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1. Feed Port Specifications Location Amplitude fi It xps 4 C X Directed E DIE Grid a zi i Di Brase i JeGtees Men we fig Y Directed WEG je 4 7 Di zuj 6 cu Resistance 50 Ohms C No Source E z Capacitance None Farads Voltage Source Series 9 poan C Cunant Source C Parallel C Polarity Inductance None Henrys S Parameter Calculation C No all ports active i Active port 1 Add feed to list Modify Selected Feed Delete feed from list Delete All Feeds Type Dir xX Y Z Grid Amp Phase R L C 1 Series Voltage zZ 33 19 46 Main 1 00 0 00 50 00 N N Click on the feed number to select Hoe f omo Figure 64 The sources loads menu after entering the appropriate data for the monopole on a box example 11 After closing the Stimulus Sources Loads menu click on Planar Transient Fields in the Edit menu Here choose to save fields in the xz plane at y 19 every 20 time steps from time step 20 to time step 320 This will give 18 snapshots for later display Select Add Sequence and press OK See Figure 65 for an example of this menu 12 To view the input impedance FFT size open the Edit menu and look for Compute Input Impedance The FFT size should default to 2048 Select Compute Input Impedance to open this window Then change the FFT size to 4096 Pressing on this option toggles the input impedance so if it is already selected with a check m
2. 0 0000 ees 84 12 SU ONIGS i epe EE 87 13 CALCFDTD Computer Program uu rtm mE ETE RA EE ete ee es 92 TAE EXample PIOCBUfes xxu are Peay ayn cee ere ase ere woe Sew Be eo Sere ET 93 14 1 Monopole Antenna on a Conducting Box 20000 eee 93 14 2 Microstrip Meander Line sellers 100 14 3 Stripline Wilkinson Power Divider 00 cee eee eeees 102 14 4 Dipole Near Lossy Sphere 2 0200 c eee eee eee 104 14 5 CDROM Example Files s 232 2 492242 RE LER 4492442 2008845 108 14 5 1 Antenna Examples 0 00 0c eee ees 108 14 5 2 Microwave Examples 22 22 ce eee eee 112 14 5 3 Biological Examples 29 ELRTRRBRIBTSRRRRLABEY 114 15 Trouble Eos 115 15 1 Problems with XFDTD 5 0 on Windows 20000000 115 15 2 Problems with XFDTD 5 0 on Unix sslllesssss 115 16 The Human Head and Shoulders FDTD Mesh esl 118 16 1 The 3mm Head and Shoulders Mesh sus 118 16 2 The Remcom High Fidelity Head and Shoulders Mesh 121 17 the Human Body EDD Meshi 27e dure eed et ud aad uda eat 122 17 1 The Original 5mm Body Mesh 0020 02 e eee eee 122 17 2 The Remcom High Fidelity Body Mesh 22000005 123 18 OUNOUE File BOM alice Soe wss AREE See wos EN DU wos iene 538 WE heed Moers Send Laid dE 125 19 REIGIONCGS
3. as a geometry file The file dialog as shown in T EE 30 will appear except this time it will display any ecto available project files files with the fdtd ipeopleicwphetatesticellphonelantuplant amp Oid extension Selecting a project file will automatically load the associated geometry file OK Filter Cancel Help 6 2 3 Open Geometry File and Merge Figure 11 The File dialog box for with Present Geometry selecting a geometry file Often it will be useful to modify a geometry file either by making the space larger or smaller or by adding or deleting some part of the file One way this can be done is by Merging one geometry with another For example to take a certain geometry file and increase the size of the entire space so as to add extra cells to the outer radiation boundary a new geometry can be created with a larger size and the existing geometry can be merged into it To do this the new geometry must be defined first then select the option to Merge the geometry The offsets of the old geometry in the new must be entered for positioning Entering 0 0 0 for the offsets will position the new geometry in the same cellular locations as before If the new geometry is 30 cells larger in every dimension and the merged space is to be centered enter offsets of 15 15 15 6 2 4 Adjust Merge Characteristics This option is used for defining which materials will take precedence over others when merging When loading an existing g
4. 7 7 3 2 Helix conic edit menu The helix is a complex object to mesh and since it is a commonly used antenna Units Celis in the telecommunication industry a Two Points Defining Centerline Helix Starting Point primitive of the helix has been added to Paint 1 Point 2 Start Stop the XFDTD library There are numerous HEE xfs 2 x n2os z x Bes parameters that must be set for the helix yes S vies A ves ij v peso primitive Figure 23 Two data points z es sj z es sii z es ij z peso are needed for defining the central axis of the helix This line does not need to CelsperTum 6 i Radius 400 align with the grid Next a starting point NumberotTums 5 i Length i800 of the helix is required Again this is an X Y Z coordinate of the first cell of the amp Single Component helix The stopping point will be C OylinderRadius 4 computed automatically but can be viewed to check for accuracy The He Cancel number of cells per turn of the helix is used for entering the helix pitch while the Figure 23 The helix primitive menu number of turns is self explanatory The polarity direction of the turn is requested along with the wire thickness of the helix If the wire of the helix is small compared to the dimensions the Single Component choice should be selected Otherwise a radius in cells may be entered Helix Thickness Polarity Clockwise C Counterclockwise 41 7 7 3 3 Plate
5. T lwasaki A P Freundorfer K lizuka A unidirectional semi circular spiral antenna for subsurface radars IEEE Trans Electromagn Compat vol 36 pp 1 6 Feb 1994 J D Dyson The equiangular spiral antenna IRE Trans Antenna Propagat vol 7 pp 181 187 April 1959 H Nakano K Nogami S Arai H Mimaki and J Yamauchi A spiral antenna backed by a conducting plane reflector IEEE Trans Antennas Propagat vol 34 pp 791 796 June 1986 K Chamberlin and L Gordon Modeling Good Conductors Using the Finite Difference Time Domain Technique IEEE Trans EMC vol 37 no 2 pp210 216 1995 C A Balanis Advanced Engineering Electromagnetics Section 2 8 3 Ramo Whinnery and Van Duzer Fields and Waves in Communication Electronics Section 13 12 R E Collin Foundations for Microwave Engineering Section 6 7 B Lax and K J Button Microwave Ferrites and Ferrimagnetics Sections 4 1 4 2 Z P Liao H L Wong G P Yang and Y F Yuan A transmitting boundary for transient wave analysis Scientia Sinica vol 28 no 10 pp 1063 1076 Oct 1984 J P Berenger A perfectly matched layer for the absorption of electromagnetic waves J Computat Phys Oct 1994 J Basterrechea and M F C tedra Computation of Microstrip S parameters using a CG FFT Scheme IEEE Transactions on Microwave Theory and Techniques vol 42 no 2 pp 234 240 February 1994 Robert S Ledlet H K Huang a
6. 16 The Human Head and Shoulders FDTD Mesh You may have received one of our FDTD meshes of a male human head and shoulders This was created using digitized data in the form of transverse color images The data is from the Visible Human Project sponsored by the National Library of Medicine NLM and is available via the Internet at no cost For information browse http www nim nih gov research visible visible_human html The male data set consists of MRI CT and anatomical images Axial MRI images of the head and neck and longitudinal sections of the rest of the body are available at 4 mm intervals The MRI images have 256 pixel by 256 pixel resolution Each pixel has 12 bits of gray tone resolution The CT data consists of axial CT scans of the entire body taken at 1 mm intervals at a resolution of 512 pixels by 512 pixels where each pixel is made up of 12 bits of gray tone The axial anatomical images are 2048 pixels by 1216 pixels where each pixel is defined by 24 bits of color about 7 5 megabytes The anatomical cross sections are also at 1 mm intervals and coincide with the CT axial images There are 1871 cross sections for each mode CT and anatomy The complete male data set is 15 gigabytes in size Our mesh of the human head and shoulders used the axial anatomical images since these had the finest resolution 16 1 The 3mm Head and Shoulders Mesh The choice of the problem space dimensions came from consideration of the computer resources
7. 9 3 Transient Far Zone Angles 3s ie eis iR es wis Vale We 62 9 4 Planar Transient Fields s sos PIRE PD MGuKwrereePeRTWES 63 9 5 Single Plane Steady State Data lsllllllllslssusn 63 9 5 1 Saving 3 D Surface Currents 00 00 cece 64 9 5 2 Specific Absorption Rate SAR 2 200 05 65 9 6 All Plane Steady State Data 0 0022 eee 65 9 7 Compute Input Impedance 0 020 eee 66 9 8 Adjust Time Step suse Sate ee eurem ute e ve E ne ee 67 9 9 Selecting Outer Radiation Boundary Conditions 67 9 9 1 Liao Absorbing Boundary Type 20e eee ee eee 68 9 9 2 PML Absorbing Boundary Type 2200e ee eee 68 9 9 3 PEC Perfect Electric Conductor 0 5 69 9 9 4 PMC Perfect Magnetic Conductor 70 10 Results MENU 66s s RITDLDLURRRPREPDIRSRRUEPLIUROERUROLIROR UE cee LBSS 71 TOSEMIOW BIBICIS 5e reete Lets os nets E teets aerate a VP Ee pirate orate Vae i 71 10 2 DIS DIAY PIO Us toas ode ig ay Ses tsm Vade we lew Asia wee we pis quate cus 74 10 3 Compute Far Zone Data 15 292 ee ee RR OFT 77 10 4 Compute S Parameter Data 0c ccc eee ee eens 79 10 5 Compute Averaged SAR Statistics 0 0 0 0 cee ee eee 79 10 6 Display Averaged SAR Information 000 cece eens 81 10 7 Display Steady State Data 2 r9 bee P dese anew s 82 11 User Generated Meshes
8. Finally save the necessary results Using the Save Near Zone Data menu save the Ez and Jz electric field and current density at the feed location 106 60 60 In order to 105 calculate the maximum SAR from the FDTD Save All Steady State Quantities SAR Planes menu save all SAR xz planes Then save the geometry and XFDTD project files using the appropriate menus from File Then run the calculation This calculation took approximately 55 minutes on a 400 MHz Pentium II computer Once the calculations are finished reload the project file to perform some postprocessing From the Results Steady State Data display you should see the feed point 1 impedance of 27 90 j111 82 ohms The antenna efficiency is 29 This means that 7196 of the power supplied to the antenna is absorbed in the lossy sphere In order to obtain SAR information use the Results Compute SAR Statistics menu and select the x z plane since these were the planes saved Once the SAR calculation is complete you can then use the Results Display SAR Information menu to see the resulting SAR information The input power can be scaled on this menu With the scale input power set to 1 Watt on this menu the Maximum SAR is approximately 11 4 W kg The SAR distribution can be seen in false color using XFDTD To do this load a SAR file using the Project Tree The distribution for the unaveraged SAR in the y 60 plane is shown in Figure 73 To allow the colors to be displayed more clearly th
9. X Directed os Sie C Y Directed Phase o Degrees C 2i Z Oatad Resistance po Ohms C No Source 4 Capacitance None Farads Voltage Source C Series 2 cris C Current Source gesture co Inductance None Henrys S Parameter Calculation C No all ports active Yes Active poth Add feed to list Modify Selected Feed Delete feed from list Delete All Feeds Type Z Grid Amp Phase R L C 1 Series Voltage 1 Main 1 00 0 00 50 00 N N 2 Series Voltage Z 115 121 1 Main 1 00 0 00 50 00 N N 3 Series Voltage Z 35 586 1 Main 1 00 0 00 50 00 N N 4 Series Voltage Z 115 56 1 Main 1 00 0 00 50 00 N N Click on the feed number to select OK Help Cancel Figure 33 The sources loads stimulus menu Note A port or feed may be entered easily by moving the mouse pointer to the desired cell edge and pressing the right mouse button From the popup menu select Edit Port This will open the Sources Loads menu with the location and direction of the feed already entered 9 1 1 1 Setting the Feed Port Location The Sources Loads menu contains a section which describes the location of the feed The grid of the feed must be selected appropriately If there is only a main grid in the project then this will be the only choice available If there are one or more subgrids then the proper grid must be selected Next enter the X Y Z location of the desired cell
10. 1 component thick rectangular SAAIE ida E The rectangular plate Figure 24 is a two CENE S dimensional object that may be rotated around width one of the principle axes The plate is first Units els defined aligned with one of the principle axes and Center Point Dimensions p Plane then a rotation angle can be specified The xm a Meee G XY location of the center of the plate must be entered v i E NN C Yz along with the dimensions of width and depth z e sj t KE The initial orientation is used for sizing the plate Rotation and then the rotation angle and axis of rotation go l define the final position of the plate AH esa T ee wee omen Figure 24 1 component thick rectangular plate menu 7 7 3 4 Plate 1 component thick quadrilateral The quadrilateral plate Figure 25 is more general than the rectangular plate but Is more complex and should be used when the rotation angle is around more than one axis For this plate three points are requested to define the plane of the plate A fourth point defines a desired point in the plane The program will compute the actual fourth point based on the input given This computed fourth point is shown in the Actual part of the window Units Cells Point 1 j Point 2 Point 3 3 5 22 25 X M35 a5 n0ggo2 25 s zoe i m Actual Point 4 X pass Calculate gt Y 43 60 Z 43 00 Figure 25 The quadrilater
11. 51 edge The feed will either be aligned with the X Y or Z axes so select the direction as either X directed Y directed or Z directed Note Feeds ports may not be located adjacent to each other unless the RLC values are all set to none Feeds Ports can be end to end but the can not be side by side 9 1 1 2 Feed Port Parameters Each port in XFDTD may have several parameters associated with it The port contains a source the source may be a voltage or a current The source may be added in series or parallel Otherwise if no source is desired a passive lumped load may be specified by selecting No Source Note For all voltage source specifications the values given are peak values not RMS If a source is defined the amplitude of the input waveform may be specified as well as the polarity The phase of the source may be selected if the input waveform is a sinusoid otherwise this option will be unavailable XFDTD also has the capability of simulating lumped RLC Resistor Inductor Capacitor elements at a port location The RLC elements will be added either in series or parallel depending on which choice is selected For all cases the load will be in series with the voltage source and in parallel with the current source The series and parallel choices refer to how the RLC components are added with respect to each other For the series combination all of the lumped circuit elements are in series and
12. Edit Magnetic Material Ea Type C Normal Anisotropic Description substrate Magnetic Conductivity Relative Permeability Larmor Precession Frequency rad sec 1 232504e10 Saturation Magnetization rad sec 0372e8 Damping Coefficient Theta 7 Delete Phi Help Cancel Figure 16 Defining an anisotropic magnetic material in XFDTD 5 0 ui TT c Clicking this button on the tool bar will show the Magnetic Material Palette Windows and display the magnetic components of the grid 36 7 5 Specifying Material Densities Material densities are required for performing Specific Absorption Rate SAR calculations This option is only available in the Bio Pro Version of XFDTD The Material Densities may be entered using the Edit Electric Material window in the Windows Version or the Edit Material Densities Menu in the Unix Version The densities of the material must be entered in kg m for SAR calculations Note 1 Make sure densities are entered in kg m as many handbooks provide material densities in g cm Note 2 If non biological lossy dielectric materials are present perhaps a plastic cover for a cellular phone setting the material density of that XFDTD material type to zero will indicate to XFDTD that SAR results are not desired for that material 7 6 Edit Thin Wires Thin Wire materials may be ISZBELU CAN ETS Cs 7x used in special situations where a wire with a
13. are located on one FDTD mesh edge For a parallel combination all of the lumped circuit elements are in parallel located on one FDTD mesh edge The voltage across the mesh edge electric field times edge length includes both the load and the source voltage if present The FDTD calculated current is always the total current through the cell edge and includes both current through the load and through the current source if present If you wish to place a voltage source in parallel with the load or a current source in series with the load you should place the source and load in adjacent cells side by side in the first case and end to end in the second The RLC values for the voltage or current source should be set to none for this situation Source Resistance An important advantage of including a source resistance is reducing the number of FDTD time steps necessary for convergence in transient calculations This is especially important for resonant devices such as many antenna and microstrip circuits With a hard source consisting of a voltage source without series resistance a resonant microstrip antenna may require 64 000 time steps for the transients to dissipate The addition of a 50 ohm source resistance might reduce this to 4 000 time steps Similar time savings may be encountered for microwave circuits The source 52 resistance should be chosen as closely as possible to match the source to what is being driven So for a micro
14. described later For many simulations involving antennas or microwave circuits the near zone source input is used 9 1 1 Sources Loads S Parameter Port Setup The Sources Loads window is used for FDTD calculations involving near zone voltage and or current source or lumped RLC circuit elements In antenna calculations the desired input is usually considered the feed while for S parameter calculations ports must be defined For XFDTD these two concepts are nearly identical and so the terms feed and port are often used interchangeably A feed is a cell edge on which the electric field is modified by the addition of some type of input waveform A port is also a cell edge where an input may be added or the near zone values of voltage and current may be monitored In either case the cell edge can be modified to behave like a voltage or current source or have some value of resistance inductance or capacitance 50 Regardless of whether the input is considered a feed or a port the necessary parameters are defined on the Sources Loads menu Figure 33 This menu is opened by selecting Edit gt Stimulus gt Sources Loads Sources Loads E3 Source Waveform Mod Gaussian Pulse Width 3100 00 Time steps 12000 Freq 3 00 GHz i Set Waveform Far Zone Transformation for Sinusoidal Source Transient steady stat Won In Feed Port Specifications Location Amplitude fi It
15. zone transform are between Transient Steady State or None Typically this option should be selected as Steady State since this offers the most flexibility However if only near zone values are of interest such as in an S parameter or SAR calculation selecting None will save a small amount of calculation time and a sizable amount of disk space In some instances the transient far zone calculation may be desired and 60 so that choice is available This will require that far zone angles also be specified using the Transient Far Zone Angles menu and useful results will only be available at the frequency of the input Note The Far Zone Transformations are not valid if any of the outer radiation boundary conditions are set to PEC or PMC or if any material is within 6 FDTD cells of the outer boundary The steady state far zone transformation does not require the definition of specific far zone angles before the FDTD computation Instead the FDTD calculation saves the tangential electric and magnetic fields on the far zone transformation surface at two time steps near the end of the calculation when the system should be in steady state This sampling determines the complex tangential fields on the far zone surface at the excitation frequency These fields are then used in post processing under the Results menu to provide radiation gain or bistatic scattering in any far zone direction at any pattern increment This saves considerable com
16. 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 emat03 mmat03 1 000000e 000 0 000000e 000 1 000000e 000 0 000000e 000 1 000000e 003 1 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 materials 4 26 are skipped here emat27 mmat27 000000e 000 0 000000e 000 1 000000e 000 0 000000e 000 1 000000e 003 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 0 000000e 000 000000e 000 1 000000e 000 0 000000e 000 000000e 000 0 000000e 000 1 000000e 000 Array format material 0 0 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 NNNNNNNNNNNNNNNNNNNNNNNNNNNNDN ND OOOOOOOoOo0O0o0o00000o0o0o0o0o0o0ooooooocooo OOOOOOOo0o0o0o0000o0o0o0o0o0o0o0o0oo0ooooooooo Table 1 Example id file which can be generated and read by XFDTD followed by that number of lines containing the J K indices for the magnetic mesh cells containing material and the material numbers for each of the three magnetic field components organized as for the dielectric mesh 86 12 Subgrids A very powerful feature of XFDTD is the ability to specify one or two subgrids with smaller cells than the main grid Proper use of this feature requires following several rules Improperl
17. 0 50 100 150 time ps frequency GHz B ce Figure 36 The waveform menu 56 the Set Waveform button brings up this window Figure 36 The excitation for the FDTD calculation may be a Gaussian pulse a Gaussian Derivative pulse a Modulated Gaussian pulse a Sinusoid or user defined in which case a custom waveform may be supplied The choice of the excitation should be based on the desired output results as some excitations are more appropriate than others The Gaussian pulse provides a broadband input and is suitable when results versus frequency are desired The derivative Gaussian is nearly identical to the Gaussian except that the DC component is removed This is useful for calculations where a short circuit loop exists since the regular Gaussian could excite DC current flow which would affect the quality of the output The modulated Gaussian is used when only a specific frequency range is desired This is very useful in structures where low frequencies could excite non radiating modes which could resonate and destroy the results The sinusoidal input is useful when only one frequency is of interest There are numerous output choices available with the sinusoidal input as well Depending on which waveform chosen the appropriate parameters of the excitation are available for selection The pulse width is the number of timesteps between the half amplitude points on the Gaussian pulse input For a Gaus
18. 58 calculation is not excited at frequencies for which accurate and useful results might be obtained There must be sufficient energy in the pulse for calculations to be above the numerical noise for all frequencies of interest For calculations with very small cells compared to the shortest wavelength of interest pulse widths may be set much larger than the default size to reduce the number of time steps needed for convergence and to increase stability If dielectric materials are present the wavelength will be reduced inside the material and the velocity of propagation will be less than the speed of light in free space A reasonable rule to apply is that the maximum frequency for the spectrum of the excitation pulse should be reduced by the square root of the relative permittivity or equivalently the pulse width should be increased by this factor This assumes lossless or low loss dielectric For more lossy dielectrics or conductors the frequency and pulse width should be adjusted proportionally to the change in velocity and wavelength in the material relative to the free space wavelength Of course the maximum frequency for reliable results is also reduced as the frequency spectrum of the excitation pulse is reduced For example suppose part of the calculation space is free space and part is a low loss dielectric with relative permittivity 4 0 Further suppose the cell size is 1 cm At 10 cells per wavelength one would expect reasonable resul
19. Electric Material Parameters OF rzsmesmpepmesm Edit Magnetic Materials is selected the corresponding Material Palette appears Figure 14 shows the Electrical Materials PEC Palette Each color on the palette represents a different material type Black number 0 and White number 1 always correspond to free space and Perfect Electric Conductor PEC respectively and cannot be changed To add a new user defined material type click Add Either the next available material may be selected or Edit Add a particular color Each color represents a particular material Ee ILS though and may only be used once To aid in identifying different Figure 14 Edit materials a material description may be entered in the area Electric Materials provided XFDTD will store this name with the other material panel parameters to allow easy identification of different materials If editing electrical materials there is also the option to Add Thin Wire Thin wires may be used when the geometry requires a wire with a very thin radius which is much less than the cell size It should be noted that a wire constructed of a single edge of PEC has an effective radius of approximately 1 4 of a cell Thin wires always appear with cross hatched color 7 3 Specifying Electrical Materials Often materials other than free space and perfect electric conductor are needed for a particular geometry To create a new material in Windows select Add from the Material
20. GHz Set Waveform Far Zone Transformation for Sinusoidal Source C Transient Steady State C None m Incident Direction Polarization Incident Amplitudes Phi 45 C EPhi Ex 499 999983 a Ey 499 999991 Theta 48 EThete Ez 707 106769 OK Help Cancel Figure 34 The incident plane wave menu 9 1 3 TEM Excitation Plane The final excitation choice is the TEM Excitation Plane Figure 35 This is a very specialized excitation option and may only be used with a special class of geometries This option is designed to excite a Transverse Electro Magnetic mode in the FDTD space and requires a suitable geometry for propagating such a mode A typical TEM geometry will have two to four parallel walls of the FDTD space set to perfect conductor see the section on the Outer Radiation Boundary Types and should have some type TEM Excitation Plane x l Source Waveform Sinusoid Time steps 20000 Freqency 0 84 GHz TEM Plane Specifications XY LES Slice fi Preview Fields C XZ OK Help Cancel Figure 35 The TEM excitation menu of center conductor 55 An example TEM geometry might be a coaxial cable with square outer conductor defined by setting PEC Outer Radiation Boundary Types and an inner conductor Multiple inner conductors are acceptable XFDTD will set up the TEM mode excitation assuming that the outer conducting walls are at ground potential and the inner conductor s are all
21. In Unix XFDTD the same options as mentioned above are accessed through the Edit ple Xp DISPLAY FDTD DATA Salet Type nf Data to Fin reus roe mnes v Pinten Angle Data Availlale Fr Eletting Maur tona Ez Total Field W m ws Tipe ba at 33 13 45 main grid Food peint M Volteg and Current va Ties mz Belici Wane Fid Polartastions Data Component Lina Typ gt E Phl Palarigarisn gt Magnitude 1B dBierdBEsen Valtage Vales Linus a E Theta Polarization ar Phasa degrens er Currant irp e Poin L ft Circular Polarization x Real Pow Watts Horie x Beth x Right Cirralar Folarization imaginary x Normalised Fower dB Data Selected for Fling Waur Eenma Ev Tota Flald Mmi E Tise mul at 33 15 45 sain arid with limas Feed palat H Voltage and Current wa Tine iz Currant with Lines Feed p lat si Voltage and Current ve Time rg Voltage with lima Came Mep Figure 50 The Plotting tool in XFDTD 5 0 on a Unix computer Plot Parameters and Labels buttons see Figure 50 The plot is displayed by pressing the Generate Plot button and closed by pressing the Close Plot button Note To set the axis value back to automatic simply type an a in the axis range window Note There is currently not a function for printing plots from XFDTD All of the data from a calculation of XFDTD is stored in ASCII files which can be loaded into a third party plotting package such as Gnuplo
22. Time Estimation 2 2 diera wea Tta To d eva eee u 14 Sw Goordinate Systemi lt s steen wh ae eka a ae Dene a ae ene Aas ee 16 4 XFDTD Graphical User Interface 0 0020 es 17 Z1 Starting SPD TD es aren eo tat dps rs an rer ua S ou 17 4 1 1 Starting XFDTD in Windows NT 95 98 LLn 17 4 1 2 Starting APO TD in UNIX xc ese ee eke NC Ae ee ee ee tees 17 4 2 The XFDTD User Interface llle 17 SXJI MIUs MU M xc 23 5 1 Geometry Files 1 25 9 Sor ere Ebr Eb ELE P EE P ELDER Ep ai 23 Dre PIGIECEBIBS coo oret etc Sieecte oe eto Dort rete Dto Stroke Merwe coit 24 5a CUIDHMEIBS 27 7 a weer amu esr aren wre mrer ers euge etd eT et aac dud 24 b The File Men sso toe ewe ee ke eee PE CEE ee ee RU ILE RES 26 6 1 The File Menu in Windows NT 95 98 2 2 0 eee 26 SENSIT Rr HEP 26 A Z DB SS ados dc arcte dilecte obe dose dtes qe eicere anaes 28 6 1 3 MSIUG ee xs es HEX LEPIDE x EE PE I aae 28 Gala AVG doc ptas ctu ota ceu oto cerea cer ue ar pest ot 28 TS ANS oai uti vidit dei tiquitl MILI MISI MILI Eton 28 Dole IOS a cya Spay a tone tius i to rte ito syrtes ato artes it Kor rete 29 OL E XI ee enn SuSE mius dA REL BL AR EG RG Re E SS 29 6 2 The File Menu in UNIX XFDTD sessleee ee 29 6 2 1 Open Geometry File esse s Erste reed was M EE dE 29 6 2 2 Open XFDTD Project Fil 59 9 IRSEDRRR ITTEARIETSG 30 6 2 3 Open Geometry File and Merge with Present Geometry 30 6 2 4
23. are to be saved in subgrids if present note that the timestep in a subgrid is 1 3 or 1 5 the size of the timestep in the main grid 9 5 Single Plane Steady State Data The windows for saving the different steady state quantities are quite similar The window for saving SAR quantities is shown in Figure 40 The steady state quantities 63 available are Specific Absorption Rates SAR sinusoidal peak electric field magnitudes EFM magnetic flux density B field magnitudes BFD and conduction current magnitudes CCM An example of the Save Conduction Current Magnitudes is shown in Figure 41 It is slightly different from the windows for the other steady state quantities basic choices on the window are the same Note that these choices are only available with the BioPro version of XFDTD For each steady state quantity the choice is to save data in a specify slice plane of the geometry These menus are useful if steady state data is desired in one particular plane However a more useful choice is often the All Plane State State Data menu which is pe Pe discussed later Slice a Grid Main Save SARs in XY plane at Z 11 main grid a Save SARs in XY plane at Z 12 main grid Save SARs in XY plane at Z 13 main grid Save SARs in XY plane at Z 14 main grid Save SARs in XY plane at Z 15 main grid Steady state values for SAR and conduction Save SARs in XY nlane at 7 1A main arid zl currents wil
24. averaging calculation uses an interpolation scheme for finding the averages Cubical spaces centered on a cell are formed and the mass and average SAR of the sample cubes are found The size of the sample cubes increases until the total mass of the enclosed exceeds either 1 or 10 grams The sample cube increases in odd numbered steps 1x1x1 3x3x3 5x5x5 etc to remain centered on the desired cell The mass and average SAR value of each cube is saved and used to interpolate the average SAR values at either 1 or 10 grams The interpolation is performed using two 80 methods polynomial fit and rational function fit and the one with the lowest error is chosen The sample cube must meet some conditions to be considered valid The cube may contain some non tissue cells but some checks are performed on the distribution of the non tissue cells A valid cube will not contain an entire side or corner of non tissue cells If the cube is found to be invalid the averaging for the center cell will stop and move on to the next cell It is possible and probable that some cells will not be the center of an average However these cells will often be part of an average cube for an adjacent cell If the FDTD cells are too large in terms of mass the results obtained may be of lesser accuracy If one cell has a mass greater than 1 or 10 gram an error message will be displayed indicating this The interpolation will not produce accurate results for values ou
25. cells Automatic meshing of basic shapes Copy regions of mesh Rotate mesh coordinates by 90 degrees 2D slices and 3D view of meshed objects Merge geometries together to combine objects Menu control of FDTD calculations Multiple Voltage Sources with series resistor Liao PML PEC and PMC outer boundaries Incident Plane Wave excitation Sample fields and currents versus time Line Plots of Results Color Display of 2D Field current slices Color Display of 3D surface currents XFDTD 5 0 XFDTD 5 0 Pro 4 XFDTD 5 0 Bio Pro 4 Feature XFDTD 5 0 XFDTD 5 0 Pro XFDTD 5 0 Bio Pro Movie sequences of steady state fields through geometry Movie sequences of transient A fields vs time Multiple Voltage Current Sources with Series Parallel RLC Input Impedance vs Frequency A Single Frequency Input Impedance A Multi Port S Parameters vs Frequency Multi Port steady state S Parameters Specific Absorption Ratio SAR Display Planes of steady state E B fields Display Planes of steady state current density Adjust SAR level to specified input power Calculate 1 and 10 gram SAR averages Location of peak SAR SAR movies by slicing through the mesh TEM cell excitation Pre Meshed human head and body Module for remeshing dielectric with different cell sizes and or rotation Module for removing mesh rotation from antenna patterns Circular Polarization Antenna Gain 4 P
26. current magnitudes or surface currents Open Steady State Data Sequence File This option is used for opening individual sequences of steady state files There is also an option to create these files if they were not already computed by the calculation program 6 2 6 Create New Space Use this option for creating a new space A menu similar to that shown in 26 will open Define the parameters of cell size number of cells in each direction and the grids to create Unless magnetic materials non free space permeability will be used the magnetic grid should not be defined 3l 6 2 7 Show Information Window This option opens a separate window with information about the loaded geometry 6 2 8 Save Geometry Select this option to save a geometry file Select whether the file should be saved as either a main grid or a subgrid A File box will open allowing the directory and filename of the geometry to be entered 6 2 9 Save XFDTD Project File This saves the Project file currently loaded 6 2 10 Destroy Existing Space If a geometry is loaded but no longer desired it can be removed with this option This is useful for removing a subgrid from a project 6 2 11 Quit Select this option to exit the XFDTD program 32 7 Edit Menu Geometry In the Windows version of XFDTD the Edit menu fdg Sil performs different functions depending on whether face M a geometry or project file is active This chapter Sut Bike describes the features
27. current project Selecting items in the Project Tree will switch the geometry in view or open output files Calculation Progress Toggles the output window showing the status of any calculation which may have been started Tool Bar Toggles the toolbar display The toolbar is the row of buttons which provide instant access to various commonly used functions Status Bar Toggles the status bar located across the bottom of the XFDTD frame window The Status Bar shows the file loading progress and the status of other operations More importantly the status bar displays location of the pointer in a geometry as well as information about the active geometry The following items are only available when a geometry view is active v v SS Grid Toggles drawing of the grid The grid is drawn as a medium gray graph that designates the size and position of the geometry The drawing grid is in alignment with the electric components of the geometry Normal Elements Toggles the drawing of the components normal to the current viewing plane Normal components are drawn as circles in the color of the material This setting is independent for each of the principle planar views Electric Components Toggles the drawing of the electric components When both an electric and magnetic grid are present or when fields displayed it is sometimes useful to turn off the electric components Magnetic Components Toggles the drawing of the magnetic componen
28. different data For the EFM and BFD files the data written for each cell following the same loops as given above for the transient fields is EFMx EFMy EFMz EFMtotal or BFDx BFDy BFDz BFDtotal For the SAR and Conduction current files the data only exists in certain cells Therefor the data is only saved for those cells with non zero values After the header there is a string followed by an integer indicating the number of cells with data After this integer follow the lines containing the cell location and the field values For SAR this might look like header array format material 1640 40 69 30 2 639620e 05 this repeats for 1639 more lines In this line X240 Y269 2230 SAR 2 63 Note that the X Y Z values are one less than what is displayed in XFDTD This SAR value would actually appear at cell 41 70 31 For the Conduction currents the file would look like this header array format material 3 13 10 20 0 000000e 00 1 397751e 01 5 143908e 01 13 11 20 0 000000e 00 0 000000e 00 4 806674e 01 13 10 21 0 000000e 00 8 427364e 02 0 000000e 00 Here there are only 3 lines The first line has data for X213 Y 10 Z 20 CCMx 0 0 CCMy 1 397751e 01 and CCMz 5 143908e 01 Again the x y and z values are one less than what is displayed in XFDTD 128 19 References 7 K Kunz and R Luebbers The Finite Difference Time Domain Method for Electromagnetics 1993 CRC Press Catalog Number 8657 496 pages
29. entered into the appropriate mesh variables The mesh must be saved after adjusting the parameters for the new values to be used in the XFDTD calculation but the parameters can be adjusted as many times as required 125 18 Output File Formats The file formats for several of the XFDTD 5 0 data files are provided in this chapter for users who wish to display the data in some format not provided by XFDTD The most common output files will be discussed here while some files used by XFDTD for internal processing will be omitted The geometry files are discussing in a separate chapter All output files have some type of header information which is terminated by the character string See the coordinate system figure at the beginning of this manual for the angular measures Near Zone Data Example monboxEZT x00011 y00020 z00005 g0 Near zone values are saved at every timestep The data file contains two columns the time in seconds and the field value in the appropriate units Far Zone Data Example monbox pafpOtO or monbox pvt90 pb0 pe360 in10 or monbox patpOf1 030 There are many possibilities for far zone data files depending on the far zone transformation used and the output data The output files will have similar formats though For transient far zone files the choices are gain RCS vs frequency theta or phi and far zone electric fields versus time For the far zone fields versus time the format is three columns time S
30. fields sequence files single steady state files and steady state sequence files Sequences of steady state files are created through this menu The Refresh option will regrow the Project Tree This is useful for viewing intermediate output files while a calculation is running The tree will regrow automatically as needed UNIX VERSION i The functions for amp B Conduction Current Magnitude Data x loading steady state field files and creating steady state sequence files Figure 6 XFDTD Project Tree are all available through the FILE menu on the main menu bar Refresh Figure 7 XFDTD Project Tree pop up menu in the Windows version 22 5 File Types XFDTD creates many different files for storing the geometry calculation parameters and output This chapter focuses on the types of files written by XFDTD All output data from the calculation are viewed through the XFDTD interface and knowledge of the actual filenames is not required For users who wish to use the output data from an XFDTD calculation in another program a detailed listing of the output file formats is given in a later chapter Here a brief listing of the files created is given here as a guide Note In this chapter the base file names of monbox and monrun will be used as examples In actual use of XFDTD these names are given within the program 5 1 Geometry Files Geometry files contain the data describing the location and content of the FDTD
31. first assures that there will be no air gaps where the layers join Next mesh the dipole This could be done manually with the mouse but can also be done with the wire function from the library The dipole is 53 cells long so each dipole arm is 26 cells and there is a 1 cell gap at the center We choose to put the dipole in the xz plane at y 60 The x location of the wire is 46 cells from the center of the sphere or x 106 The center of the dipole will be cell edge 106 60 60 To use the wire library function for the upper half of the dipole wire set end 1 to 106 60 61 and end 2 to 106 60 87 with material PEC then click on add object If the XFDTD slice is set to xz plane at y 60 the upper half of the dipole should appear To mesh the lower half set end 1 in the wire function to 106 60 60 and end 2 to 106 60 34 The result should be the wire dipole with each arm 26 cells and a 1 cell gap in the middle Be sure to set the relative permittivity and conductivity of materials 2 and 3 to the parameters given above for brain and skull Also set the densities for materials 2 and 3 to the brain and skull parameters given above Next set the excitation of the calculation From the Stimulus Sources Loads menu add a Z voltage source at location 106 60 60 with a zero resistance source resistor Then set the frequency to 900 MHz 0 9 GHz with 2500 time steps Choose the steady state far zone transformation so far zone patterns can be calculated
32. higher frequencies that would be excited by the narrower pulse will not be accurate Figure 70 Detail of the Meander Line feed As this geometry is already meshed and the project file is defined the calculation can be run using Results Run CalcFDTD When the run is complete the results can be displayed using the Display Plot submenu Figure 71 XFDTD calculation of S for meander line compared with measurements 101 The result S is plotted in Figure 71 and compared with measurements from 18 The agreement is quite good comparable or better than the calculated results given in 18 and much better than the Touchstone results also shown in 18 14 3 Stripline Wilkinson Power Divider This example is for a stripline Wilkinson power divider The wilk50 id and wilk50 fdtd files that correspond to this example are included with XFDTD50 You are encouraged to load these files into XFDTD50 and follow along with the following discussion The layout of the power divider will be shown in XFDTD50 in the x y plane at z 7 Port 1 is at the bottom Port 2 at the upper left and Port 3 at the upper right The FDTD cell size is 112 x 112 x 127 mm with the total FDTD space being 155 x 199 x 12 cells The overall dimensions of the stripline conductors are 19 94 mm or 178 cells from Port 2 to Port 3 and the overall distance from Port 1 to the far edge of conductor is 15 57 mm or 139 cells The dielectric has permittivity 2 94 and the t
33. lower left corner of the field image in the H A m 6 1817e 002 geometry window The peak value is J A m 3 1405e 001 3 1405e 001 Reset the 0 dB or 100 number while the S Ww m3 7 0543e 000 1 0543e 000 Reset other colors are based on field values From presently loaded field file s related to this peak The MOUSE pointer may also be used to find the field Hep Cancel value at a specific location in the geometry Move the mouse pointer over Figure 46 The Set Full Scale window for a time the geometry image while a field is domain field file loaded and the field is displayed in the geometry window 12 Any of the transient field files or steady state quantities listed in the sequence Field Type Mex Value file may be displayed individually or XFDTD can automatically run through SARQW ks 3 6560e 005 ERIE any set or subset of the files listed in From SAR Calculation the sequence file The sequence can be viewed as a looping movie by nene aan Eien i Calculated 5 0297e 004 Scaled 5 0297e pressing the PLAY button For a time e iii domain field sequence this movie will display the field propagation over time 2 Hep ance For a steady state quantity sequence the movie will show slices through the geometry The other functions available include the frame advance fast forward rewind move to end and move to beginni
34. more than one geometry is open the additional windows are visible with the title Sub Grid 1 and so on Also in this case an extra window containing All Grids is open This window shows the main grid and the subgrids 18 together Each of these windows allows selection of the viewing plane and provides specific tools by which to manipulate the geometry Note that editing is disabled in the All Grids window When any one of these windows is active features such as the background grid the electric or magnetic components and normal elements can be turned on and off Also the zoom and slice features are functional Select the coordinate plane in which to view the geometry by clicking on one of the three panes along the left side of the window For each window except the All Grids window the 3D View is available displaying the entire problem space in three dimensions Panning in XY YZ and XZ planes in Windows If the Geometry window is active the current coordinate system of the geometry is shown in blue along the left hand side of the window When the mouse pointer is moved over these panes a hand icon appears By holding down the left mouse button while the cursor is over a coordinate system window the hand grabs the window and allows panning of the viewed portion of the geometry to center features of interest Furthermore each coordinate plane zooms independently of the others Other controls of the geometry w
35. of the other feeds if any have been specified Voltage and current samples beyond the number of time steps specified for the FDTD calculation will be set to zero Input impedance for each source feed is always available if steady state far zone transformation is selected Note If Steady State far zone transformation has been selected the single frequency input impedances for each source are always calculated and the Compute Input Impedance menu choice is not active The input impedance is displayed from the Steady State Antenna Data entry of the Results menu Again this input impedance is 66 Compute Input Impedance x Setthe FFT Size Cancel Figure 42 Menu for entering the FFT size for the input impedance the total complex voltage divided by the total complex current and therefore includes effects of other feeds if they exist 9 8 Adjust Time Step This menu item may be used to reduce the timestep in the FDTD calculation The time step size is determined automatically by XFDTD and normally should not be modified Situations may occur where this control is desired One situation may be where a frequency dependent dielectric or magnetic material is specified with parameters that cause instability in the FDTD calculation This instability may sometimes be removed by reducing the time step The timestep may also be reduced when the impedance or antenna gain is needed at a specific frequency Reducing the timestep may adjust t
36. of XFDTD these options are found Sample Near Zone Data Cirle simply under the Edit menu while in the Windows Transient Far Zone Angles Ctrl F Version the Run Parameters window must be Planar Transient Fields Ctri l active to view these menu choices Some of the Single Plane Steady State Data calculation parameters menus may be accessed All Plane Steady State Data through the toolbar v Compute Input Impedance FFT Size 4096 Adjust Timestep There are many calculation options with XFDTD Main Grid Outer Radiation Boundary Conditions Ctrl B and the available outputs are dependent on the Preferences type of input selected The inputs which are covered in the first section of this chapter must be chosen carefully according to the type of result desired XFDTD can generate both broadband and single frequency results and due to the different calculation methods used for generating output one type often is more useful than another for a particular project Figure 32 The Edit Run Parameters menu in the Windows version of XFDTD 9 1 Stimulus The Stimulus refers to the input used by XFDTD There are three broad types of inputs near zone sources incident plane waves and TEM excitation planes The most commonly used input is typically the near zone source Incident plane wave calculations are useful for applications where the scattering or absorption of fields by an object is desired The TEM excitation mode is a specialized input which is
37. of the Edit menu for a Copy Ciria geometry window The Edit menu in the Unix Ease ia version of XFDTD is analogous to the Windows _ wes Geometry Edit menu The Edit sub menu choices Geometry Geometry Editing Tools Ctrl E of the Windows version are shown in Figure 13 Electrical Material Parameters The editing tools Undo Redo Cut Copy Paste idagnetic rleierial P ararnieien and Delete are included in the Windows Version only Other panels for entering and modifying the Geometry dielectric and magnetic Material Parameters and the subgrid location within the main grid are available The spatial increments for a geometry can be modified from this menu as well as the orientation of the geometry If a dual grid is Preferences required for example when a complicated Figure 13 The Edit menu of the geometry was generated assuming only dielectric Geometry window in the Windows materials and at a later time magnetic materials are version of XFDTD 5 0 desired it can be added here The Remesh and Rotate optional features are accessed through this menu if that module has been added to the basic XFDTD package The Tissue material parameters of the Remcom High Fidelity human meshes an optional feature available for purchase can be automatically adjusted to a specific frequency using the Adjust Tissue Material Parameters menu Finally preferences controlling the functionality and appearance of XFDTD can be modified Spatial Incremen
38. of the Project Tree The Project Tree can either display a text description for each item in the tree or the actual filename for that data The Quick Draw field display option controls how the field snapshots are drawn on the screen The fields may be drawn using the actual field values at each cell location or an interpolated version of the fields may be shown which presents a smoother transition of the fields When Quick Draw is selected the actual field values will be displayed 46 rather than the interpolated fields The selection of Quick Draw will increase the speed in which fields are loaded and movies are presented The number of Undo levels for editing may be adjusted as well The default setting for Undo is 2 but this can be increased as needed The limitation on increasing the number of Undo levels is the memory requirement for storing changes to large areas of the geometry When actions are stored in the undo list the Information button will provide an estimate of the amount of memory used 47 8 View Menu 8 1 The View Menu in Windows XFDTD Like the other menu items the menu has different contents depending on which window is currently active View has different contents for depending whether the active window is a geometry the run parameters or a plot The following items are common regardless of which view is active XFDTD Project Tree Toggles the XFDTD Project tree The Project Tree displays all the files in the
39. option Also available are the near zone field values at the feed versus time The broad band example helgaus fdtd also contains field sequences in both grids The input impedance and S11 versus frequency may be plotted Time domain data 108 available includes the feed voltage and current Coplanar Waveguide Slot Measured and calculated results for a Coplanar Waveguide Slot antenna are given in the paper FDTD Analysis of CPW Fed Folded Slot and Multiple Slot Antennas on Thin Substrates by Tsai and York IEEE APS Transactions February 1996 XFDTD has been applied to a folded slot antenna as shown in Figure 1 of the paper Using the Magnetic Wall capability of XFDTD only half of the slot geometry needs to be included in the calculation Figure 75 shows a comparison between results obtained using XFDTD and measurements from the paper Many more results can be seen by loading the XFDTD project file cpwfslot fdtd into XFDTD Situs 511 cdd Co Flanar Harpide Folded Sick items Figure 75 XFDTD 5 0 calculations of S11 compared with measurements Patch Antenna XFDTD Version 5 0 is used to calculate the S11 scattering parameter for a microstrip patch antenna The geometry and measured results for S11 are given in the paper Applications of the Three Dimensional Finite Difference Time Domain Method to the Analysis of Planar Microstrip Circuits by Sheen et al in the July 1990 issue of IEEE Transactions on Microwave Theory and Technique
40. portions of a geometry To save Surface Currents in the Save Conduction Current Magnitudes window Figure 41 pick Surface in the Plane box Select the grid if subgrids are present and specify whether the surface currents should be saved over the entire 64 geometry or only in a specific sub region If the sub region choice is selected enter the extent in cells of the sub region in the spaces provided 9 5 2 Specific Absorption Rate SAR For FDTD calculations SAR is defined for each FDTD cell as o o o x 2 y 2 z 2 IE P P P x y z where is the root mean square RMS amplitude of the X component of the sinusoidal electric field in a particular FDTD cell o is the corresponding conductivity in S m and p is the corresponding material density in kg m The remaining two terms are for the Y and Z components of the same FDTD cell same I J K values in the mesh The conductivity values used by XFDTD are those entered in the material parameter menu The code does not convert complex permittivity values such as from frequency dependent materials into conductivity terms The SAR calculation is a only valid with a single frequency input so only normal dielectric materials should be specified If material parameters are given in as complex permittivity the static conductivity can be computed as O OSE where wo is the radian frequency desired The SAR by definition uses RMS electric field values but the
41. r Open XFDTD Project File Ctrl O Open Geometry File amp Merge with Present Geometry Adjust Merge Characteristics Open Single Transient Field File Open Transient Field Sequence File Open Single Steady State Data File z Open Steady State Data Sequence File z Create New Geometry Show Information Window Save Geometry Save XFDTD Project File Ctrl S Destroy Existing Space z Quit Ctrl Q Figure 10 The File menu in the UNIX version of XFDTD 5 0 6 2 1 Open Geometry File Choose this option to open a geometry file by itself A sub menu gives the options of Main Grid Sub Grid 1 and Sub Grid 2 Select the desired option while keeping in mind that the first grid loaded should be the main grid the second should be sub grid 1 and so on Selecting Main Grid will open a File window Figure 11 which will display the 29 available geometry files in the current directory Select a geometry file or use the other features of the window to select a different Pier directory If one of the Sub Grids is selected the usc peopleicwplbetatesticellphone antup id ratio of the subgrid cells to the main grid cells Directories Files must be specified before proceeding to select the file Le fusr2 peopl fusr2 peopl fusr2 peopl usr2 peopl fusr2 peopl usrZ peopl ellphone antup 7E 6 2 2 Open XFDTD Project File The Project file is selected in the same manner
42. relationship can be used fields bytes materials bytes storage NC x d MM S M 2 cell field cell material Note If no magnetic materials are present and the magnetic grid has not been defined the factor of six multiplying the materials cell factor is reduced to three 13 This equation neglects the relatively small number of auxiliary variables needed by the program It also neglects the memory needed to store the executable instructions Since this overhead is nearly independent of the number of cells in the problem space as the total number of cells increases it will become a smaller fraction of the total memory required However if the computer memory storage as computed above exceeds the memory capacity of the computer then fewer FDTD cells must be used This estimate will be low if many far zone field directions are specified with transient calculations especially if the calculation has a large number of time steps For each far zone direction the program will require six floating point 4 byte arrays with a single array index slightly larger than the number of time steps specified This additional storage can be easily estimated and added to the above For a 100 cell problem space approximately 30 MBytes of memory would be required with the actual amount being somewhat greater due to storage of other variables and instructions plus memory needed by the operating system Problems of this size can be run on machines ran
43. resulting plot as it would appear on the computer screen is shown in Figure 69 It compares very well with measured results shown in Figure 14 27 of 7 99 1 St Hango Arigna on Seer Hoe De yw edo jp m aleia IBIS ze i l l EEA Figure 69 The input impedance plot of the monopole 14 2 Microstrip Meander Line The next example is of S parameter results for a microstrip meander line The meander50 id and meander50 fdtd files that correspond to this example are included with XFDTD This example can be loaded and the results viewed in XFDTD The meshed meander line geometry is in the x y plane at z 3 This can be viewed using XFDTD50 and going to the z 3 plane The geometry and measured results are taken from 18 The meander line is on a dielectric substrate 0 49 mm thick with dielectric constant 2 43 The FDTD cell size is 0 245 mm cubes so that two cells correspond to the thickness of the substrate The electric field mesh locations on the surface of the substrate are assigned a dielectric constant of 2 43 1 2 1 72 to correctly model the air dielectric interface in the FDTD equations The stripline width is 1 41 mm which was meshed using 6 FDTD cells The lengths of the meanders are 9 87 mm or 40 cells and the spacing between meanders is 0 94 mm or 4 cells The distance from end to end of the line is 60 mm or 245 cells The Liao absorbing boundary is chosen With ample spacing to the absorbing outer b
44. that would be required to make the calculation An FDTD mesh of two million cells will require about 96 MBytes of RAM A cell size of 3 mm was chosen for the original mesh since it will allow the head and shoulders region including a 20 cell border to be modeled in a space of 153 x 118 x 120 or 2 166 480 cells Creating the XFDTD id file from the axial anatomical images Each of the axial anatomical images contains 33 mm x 33 mm pixels We sample each image every 9 x 9 pixels such that we represent an area 3 mm x 3 mm with one pixel or 24 bit value We convert this 24 bit data value to a corresponding set of constitutive parameters by assigning tissues to five different tissue types Each of these is also assigned a material type number in XFDTD In addition we add a group for skin It was not possible to separate skin from the other tissues from the files so a one to two cell layer of skin was added manually This grouping or conversion process was done by inspection Each 24 bit value that corresponds to an FDTD cell was originally examined with the help of 19 20 and properly placed into one of the above six groups 119 Dr Michael Smith and Mr Chris Collins of The Milton S Hershey Medical Center Hershey Pa reviewed the original FDTD mesh developed by Remcom Inc and revised it These revisions included improved fidelity additional shoulder region and removal of small regions of blood which do not correspond to a living hum
45. the XFDTD window are listed below 1 Title Bar across the top This contains the name of the window and is colored shown in blue in the figure when the window is active 17 SATO hian Gnd wiin Be Edi yie Wedre Help oleja anle e co Teil nam LLL TIT NN du Buscan 1 Fike Snap Shots 4 HaeeZone Dena de FerZare Deis Boundary Coubsens Tormos Type aija Feud Brune Memor m eit Wises Gild wiling A B IE am aver a T Pine i Exenetein 4 qq Omnes Losada M See Fran a x Naor Zone Dee BENEA mah Figure 2 XFDTD window as seen on a Windows NT 95 98 computer 2 Menu Bar pulldown menus for File Edit View Window when viewing the geometry file When viewing the Run Parameters window the Results entry is also added The menu bar on the UNIX version of XFDTD will always display all the options as there are not separate windows for Geometry and Run Parameters 4 Tool Bar a row of icons which provide one touch operation of frequently used functions Figure 3 Pop up balloons describe each button when the pointer is above the button If a particular function is not available the button is disabled For example if no geometry is active for editing the edit geometry button will be disabled olsa ee oc Cale e ee E3 Figure 3 The Tool Bar in XFDTD 5 0 5 Main Grid WINDOWS VERSION The Main Grid Window displays the actual problem space When
46. the size of the FFT used for the S parameter calculation so that the plot over this frequency range would be smooth 103 Fraqumacg iri Figure 72 Magnitude of S for stripline Wilkinson power divider calculated using XFDTD 14 4 Dipole Near Lossy Sphere This example is based on the COST 244 canonical model of a layered lossy sphere The sphere is intended to be a rough approximation to a human head The sphere has an outer diameter of 20 cm which includes a 0 5 cm thick outer layer representing the skull bone Calculation frequencies for the model are 900 and 1800 MHz The example here uses FDTD cells small enough for 1800 MHz calculations but only 900 MHz results are considered For the SAR calculations the material parameters at 900 MHz are relative permittivity 17 conductivity 0 25 S m and density 1200 kg m for the outer skull layer For the inner brain volume the parameters are relative permittivity 43 conductivity 0 83 S m and density 1050 kg m The sphere is excited by a 0 4 wavelength long dipole with a 0 25 cm feed gap and a wire diameter of 0 25 cm The dipole is located 1 5 cm from the outer surface of the sphere At 900 MHz the wavelength in free space is 33 33 cm so the dipole then has a total length of 13 33 cm Desired output results are the SAR distribution relative to a maximum value the total absorbed power with reference to the total radiated power the input impedance of the dipole and the radiation pattern T
47. 1991 J Beggs R Luebbers K S Yee K Kunz Finite Difference Time Domain Implementation of Surface Impedance Boundary Conditions IEEE Transactions on Antennas and Propagation vol 40 no 1 pp 49 56 January 1992 R Luebbers K Kunz FDTD Modeling of Thin Impedance Sheets IEEE Transactions on Antennas and Propagation vol 40 no 3 pp 349 351 March 1992 R Luebbers K Kunz Finite Difference Time Domain Calculations of Antenna Mutual Coupling IEEE Transactions on Electromagnetic Compatibility vol 34 no 3 pp 357 360 August 1992 130 R Luebbers F Hunsberger FDTD for Nth Order Dispersive Media IEEE Transactions on Antennas and Propagation vol 40 no 11 pp 1297 1301 November 1992 R Luebbers J Beggs FDTD Calculation of Wide Band Antenna Gain and Efficiency IEEE Transactions on Antennas and Propagation vol 40 no 11 pp 1404 1407 November 1992 F Hunsberger R Luebbers and K Kunz Finite Difference Time Domain Analysis of Gyrotropic Media I Magnetized Plasma IEEE Transactions on Antennas and Propagation vol 40 no 12 pp 1489 1495 December 1992 R Luebbers L Chen T Uno and S Adachi FDTD Calculation of Radiation Patterns Impedance and Gain for a Monopole Antenna on a Conducting Box IEEE Transactions on Antennas and Propagation vol 40 no 12 pp 1577 1583 December 1992 R Luebbers T Uno K Kumagai Pulse Propagation in a Linear Causally Dispersive Medium Proceedings
48. 33 Y 19 Z 46 Main Grid Figure 37 Sample Near Zone Data menu 61 surrounding that cell edge Thus the current density only includes the conduction current When a near zone or TEM source is used as the input the total field values are available With an incident plane wave input the scattered and total electric and magnetic fields may be saved in addition to the total current density The location of the field quantity must be specified by its X Y Z location in the geometry grid If subgrids exist the desired grid must also be specified Note Near zone fields in the main grid may not be saved in areas covered by a subgrid The subgrid fields overwrite the main grid fields so saving the subgrid field provides the same information as saving the main grid field Note The location of a near zone quantity may be specified simply by positioning the mouse on the desired cell edge and pressing the right mouse button Choose Save Data from the popup menu This will open the menu shown in Figure 37 Each quantity added to the list at the bottom of the window will be saved by the calculation program The output will be a file containing the time and the near zone quantity After the entire calculation is complete these files may be displayed in XFDTD with the plotting features 9 3 Transient Far Zone Angles The Transient Far Zone Angles menu Figure 38 is used for specifying far zone ung Methods mn directions with a transient
49. 5 cm from the bottom of the sphere The specific absorption rate SAR values in all planes of the liquid are saved for viewing 114 Movies of the SAR through the liquid may be created The SAR data is available for averaging using the Results gt Compute SAR statistics menu The maximum whole body average and maximum 1 and 10 Gram averaged SAR values are available after computing the SAR statistics from the Results gt Display SAR Information menu Additionally some data regarding the dipole is available including the steady state input impedance input power and efficiency and the S11 values at the input frequency Antenna patterns of the dipole sphere geometry may be computed if desired Comparisons of XFDTD impedance and SAR simulations of this geometry with experimental data is available in the report Measurements and FDTD Computations of the IEEE SCC 34 Spherical Bowl and Dipole Antenna by Martin Siegbahn and Christer Tornevik of Ericsson Radio Systems This report is included with the CDROM as an Adobe Acrobat file called ericsson pdf 115 15 Trouble Shooting The XFDTD programs have been extensively tested and should operate reliably on all supported platforms Should you encounter any difficulties you may contact Remcom Inc by phone fax or electronic mail REMCOM Inc Calder Square PO Box 10023 State College PA 16805 Phone 814 353 2986 Fax 814 353 1420 E mail xfdtd remcom com URL http www remcom com Be
50. Adjust Merge Characteristics 0000085 30 6 2 5 Open es File a scie pee eee a ee oe HAA eae 31 6 2 6 Create New Space 6 4 4 4 ce ne eee EDS CUPS EXPEDIRE 31 6 2 7 Show Information Window 00000 eee eee ee eee 32 6 2 8 Save Geometry secas an ie ale wate ws ius wee a UE 32 6 2 9 Save XFDTD Project File rir r8 RA 32 6 2 10 Destroy Existing Space 0 42 24402442 2cn9 84h ces EEG 32 6 2 SIT DEN 32 T Edit Menu Geop y once aeter P T adr P ROME ESI E DeC aeri s 33 7 1 Geometry Editing 5 eo aor pu Rx DR EDEN EE SUE 33 7 2 The Material Palette Windows Version Only lslssuuss 34 7 3 Specifying Electrical Materials ion m is wre elas wis oo ewes ee 34 7 4 Specifying Magnetic Materials 0 0000 eee 35 7 5 Specifying Material Densities 0 0222 eee eee 37 7 6 Edit Thin Wires ci See riae ew ad pe dace oce ae ich yu EE Seo ne Se 37 737 Geometry Editing TOOS eim EIE EAS PEUPLE EAS 38 7 7 1 User Defined Objects 29e RR IR IB I ABRE 39 7 7 2 Additional Layers in Geometry lslslllllsssn 40 PRO EIDA zi oe eats oic e ea medie a ca biete es Ba he Data E 40 7 7 3 1 Circular Cylinder and Conic 41 Vf ae elt s doti dos mtd tere ics ee beers rre ces 41 7 7 3 3 Plate 1 component thick rectangular 42 7 7 3 4 Plate 1 component thick quadrilateral 42 7 1 3 9 Rectangular BOX srne 3e tuno ea awe m eu g
51. FFT size for increasing the resolution of the results in the frequency domain To do this simply open the Compute S Parameter Data window and set the desired FFT size Press the OK button to compute the new S parameter data Note The S parameters computed will depend on which port is currently designated as active For example if active port 1 is selected than S11 S21 S31 and so on will be calculated 10 5 Compute Averaged SAR Statistics Note In XFDTD 5 0 the SAR statistics are computed during the execution of the CalcFDTD program rather than in post processing This menu will perform the same function but it is more efficient to use Edit gt All Plane Steady State Data gt 1 or 10 Gram Averaged SARs when defining the project before executing the CalcFDTD program XFDTD 5 0 computes the Specific Absorption Rate SAR in each complete cell containing lossy dielectric material and with a non zero material density To be 79 considered a complete cell the Compute SAR Statistics E3 twelve cell edges must be lossy dielectric material With the ek ovr ce Compute SAR Statistics menu the Ere maximum SAR in the geometry can Type be found both the value and the Find Max Whole Body Avg Only cellular location as well as the C 1g Averages whole body average the average of C 10g Averages the SAR in all the lossy dielectric aig and ieaveres materials If desired a 1 or 10 gram averaging calculation ma
52. Palette You can choose whether you want the next available color or whether you want to select a specific color Either choice brings up the Edit Electric Material window Figure 15 In the Unix version the equivalent operation is to open the Electrical Materials Parameter Window from the Edit gt Geometry menu b Clicking this button on the tool bar will display the Electric Materials Palette Windows and display the electric components of the grid The Edit Electric Material window for Windows or the Electrical Material Parameters window for Unix is used to edit the values of constitutive parameters for dielectric materials including frequency dependent dielectrics XFDTD has three options for dielectric material models For a normal dielectric one in which the electrical properties do not vary significantly with frequency the conductivity in Siemens meter 34 Edit Electric Material Ea Type Description LO N mal C Debye C Lorentz Conductivity D Permittivity Infinite Freq P resonant Rrequency He a Damping Gaeficient He ae SARDensity kg m 1000 Delete Help Cancel Figure 15 Edit Electric Material window and relative permittivity may be set These values may be found in tables or other sources Typically when a good conductor is to be included in an FDTD calculation a perfect conductor should be used as an approximation Trying to include the effects of a good conductor rather than perfect conduc
53. REMCOM Inc Phone Fax e mail URL USER S MANUAL FOR XFDTD THE Calder Square P O Box 10023 State College PA 16805 814 353 2986 814 353 1420 xfdtd remcom com http www remcom com FINITE DIFFERENCE TIME DOMAIN GRAPHICAL USER INTERFACE FOR ELECTROMAGNETIC CALCULATIONS Version 5 0 4 9 Sept 1999 Copyright O 1994 1999 REMCOM Inc All Rights Reserved XFDTD is a Registered Trademark of Remcom Inc Table of Contents T Introduction seeren TP 6 t Operating System sirri ra irna n a E ACUTA EEN 6 1 2 General Technique for FDTD Calculations 005 6 1 2 1 Define Geometry serre eee ees edt eee hee e ees 6 1 2 2 Define Project Parameters 000 02 eee 7 1 2 3 FRESUITS and QUIUBE 52r deerat us av alg avs Tae dro qe iuo a 7 1 3 Summary of XFDTD Features on tcr to eta teeta Ron eee 7 2 Installation and Licensing 2 sere sere ott EE ats Meo Eon Sees I ct Se SS 11 3 Estimating Computer Resource Requirements 0000 eee eee 12 3 1 Defining the Cell SiZ s i eate ee c Che Bok Cee Bee ws 12 3 1 1 Creating a Geometry with FDTD Cells 12 3 1 2 Free Space Boundaries n 2 reta ahaa aed es a ed 13 3 2 Determining the Total Number of Cells 200000005 13 3 3 Estimating the Necessary Computer Resources 13 3 3 1 Far Zone Radiation angles at a single frequency 14 3 3 2 Execution
54. Sequence XZ Plane Y 19 Timstep 20 to 320 by 20 amp 23 S Parameters Figure 66 The project tree after the calculation 15 Open the Field Controls tool if it is not already opened either through the Results View Fields menu or from the icon on the Tool bar Choose to display Ez with a dB scale with dB increment of 15 Then start the sequence by pressing the Play button The field snapshots of the fields will be sequentially displayed A view of the fields after 80 time steps is shown in Figure 67 BL Ic aie do 1 28 AWENA 1 44th ia T S Sale E g kerman l surasa en Hoe Bra Mif o gwp Pa did eaded TE 3 mmberi d Herbir ine Figure 67 The field display of the monopole on a box geometry 16 Next consider the input impedance for the monopole From the Results menu click on Display Plot Choose to view Data versus Frequency and then in the Available Plots window find Input Impedance vs Frequency entry Select this entry and choose Real and press Add to Plot Press Imaginary and again press Add to Plot The Plot window should look like Figure 68 Chace Piri Don cm Figure 68 The Plotting tool after selecting the Real and Imaginary parts of the monopole impedance If using the Windows version press Next and then set xmin to 0 2 xmax to 6 0 ymin to 1000 and ymax to 1000 In the Unix version this is done by pressing the Edit Plot Parameters button After specify titles the
55. a plane at various moments in time The file has a header which contains five lines Below is an example with the definitions of each item t means the file contains total field data This is always the case 80 12003180 timestep number maximum timestep number slice direction 1 xy 2 yz 3 xz the slice number which is always one less than what is shown in XFDTD and the grid number O main grid 1 subgrid 1 etc 67 37 91 the dimensions of the space in cells 3 216099e 00 the timestep in picoseconds 1 670000e 03 1 670000e 03 1 670000e 03 the spatial increments of the geometry Following this header there are 9 floating point numbers for every cell in the space starting in the lowest corner and working up to the highest So if this is the xz plane the first point will be for x21 z 1 The loop will be as follows from z 1 to maximum z From x21 to maximum x Write gt Ex Ey Ez Hx Hy Hz Jx Jy Jz In the xy plane it will be from y 1 to maximum y From x 1 to maximum x Write gt Ex Ey Ez Hx Hy Hz Jx Jy Jz In the yz plane it will be from z 1 to maximum z From y 1 to maximum y Write gt Ex Ey Ez Hx Hy Hz Jx Jy Jz 127 Steady State Data Steady state data files have the same header as the transient field files The SAR and conduction current files have a different body while the electric field magnitude and magnetic flux density files have the same format as the transient field files only with
56. al anatomical images contains 33 mm x 33 mm pixels We sample each image every 15 x 15 pixels such that we represent an area 5 mm x 5 mm with one pixel or 24 bit value We convert this 24 bit data value to a corresponding set of constitutive parameters by assigning tissues to six different tissue types Each of these is also assigned a material type number in XFDTD The six groups of tissue types and their XFDTD material numbers are group 1 XFDTD 14 fat bone cartilage group 2 XFDTD 4 intestine liver kidney muscle spleen pancreas skin group 3 XFDTD 9 nerve brain group 4 XFDTD 7 eye group 5 XFDTD 15 blood group 6 XFDTD 13 lung This grouping or conversion process was done by inspection Each 24 bit value that 123 corresponds to an FDTD cell must be examined with the help of 19 20 and properly placed into one of the above six groups For each tissue group we have found reasonable approximations to the material density in kg m 3 conductivity sig in S m and relative permittivity The electrical constitutive parameters change with frequency and values for 5 different frequencies are given in the table Constitutive Parameters for FDTD Human Body Mesh tissue type density 150 MHZ 300 MHZ 500 MHZ 700 and 915 MHZ kg m sig eps sig eps sig eps sig eps fat bone 1130 07 6 7 09 8 3 07 5 1 07 5 1 cartilage intestine 1020 88 69 92 57 85 56 1 0 52 6 liver kidney muscle spleen pancreas skin ne
57. al plate menu 7 7 3 5 Rectangular Box The rectangular box is used for defining a large volume of cells quickly Figure 26 Three points on the box are requested along with the thickness of the box The three points should be Units Cells s three corners on a plane through the center of Point1 Point Point 3 the box The thickness will set the extent in cells x x foz 4 xps 4 of the box above and below this plane The y pos 4 ypo 4 v 2075 4 thickness does not need to be an integer number z jos 3j z fos 4 zpos 3 but it will be rounded to the nearest cell i Thickness jar a Note To make an odd numbered thickness Help Cancel select the center point of the box to be in the middle of a cell Figure 26 Rectangular Box menu 7 7 3 6 Sphere The sphere Figure 27 requires a center point and l an inner and outer radius The sphere may also pirata aoe be meshed using fuzzy cells on the outer edges b ij Outer 21 if desired gt p 4 Inner Additional Fuzzy Levels o Cancel Figure 27 The sphere primitive menu 7 7 3 7 Spiral antenna Spiral antennas are complicated objects to enter Plane Center in FDTD cells Figure 28 A primitive has been i sw oE i added to XFDTD for three possible spiral antenna aes ae B UE i designs semi circular 8 equiangular 9 and i Archimedean 10 The parameters r
58. alues that can be saved include SAR specific absorption rate files electric field magnitudes magnetic flux density magnitudes or conduction currents These files can be made into movies that show the fields versus position in the geometry Diagnostics file fdtd diag This file provides some basic information about the FDTD calculation parameters including problem space size cell size time step size and number of time steps calculated Information on excitation either pulse or sinusoidal is also provided Progress file tsfdtd This file contains information regarding the progress of an FDTD calculation Typically it contains three numbers current time step total number of time steps percent completion There are various other files created by the FDTD calculation program that are used for postprocessing data For example files ending in fza fzb and fzin are used only by the postprocessors xpostpss50 and xpostp50 Additionally there are files created by the postprocessors such as antenna gain patterns or averaged SAR values 25 6 The File Menu The menus in the Windows version of XFDTD are standardized to match common Windows NT and Windows 95 98 applications This chapter will discuss the first menu option the File menu As the UNIX version of XFDTD follows a different format it is covered in a separate section of the chapter that follows the Windows section 6 1 The File Menu in Windows NT 95 98 Clicking on Fil
59. an but pooled after the death of the human subject Information about their research efforts can be obtained by browsing http nmr hmc psu edu The six groups of tissue types in the original mesh and their XFDTD material numbers are XFDTD 2 cartilage XFDTD 4 muscle XFDTD 7 eye XFDTD 9 brain XFDTD 12 dry skin XFDTD 14 skull bone These correspond roughly to the tissue groups of the entire body mesh except that the entire body mesh 1 has lung tissue and internal organs which are absent from the head shoulders mesh 2 combines cartilage with fat and bone and 3 includes blood For each tissue group we have found reasonable approximations to the material density in kg m In particular the values given by Camelia Gabriel Ph D and Sami Gabriel M Sc Physics Department Kings College London London WC2R2LS UK for average brain 1030 average skull 1850 and average muscle 1040 are used Their values of conductivity in S m and relative permittivity are also recommended for the head shoulders The electrical constitutive parameters change with frequency and can be obtained from the www site http www brooks af mil AL OE OER Title Title html which is supported by Armstrong Laboratory AFMC Occupational and Environmental Health Directorate Radiofrequency Radiation Division 2503 D Drive Brooks AFB TX 78235 5102 Approximate values for different frequencies as given by Camelia Gabriel Ph D and 120 Sa
60. ark you will need to select this item twice to make the FFT menu appear 12 Choose File then Save from the main menu and enter a name for the Project file The project is now ready to run 96 DE Hap Carnai Figure 65 The Transient fields window after entering the appropriate data 13 The calculation is started by selecting Results and then Run CalcFDTD On the Windows version a window will appear asking for the priority select Normal In Unix simply select Run CalcFDTD The calculation will then begin and a status window will open to display the progress of the calculation This calculation required just over 3 minutes on a 400 MHz Pentium Il Note On a Unix computer the calculation can be run as either a batch job or from the command line The command for executing the calculation is calcfdtd50 monbox50 where calcfdtd50 is the calculation program and monbox50 is the name of the project file Insert the correct file name in place of monbox50 14 Once the calculations are finished the data is ready for display Note In the Unix version of XFDTD the project file must be reloaded first Do this by selecting File then Open Project File 15 From the Project Tree click on the project name then on output files then on Transient Field Sequence as shown in Figure 66 Select the sequence 97 FDTD Project aX monobox fdtd Geometries Loaded 8 Output Files f Single Transient Fields s Transient Field
61. as similar features for viewing the geometry as mentioned above but all views are contained in one window To switch between grids or to view all grids the menu option View gt Set Viewing Space is available Additionally the grid pushbuttons to the left of the viewing window allow switching between the main and sub grids afiti PoE eut File Edit View Remit tidy SHOT eg nu FE L EA Ge amp EMOH Sin XFDTD Preject Files ax fiam ng id Acima li asmatry Fla mar ack mh Apa MEE epum main grid larg acidi Aonik la wd maa DO ac E OCRXI x E DET ee tirzestep 171 E a Figure 4 The XFDTD 5 0 interface on a UNIX computer 6 Geometry Information WINDOWS VERSION The pane on the right side of the status bar at the bottom of the XFDTD window shows the position of the cursor within the geometry When the cursor is outside the geometry this pane becomes Remcom Inc Also in the status bar is a pane with information that describes the current geometry The arrow button opens a menu with options for viewing the spatial increments and the dimensions of the geometry in cells and in physical units 20 UNIX VERSION The display for the location of the pointer is in the upper left corner of the geometry window The spatial increments number of cells and other information is displayed in the information area at the left of the geometry display 7 Run Parameters WINDOWS VERSION When a pro
62. at no cost The male data set consists of MRI CT and anatomical images Axial MRI images of the head and neck and longitudinal sections of the rest of the body are available at 4 mm intervals The MRI images have 256 pixel by 256 pixel resolution Each pixel has 12 bits of gray tone resolution The CT data consists of axial CT scans of the entire body taken at 1 mm intervals at a resolution of 512 pixels by 512 pixels where each pixel is made up of 12 bits of gray tone The axial anatomical images are 2048 pixels by 1216 pixels where each pixel is defined by 24 bits of color about 7 5 megabytes The anatomical cross sections are also at 1 mm intervals and coincide with the CT axial images There are 1871 cross sections for each mode CT and anatomy The complete male data set is 15 gigabytes in size Our mesh of the human body required the axial anatomical images since these had the finest resolution of the entire body 17 1 The Original 5mm Body Mesh The choice of the problem space dimensions came from consideration of the computer resources that would be required to make the calculation An FDTD mesh of six million cells will require about 180 MBytes of RAM and about 6 hours of run time on a fast work station A cell size of 5 mm was chosen since it will allow the entire human body including a 20 cell border to be modeled in a space of 157x102x396 or 6 341 544 cells Creating the XFDTD id file from the axial anatomical images Each of the axi
63. at the excitation potential A plane perpendicular to the conducting walls must be specified on the TEM Excitation Plane window The electric and magnetic fields of the TEM mode will be excited in this plane The excitation plane is typically located a few cells from the end of the geometry but may not be closer than 4 cells from the absorbing boundary Normally the propagation direction is into the geometry The TEM wave will propagate in the positive coordinate direction from the excitation plane so a typical selection for the slice number is 5 The calculation of the TEM mode fields may be verified by pressing the preview fields button and viewing the geometry in the appropriate slice plane The electric field vectors tangent to perfect conductors should be zero and should be directed away from normal to the conducting surfaces 9 1 4 Specifying the Source Waveform Regardless of whether the excitation is a plane wave near zone feed or a TEM mode the time variation of the excitation must be determined The Set Waveform button in the upper right corner in each of the stimulus definition windows controls this Pressing Stimulus Waveform EG Waveform Parameters C Gaussian Pulse Width time steps 3100 C ee Gaussian Derivative Amplitude valle iem C Sinusoid Frequency GHz 3 C User Defined Number of Time Steps fi 2000 Time Domain Frequency Domain
64. ata is displayed in the Data To Plot area Selecting one of these choices with the mouse will cause the corresponding options to become available The options depend on the type of plot As an example selecting the Input Impedance versus frequency choice will make the options Real and Imaginary active Any of the active plotting options may be selected and then the data can be added to the list of plots by pressing the Add to Plot button If a mistake is made the undesired plot should be selected with the mouse from the Data to Plot area and then pressing the Remove from List button will remove it For a completely new plot press the Remove All Plots button Changing the X axis type will also remove all plots from the list 75 The Windows version of XFDTD 5 0 uses a wizard for entering the plot data So after entering all the desired plots to the list press the Next button to view more options see Figure 49 or to display the plot The next screen will display windows for entering legends and line types for the data and labels for the axes The maximum and minimum X and Y axis values can be defined or set to automatic default which will scale according to the data There are also options for setting the location of the Label Setup Figure 49 The labels window on the Display Plot wizard on Windows legend drawing grid lines and axis tick marks Display the plot by pressing the Finish button 76
65. atios of either one third or one fifth may be selected Note the subgrid mesh appears to overlap slightly the main grid mesh This is normal and is caused by the mesh interpolation of the magnetic fields rather than electric fields For a cell size ratio of one third each of the grid dimensions NX NY NZ for the subgrid must be evenly divisible by three ie NX 3 is an integer For proper field interpolation each subgrid dimension should be at least 4 main grid cells Thus for a one third cell subgrid the minimum grid dimensions are 12 x 12 x 12 subgrid cells In addition if two subgrids are specified both must have the same cell size After setting the offset and ratio of the new subgrid the Create New Geometry panel Figure 9 will open and prompt for the same information as a main grid However when a subgrid is created the spatial increment has already been selected automatically and should not be modified The Number of Cells requested is in main grid cells not subgrid cells So entering an NX value of 4 with a 3 1 subgrid will create a new subgrid with an NX of 12 Subgrids may be specified to contain magnetic materials but for all calculations the subgrid space is assumed to have free space permeability and no magnetic materials will be visible in the subgrid If the subgrid is also used as a main grid in a separate project then the magnetic grid may be edited and used 27 6 1 2 Open This option opens geometry or projec
66. atterns Antenna Impedance vs Frequency vA Transient Far Zone Transformation A Feature XFDTD 5 0 Steady State Antenna Impedance Efficiency Antenna Gain vs Frequency Single Frequency Far Zone Transformation Linear Polarization Antenna Gain vs Angle Automatic Meshing of Spiral Antennas Thin Wires with different wire radii Incident Plane Wave Scattering Cross Sections vs Frequency Bi Static Scattering vs Angle XFDTD 5 0 Pro XFDTD 5 0 Bio Pro 10 2 Installation and Licensing The installation and licensing procedure for XFDTD depends on what operating system Unix or Windows you have and what version of XFDTD permanent license or evaluation license you are installing There are detailed descriptions of the installation procedure provided in two separate documents e For evaluation versions of XFDTD see the document demo install pdf e For permanent license installations purchased versions of XFDTD see the document permanent install pdf 11 3 Estimating Computer Resource Requirements This chapter discusses basic relationships for estimating computer resources required for FDTD calculations The important aspects of entering the geometry and calculation parameters are discussed Equations for estimating the amount of memory and computer CPU time required for a typical FDTD calculation are provided 3 1 Defining the Cell Size The starting point of an FDTD calculation is often deciding the
67. be is then added a TEM wave can propagate along the tube and be absorbed at either end in the two remaining absorbing boundaries This geometry is useful in making calculations of the electromagnetic fields inside a TEM exposure cell To excite the TEM wave inside such a geometry a special menu item in the FDTD menu allows for the TEM mode for any conductor geometry which includes at least one conducting FDTD wall and one other conductor to be generated and used to excite the FDTD calculation If the outer boundary of the calculation is not free space a plane wave should not be used to excite the calculation and the far zone transformations will not provide accurate results for far zone fields Note An edge of the FDTD space should be set to PEC using the PEC Boundary Condition DO NOT set FDTD cells to PEC material in the geometry and set the outer boundary to Absorbing as this will cause instabilities in the calculation 9 9 4 PMC Perfect Magnetic Conductor The final choice of outer boundary is PMC that is perfect magnetic conductor This may be useful in taking advantage of geometry symmetries to reduce the size of the FDTD mesh and therefore the memory and calculation time required 70 10 Results Menu The interface to the FDTD calculation v View Fields Ctrl ev program and the numerous options for Display Plot Ctrl P processing the output from an XFDTD calculation are found on the Results menu Figure 44 of the Run Parameter
68. can be checked by making a calculation and observing the transient field results by sampling near zone field points For a sinusoidal excitation sufficient time steps to reach steady state must be chosen Again near zone values should be saved and observed so ensure that the system has reached steady state Results that require the application of an FFT any results which will be displayed versus frequency or that assume steady state sine wave conditions have been reached such as antenna efficiency or steady state far zone transformation will not be accurate if sufficient time steps to not been specified lt is vital that the near zone results be observed to determine convergence before attempting to make conclusions about the output of a calculation Note The only way to be ensured of convergence of the FDTD calculation is to view the time records of near zone field values or the feed point current voltage XFDTD does not send an error message when an insufficient number of timesteps have been calculation The determination of convergence or steady state is left up to the user and is best viewed by plotting near zone field values 9 1 6 Far Zone Transformation for a Sinusoidal Source In the Sources Loads and Plane Wave Run Parameter sub menus there is a choice for the Far zone transformation type for a sinusoidal input Figure 33 If a transient input gaussian pulse etc is chosen this option will not be available The choices for the far
69. ce Time Domain Codes IEEE Antennas and Propagation Magazine vol 36 no 6 pp 66 71 December 1994 D Steich R Luebbers K Kunz Absorbing Boundary Condition Convergence Comparisons IEEE Antennas and Propagation Society International Symposium Ann Arbor MI June 28 July 2 1993 D F Kelley R Luebbers Comparison of Dispersive Media Modeling Techniques in the Finite Difference Time Domain Method IEEE Antennas and Propagation Society International Symposium Seattle WA June 19 24 1994 J Schuster R Luebbers Application of FDTD to Anisotropic Materials IEEE Antennas and Propagation Society International Symposium Seattle WA June 19 24 1994 R Luebbers and H S Langdon Reducing the Number of Time Steps Needed for FDTD Antenna and Microstrip Calculations 11th Annual Review of Progress in Applied Computational Electromagnetics Naval Postgraduate School Monterey CA March 20 25 1995 D F Kelley and R Luebbers The Piecewise Linear Recursive Convolution Method for Incorporating Dispersive Media into FDTD 11th Annual Review of Progress in Applied Computational Electromagnetics Naval Postgraduate School Monterey CA March 20 25 1995 J Schuster and R Luebbers Application of the FDTD Method to Three Dimensional Propagation in a Magnetized Ferrite 12th Annual Review of Progress in Applied Computational Electromagnetics Naval Postgraduate School Monterey CA March 18 22 1996 C Penney R L
70. cells These files always have the extension id For example the geometry of a monopole on a rectangular box might be saved as the file monbox id A geometry often referred to as id file may be either a main grid or a subgrid Thus a geometry file may be used alone for calculations or it may be used as a subgrid with a different geometry file serving as the main grid This removes the necessity for having two different types of geometry files while also allowing the use of the same mesh in a different calculation For example an antenna can be meshed and calculations made on it as a main grid Then this same antenna geometry file can be used as a subgrid in conjunction with a main grid mesh using larger cells of a vehicle on which the antenna is located When used as a subgrid the cells for the geometry must be smaller than those of the file used as the main grid mesh Alternatively the two grids can be merged into one mesh with the same cell size Ratios between Main Grids and Subgrids There is a constraint on subgrid meshes that the cell ratios between the main grid and subgrid must be fixed at odd integer ratios That is the subgrid cells must be one third or one fifth the size in each edge dimension of the main grid cells Also the number of cells in each dimension of the subgrid geometry must align properly with the main grid For proper alignment the subgrid dimension NX NY and NZ must be evenly divisible by either three or fiv
71. cells The button labeled X will set only the X directed components inside an area defined by the mouse The Y and Z labeled buttons function similarly The button with an icon of one square above another draws two dimensional sheets of cells in an area defined by the mouse The editing button with the two cube icon will set all geometry edges in the area selected This includes those components normal to the view The last two buttons on the bar are for copying an area and for rotating an area of cells When finished press Library gt End user defined Unix or End Object Windows to complete the user defined object When editing electric components the dielectric material locations naturally align with the grid However when placing magnetic components in the grid the material locations are offset by 12a cell in all directions This convention is used to represent the locations for the electric and magnetic materials in the Yee cell geometry 7 This may seem confusing when using the interactive mouse controlled editing of a magnetic mesh but it is easy to adapt to this 39 To aid in finding specific locations in the geometry XFDTD displays the position of the mouse pointer In the Windows version the mouse pointer location is displayed on the right most pane of the status bar In the Unix Version the pointer location is drawn in the upper right corner of the geometry window As the pointer is moved in the geometry window
72. ces are available immediately after the FDTD calculation finishes if the All Planes option was chosen for the steady state data Each different type of field display has a different menu laisse for controlling the fields The View Fields menu for a ViewField MagE Planar Transient Fields Sequence File is shown in Scale dB Figure 45 This menu is used for controlling the Se e display of the transient color intensity file snapshots in theme diver coral time domain ae maps the mE FDTD space that were selected prior to the calculation e oe pr pd Choose the field component to display from this menu Stet Er ET el BUS Choices are electric or magnetic field vector NNNM z components current density components total electric 1 runltrliaonz yz24 t100 fld Figure 45 The field control 7 panel or magnetic field or current density amplitudes obtained by combining all three field vector components and Poynting vector components The color intensity areas are the same size as one FDTD cell face when using the Quick Draw Fields Preferences menu Otherwise the fields of neighboring cells are interpolated to create a smoother field transition The display is centered on the spatial location of the current field component Some quantities such as total electric or magnetic fields or steady state SAR involve three vector components For these the color intensity area is centered on the spatial location of the field component no
73. compute 1 or 10 gram Average SAR values the SAR values must have been saved in at least one direction XY YZ or XZ for all planes using the All Plane Steady State Data menu To edit the planes selected to view the listing of planes or to add more planes use the Single Plane Steady State Data menu described in the previous section If the All Plane menu is used the steady state sequence files for that particular quantity will be computed automatically Note In previous versions of XFDTD the average SAR calculation was performed in post processing This function must now be defined before executing the calculation program using the All Plane menu Select All Plane Steady State Data gt 1 or 10 Gram Averaged SAR from the Edit menu and then select the desired direction 9 7 Compute Input Impedance If the transient far zone transformation has been selected the input impedance versus frequency may be computed for the first voltage source To do this select the Compute Input Impedance option Figure 42 Enter the desired FFT size on the menu which must be larger than the number of timesteps to be computed Selecting a larger FFT size will provide more sample points of the impedance in the frequency domain This will result in a smoother impedance plot The input impedance is determined as the complex FFT of the total source voltage divided by the FFT of the total source current at each frequency This input impedance will include the effects
74. d takes precedence over the materials specified in the same region of space in the main grid When materials cross the main grid subgrid boundary the alignment can be checked by choosing to view All Grids This is done by selecting the appropriate window in the Windows version of XFDTD or through the View Set Viewing Space menu in the Unix version of XFDTD If the Grid is displayed then a slight overlap of the main and subgrids is evident This is due to the interpolation scheme used between the two grids For materials that cross the boundary the same material type should be set in the outer subgrid cells and the inner main grid cells that touch the main grid subgrid boundary To help setting the alignment the mouse cursor position for both grids is displayed when the view is set to All Grids If material is to cross the boundary the exact cellular coordinates of the material can be found in both grids The subgrid interpolation scheme is designed to allow dielectric materials to have boundaries which cross the main grid subgrid boundary However magnetic materials if they cross the main grid subgrid boundary must be uniform within 5 cells of the boundary in order to avoid instability and inaccuracy The subgrid position within the main grid can be adjusted easily by changing the offset of the subgrid This is done by selecting the Subgrid Location in Main Grid option from the Edit menu The subgrid location is offset by slightly from what ap
75. dy state far zone transformation The steady state far zone transform only provides a pattern at the input frequency but patterns in any direction at any resolution may be computed in postprocessing 9 4 Planar Transient Fields Location C XY The Planar Transient Fields window Grid Main Sr Slice js 3 Figure 39 is used for saving a movies of fields in specific planes of rimesispe the geometry during the FDTD Beginning 20 calculation The principle plane XY Increment 20 YZ or XZ must be specified along Ending 200 with the slice number ie Z 25 and the grid if subgrids as Te _Add Sequence _Delete Sequence Dele Ar starting ending and increment values in timesteps must be entered as well A field file containing the electric and magnetic fields and the current will be created for each timestep specified mr Help ERE For example setting the entries to m ae Beer Z 25 beginning at timestep 100 ending at timestep 1000 with an increment of 100 will create 10 field files which may be viewed as a movie after the FDTD calculation is performed Main Grid Y 19 increment 20 begin 20 end 200 Figure 39 Planar Transient Fields menu Note Great care should be taken when specifying the number of field slices to save as they can store enormous amounts of data Single field files may contain megabytes of data depending on the number of cells in the specified plane If field slices
76. e depending on the ratio of the subgrid If a geometry file does not fit properly a new mesh can be created that has the correct dimensions and the geometry can be merged into it The Merge feature is covered in a later section of the manual If a main grid is first created or read into XFDTD and then a subgrid is created the subgrid dimensions are entered as a number of main grid cells and XFDTD 23 automatically provides the correct number of subgrid cells to fit into the specified portion of the main grid 5 2 Project Files Project files contain the calculation parameters and the filenames of any geometry files associated with a particular calculation Project files have the extension fdtd Continuing the example from above with the monopole on a box the project file might be named monrun fdtd The project file may also have the same name as the geometry file 5 3 Output Files After the execution of the FDTD calculation program many files might exist Which files are created by the calculation program depends entirely on the run parameters specified in the project file A listing of some common files created are listed here In this section the assumption is made that the project file was named monrun fdtd Transient field slice files monrun varies fld These files contain near zone field data in particular slices of the geometry The name is determined automatically depending on the location of the slice plane and the timest
77. e material display is toggled off The dipole is actually in this plane and will be visible when the file is first loaded The color display may also be changed by changing the dB increment from the 18 dB used for this figure The far zone radiation pattern can be obtained from the Results Compute Far Zone Plot Data Choose a constant theta pattern with theta 90 degrees and let phi cover from 0 to 360 degrees in 2 degree increments The pattern calculation will require some time Once it is complete the result can be displayed using the Results Display Plot menu The result for E theta polarization is shown in Figure 74 106 Figure 73 Unaveraged SAR distribution for Dipole near Lossy Sphere example in the y 60 plane with the input power scaled to 1 Watt SF OTE Pit Cipals Hem Lead Sphere M blir poches Fikah HNH Enn Baratte ii Figure 74 Azimuthal radiation pattern for Dipole near Lossy Sphere example 107 14 5 CDROM Example Files There are four groups of files on the XFDTD5 0 CDROM which include example results for viewing The various examples are discussed briefly here Refer to the actual example files for the results 14 5 1 Antenna Examples Cellular Telephone Example These files contain an example of a detailed cellular telephone handset The dimensions and internal distribution of the telephone are designed to be similar to an actual telephone but the internal components are not functional The telephone
78. e opens the menu shown in Edit View Window Figure 8 The first three entries are for creating cae CtrleN a new file opening a previously created fips Chie geometry or project file or merging two Merge geometries together Following this are Save standard Save options for saving either the Save As geometry or project file The Close option will Close close the currently selected window The Print Chl P options for printing are standard among Pit Setup Windows programs and will not be discussed Print Preview here A listing of previously opened files is attached to the bottom of the menu along with the Exit choice 1 CXXFDTD Program monbosv4 2 CNXXFDTD Program monboxv4 3 CXXFDTD Program smonboxv4 Exit Figure 8 File Menu 6 1 1 New The New option on the file menu is Spatial Increment Cellular Dimensions Components used for creating new geometry or Units CEE project files If a geometry file is E zd l already open the New option will Detax 1 M Electric create a subgrid geometry If a new Detay v n a geometry is selected a panel pez l appears for entering the spatial ees 2 fa a Magnetic increment of the grid the cellular Quick Cale dimensions number of cell edges in each dimension and whether a ae Help as Electric or Magnetic components will Ls tee Eea be in the mesh Figure 9 When Figure 9 Create New Grid no magn
79. econds phi directed electric field v m theta directed electric field v m For gain RCS versus frequency there are five columns frequency Hz phi directed gain magnitude dBi or dBsm theta directed gain magnitude dBi or dBsm phi directed gain phase degrees theta directed gain phase degrees For gain RCS versus theta or phi there are five columns theta or phi degrees phi directed gain magnitude dBi or dBsm theta directed gain magnitude dBi or dBsm phi directed gain phase degrees theta directed gain phase degrees For steady state far zone files the choices are gain RCS versus theta or phi There are no far zone time domain fields available with the steady state far zone transformation For gain RCS versus theta or phi there are five columns theta or phi degrees phi directed gain magnitude dBi or dBsm theta directed gain magnitude dBi or dBsm phi directed gain phase degrees theta directed gain phase degrees 126 S parameter Data Example monbox s11 or monbox ss s1 1 For transient S parameter calculations the file has five columns frequency Hz the real part the imaginary part the magnitude dB and the phase degrees For steady state S parameters there is only a single line of data in the same format as above Transient Field Data Example monbox xz12 t200 fld These are the field snapshot which show the electric and magnetic fields or current density in
80. electric field magnetic field and conduction current density magnitudes are saved and displayed as peak values These steady state quantities are available only if sinusoidal excitation is chosen Check near zone values ensure that steady state has been reached in the calculation If not increase the number of timesteps and run the calculation again In XFDTD 5 0 the SAR is formed from the 12 edges of the cells The four electric fields in each direction are averaged to give the x y and z directed fields using in the SAR equation Previous versions of XFDTD formed the SAR at nodes using 3 electric fields The SAR values and results in XFDTD 5 0 will vary slightly from earlier XFDTD version results Note If non biological lossy dielectric materials are present perhaps a plastic cover for a cellular phone setting the material density of that XFDTD material type to zero in the Edit Material Densities menu under Edit will cause XFDTD to predict zero SAR for that material 65 9 6 All Plane Steady State Data The All Plane Steady State Data menu should be used when any of the Steady State quantities are desired in many planes By selecting this option movies of the steady state quantities versus position in the geometry may be viewed in XFDTD after the calculation is complete This option will also automatically select which SAR and conduction current CCM planes to save based the material in the geometry in each plane Note To
81. emcom High Fidelity Head and Shoulders mesh is based on the same data as used in the 3mm mesh but it uses 2x2x2 5 mm cells and has dimensions 309x177x161 for 8 805 573 cells It contains 17 materials which are assigned as follows XFDTD 2 Skin XFDTD 8 Tendon XFDTD 4 Fat Yellow Marrow XFDTD 5 Cortical Bone XFDTD 6 Cancellous Bone XFDTD 7 Blood XFDTD 8 Muscle XFDTD 9 Grey Matter XFDTD 10 White Matter XFDTD 11 Cerebro spinal fluid XFDTD 12 Sclera Cornea XFDTD 13 Vitreous Humor XFDTD 15 Nerve XFDTD 16 Cartilage XFDTD 17 Tongue Thyroid XFDTD 19 Cerebellum XFDTD 20 Esophagus Measured values for the tissue parameters for a broad frequency range from 1 MHz to 20 Ghz are included with the mesh data The tissue parameters may be adjusted automatically for a specific frequency by using the Edit gt Adjust Tissue Material Parameters menu The correct values from the table of measured data will be selected and entered into the appropriate mesh variables The mesh must be saved after adjusting the parameters for the new values to be used in the XFDTD calculation but the parameters can be adjusted as many times as required 122 17 The Human Body FDTD Mesh You may have received one of our FDTD meshes of a male human body They were created using digitized data in the form of transverse color images The data is from the Visible Human Project sponsored by the National Library of Medicine NLM and is available via the Internet
82. ements as 1 67 millimeters the space dimensions as 67 x 37 x 91 and specify only Z Di s an electric grid Our example geometry has no ios em of s Hh a magnetic materials so the magnetic grid is not eee needed nor will we need to create a Subgrid Har Ca Figure 60 Creating the example 3 The next step is to put our geometry into the FDTD main grid Open the Geometry Editing Tools by selecting them from the Edit menu or by pressing the icon on the Tool bar From the geometry 93 Materials Palette select material PEC Then select New on the Geometry Editing Tools window and then select Rectangular Box from the library menu To locate the box with monopole in the center of the space we determine the mesh locations for the surfaces The constant x surfaces are at x 16 and x 51 cells the y surfaces at y 16 and y 22 and the z surfaces at z 16 and z 46 Using the Rectangular Box primitive construct the box by defining the three points as 16 16 31 16 22 31 and 51 16 31 Set the thickness to 30 cells The windows should appear as shown in Figure 61 Rectangular Box x Faint 1 Point 2 Point 3 X fie a x 116 x 1 E Ye 22 b fie Z 431 Z 431 Z 31 Thickness 20 Hoe omes Figure 61 The rectangular box primitive menu with the data entered for the monbox base 4 Press OK on the Rectangular Box menu to add the primitive to the list Then pr
83. eometry into a blank space this feature is not applicable However in some instances there are two existing geometries which will be merged This function defines which materials will overwrite others should the two geometries overlap Selecting this option will open the menu shown in Figure 12 where the choices of Electrical and Magnetic mask are used for defining the overlap of either the electrical or magnetic components 30 Atja Whaariges Chonra e E Canari of Geom File Merging Edit material oeerarite mass Electric Mask Magratle Mask OK Caneal Halp Figure 12 The Adjust Merge Characteristics menu 6 2 5 Open File There are four choices of output files which may be opened Each is described below Open Single Transient Field File Select this option to open a single time domain field file For the currently loaded geometry the field files can be selected from the Project Tree However occasionally a field file from a different calculation is desired This menu option can be used for opening field files that are not in the Project tree or simply as an alternative to the Project tree Open Transient Field Sequence File This option has the same function as the time domain field file menu item mentioned above but it is for sequence of time domain field files Open Single Steady State Data File Used for opening single steady state files which may be either SAR electric field magnitudes magnetic flux densities conduction
84. ep during the sample For example monrun xy10 t100 fld indicates fields in z 10 plane at time step 100 Field screen show files monrun varies fss These files contain a list of transient field slice file names for automatic display in a movie format The slice plane of the geometry remains fixed and the movie shows the field propagation versus time The name is automatically determined For example monrun xy10 fss indicates a screen show file of fields in z 10 plane Feed voltage and current file monrun vc When a transient far zone calculation is performed this file contains three columns of time voltage and current at the feed With the steady state far zone the file contains values for just two time steps just below the maximum number of time steps Input impedance file monrun imp This file contains the input impedance versus frequency There are three columns frequency Hz real and imaginary Near zone field samples files monrun varies These files hold near zone values versus time at any location within the geometry The near zone value saved can be electric or magnetic fields or currents As an example monrunEXS x00010 y00020 200030 90 would contain 24 the x directed electric field component at cell location x y z i j k 10 20 30 is saved Steady State Field Quantities monrun varies sar cef ofd ccm These files contain steady state field magnitudes in a particular slice of the geometry The steady state v
85. equired vary Tums 15 Zentren jus depending on the type of spiral being built Each Width 0 000866 Ara Lent of the types may be constructed using the dilinirmum Festive Crooner suggested parameters below but the references Esgansion Fieis U for each antenna should be used for an exact Pas sul E A determination of the parameters required for a He cm specife design Figure 28 The spiral antenna primitive menu Semi Circular Create an FDTD space with dimensions in cells of 178x179x31 with 2 5 mm spatial 43 increment In the spiral antenna parameters window choose Semi Circular Set the Width to 1 cm and the Turns at 3 Mesh the antenna in the XY plane at the center of the space Equiangular Create an FDTD main grid space 124x158x31 cells with 2 0 mm spatial increment Use the edit panel to set the cell edges in the z 16 plane to PEC In the spiral antenna parameters menu choose Equiangular Set the Min Radius at 0 005 m the Expan Rate at 0 303 the Ratio at 0 75 and the Length at 0 428 Mesh the antenna in the center of the XY plane at z k 16 Archimedean Create an FDTD main grid space 180x180x31 cells with 0 3 mm spatial increment In the spiral antenna parameters menu choose Archimedean Set the width at 0 00334 the minimum radius at 0 00334 the expansion rate at 0 00835 and the circumference at 0 167 Units c ells z Feint 1 7 7 3 8 Wire The wire Figure 29 is a very useful primi
86. ero The next part of the file is organized into 25 sets of 5 lines each one set for each of the 25 material types that can be defined The labels start at Material 2 since Material type 0 is reserved for free space type 1 for perfect conductor The first two lines of each material definition are used for labels and must contain the labels emat02 and mmat02 etc exactly as shown The label if defined may be written after the descriptor but is best left blank at this point The next line holds five floating point numbers for relative permittivity conductivity Siemens meter relative permeability magnetic conductivity and material density kg m The next line holds four floating point numbers and one integer for defining the dispersive material parameters of static relative permittivity relaxation time resonant frequency damping coefficient and the integer indicating the dispersive material type 0 for normal 1 for Debye 2 for Lorentz The last line contains five floating point numbers and one integer for anisotropic magnetic material parameters of Lamor Precession Frequency rad sec saturation 84 magnetization rad sec damping coefficient theta and phi of the static magnetic field and finally the integer indicating the magnetic material type 0 for normal 1 for anistotropic Note While the parameters for a material may be defined this way it is strongly recommended that the materials be left at the default va
87. ers of the adjoining material 7 8 Spatial Increment With the Change Spatial Increment window the cell size of the cells in an FDTD geometry may be adjusted Figure 30 This will not change the numbers or locations of FDTD cells only the cell size DeteX 167 Deka 157 Delta fis This option should be used for make adjustments or changes of scale Help Cancel Remember than a 10x10 cell plate will still be 10x10 cells but the actual dimension Figure 30 Change Spatial Increment window in physical units will change based on the values entered on this window 7 9 Add Dual Grid UEG Y Add Dual Grid may be used to add either the magnetic or electric grids to a geometry In most circumstances this feature would be used if a geometry was defined with only the electric grid and at a later time some magnetic material was desired By using this feature the dual grid will be added to the geometry and will be available for editing 45 Adding the dual grid will increase the memory storage requirements of the geometry because three new three dimensional arrays will be added Also the calculations of the field equations by the calculation program will become slightly more complex So the dual grid should only be added when it is required Note that subgrids will not use magnetic materials in the FDTD calculations Magnetic materials may be defined in a subgrid geometry for cases where the subgrid will also be used as a main g
88. ers that have been calculated to Input Rower WY egies renee SEES be displayed If several calculations have pon 0 0000 Qn 0009500 been made the results of the most recent Normalized S Parameters Calculation will be displayed These results are also available in ASCII files ending in ss s11 ss s12 etc if the user wishes to work with the results directly If more than one FDTD calculation has been made in the same directory with the same 4 Project file name all of the results will be OK Hel Cancel E oem saved in the ss s11 etc files Figure 55 The Steady State data available 8 2843e 001 2 6435e 001 2 0000 GHz When an S Parameter calculation is made 82 with the steady state far zone transformation selected then both the antenna data and the S Parameter data will be displayed This may be useful for example when making calculations for a microstrip antenna when both S and input impedance are of interest 83 11 User Generated Meshes While XFDTD can be used interactively to generate complicated objects in some cases it is preferable to generate the meshed geometry by some other means This might be by writing special Fortran or C code to generate an object that can be described by equations or it might be by translating an object described from another program into a cubical mesh This process is described in 7 A material type number must be a
89. ess the Mesh All button to add the box to the geometry 5 The next step is to add the monopole antenna We ii ME want this monopole antenna to be fed with an Ez field Line p a at location 33 19 46 in the center of the box So this ME enda cell edge is left as free space to accommodate the xp Jm feed The monopole itself is built by setting Ez cell jr a im a edges from 33 19 47 to 33 19 76 as perfect conductor Add this wire with the Wire primitive in m a the object library by selecting New and then Wire on the Geometry Editing Tools window Enter the two Figure 62 The Wire primitive data for the monopole 94 points as shown in Figure 62 Press OK and then Mesh All to add the wire Note The box and the wire monopole can also be defined using the mouse driven tools User Object The primitives are used here for simplicity 6 When we are finished we can close the Edit Geometry Tools then slice through the space to check the geometry The geometry may also be displayed in three dimensions by selecting the 3D view 7 If the geometry looks correct save the file by selecting File and then Save from the menu bar 8 The next step is to define the parameters for the XFDTD calculation Start by selecting File then New then Project Note This step is not required with the Unix version of XFDTD as the Project file is created with the Geometry file 9 Now open the Edit menu be sure the Run Parameters window is ac
90. etic materials those with permeabilities other than free space are required the magnetic components should 26 not be selected The Quick Calc option displays the frequency and wavelength that correspond to 10 cells per wavelength at the current spatial increment If no geometry files are already open in XFDTD selecting New will create a new main grid When specifying the spatial increments cell size in the x y and z directions the cells should not deviate greatly from cubical A reasonable rule is to keep all cell increments cell edges to within a factor of two in size The cell size is determined by both the geometry features and by the highest frequency The cells should be small enough to describe the important geometry features and no larger than approximately one tenth of the shortest wavelength of interest If the geometry includes dielectric and or magnetic material the wavelength inside these materials must be considered since it will be shorter than in the free space region of the FDTD space If a geometry already exists when the New geometry is selected the Configure Subgrid menu opens This menu prompts for the subgrid offset within the main grid and the ratio of the subgrid cells The offset refers to the displacement of the origin of the subgrid relative to the origin of the main grid This positions the subgrid within the main grid The ratio refers to the cell size of the subgrid in relation to the main grid cells R
91. etry feature Thus the outer boundary specification is stored in the XFDTD project file not in the geometry file A conducting outer boundary will not be evident in the geometry view until the project file has been loaded xz Plane atj 1 Absorbing JPEG C PMC XZ Plane atj NY Absorbing PEC C PMC xY Plane atk 1 Absorbing PEC C PMC XY Plane atk NZ Absorbing C PEC C PMC Absorbing Boundary Type Liao PML layers e EFE Figure 43 The menu for setting the outer radiation boundary condition 9 9 1 Liao Absorbing Boundary Type It is important to understand the differences between the Liao and PML options Liao is an estimation method By looking into the FDTD space and back in time it estimates the electric fields just outside the limits of the FDTD mesh These estimated values are then used in the FDTD equations inside the space The Liao estimation is made assuming that waves are allowed to travel outwardly from the space but not reflect back in The Liao method works well provided that there is enough space between the radiating geometry and the outer boundary Typical limits are at least 15 cells spacing A homogeneous dielectric may be located up against the Liao boundary For example in a lossy earth or stripline calculation the earth or dielectric layer may touch the outer boundary Liao will usually function well in this situation provided that there are no air gaps within 5 cells of the Liao boundary Lia
92. fore contacting us however please consider the following difficulties that may arise and the suggested remedies 15 1 Problems with XFDTD 5 0 on Windows b Colors on screen are incorrect on Windows 98 There are some problems with Video acceleration for some cards with Windows 98 To disable the acceleration from the desktop click on Properties gt Settings gt Advanced gt Performance and set Hardware Acceleration to none 15 2 Problems with XFDTD 5 0 on Unix b xfdtd50 and or calcfdtd50 will not execute Possibly the files are not set as executable Use Unix chmod command P xfdtd50 gives a message about missing libraries On Sun Solaris On some computers running the Sun Solaris operating system the path to the Motif libraries must be in the LD LIBRARY PATH declaration 116 For the C Shell edit the cshrc file in your home directory search for the LD LIBRARY PATH variable Add usr dt lib to this line EXAMPLE setenv LD_LIBRARY_PATH 0PENWINHOME lib usr new X1 1 R5 lib usr lib usr dt lib For the K Shell edit the profile file in your home directory search for the LD_LIBRARY_PATH variable Add the usr dt lib to this line EXAMPLE LD_LIBRARY_PATH usr openwin lib usr ucblib usr 4lib usr lib usr dt lib E xfdtd50 and or calcfdtd50 write license problem message to screen and stop For Unix installation check that license procedure was followed and that xfdtd5 0 license and calcfdtd5 0 license file
93. form must be chosen as either a transient pulse or sinusoid and the desired output quantities selected The outputs can include far zone fields in particular directions for a transient pulse excitation near zone field quantities at particular points or in particular slices of the geometry steady state field magnitudes and many more In addition wide bandwidth impedance and S Parameters versus frequency can be computed with a transient pulse excitation Many other results are available and these are described in detail in this manual 1 2 3 Results and Output After the geometry and project parameters are defined and saved to files the actual FDTD calculations may be performed Depending on the number of cells in the FDTD space and the number of time steps specified the calculation may require from minutes to hours to days All results can be viewed from within the XFDTD interface and some further post processing calculations may be done In addition the FDTD calculation output files which are in plain ASCII format are available for custom post processing 1 3 Summary of XFDTD Features The features available in each version of XFDTD 5 0 are listed in the table attached below Feature Lossy Dielectric Materials Lossy Magnetic Materials Perfect Conductor Frequency Dependent Dielectrics Anisotropic Ferrites Display of geometry with slice translate zoom Interactive geometry editing with mouse control Local Regions of smaller
94. ging from super computers to 32 bit personal computers As available memory is reduced the maximum number of cells which can be accommodated is correspondingly decreased With 16 MBytes of memory the problem space size would be estimated from the above relationship as 79 cells Note In actual experience 16 MBytes will accommodate approximately 72 cells indicating a memory overhead for instructions and auxiliary variables for this problem size of about 30 of the memory needed to store the field components Again for larger problem spaces with more cells this overhead percentage would be reduced 3 3 1 Far Zone Radiation angles at a single frequency The steady state calculation option and its associated steady state far zone transformation allow for unlimited far zone calculations in post processing With this option the complex tangential fields on a closed surface surrounding the radiating structure are determined at the end of the FDTD calculation These tangential fields are then used by XFDTD to obtain far zone radiation gain or bistatic scattering in any direction during post processing This eliminates the time and memory required for many transient far zone radiation directions However this method provides results only at the frequency of the input 3 3 2 Execution Time Estimation Another way to estimate the computational cost is by calculating the number of floating point operations required This method involves estimati
95. gnetic fields For an FDTD calculation with no magnetic materials present the magnetic fields are computed very quickly However when PML is added the magnetic field update equations are more complicated even when no actual magnetic fields are present and this adds to the time penalty Benefits of PML It may be that the PML layers might provide better absorption than Liao even with only a 5 cell border of free space And perhaps only 6 PML layers would provide this So in such a situation calculation time would be saved Making this comparison would require meshing the object again with less free space margin to the outer boundary This can be done in XFDTD using the mesh merge function Both PML and Liao are offered to provide flexibility Both methods should provide similar results when properly used 9 9 3 PEC Perfect Electric Conductor Radiation and scattering calculations require that all six outer boundaries be set as absorbing In some situations there are advantages terminating one or more faces of the FDTD geometry space with a perfect electric conductor PEC For example the conducting ground plane of a microstrip could be located on one face of the FDTD space 69 A special utilization of this capability involves setting four of the FDTD surfaces to PEC forming a rectangular conducting tube These may be considered as the outer walls of a Transverse Electro Magnetic TEM cell If a center conductor along the length of the tu
96. has a helical antenna which is simulated in XFDTD with a subgrid To view both the phone and the helix choose the All grids option for viewing The phone is fed with a 1 9 GHz sine wave Several time domain near zone electric fields and current densities can be viewed with the plotting tools There are also two field sequences for watching movies of the field propagation The steady state input impedance input and radiated power efficiency and S parameters can be seen by selecting Steady State Data from the Results menu Antenna patterns in any plane can be computed by selecting the Compute Far Zone from the Results menu Enter the desired pattern add it to the list and then press OK The pattern can be viewed with the plotting tool by choosing Plots vs Angle Simple Subgrid Example Helix on a Box These files demonstrate the use of a subgrid by showing a simple PEC box in the main grid and a helical antenna in the subgrid Two cases are computed a steady state calculation with a sine wave input and a transient calculation with a broad band gaussian pulse input The steady state example helix fdtd displays field sequences in the main grid and in the subgrid The steady state port information is available from the Results gt Steady State data menu Antenna patterns in any plane may be computed by selecting Results gt Compute Far Zone Data The antenna patterns may be view with the plotting tools by selecting the plot versus angle
97. he FFT bins so this frequency may be selected Note It is not recommended that the tmestep size be modified except in cases where it is absolutely necessary Modifying the timestep size can lead to incorrect results or instabilities in the calculation The time step is specified as a fraction of the maximum Courant limit time step in the main grid The Courant limit may not be exceeded nor can a timestep of 0 be entered If subgrids or anisotropic ferrite materials have been specified will automatically be reduced below the Courant limit by XFDTD 9 9 Selecting Outer Radiation Boundary Conditions The default boundary condition for XFDTD is a second order stabilized Liao radiation boundary This is a numerical absorber designed to allow electromagnetic fields 67 radiated or scattered by the FDTD geometry to be absorbed with very little reflection from the boundary The Perfectly Matched Layers PML outer boundary is also available see Figure 43 The Liao and PML boundaries may not be mixed together in the same calculation Furthermore PML may not be used with the Perfect Magnetic Conductor PMC boundary while Liao may be used with both Perfect Electrical Conductor PEC and PMC boundaries Boundary Conditions Ea rupeerecepingie dida YZ Plane ati 1 e Absorbing C PEC PMC YZ Plane ati NX Absorbing l PE C PMC Note XFDTD treats the specification of the outer boundary as a calculation parameter nota geom
98. hese quantities are all easily obtained using XFDTD We first determine the cell size and spatial volume With the relative permittivity of the 104 brain tissue of 43 the shortest wavelength in the problem space is inside the brain and is the 1800 MHz free space wavelength divided by the square root of 43 or approximately 0 25 cm This is also a convenient cell size for modeling the dipole gap and wire diameter since the wire diameter is approximately the cell size We could use the XFDTD capability to include thin wires but for this cell size and wire diameter it is not needed This cell size will provide 20 cells per wavelength at 900 MHz This is more than needed but lets us use the same mesh for both frequencies With 0 25 cm FDTD cells the sphere diameter is 80 cells and the dipole is 6 cells away from the sphere surface With a 20 cell free space border on all sides this results in a 130 x 120 x 120 cell space where we have allowed a few extra cells to separate the dipole from the outer boundary To set up the calculation start XFDTD and create a space 130 x 120 x 120 cells with 0 25 cm cells From the Geometry Editing Tools window choose the sphere One way to mesh the two layers is to first mesh a 40 cell radius sphere centered at 60 60 60 with material type 3 Then mesh a 38 cell sphere centered at the same location with material type 2 The two cell layers corresponds to the 0 5 cm skull outer layer Meshing the larger sphere
99. ic material fuzzy cells should not be used Note that if a cell is on the boundary between two dielectric materials the cell is in effect halfway in one material and halfway in the other For example consider the mesh edge locations tangent to a flat dielectric air interface at the surface of a dielectric substrate for example The permittivity of these mesh edges should be set to 1 2 the 1 for relative permittivity of free space and the conductivity to 0 2 where and o are the relative permittivity and conductivity in Siemens meter of the dielectric This corresponds to selecting the 50 Fuzzy level from the edit menu for the dielectric at these surface mesh locations If the adjoining dielectric is not air then the permittivity and conductivity are set to the average values of the two materials In XFDTD it is assumed that the material is adjacent to air and a fuzzy level of x96 means that the relative permittivity for that mesh location is set to x 100 x 100 and the conductivity is set to xo 100 Other situations can be accommodated by using a different dielectric material number for the intermediate fuzzy layer and setting its constitutive parameters appropriately This same correction should be applied to magnetic materials Of course if the adjoining material is perfect conductor then any electric fields tangent to the surface of a perfect conductor are set as perfect conductor regardless of the constitutive paramet
100. indow The zoom button increases or decreases the scale of the geometry Q oo drawn in the window By pressing the magnifying glass at the left of the zoom figure the mouse buttons may be used to perform the zooming The left mouse button zooms in and the right mouse button zooms out A region may be defined with the mouse in when the icon is a magnifying glass and this view will zoom in on this region To turn off zooming click the magnifying glass button again Double clicking on the magnifying glass sets the zoom back to 100 The zoom can also be changed by simply pressing the up and down arrows next to the text displaying the zoom scale or by typing a zoom amount into the text area je 3 The slice currently in view is changed by pressing the up or down arrows or by simply typing the desired slice into the text area This button toggles the normal components view Since the window is two dimensional components normal to the view are be displayed as dots H This button toggles the drawing of the grid representing entire geometry space Turning on this grid is especially helpful when editing the geometry n This button toggles the drawing of the electric components of the geometry When viewing fields or editing the magnetic grid it is sometimes useful to turn off the geometry 19 le This button toggles the drawing of the magnetic components of the geometry UNIX VERSION The UNIX version of XFDTD Figure 4 h
101. input When a l steady state far zone has been selected a E Theta 0 from the input menu this menu is not Constant Theta Pattern Final Phi 360 available and is not needed because all auian E far zone directions are available in Mods edi oe T postprocessing in that case However with a transient input the far zone directions Add Bisi Delete All must be specified before the calculation A with this menu m The far zone directions must be specified as angles in spherical coordinates The He o same coordinate system shown in Chapter 3 and used for specifying the incident plane wave direction is used here Figure 38 Transient Far Zone Angles menu With Single Far Zone Angle only a value for Phi and Theta in required This is useful for cases where only one far zone direction is of interest such as in back scattering calculations The angle will be added to the list only if it has not been specified previously 62 Constant Theta Pattern is used for a specifying series of angles at a single Theta direction The starting and ending Phi angles must be entered as well as an increment A Constant Phi Pattern may be specified for patterns that vary with Theta Transient far zone angles add a noticeable overhead to the FDTD calculation both in terms of memory and execution time Care should be taken to specify only those angles where are required If a detailed pattern is required another option is using the stea
102. is sometimes required for accurate results If extremely small cells relative to the wavelength are used an outer boundary of approximately 1 3 of a wavelength at the lowest frequency of interest should be used if possible 3 2 Determining the Total Number of Cells Once the cell size has been chosen the total number of cells needed for the calculation can be found The number of cells in the x y and z directions often called NX NY and NZ is determined from the sum of free space boundary cells and the dimensions of the structure in each direction divided by the cell size The total size of the FDTD space in cells is determined by the product of the cells in each dimension The memory requirements of XFDTD are directly related to the number of cells in the calculation space A computer with 128 MB of memory can accommodate calculations involving up to three million cells 3 3 Estimating the Necessary Computer Resources This section discusses the computer resources required for a given calculation Let the total number of cells in the problem space be designated as NC NX NY NZ If subgrids are being used their cells must also be added to the cells in the main grid to give a total cell number NC The material information is stored in 2 byte integer arrays on most computers some require 4 byte integers Assume that both dielectric and magnetic materials are included Then to estimate the computer storage in bytes required the following
103. ject file FDTD is loaded the Run Parameters window is active as shown in Figure 5 This window displays the FDTD run parameters and the output data selected In the figure the Sources page is active This shows the type of excitation Voltage Feed and the waveform Sinusoid The window also shows time and frequency domain representations of the input waveform Note that this is a steady state calculation so the tabs corresponding to that type of input are visible When using a transient input such as a gaussian pulse the BFD CCM EFM and SAR tabs would not be present but an additional tab for Far Zone Directions would smi Run Parameters monbox50_fdtd GE x D Electric Field Magnitude Data EFM G Magnetic Flux BFD Magnitude Data E3 Conduction Current Magnitude Data CCM Boundary Conditions LJ Sources B Field Snap Shots 4 Near Zone Data 3 Specific Absorption Rates SAR Source Type c Voltage Feed C Plane Wave Excitation C TEM Mode Source Waveform C Gaussian Gaussian Derivative C Modulated Gaussian Sinusoid User Defined Time Domain Frequency Domain f time ps frequency GHz Figure 5 The XFDTD Run Parameters window available in the Windows Version UNIX VERSION The UNIX version of XFDTD does not have a Run Parameters window To view the Run Parameters select the menu options for e
104. l not exist in all planes as they require lossy dielectric material Saving the SAR Hep Cancel_ in a plane of free space will not produce any useful output as all values will be zero The E Figure 40 The Save SAR Data menu field and B field magnitudes may be saved in any The menus for saving steady state E plane of the geometry though fields and B fields are similar Plane Note To save the e KY Grid Mem s ern eco 77 4 MA steady state quantities cyz vnde o A in a particular slice of fs PP con FO ce the geometry simply C Surface s lt press the right mouse Add Delete Delete All button in the desired slice plane of the Save Conduction Current Magnitudes on Surface in Sub Region i 1 151 j 1 135 k 1 135 main grid Save Conduction Current Magnitudes on Surface in Sub Region i 1 27 j 1 45 k 1 27 sub grid 1 Save Conduction Current Magnitudes in YZ plane atx 15 main grid geometry window and Save Conduction Current Magnitudes in YZ plane atX 16 main grid i tudasi ingri choose Save Data Save Conduction Current Magnitudes in YZ plane atx 17 main grid Save Conduction Current Mannitudes in YZ nlane at 18 main arid zi then Steady State Help Cancel from the popup menu Figure 41 The menu for saving steady state conduction current magnitudes and surface currents 9 5 1 Saving 3 D Surface Currents Surface currents may be saved over entire geometries or over specific
105. lion Floating point Operations Per Second for a fast workstation through 10 to 80 MFLOPS for typical workstations Keep in mind that manufacturer s ratings are often inflated with a realistic speed usually being less than half of that claimed The run CPU time for a 65 cell problem containing about 1 4 million cells which requires 1000 time steps or approximately 22 x 10 floating point operations would be estimated as 3 7 minutes for a 100 MFLOPS workstation and 30 minutes for a 14 MFLOPS workstation A AIL Figure 1 Coordinate system used in XFDTD X 15 3 4 Coordinate System The coordinate system used in XFDTD is shown in Figure 1 Geometries are described in Cartesian X Y Z coordinates Distances may be measured in spatial increments Ax Ay Az with integer indices l J K locating points in the FDTD space as x lAx etc Far zone directions are measured using spherical coordinates and For far zone field amplitude calculations the far zone distance is normalized to 1 meter 16 4 XFDTD Graphical User Interface XFDTD is a graphical user interface to an FDTD calculation program With XFDTD electromagnetic simulations can be performed quickly and easily From within XFDTD the object under consideration can be entered with the editing tools the calculation parameters for the input and output selected using informative menus and the results displayed in a variety of formats This chapter of the manual contains an o
106. lues and the correct parameters be set in XFDTD after loading the geometry In the file shown if a dielectric mesh cell edge is set to material type 2 this material would have a relative permittivity of 1 a conductivity of 0 If a magnetic material mesh cell edge is set to type 2 it would have a relative permeability of 1 and a magnetic conductivity of 0 0 The material density at this mesh edge for calculating SAR is 1 kg m These parameters may be updated from within XFDTD At the end of the 27 material definitions there is a line with a single integer indicating whether thin wire materials are used in the geometry The zero in this line indicates that there are no thin wires used If a thin wire had been specified this number would be a 1 andt would then be followed by four floating point numbers indicating the four thin wire radii available even if all four are not used The next four lines contain three numbers each that are the direction cosines of the previous mesh rotation applied by the XFDTD mesh rotation module If no rotation has been applied this represents a 3 x 3 identity matrix The next line indicates that the material file format is used This is the standard format for XFDTD geometry files In this format only cell locations which contain at least one edge with material other than free space are listed in the geometry file The next line of the example file indicates whether dielectric and or magnetic material meshes are
107. lution due to various factors including curved surfaces wire radii and small details of the structure An example might be a microstrip circuit that has a small lt lt A separation distance between the ground plane and the trace In this case the driving factor on the cell size will probably be the separation distance between the ground plane and trace rather than the highest frequency of interest XFDTD uses a staircase method of approximating curved surfaces with rectangular cubes If the structure contains curves a higher number of cells per wavelength will be required to reduce the error from the staircased approximation The exact resolution required will vary but a good starting point is between 20 and 30 cells per wavelength 12 XFDTD has a feature known as subgridding for approximating small regions of the structure at a higher resolution The subgrid can have a resolution of either one third or one fifth the cell size and is useful in situations where only a small part of the structure requires the higher resolution for producing an accurate approximation Subgrids are described in more detail in a later chapter 3 1 2 Free Space Boundaries Typically XFDTD makes use of a free space or absorbing outer boundary A number of cells must separate the structure from this outer boundary to allow better absorption of the fields The minimum spacing between the geometry and outer boundary is ten cells although fifteen or more
108. ly frequencies in the band of single mode operation are excited Another useful situation is when band limited devices are being analyzed For example a broadband antenna such as a spiral may be designed for a specific frequency range Exciting the antenna at frequencies outside this range may greatly increase the number of time steps need for convergence since the out of band energy cannot readily radiate or be otherwise dissipated by the antenna structure In order to set the frequency spectrum of the modulated Gaussian excitation fmax iS defined as the highest frequency of interest in Hz and fin as the lowest frequency and At the time step In XFDTD the modulated Gaussian frequency is then fmax fmn 2 The Gaussian envelope varies as exp a t To find where the specturm of the modulated Gaussian is down x dB from the pak at frequencies fmax and fmin the expression x In 10 is solved Once a is determined from this expression the pulse width B in time steps used in the XFDTD menu is given by where At is the time step in seconds For example with fmax 19 GHz and fmin 11 GHz and the attenuation of the spectrum at these frequencies is x 60 dB and the time step At 1 059 ps the modulated Gaussian frequency is 15 GHz and the pulse width in time steps is 789 Note The pulse width should not be so short as to introduce energy at frequencies too high for the FDTD method to produce accurate results nor so long so that the
109. material 8 The two dielectrics must have the same constituitive parameters though LLLLLLELLLI o Figure 57 An example of an improper main grid subgrid geometry Here there is a discontinuity near the interface which can lead to instabilities 88 PEC may pass through the main grid subgrid interface but it must do so in the normal direction and continue for several cells on each side See Figure 58 for an example of a wire passing through the boundary properly Figure 58 A PEC wire passing through the main grid subgrid interface correctly Once again there must not be any discontinuities in the normal direction near the main grid subgrid boundary See Figure 59 for an example of a poorly formed subgrid Here the PEC wire runs parallel to the boundary only two cells away There should be at least four subgrid cells between the boundary and this turn in the wire SESEBSESED Figure 59 A poorly formed subgrid with a discontinuity near the main grid subgrid boundary Note that the material types are specified independently in the main and subgrids That is material type 2 may be specified with different permittivity in the main and each subgrid Material type 2 can even be a totally different type of material in each grid For example material type 2 could be a normal dielectric in the main grid a Debye material in subgrid 1 and a Lorentz material in subgrid 2 When making FDTD calculations the material inside the subgri
110. mi Gabriel M Sc and obtained from the indicated www pages are given in the table below for convenience 150 MHZ 300MHz 500 MHZ 700 MHZ 2 0 498 0 552 0 621 0 697 cartilage 51 4 46 77 44 60 43 46 4 0 749 0 791 0 844 0 902 muscle 62 68 58 98 57 32 56 50 7 0 926 0 975 1 033 1 096 eye 63 47 58 90 56 89 55 91 9 0 479 0 553 0 626 0 695 brain 60 19 51 90 48 42 46 80 12 0 543 0 641 0 728 0 800 dry skin 61 50 49 82 44 91 42 70 14 0 127 0 149 0 177 0 208 skull 19 98 18 30 17 45 16 97 900 MHZ 1 2GHz 1 5GHz 1 9GHz 2 3GHz 2 0 782 0 929 1 098 1 354 1 641 cartilage 42 65 41 72 40 93 39 98 39 10 4 0 969 1 088 1 228 1 448 1 705 muscle 55 95 55 36 54 87 54 30 53 77 7 1 167 1 290 1 435 1 662 1 925 eye 55 27 54 58 54 04 53 42 52 84 9 0 766 0 882 1 010 1 204 1 423 brain 45 80 44 82 44 11 43 37 42 75 12 0 867 0 967 1 072 1 224 1 395 dry skin 41 40 40 21 39 43 38 71 38 18 14 0 242 0 298 0 362 0 456 0 559 skull 16 62 16 21 15 87 15 46 15 10 Table of Constitutive Parameters for FDTD Human Head Shoulders Mesh for various frequencies Material column is the XFDTD mesh material number for that particular tissue type Upper number in each entry is conductivity in Siemens meter lower is relative permittivity Average values used for muscle brain and skull Based on the values of Camelia Gabriel Ph D and Sami Gabriel M Sc as described above 121 16 2 The Remcom High Fidelity Head and Shoulders Mesh The R
111. n Figure 14 of the paper In this set of example files we have included comparison plots of the measured results and XFDTD 5 0 calculations They are shown in Figure 80 Display the XFDTD results by loading the XFDTD project file cps13 fdtd into XFDTD 113 Magnitude S dB Co Planar Stripline Bandstop Filter 10 521 FDTI Measured 1 6 1 8 Frequency GHz Figure 80 S11 of Co planar Stripline Bandstop filter compared with measurements 14 5 3 Biological Examples Simple Dielectric Sphere This example shows a simple dielectric sphere with a radius of 7 33 mm a relative permittivity of 72 2 a conductivity of 1 808 Siemens meter and a material density of 1000 kg m The sphere is exposed to an 837 MHz incident plane wave with an amplitude of 2500 V m The Specific Absorption Rate SAR values in the sphere are saved in one direction the xy plane and the 1 and 10 gram averaged SAR values are computed The Results gt Display Averaged SAR Information option may be used to display the maximum and whole body average SAR values and the the 1 and 10 Gram Averaged SAR maximums Movie sequences of the SAR files may be viewed by selecting the SAR Sequences entry from the Project Tree Spherical Bowl and dipole example In this example a liquid filled spherical bowl exposed to radiation from a dipole antenna is simulated The bowl is filled with a brain simulating liquid and the 835 MHz half wave dipole radiates at a distance of
112. n when specifying the number of timesteps The minimum number of time steps that will allow convergence to steady state or quiescent field values should be chosen A subgrid must have dimensions that are at least four main grid cells as a minimum If instability is encountered the symptom is rapidly growing field values that oscillate rapidly If this happens some possible ways to attempt to remove the instability are by specifying fewer time steps by changing to 1 3 size subgrid cells if 1 5 size cells have been specified or by enlarging the subgrid size to allow a larger boundary between the grids 91 13 CALCFDTD Computer Program The actual FDTD calculations are not made by the XFDTD graphical user interface Once the geometry and project file are specified using the XFDTD menus they must be saved before any calculation can be run A separate computer program called CalcFDTD makes the actual FDTD calculations The XFDTD Graphical User Interface then will operate on and display the results of the FDTD calculations The CalcFDTD computer program reads the project and geometry files written by XFDTD and performs the actual FDTD calculations It is an executable program written in the C language It includes dynamic memory allocation so that different size FDTD spaces may be accommodated without allocating more computer memory than necessary To run the CalcFDTD program simply start it by selecting Run CalcFDTD from the Results menu The pr
113. nd John C Mazziotta Cross Section Anatomy An Atlas for Computerized Tomography The Williams and Wilkins Co 1977 129 20 Richard A Boolootian Elements of Human Anatomy and Physiology West Publishing Co 1976 20 Bibliography K Kunz R Luebbers The Finite Difference Time Domain Method for Electromagnetics CRC Press 496 pp 1993 R Luebbers K S Kunz K A Chamberlin An Interactive Demonstration of Electromagnetic Wave Propagation Using Time Domain Finite Differences IEEE Transactions on Education vol 33 no 1 pp 60 68 February 1990 R Luebbers F Hunsberger K Kunz R Standler A Frequency Dependent Finite Difference Time Domain Formulation for Dispersive Materials IEEE Transactions on Electromagnetic Compatibility vol 32 no 3 pp 222 227 August 1990 K Kunz R Luebbers F Hunsberger A Thin Dipole Antenna Demonstration of the Antenna Modeling Capabilities of the Finite Difference Time Domain Technique Applied Computational Electromagnetics Society Journal vol 5 no 1 pp 2 18 Summer 1990 R Luebbers F Hunsberger K Kunz A Frequency Dependent Time Domain Formulation for Transient Propagation in Plasma IEEE Transactions on Antennas and Propagation vol 39 no 1 pp 29 34 January 1991 R Luebbers K Kunz M Schneider F Hunsberger A Finite Difference Time Domain Near Zone to Far Zone Transformation IEEE Transactions on Antennas and Propagation vol 39 no 4 pp 429 433 April
114. ne field values port feed voltages and currents and far zone electric fields The next category is for plots versus frequency for data such as input impedance S parameters gain or radar cross section RCS input incident power or port power Finally plots versus angle may be viewed for gain or RCS patterns versus azimuth or elevation 74 Choose Plot Data Plot Type Data Vs Frequency Available Data of Selected Type Input Voltage dB vs Frequency GHz Bi vs Fi GH z at Phi 45 00 Theta 10 00 Gain dBi vs Frequency GHz at Phi 45 00 Theta 20 00 Gain dB v vs Frequency GHz at Phi 45 00 Theta 50 00 CP Gain dBi vs Frequency GHz at Phi 45 00 Theta 10 00 CP Gain dBi vs Frequency GHz at Phi 45 00 Theta 20 00 zl Components Parts Power G Ege CECE C EPhi Magnitude Peal R Norrelize Current C ERCP ETheta Phase ineginety Add To Plot Bemove From Plot Remove All Plots Data to Plot Gain dBi vs Frequency GHz at Phi 45 00 Theta 10 00 Magnitude EPhi Gain dBi vs Frequency GHz at Phi 45 00 Theta 10 00 Magnitude E Theta i vs Frequency GHz at Phi 45 00 Theta 20 00 Magnitude EPhi i vs Frequency GHz at Phi 45 00 Theta 20 00 Magnitude ETheta Cancel Figure 48 The Display Plot tool in XFDTD 5 0 on a Windows computer After selecting the basic plot category of interest a listing of the available plot d
115. ng The sequence can be modified to only play over a certain portion by setting the starting and stopping frame numbers Figure 47 The Set Full Scale menu for an SAR file To clear the field display click on the Clear button of the Field Control menu This will remove the fields from the screen and close the Field Control window When a steady state SAR file or sequence has been loaded an additional capability the option to adjust the input power If a specific input power is desired this value can be entered and the SAR fields display will be scaled accordingly This feature is accessed through the Set Full Scale button see Figure 47 The computed input power will be displayed along with a window for setting the desired input power Three Dimensional Surface Current Display The display of currents flowing on a three dimensional surface is somewhat different than the planar display of SAR fields and currents discussed previously The file containing the surface currents of extension ccms is grouped with the Conduction Current Magnitudes on the Project Tree Once this file is loaded the Field Control window can be opened as with planar files For best results the 3D viewing option should be selected Capturing XFDTD Screen Views With the Windows version of XFDTD there are two options for capturing screen views On the geometry window select View Export Bitmap to save the image in the geometry window This image may be the geome
116. ng it and starting one cell inside the mesh This would correspond physically to a stripline constructed inside a metal box with all sides closed and fed by coaxial cables with the outer conductor attached to the metal box and the center conductor going through the metal box surface to feed the stripline This feed geometry while a reasonable approximation to a realistic stripline circuit 102 does not yield good FDTD results in some situations The difficulty is that with the FDTD calculation entirely enclosed by conductor the only means of dissipating the energy supplied to the calculation is by dissipation in the characteristic resistors and of course in any other lossy dielectric materials But many devices are made entirely or almost entirely from lossless dielectric and conductor and some of the induced energy may be at frequencies such that it is not absorbed by the characteristic resistors This energy then rattles around inside the conducting walls of the FDTD space greatly increasing the number of time steps needed for convergence It is therefore desirable to have the four side walls of the FDTD stripline calculation mesh be absorbing rather than conducting Given this consideration a feed location that drives the stripline with voltages relative to the top or bottom conductor is desired so that the sides of the FDTD mesh may then be set as absorbing boundaries However feeding from just the top or just the bottom conducto
117. ng the total number of time steps to be calculated As a preliminary estimate the time required for energy traveling at the speed of light to traverse the geometry five times may be used With a transient input convergence of the calculation can be determined by observing the feed point 14 voltage and current or some other near zone value With a steady state input near zone values in the space should be saved and observed to ensure the calculation has reach steady state This is especially important in calculations involving large amounts of dielectric material where fields propagate more slowly Lossy geometries typically will require fewer time steps while resonant geometries will require more With NC representing the total number of cells and with the total number of time steps designated as N the total number of floating point operations is estimated by Operations NC x 80 operations cel time step x N The actual number of calculations for each component depends on the material type and excitation of the incident field at a particular time step There are also logical statements which must be executed to determine what type of material free space perfect conductor dielectric is located in a particular cell The number of seconds required for a calculation can be estimated by dividing the Operations given by the above equation by the FLOPS rating of your computer Speeds of available machines range from 120 or more MFLOPS Mil
118. ntering the parameters 8 XFDTD Project Tree Figure 6 This window displays the parameters of the calculation in another form The Run Parameters are displayed hierarchically Clicking expands the branch and clicking condenses it Double clicking on the text of the 21 parent item will also expand a branch In this figure the parent item monbox50 fdtd is shown expanded The Output Files branch is expanded showing all the outputs specified for the loaded project When an item is in bold print it is available for display by double clicking An item in the tree that is not in bold print is not available Smee monbox50 fdtd Geometries Loaded S E Output Files amp 4B Single Transient Fields iB XZ Plane at Y 19 Timstep 20 iff XZ Plane at Y 18 Timstep 40 iB XZ Plane at Y 19 Timstep 60 iB XZ Plane at Y 19 Timstep 80 iB XZ Plane at Y 19 Timstep 100 iB XZ Plane at Y 19 Timstep 120 iB XZ Plane at Y 19 Timstep 140 iB XZ Plane at Y 19 Timstep 160 iB XZ Plane at Y 19 Timstep 180 iB XZ Plane at Y 19 Timstep 200 1 Transient Field Sequence 00 Far Zone Data amp 00 Near Zone Data 20 EZT at 33 19 46 in Main grid 00 JZT at 33 19 46 in Main grid Electric Field Magnitude Data amp Ga Magnetic Field Data WINDOWS VERSION Clicking the arrow at the top right corner of the XFDTD Project Tree displays the menu shown in Figure 7 It provides the ability to load single transient field files transient
119. o assumes homogeneous material within 5 cells and if this is not the case then the FDTD calculation will usually be unstable with rapidly rising field amplitudes 68 Since Liao is an estimation method the size of the FDTD mesh is not increased by using it Some storage is needed for saving electric values at previous time steps but this is usually negligible in a typical calculation 9 9 2 PML Absorbing Boundary Type PML is an artificial absorbing material It absorbs the incident energy as it propagates through the PML layers Better absorption that is smaller reflection is obtained by adding more layers at the expense of increasing the size of the FDTD mesh For example consider an FDTD calculation on a mesh using the Liao absorber that is 50 x 60 x 70 cells or a total of 210 000 cells There is a 15 cell free space border all around the geometry so that the Liao boundaries can provide small reflections If the Liao is changed to 8 PML layers the geometry mesh will not change However outside of this defined mesh region 8 additional FDTD mesh layers are added on each side of the geometry This means that the actual number of FDTD cells that must be calculated grows to 66 x 76 x 86 or 431 000 cells more than double Since PML cells require more arithmetic operations than normal FDTD cells the time penalty is actually greater This time penalty for PML is also increased since the PML cells have special equations for both electric and ma
120. of the IEEE vol 81 no 4 pp 631 636 April 1993 R Luebbers J Beggs K Chamberlin Finite Difference Time Domain Calculation of Transients in Antennas with Nonlinear Loads IEEE Transactions on Antennas and Propagation vol 41 no 5 pp 566 573 May 1993 R Luebbers D Steich and K Kunz FDTD Calculation of Scattering from Frequency Dependent Materials IEEE Transactions on Antennas and Propagation vol 41 no 9 pp 1249 1257 September 1993 J Beggs R Luebbers and B Ruth Analysis of Electromagnetic Radiation from Shaped End Radiators using the Finite Difference Time Domain Method IEEE Transactions on Antennas and Propagation vol 41 no 9 pp 1324 1327 September 1993 R Luebbers Lossy Dielectrics in FDTD IEEE Transactions on Antennas and Propagation vol 41 no 11 pp 1586 1588 November 1993 C Penney and R Luebbers Radiation and Scattering of a Square Archimedean Spiral Antenna using FDTD Electromagnetics vol 14 no 1 pp 87 98 January March 1994 R Luebbers and C Penney Scattering from Apertures in Infinite Ground Planes using FDTD IEEE Transactions on Antennas and Propagation vol 42 no 5 pp 731 737 May 1994 131 C Penney and R Luebbers Input Impedance Radiation Pattern and Radar Cross Section of Spiral Antennas using FDTD IEEE Transactions on Antennas and Propagation vol 42 no 9 pp 1328 1333 September 1994 R Luebbers Three Dimensional Cartesian Mesh Finite Differen
121. ogress of the calculation will be displayed in a window Additional options in Unix In a Unix environment it is often more desirable to run CalcFDTD as a batch job or from the command line To do so simply enter the following calcfdtd50 options filename fdtd where filename is the name of the Project file The fdtd suffix need not included in the calcfdtd50 command line For normal operation no options need be specified There are several options available should they be of interest rev print revision date ver print version number Z compress the field snapshot files fld files after creating them in order to save disk space XFDTD will read the compressed files gZ gzip the field snapshot files fld files after creating them in order to save disk space For this function to be used the gzip and gunzip programs must be executable and in the path 92 14 Example Procedures In this section procedures for making an FDTD calculation will be illustrated by some examples Four cases are examined in detail These are a monopole ona conducting box a microstrip meander line a stripline Wilkinson power divider and a dipole near a lossy dielectric sphere Several other examples are briefly discussed in a separate section The XFDTD files for the geometry and run parameters for all examples are included with the XFDTD50 CDROM The monopole on conducting box example is considered first and in some detail New users are enc
122. om Inc by request All of the calculations in the dissertation were made using XFDTD 4 Finger Lange Coupler These files show XFDTD results for a 3 dB Lange coupler After loading the lange29 fdtd file the output available for display includes the time domain voltage and 112 current at each port for the case where port 1 is fed The S parameters S11 S21 S31 and S41 may be viewed through the plotting menu as plots versus frequency Also available is the port power versus frequency Wilkinson Power Divider These files show XFDTD results for a Wilkinson Power Dividor After loading the wilk fdtd file the output available for display includes the time domain voltage and current at each port for the case where port 1 is fed The S parameters S11 S21 and S31 may be viewed through the plotting menu as plots versus frequency Also available is the port power versus frequency Loading the time domain field sequence file wilk xy9 i100 b100 e1000 fss will show a movie of the field propagation through the power divider Coplanar Stripline Bandstop Filter Measurements and calculations for several Coplanar Stripline geometries appeared in the paper Coplanar Stripline Component for High Frequency Applications by Goverdhanam Simons and Katehi IEEE MTT Transactions October 1997 Here we have applied XFDTD to the Bandstop Filter of Figure 13 of the paper Using XFDTD 5 0 we have obtained excellent agreement with the measured results shown i
123. ore Silicon Graphics IBM RISC Hewlett Packard Sun Solaris DEC Digital Unix SCO Unix and Linux Unix operating systems 1 2 General Technique for FDTD Calculations 1 2 1 Define Geometry To apply the FDTD method the geometry of interest must be approximated as discrete material cells Each cell edge may be defined with different dielectric properties Since XFDTD uses rectangular cells the geometry is approximated using the edges surfaces or entire volumes of small rectangular boxes The cell edges must be smaller than approximately one tenth of a wavelength for accurate results They must also be small enough to approximate the important geometry features XFDTD provides several methods for meshing the desired geometry such as 4 importing an existing geometry file V building the geometry from a library of basic objects including plates cylinders spheres and boxes V setting the cell edges manually in user defined objects using the mouse 1 2 2 Define Project Parameters Once the geometry is defined the FDTD calculation parameters for the specific project are chosen These parameters include the location and type of excitation For example the geometry may be excited by an incident plane wave for a scattering or penetration problem or by voltage and or current sources connected to the geometry for a microstrip or antenna radiation problem If a TEM cell is being considered XFDTD can provide the TEM wave excitation The wave
124. otal dielectric thickness is 1 524 mm with the stripline conductor sandwiched in the middle The blue square is a 100 Ohm isolation resistor fabricated using 100 Ohm square resistive material Care must be taken in meshing the power divider First the stripline planes of the FDTD space are set to conductor while the 4 sides are terminated in Liao absorbing boundaries The entire FDTD space is filled with dielectric except for the stripline conductor and the isolation resistor The stripline conductor is meshed as one plane thick perfect conductor The isolation resistor is meshed using one plane thick lossy dielectric with permittivity of free space and conductivity of 78 74 Ohms This is obtained using a simple sheet impedance model 1 as the reciprocal of the product of the sheet resistance and the cell thickness The cell thickness is set at 0 127 mm in this dimension so that 12 cells correspond exactly to the dielectric thickness The other two cell dimensions in the plane of the conductor were chosen to allow precise alignment of the mesh edges with the conductor steps A very important consideration is location of the mesh edges where the port sources and terminations are to be located One approach might be to terminate the side boundaries of the FDTD mesh normal to the stripline conductor with perfect conductor planes Then a mesh edge normal to the outer conductor plane could be used as the source location with the stripline conductor touchi
125. oundary a calculation space of 286 x 122 x 25 cells results Using the Courant limit time step size the FDTD calculation required approximately 6 000 time steps to converge The calculation took about 2 hours on a Pentium Pro 200 MHZ processor PC using the SCO ODT 5 operating system and optimizing C language compiler 100 Details of the port feed geometry FDTD mesh at one end of the meander line can be seen in XFDTD50 in the y z plane at x 21 see Figure 70 Use the m mi w translate and zoom function to see the feed region in detail The green rectangle indicates the FDTD mesh edge where the feed port is located The simple transition from the feed port m location to the wider stripline conductor has been observed to provide more accurate results especially at higher frequencies The lowest plane of mesh edges is set to perfect conductor to simulate the ground plane This mesh geometry is an approximation to a coaxial feed or termination connected to the bottom of the ground plane with the center conductor flaring and connecting to the microstrip For the FDTD meander line calculation both R and R are set at 50 Ohms corresponding to a coaxial cables with 50 Ohm characteristic resistance This can be seen in the Stimulus Sources Loads sub menu The Gaussian pulse width has been set to 50 time steps This will converge faster than a pulse width of 32 time steps and with the dielectric present accurate results at the
126. ouraged to follow this example before loading the provided files as it explains the basic operation of XFDTD 5 0 14 1 Monopole Antenna on a Conducting Box This example was considered in 7 on pages 279 289 Here we will calculate the impedance vs frequency for a 50 mm long monopole antenna on a 60 x 10 x 50 mm box The XFDTD50 input files monbox50 id and monbox50 fdtd furnished with XFDTD50 correspond to this example Following the description in 7 on page 283 we will use 1 67 mm cubical FDTD cells This will give us 30 cells per wavelength at 6 GHz which should provide very accurate results With this cell size the box will be 35 x 6 x 30 cells and the monopole will be 30 cells long With a 15 cell border our FDTD space will be 67 x 37 x 91 cells For the calculations in 7 a space of 130 x 90 x 180 cells was used since the absorbing outer boundary used for those calculations required a much larger border in order to provide adequate absorption of the radiated fields The savings for XFDTD are considerable The calculation in 7 required over 2 million cells while the calculation here needs just over 1096 of that number 1 After starting XFDTD by entering xfdtd50 or launching from the Programs bar click on File then on New or select the New Geometry icon from the Tool bar 2 Choose to create a Main Grid This will bring up Teac cpa fo aan the menu shown in Figure 60 For our example we ue Pm a me set the spatial incr
127. pace during the calculation There is no need to define the geometry in the main grid in the region of the subgrid but if there is something there it will not be part of the calculation As an example if there is a box in the main grid and an antenna will be added in a subgrid any part of the box overlapped by the subgrid must be added to the subgrid geometry Otherwise the overlapped box will be considered free space To further illustrate proper and improper subgrid techniques in XFDTD some example geometries are shown here First if a dielectric material passes from the main grid into the subgrid there must not be discontinuities in the normal direction for the first few cells of the subgrid Also the dielectric in the main grid must be reproduced in the subgrid See Figure 56 for an illustration As is mentioned in the caption the two dielectrics may be chosen as different XFDTD materials but the constituitive parameters must match A material in the subgrid may not end near the main grid subgrid boundary as shown in Figure 57 This is an improperly formed subgrid which will possibly lead to an unstable calculation 87 Figure 56 An example of dielectric passing from the main grid into a subgrid Note that the subgrid dielectric must have the same material parameters as the main grid dielectric but it does not have to be the same XFDTD material number Here the main grid dielectric is material 10 while the subgrid dielectric is
128. pears on the screen due to some hidden cells in the subgrid For example setting the offset of a 3 1 subgrid to 5 cells will start the subgrid just past cell 6 This is because there are two or 3 with 5 1 ratio extra subgrid cells which are not drawn that are used as boundaries Computational Price for Subgrids There is a computational price that must be paid in order to have the higher spatial resolution A part of this price is additional memory requirements For a 1 3 cell size ratio each main grid cell is replaced by 27 subgrid cells For a 1 5 cell size ratio each main grid cell is replaced by 125 subgrid cells Even a fairly small subgrid region may quickly need more memory than the entire main grid So subgridding should be used only when absolutely needed Another computational burden imposed by subgrids is that since the subgrid has smaller cells the time step in the subgrid is smaller than in the main grid Furthermore in order to increase stability even the main grid time step is reduced below its normal value when subgrids are present This is done automatically but does mean that for 90 the same simulation time in seconds more FDTD time steps in the main grid are required While the XFDTD implementation of subgrids is designed to give greater freedom in application the possibility of instability remains This is due to the interpolation of the fields between the main and subgrids When using subgrids care should be take
129. ports are to be excited a separate FDTD calculation must be performed with the another port active For example if the full S parameter matrix for a 2 port problem is desired two calculations must be performed with a different port active in each The Project file should be saved with the same name in each case XFDTD will save the S parameters for each run in separate files differentiated by the active port number 9 1 2 Plane Wave The second stimulus form available is the incident plane wave Calculations of Radar Cross Section or scattering may be performed using this input The plane wave source is assumed to be infinitely far away All calculations with the incident plane wave input are performed in SCATTERED FIELD Total field values may be saved and displayed as they can be determined by adding the specified incident field with the computed scattered field The incident plane wave is specified using the menu shown in Figure 34 The incident direction defined by phi and theta must be specified in degrees Phi is measured from the X axis to the Y while Theta is measured from the Z axis to the XY plane see the 54 coordinate system in Chapter 3 The incident waveform may be Phi or Theta Polarized The electric field values in the X Y and Z directions are displayed on this window and are updated each time the polarization or incident direction is modified Plane Wave x Source Waveform Sinusoid Time steps 20000 Freqency 0 84
130. present The 1 0 variables in the example indicate that a dielectric mesh is present the 1 but that a magnetic material dual mesh is not present the 0 Since only a dielectric mesh is present only information about this mesh is included in the geometry file The next number indicates that 30 FDTD dielectric mesh locations contain material other than free space The remaining lines of the geometry file contain the meshed geometry information Each line corresponds to a corner of one FDTD cell The first three numbers give the I J K index location of that corner 21 21 21 in the example A position in the mesh is described by integer variables J and K where the coordinates of the particular mesh corner are then x IAx y JAy and z KAz The next three numbers in the line O O 1 in the example geometry file indicate the material type number for the x y and z edges at that corner For this position the z components of electric field interact with perfect conductor material type 1 or in other words this cell edge will be drawn as PEC material in the geometry If the dual magnetic material mesh had been specified the file would continue with one line containing a single number indicating the number of magnetic mesh cells containing magnetic material 85 Geometry file version 3 8 41 41 72 1 000000e 002 1 000000e 002 1 000000e 002 000 0 emat02 mmat02 1 000000e 000 0 000000e 000 1 000000e 000 0 000000e 000 1 000000e 003 1 000000e 000
131. pressing Selected gt Move up down to top to bottom Other features of the Selected menu include meshing unmeshing and deleting an object from the list To add a new object to the list press the New button and select one of the choices from the library or primitives Each of the primitives is described later in this chapter After adding the item to the list it can be meshed by pressing the Mesh All button If the order of the items on the list has changed the display of the mesh can be refreshed by pressing the Remsh All button To clear the list of all objects press the Delete All button 7 7 1 User Defined Objects A user defined object can be created using the edit mode buttons shown in Figure 20 which are for different manual mouse driven editing modes To create a user defined object select Library gt Begin user defined UNIX or New gt User Object Windows from the Geometry Editing Tools window The edit mode buttons will then become D E FH 8 q lo available for use There is also a space provided for naming the user defined object Figure 20 Editing tools for future reference Otherwise the object will appear on the list as simply User Object The first three buttons are single click operations The first button sets single edges of cells The second sets one face of a cube while the third sets an entire cube directed normal to the viewing plane The next five buttons allow definition of areas
132. puter time and memory if many far zone directions are required The selection of a Steady State Far Zone transformation also computes the the single frequency input impedance total input power radiated power and antenna efficiency All values computed require that the calculation has reached steady state XFDTD does not evaluate calculations for convergence or steady state though and so near zone values should be observed to ensure these conditions exist 9 2 Sample Near Zone Data With the Sample Near Zone Data menu Figure 37 Available Field Quantities transient near zone field C ExScattered C ExTotal HxScattered C Hx Total C Jx quantities at specific points C EyScattered EyTotal HyScattered C HyTotal C Jy within the bounds of calculation C EzScattered Ez Total HzScattereed C Hz Total Jz space may be saved The field quantities of X Y and Z Locetion directed electric and magnetic Grid Man A x ps Sy fs Sz fe 4 E and H fields may be saved Add Point Delete Point Delete All as well as the X Y and Z oin elete Poin age directed current density J Ez Total x 33 Y 19 Z 46 Main Grid Current densities are determined by multiplying the conductivity of the material at the specified cell location by Lose ewe the Electric field in the given direction When a PEC material is present the current density will be computed by the loop of magnetic fields Jz x
133. r 1 00 Gain dBi at Phi 45 00 from Theta 0 00 to 180 00 Incr 5 00 Gain dBi at Theta 90 00 from Phi 0 00 to 360 00 Incr 2 00 I Prn45 0l Theta bt FhislE dn Thoi 2B d FhizAt D Themas JEn Bee nfi Thee fi i a Fred eres OHH ot Prim l5 DO Talem ED DO Aa Thais st his 00 Fem 0341 B Caes DLC E H m Thes nt hn SD Fegi 512 j Blecic Figli gj vi Tieia irra el Phesd5 EU Thee 09 OK Help Cancel Se tien EB Figure 52 The Compute Far Zone Data window Figure 51 The Compute Far Zone Data with a Steady State calculation window for a Transient Far Zone calculation Because of the inherent differences between the transient and steady state transforms the menu that appears when the Compute Far Zone Data option is pressed will have slightly different choices The transient far zone menu shown in Figure 51 has four options at the top for selecting the type of transform If the Plot vs Frequency or far zone electric field option is selected all of the available far zone angles will be displayed in the angles window For a plot versus theta or phi the available angles will be shown in the angles window and the list of FFT frequency bins will be shown in the Frequency window The FFT size may be modified for a higher resolution graph Multiple far zone calculations may be made at a time simply by adding to the list Pressing OK will start the post processing calculation When the steady
134. r does not provide the symmetry necessary to excite the dominant field modes of the stripline A symmetrical arrangement for exciting and terminating the stripline can be seen in the XFDTD50 display of the geometry by viewing the y z plane in the x 12 slice Using zoom and translate get a clear view of the mesh surrounding edge 12 189 7 the location of one of the ports The medium intensity white horizontal line is the center of a stripline conductor This conductor is several meshes wide perpendicular to the plane of this slice of the FDTD mesh The vertical white line is a line of FDTD mesh set as conductor which connects the port to both the upper and lower conducting surfaces This arrangement allows the port voltage and current to be symmetrical with respect to both stripline conducting surfaces and is used for all three ports of the stripline circuit The procedure used for the meander line example is followed again with the extension to a three port circuit The characteristic resistances at each port are set to 50 Ohms Port 1 is fed so that S parameters S S and S will be determined The Gaussian pulse is made very wide 1024 time steps to reduce the number of time steps needed to reach convergence Results are higher frequencies that would be excited by a narrower pulse are not of interest Figure 72 shows the S calculation made by XFDTD50 for the Wilkinson power divider The Compute s parameter plot data menu was used to increase
135. radius Units uan much smaller than the cell i Radius 0 167 size is required Figure 17 shows the window for editing eee e the thin wire radii in the Windows version In most cases material 2 PEC will Delete Help Cancel serve well as a wire The Edit Thin Wire Parameters Figure 17 Edit Thin Wire Parameters window window is accessible through the Electrical Materials Palette in Windows and from the Utilities Menu on the Geometry Editing Tools panel in UNIX Note Thin wire materials may not be located adjacent to each other and may not cross each other There must always be at least two cells between any non colinear thin wires 37 7 7 Geometry Editing Tools The geometry for a calculation can be entered into XFDTD through the Geometry Editing Tools The geometry may be edited by creating user defined objects with mouse driven tools or from a library of primitive shapes The Geometry Editing Tools in the Windows version are shown in Figure 18 The corresponding Geometry Editing Selected Material 1 PEC Editing Electrical Grid Tools m Object Library MRectangle P1 16 75 9 25 45 50 P2 50 25 8 25 45 50 P3 33 50 27 75 45 50 Th Cylinder P1 33 00 18 00 22 00 P2 33 00 18 00 68 00 R1i 9 00 R10 0 00 R2i New i nj ERE Bemesh All Mesh All Delete All User Object maals 7 T z TIT n
136. rately If the file has not been saved before a filename must be entered Otherwise the file will be saved with the same name XFDTD automatically supplies the suffix to the file name either id for a geometry file or fdtd for a project file The filename for geometry and project files can be the same but it does not have to be Before writing a project file the corresponding geometry file for the main grid and for any subgrids must be saved Also some calculation parameters for both inputs and outputs must be set before a project file can be saved 6 1 5 Save As This option functions identically to the Save function above except it prompts for a filename Save As will not automatically save a file under the same name 28 6 1 6 Close The Close option closes the currently active window which may be a geometry or project file Typically before loading a new geometry or project any existing file should be closed Before closing a file XFDTD determines if the file has been modified and asks if the file should be saved before closing 6 1 7 Exit Select this option to exit XFDTD XFDTD will ask if any unsaved files should be saved 6 2 The File Menu in UNIX XFDTD The File menu Figure 10 is structured in a slightly different manner in the UNIX version of XFDTD 5 0 The features of the UNIX version are also present in the Windows version This section briefly describes the menu items on the Unix File menu Open Geometry File as
137. re Es Additonal Layers Ld EE ES EH ee poa Fuzzy Level fos 7 Below b a Desciptian Figure 18 G eometry Editing Tools Windows Version window from the UNIX version is shown in Figure 19 oa Click this button in the tool bar to show the Geometry Editing Tools window Soloted Materat i PEC Mech All Beene AN Mifiiics n phan C013 DO 11 0 13 000 Ha DO Re DUX cerned Maiana 8E Fory d Least mila 1 Extangla FING 2818 23 22 STI PAAA TI LGH 22 STI PEAL SE AR 73 22 511 Thik i Mam Puy eel 100 um d bl mox 1 zu 5 8 12 2 gj iB eel iN Standard Manera Noo GE NE 1 69 1 8 8 nd UN o nn 1a 1E Bj Mj se ga ej sj ss 5 ss NH 55 n5 This Wire BN BN a Ei Figure 19 Geometry Editing Tools in the Unix Version The Geometry Editing Tools are controlled by a series of buttons which appear in the middle of the panel The list of objects in the space shows all items in the geometry 38 whether they are meshed or not If an object is meshed the letter m will appear in the first column of the list If it is unmeshed the letter u will be displayed The objects in the list are meshed with items at the top of the list having priority over items at the bottom of the list Items are added to the list at the top so the last object added will have the highest priority in meshing The order of objects on the list can be change by clicking on an item in the list and then
138. resulting menu is Bectengular box shown in Figure 21 Sphere Spiral antenna Wire The primitive library contains several objects that can be used to create many parts of a complex geometry Included in the library are a circular cylinder and conic a helix a plate either aligned with the grid or tilted a rectangular box a sphere some basic spiral antennas and a wire The positioning size and composition of the objects is controlled by the individual menus For all of the menus unless otherwise noted the units requested are FDTD cells Figure 21 Library menu 40 7 7 3 1 Circular Cylinder and Conic The circular cylinder and conic menu Figure 22 is used for adding cylindrical objects of any material to the geometry Two points along the centerline of el IL the cylinder are needed for determining the location of the cylinder in the grid The cylinder does not ums a need to be aligned with the grid The inner and ara dosi outer radii of the cylinder at each point define the shape of the cylinder By setting one outer radius zi 3 zs 3 to zero a cone is made rather than a cylinder If I Ta the cylinder is constructed of dielectric or magnetic ERN a materials either 1 or 3 levels of fuzzy cells may be ower F Owen F used on the out edges of the cylinder Fuzzy cells EN are described in another section of this manual Unuda E s ok Heip Gencel Figure 22 The circular cylinder and
139. rid However any magnetic materials in a subgrid will be treated as free space by the calculation program 7 10 Preferences The Preferences window allows control over numerous features of XFDTD The values entered on the Preference window will be stored and used every time XFDTD is run in the future The default units in both spatial and frequency terms may be modified to fit individual situations The options for frequency can range from Hertz to TeraHertz while spatial units may be displayed in both metric or English values XFDTD will use these units for any display of data Windows Version Preferences The Windows version of XFDTD has some specialized preferences for controlling the appearance and function of XFDTD The Interface preferences allows selection of which windows in XFDTD are dockable Dockable windows are those that can be attached to the sides of the main frame window To dock a window click and drag it to the edge of the XFDTD frame window The outline of the window will shrink when it will dock To undock or float a window double click on it or drag the window off the frame If windows are set as dockable they may be moved without attaching by holding the Control key while moving The Material Palette section controls the display of materials on the material palette Materials will be display either with the material descriptions entered or by the material number The XFDTD Project Tree section controls the behavior
140. rmal to the viewing plane The fields may be displayed on either a linear or dB scale The default is the dB scale with 3dB separating each color on screen When the scale is set to linear the step defaults to 20 between adjacent colors so that the red highest intensity represents 100 and blue represents 20 The display colors are graduated so that a color intensity between yellow and red would indicate a field magnitude between those two levels on the color bar Since FDTD is spatially discrete some volumetric quantities may be offset by a fraction of an FDTD cell since the quantities from which they are calculated are not co located in space Initially the fields are automatically normalized to the peak value in that plane With each new field file loaded the peak value and thus the scale changes With sequence files the peak value for all files is used as the normalizing value However for additional flexibility the Set Full Scale Figure 46 and Figure 47 option may be used to force a certain peak value on the display This is useful if small regions of the field display region such as near the antenna feed have very intense field levels For display purposes all values greater than the Full Scale value are displayed as if they were equal to the full scale value Set Full Scale Values x Jm NM The normalization value is displayed Field Type Max Value Full Scale with the fields and can be found at the EV M 32641e 001 SEET
141. rrent several parameters are computed and may be viewed on the Steady State Data menu Figure 55 The input impedance input power radiated power and antenna efficiency are displayed at the top of this window If steady state S parameters have been selected the values will be displayed in the lower part of this window The values displayed on this menu are computed either when a project file is loaded or when a steady state far zone transformation is computed Otherwise the menu will not be available for opening If no steady state far zone transform data has been saved this menu will not be available If more than one feed has been defined the input impedance calculation is not performed and will not be displayed When only one feed is used the impedance is computed by dividing the complex input voltage by the the total complex input current Note If any of the boundaries have been set to PEC or PMC or if any materials are within 6 cells of the outer boundaries then antenna results displayed here will not be accurate since the far zone transformation is not valid S Parameter results do not depend on the far zone transformation and these restrictions do not apply Steady State Data x Feed Point Impedance R jx Ohms Feed Point 1 8 9728e 001 j 2 7805e 002 If an S Parameter calculation was made with sine wave excitation then this menu will provide the single frequency S Power and Antenna Efficiency Paramet
142. rve brain 1050 57 72 61 55 7 46 5 44 eye 1000 1 9 84 1 7 74 1 9 70 1 9 70 blood 1000 1 12 70 1 19 74 1 09 63 1 18 62 lung 330 28 22 22 12 24 12 24 12 sig conductivity in Siemens m eps relative permittivity 17 2 The Remcom High Fidelity Body Mesh The Remcom High Fidelity Body mesh is based on the same data as used in the original mesh It uses 5x5x5 mm cells and has dimensions 136x87x397 for 4 697304 cells The High Fidelity mesh is much more detailed than the original mesh and it contains 23 materials which are assigned as follows 124 XFDTD 2 Skin XFDTD 3 Tendon pancreas prostate aorta liver other XFDTD 4 Fat Yellow Marrow XFDTD 5 Cortical Bone XFDTD 6 Cancellous Bone XFDTD 7 Blood XFDTD 8 Muscle heart spleen colon tongue XFDTD 9 Grey Matter cerebellum XFDTD 10 White Matter XFDTD 11 Cerebro spinal fluid XFDTD 12 Sclera Cornea XFDTD 13 Vitreous Humor XFDTD 14 Bladder XFDTD 15 Nerve XFDTD 16 Cartilage XFDTD 18 Gall Bladder bile XFDTD 19 Thyroid XFDTD 20 Stomach Esophagus XFDTD 21 Lung XFDTD 22 Kidney XFDTD 24 Testes XFDTD 25 Lens XFDTD 27 Small intestine Measured values for the tissue parameters for a broad frequency range are included with the mesh data The tissue parameters may be adjusted automatically for a specific frequency by using the Edit gt Adjust Tissue Material Parameters menu The correct values from the table of measured data will be selected and
143. s pp 849 856 The XFDTD 5 0 calculations are on an FDTD mesh with the same size cells as in the Sheen paper but in a space only 60x75x16 FDTD cells due to improved methods of 109 feeding the antenna and in performance of the absorbing outer boundary The XFDTD 5 0 calculation also requires only 4 000 time steps rather than the 8 000 time steps needed by Sheen again due to improvements in the feed method incorporated into XFDTD 5 0 Finally the agreement with measurements is better than shown in the Sheen paper The XFDTD 5 0 calculation required approximately 4 minutes on a Pentium 400 MHz Computer using Windows NT Operating System See sample output in Figure 76 Figure 77 Figure 78 and Figure 79 Figure 76 Geometry of microstrip patch antenna as meshed in XFDTD 5 0 110 Figure 77 Ez out of plane electric field after 160 time steps due to Gaussian Pulse excitation Figure 78 Jy vertical current density after 160 time steps due to Gaussian pulse excitation 111 Figure 79 Comparison of S11 computed by XFDTD 5 0 and measurements 14 5 2 Microwave Examples The Lange coupler and Wilkinson Power Divider results in the directories examples lange and examples wilkinson on the CDROM are both taken from the PhD dissertation of Dr Jose G Colom With his permission a portion of his dissertation is included on the CDROM as an Adobe Acrobat file colompart pdf The complete dissertation may be obtained from Remc
144. s exist in etc directory and contain only the license number supplied by Remcom NOT your computer serial number Contact Remcom Inc for correct license number if necessary This applies only to the Remcom supplied licensing If a special licensing situation such as FlexLM is being used this message does not apply P XFDTD colors appear strange or some materials are not visible in the mesh Other Unix applications may be using colors that are needed by XFDTD Close all other applications running on the computer platform and start XFDTD again After you start XFDTD look at the window from which you gave the xfdtd50 command If there is a Unix warning that not all colors could be allocated then you still have an application running that is using some of the colors required by XFDTD P difficulty reading files with XFDTD Unix allows a limited number of files in the same directory Try to separate files from different XFDTD calculations into different directories P Can t read files into XFDTD after Upgrade to Newer Version XFDTD should be fully backward compatible This means files created by older versions of XFDTD should be functional with XFDTD 5 0 Files created by XFDTD 5 0 117 can not be read in older versions of XFDTD 2 4 since the formats are different It is recommended that when you receive your new version of XFDTD that you remove all the XFDTD executable files from the previous version from your computer 118
145. s manual for details For transient calculations including a source resistance equal to the impedance of the coaxial cable being approximated should reduce the number of time steps needed for the transients to dissipate It is similar to driving an actual circuit or antenna using a matched source 9 1 1 5 S Parameter Calculations Any number of individual ports for S parameter calculations may be specified in the Sources Loads window Each port can have a different source resistance Lumped reactive elements should not be used in the active port specification The S parameters at each port will be calculated relative to the source resistance as the value of the characteristic impedance of the transmission line feeding the port For instance if the S parameters would be measured using 50 Ohm cables then the source resistance should be specified as 50 Ohms Examples for both stripline and microstrip circuits are given in this manual For antenna calculations all feeds are normally excited However for S Parameter calculations only one feed can be excited for a particular FDTD calculation If an S Parameter calculation is to be made the yes option next to the S Parameter specification box must be selected Also the active port must be entered as well for this particular calculation XFDTD then provides that column of the S parameter matrix For example if port 1 is excited in a 3 port circuit XFDTD will determine S S and S4 If different
146. s window Compute Far Zone Data Compute S Parameter Data After all parameters for an FDTD calculation Cami Bule art NENE have been entered and saved selecting Disney SAP hGnneton Results Run CalcFDTD will begin the Display Steady state Weta simulation After all timesteps have been calculated and the output files have been Run CalcFDTD Ctrl U written some post processing option may be Figure 44 The Results menu available on this menu Not all choices will be available on this menu as the post processing depends on the input parameters and data saved during the calculation All of the possible choices and when they are available are described in this chapter 10 1 View Fields Several choices for color intensity displays are available in XFDTD After field file of the appropriate type is loaded this menu choice will become available In XFDTD 5 0 this menu is activated after loading either a planar transient field file or sequence or any one of the steady state data files or sequences such as SAR electric field or magnetic flux densities or conduction currents The time domain field files will display either the electric or magnetic fields the current density or Poynting vector in a single slice of the geometry at various moments in time The steady state quantities files are magnitudes in specific planes so the sequences slice through the planes of the object rather than through time Both the time domain and steady state sequen
147. sian modulated pulse there is a Gaussian envelope of the specified pulse width enclosing a sine wave of the specified frequency The sine wave is centered in the Gaussian envelope so that the average value of the pulse is zero The two graphs in this window show the time variation and frequency spectrum of the waveform to aid in correctly specifying the parameters When choosing the pulse width and or frequency bear in mind the constraints of the FDTD method The time rate of change of the pulse maximum frequency with significant energy or the sine wave frequency must be chosen low enough so that a sufficient number of time steps occur during one period for reasonably accurate sampling The Courant limit for the time step size is where Ax is the size of the cell edge At is the time step and c is the speed of light Assuming the often applied constraint that Ax lt A 10 the maximum frequency specified is then constrained by Frequency ite The default size for the Gaussian pulse width is 32 time steps This provides a reasonable frequency bandwidth for the Gaussian pulse For the Gaussian derivative pulse the time duration should be set somewhat greater since the Gaussian derivative pulse will have a higher frequency spectrum than a Gaussian pulse of the same time duration 57 The pulse width for the modulated Gaussian may be adjusted to enclose a specific frequency range This may be useful for example in waveguide calculations so that on
148. so cd deck eect Cee Ree NC ee toe ee Cet Lp RET Lee ee eee ESI 128 20 Bibliogra phy sis oso ues on cse os he arg a as See eg Sa ssi See ao Say ay Sands 129 1 Introduction The Finite Difference Time Domain FDTD method of electromagnetic calculation is widely used in a variety of electromagnetic radiation interaction and scattering applications The method is a transient marching in time approach in which time is divided into small discrete steps and the electric and magnetic fields on a fine grid are calculated at each step Although a discussion of the fundamentals of the FDTD method is beyond the scope of this manual The Finite Difference Time Domain Method for Electromagnetics by Kunz and Luebbers 1 provides an in depth exploration of the method and offers many example results To obtain reliable and accurate results from the XFDTD program a familiarity with the basic FDTD method is essential In addition a working knowledge of either the Unix operating system or Windows NT 95 is required 1 1 Operating System The FDTD method is very general in terms of geometries and materials that can be considered However even for general problems such as resonant frequency simulations where the geometry extent is several wavelengths the program requires the capabilities of a workstation or powerful PC XFDTD 5 0 is available for Windows NT and Windows 95 98 operating systems As with previous version of XFDTD Version 5 0 is also available f
149. spatial increment or cell size of the structure being simulated The fundamental constraint on the cell size is that it must be much less than the smallest wavelength for which accurate results are desired A commonly applied constraint is ten cells per wavelength meaning that the side of each cell Ax Ay Az should be 1 10 A or less at the highest frequency shortest wavelength of interest If the cell size is much larger than this the Nyquist sampling limit A 2Ax is approached too closely for reasonable results to be obtained Significant aliasing is possible for signal components above the Nyquist limit Choosing a cell size of 1 10 A is a good starting point but other factors may require a smaller cell size to be chosen This topic is covered in more detail later Note FDTD is a volumetric computational method If some portion of the computational space is filled with penetrable material the wavelength in the material must be used to determine the maximum cell size Geometries containing electrically dense materials require smaller cells than geometries that contain only free space and perfect conductors 3 1 1 Creating a Geometry with FDTD Cells Before any FDTD calculation can be done an accurate approximation of the structure under test must be entered into XFDTD As was mentioned above a resolution of one tenth of a wavelength is the minimum required for accurate FDTD results However many structures require a higher reso
150. ssociated with each edge of the mesh These material types correspond by number to those on the Material Palettes so that 0 is free space 1 is perfect conductor 2 N are dielectrics In XFDTD 5 0 the maximum number for dielectrics is 27 If only dielectric materials are present only one set of edges need to be defined If magnetic materials are present a separate set of mesh edges must be defined Once the mesh has been generated it can easily be put into a form that can be read by XFDTD Note XFDTD expects the geometry file to have the extension id An example geometry file is shown in Table 1 The first line of a geometry file contains the file version number This indicates to XFDTD the format of the file and allows for backward compatibility The next line contains the variables which are the number of cells in the FDTD space in the x y and z directions NX NY NZ This is followed by three floating point variables giving the cell x y and z dimensions Ax Ay and Az in meters In the example file shown the space is 41 by 41 by 72 cells and each cell is a 1 cm cube The next line has three integer numbers which are the offsets in cells of the geometry if it is to be used as a subgrid For the example file these are all zero since this file was meshed as a Main Grid and never used as a subgrid The next line contains a flag which indicates whether or not fuzzy cells are used in the mesh No fuzzy cells are used and the value is z
151. state far zone is selected the Compute Far Zone Data menu is simplified A pattern made be computed versus Theta or versus Phi Select one of 78 these options and then set the fixed angle the starting and stopping angles and the increment For example for a pattern versus Theta from 0 to 180 in 1 degree steps at Phi 45 set phi to 45 theta to 0 theta final to 180 and increment to 1 As with the transient far zone multiple patterns can be made at a time simply by adding more on to the list Pressing OK starts the post processor Note As with all steady state calculations accurate results can only be obtained if the System has actually reached steady state Sufficient timesteps must be specified and near zone values monitored to ensure that there are no transients in the system Far zone calculations cannot be made unless all outer boundaries of the FDTD space are set to absorbing Liao or PML before the calculation of the data The far zone transformation is performed over a box 5 cells in from the outer boundary Therefore no part of the geometry may pass through this box or else invalid results will be computed 10 4 Compute S Parameter Data Whenever S Parameter calculations are performed with transient pulse excitation XFDTD can provide files for plotting S parameters vs frequency The S parameters will be computed by the calculation program using the default FFT size However the S parameters may be post processed at a different
152. strip problem with 50 ohm characteristic impedance a source resistance of 50 ohms would be a good choice When making calculations that include the input voltage current and or power in the calculation formula such as antenna gain or S Parameter values the input voltage current and or power will be that provided at the terminals of the mesh edge In particular the power dissipated in the source load resistor will not be included in the input power For example the gain of antenna is reduced if any power is dissipated in lossy materials in the antenna since this power is therefore not radiated In XFDTD since the voltage current and input power are calculated at the mesh edge the gain of antenna will not be affected by the value of the source resistance Similarly for input impedance calculations the source resistance capacitance and inductance values will not be included in the input impedance Note The source resistance cannot be made too high or instability may result In the source resistance calculation the displacement capacitive current through the FDTD cell is neglected If the source resistance is made high enough so that the neglected displacement current become larger than the conduction current through the source resistance Maxwell s equations will not be satisfied and the FDTD calculation may go unstable 9 1 1 3 Modifying Feed Port Parameters If a feed location was entered incorrectly or it has moved the entry ma
153. t none Location in Men Grid Add Dual Grid Remesh and Rotate gt Tissue Material Parameters Reorient Space 7 1 Geometry Editing Geometry editing in XFDTD is done by the definition of objects These objects may be chosen from a library of primitives or by creating a user defined object which is defined using mouse driven editing tools The geometry is entered by defining the electric or magnetic material parameters of cell edges which correspond to either electric field locations for the electric grid or magnetic field locations for the magnetic grid Setting the electrical or magnetic properties of a cell location such as the permittivity and conductivity changes how the electric or magnetic fields are updated by the calculation program This effectively adds a material with those properties to that location Open the Geometry Editing Tools panel to edit the geometry A window lists any objects that are defined and whether the object is meshed or not A library of objects is available for meshing which includes a user defined object The editing tools described in more detail in a later section 33 A material palette is included in Windows for adding new dielectric or magnetic materials and defining their properties The Electrical and Magnetic Material Parameters menus provide the Material Palette function in the UNIX version 7 2 The Material Palette Windows Version Only In Windows when Geometry
154. t files that have already been created To opena file either double click on the file or select it with the mouse and the select Open The project files contain the XFDTD calculation parameters and the geometry file name including subgrids so opening a project file will also open the geometry 6 1 3 Merge This feature merges two geometry files It is especially useful for modifying an existing geometry by placing it in a new mesh that may be larger or smaller than the original The Merge function prompts for a vector offset which allows for repositioning of one geometry within another Geometries can be merged into the main grid or one of the subgrids One application of using the Merge function might be when one geometry contains a human head and another contains a portable telephone The two geometries can be merged together to place the telephone near the head The resulting mesh can be saved as a new geometry file This procedure can be repeated and with the telephone in a different position Another use of the Merge function is creating subgrids from existing main grid geometry files If the grid dimensions of a geometry file are not correct for use as a subgrid the geometry can be merged into a mesh of the proper dimensions and saved as a new file 6 1 4 Save This option saves either the geometry or calculation parameters depending on which window is currently active The main grid geometry and any existing subgrids are saved sepa
155. t for printing The filenames and formats of the data files are described in a later chapter of this manual 10 3 Compute Far Zone Data XFDTD has the ability to compute both a transient and a steady state far zone near to far transform The basic purpose of the transform is to generate gain or scattering patterns in the far zone from the near zone field data There are some important 11 differences in how this is done between the two cases though The far zone angles for the desired pattern must be specified before the FDTD calculation for the transient far zone transformation In post processing a gain pattern versus angle can be generated at the angle specified The pattern can be made at any frequency in the input or at a single angle over all frequencies in the input see Figure 51 The steady state far zone transformation is only available at the frequency of the input but no angles need to be specified before the calculation and in post processing a pattern can be made at any set of angles in any increment see Figure 52 El MEME Compute Far Zone Data Eg Compete Far zZonna Doia Dana Typa Eurus Phi a C Gens Ph Comitan Thee ra Thats Consis Phi fa tiis pee Constant Theta Pattern Theta F Farions Elecinc Fiski vr Time Final Phi 360 FT Sing ii C Constant Phi Pattern fainalieta 180 Fardone Angee Increment 2 Delete Delete All Gain dBi at Phi 0 00 from Theta 0 00 to 360 00 Inc
156. terials in the subgrid 7 4 Specifying Magnetic Materials Magnetic material permeability and magnetic conductivity are specified for each magnetic material type using either a panel similar to the Electric Material Panel 35 Windows or a menu analogous to the Electrical Material Parameters menu UNIX These choices are only available if the magnetic grid was created with the geometry If the magnetic is grid is desired but does not exist it can be added through the Add Dual Grid function discussed later Simple magnetic materials referred to as normal have relative permeability and magnetic conductivity values which may be found in tables for some materials These values can be derived from complex permeabilities as well Frequency dependent anisotropic magnetized ferrites require the specification of five material parameters see Figure 16 The first three ferrite material parameters are the Larmor precession frequency in radians sec the frequency corresponding to the saturation magnetization in rad sec and the damping coefficient The fourth and fifth parameters are the theta and phi angles in degrees which specify the direction of the static magnetic field The form of the permeability tensor used for the ferrites is discussed in references 12 13 14 15 The first two references do not discuss the damping coefficient Reference 15 gives the parameters for some commercially available ferrites in Appendix 12 1
157. the location in cells is updated including the orientation of the edge under the pointer X Y or Z This position display is especially helpful in locating the voltage and or current sources and other geometry features The material number at each edge is also shown as the pointer is moved through the space 7 7 2 Additional Layers in Geometry For adding features to a User defined object which extend through several layers above and or below the current viewing plane the Edit Geometry Tools window provides the ability to duplicate editing actions through additional layers This is accomplished by setting the editing depth in the Additional Layers field For example if the view is set to the XY plane at Z 25 and the above editing depth is set to 5 the same changes made in plane Z 25 will appear in planes Z 26 through Z 30 This greatly simplifies the description of geometry shapes that have a constant cross section and extend over multiple layers of the space The vertical bar on the right of the Edit Geometry Tools window provides visual feedback of the editing characteristics 7 7 3 Library The Geometry Edit Panel also contains a library of Circular Cylinder end Conic primitive objects which may be used to build a Helix geometry These are accessed by clicking on New Plate 1 component thick rectangular in the Windows version or by selecting Library in the Plate 1 component thick quadrilateral UNIX version of the Edit Panel The
158. tive in Windows and select Stimulus We are interested in feeding the antenna with a voltage source so select the Sources Loads sub menu To set the input waveform press the Waveform button We want to set the excitation as Gaussian with a pulse width of 32 time steps and run the calculation for 1200 timesteps See Figure 63 Press OK to close the window Stimulus Waveform xi Waveform Parameters Gaussian Pulse Width time steps 32 C Gaussian Derivative l E vsrmimtitu Ev ite C Modulated Gaussian C Sinusoid Iren t User Defined Number of Time Steps 1200 Time Domain Frequency Domain L time ps frequency GHz ENTE Figure 63 The Waveform menu after setting the pulse width and number of timesteps for the monopole on a box example 95 10 The Feed is located at x 33 y 19 and z 46 in the main grid and is z directed Specify a series source resistance of 50 ohms to reduce the number of time steps needed for the transients to dissipate Select Add feed to list and if desired set the active port for an S parameter calculation The resulting window should appear as shown in Figure 64 Source Waveform Gaussian Pulse Width 32 00 Time steps 1200 Set Waveform Far Zone Transformation for Sinusoidal Source G jransient Steady State Wore
159. tive object All that is required are the two endpoints of the wire If the wire material in PEC the wire may lie at any orientation on the grid If the thin wire material has been chosen the wire must be aligned with the grid Thin wires may not be staircased as this will lead to instabilities in the calculation Figure 29 The Wire primitive menu 7 7 4 Fuzzy Cells In order to improve the fidelity of the FDTD results for dielectric objects the cylinder and sphere library objects can be meshed using fuzzy cells on the surface Fuzzy cells use values of permittivity and conductivity intermediate between free space and the values of the material The staircase error involved in meshing curved dielectric surfaces with rectangular cells is reduced using fuzzy cells The fuzzy cell values are automatically calculated and assigned The fuzzy cells are displayed in a lower color intensity That is all cells of the same material type are displayed as the same color but fuzzy cells with intermediate permittivity and or conductivity are displayed with lower intensity Fuzzy cell meshing is not helpful for PEC targets 44 While XFDTD automatically adjusts the relative permittivity on the surfaces of these dielectric spheres and cylinders the permittivity of flat surfaces of dielectric objects may be adjusted manually For this purpose a manual selection of Fuzzy levels is available from the Edit Panel If a cell is entirely within a dielectr
160. tor may be difficult since the wavelength inside the good conductor will become very small requiring extremely small FDTD cells to provide adequate sampling of the field values inside the material If only the surface losses are of interest in a cavity for example approximate methods for determining an equivalent conductivity for FDTD calculations are discussed in 11 In many FDTD calculations a normal dielectric specification for most materials will be sufficient However for wide band pulse excitations some materials exhibit significant changes in their permittivity The two most common ways to specify the frequency behavior of such materials are the Debye and Lorentz functions For a Debye material the electrical conductivity in S m infinite frequency relative permittivity static relative permittivity and relaxation time in seconds are set in the Edit Electrical Material Windows or Electrical Material Parameters UNIX window For a Lorentz material the conductivity in S m infinite frequency relative permittivity static relative permittivity resonant frequency in Hz and damping coefficient in Hz must be specified For a detailed discussion of these materials refer to Chapter 8 of 7 If one or more sub grids are included in the FDTD calculation the dielectric material parameters can be set independently for each grid The process of adding a material must be repeated for the subgrids and different parameters can be set for ma
161. try alone or the geometry with fields A second option is to simply press the Print Screen button which will capture the active window in a buffer This image may then be pasted into other software such as the Windows Paint program 43 In Unix XFDTD does not include the capability to provide users with digital files of XFDTD displays directly However other software exists that can do this very well To obtain digital images gif or tif files or other formats of any of the XFDTD screen images we recommend the free software xv It can be obtained over the Internet by anonymous FTP to ftp cis upenn edu The xv software is available from directory pub xv Executable versions of xv for many systems can be obtained using a web browser from www trilon com xv downloads html distributions Additionally the Unix XFDTD screen can be exported to a Windows machine using an X server and images may be saved using the Print Screen method described above 10 2 Display Plot Plots of most data saved by XFDTD can be displayed with the plotting tools included with the program The plotting tool may be opened either through the Display Plot Results menu or from the icon on the button bar The Display Plot window shown in Figure 48 will then open and a plot of the desired data can be made and viewed There are three basic categories of plots in XFDTD depending on the X axis abscissa type The first category is for time domain plots which includes near zo
162. ts Background Color This menu item controls the color of the geometry window background Note that the drawing background is switch to white for printing automatically Export BMP Exports the current view to a bitmap of a user defined size The size of the output bitmap must be entered followed by the filename 8 2 The View Menu in Unix XFDTD In the Unix version of XFDTD the View menu does not change as there are not separate windows for the Geometry and Run Parameters The menu will appear as shown in Figure 31 The Hide Toolbar option removes the toolbar from the interface 48 window Selecting this option again will Hide Toolbar replace the toolbar Use the Set Viewing Change Visible Grid Space item to change which grid is Turn On Grid Ctrl G currently in the view The options for Tum Off Normal Elements Ctrl A turning on and off the grid normal Turn Off Electrical Grid Components Ctrl L elements electrical components and magnetic components follow Select 3D 3DMode Ctrls3 Mode to view the geometry in three D dimensions Drawing Area Background is used to change the color of the geometry window Drawing Area Background Color P Figure 31 The view menu in XFDTD 5 0 on a Unix computer 49 9 Edit Run Parameters The input and output parameters for an FDTD Undo Mesh Wire rez calculation are defined on the Edit menu of the reda nt Run Parameters window see Figure 32 In the Stimulus UNIX version
163. ts up to 3 GHz with a Gaussian pulse 32 time steps wide But since part of the space has the dielectric material with the same cell size the Gaussian pulse width should be increased to 64 to reduce the frequency spectrum bandwidth Correspondingly the maximum frequency for reliable results would be decreased from 3 to 1 5 GHz Note When the pulse width is changed from the default values the FDTD results for some frequencies will not be valid since the energy spectrum of the modified pulse will not excite the problem over then entire spectrum When displaying such results limit the frequency range accordingly When choosing the source form remember that the Gaussian pulse has a non zero average value It should not be used for calculations if there is a closed path loop of perfect conductor connected to the electric field location unless a source resistance is also specified This is because a steady current will start to flow in the loop and never decay through loss or radiation The symptom of this will be a source current that has an average value not equal to zero If this occurs the Gaussian Derivative or Modulated Gaussian pulses can be used or a non zero source resistance included in the calculation An arbitrary source voltage vs time my be specified by choosing User Defined from the Stimulus Waveform window Pressing this option will open a menu asking for the input filename with an extension src The file format for a user defined wa
164. tside the range of sample points or when only a small number of data points is available Note To avoid computing an SAR in certain materials of the geometry simply set the material density to O 10 6 Display Averaged SAR Information After the SAR statistics have been computed select this option for viewing the results Figure 54 The information available includes the maximum SAR and its SAR Statistics x Average SAR in exposed Object W kg fi1980e 005 8 Maximum SAR W kg B 6758e 004 Location of Maximum SAR xy z 473231 Maximum 1 Gram Average SAR W kg 67589 2004 Location of Maximum 1 Gram Average SAR x y z 233230 ooo Maximum 10 Gram Average SAR W kg 9018e 004 Location of Maximum 10 Gram Average SAR xyz 493231 Computed Input Power Ww p0297e 004 Scaled Input Power vv OK Help Cancel Figure 54 The SAR Statistics available after computing both the 1 and 10 gram averages 81 location the whole body average SAR and the maximum 1 and 10 gram averaged SAR values and locations To adjust the SAR to a particular input power the computed input power is also shown Changing the power value will adjust the SAR values accordingly This power adjustment may also be done on the Field Control Panel on the Set Full Scale menu 10 7 Display Steady State Data When a steady state calculation has been performed with a near zone source voltage or cu
165. uebbers and J Schuster Scattering from Coated Targets Using a Frequency Dependent Surface Impedance Boundary Condition IEEE Transactions on Antennas and Propagation vol 44 no 4 pp 434 443 April 1996 D Kelley R Luebbers Piecewise Linear Recursive Convolution for Dispersive Media using FDTD IEEE Transactions on Antennas and Propagation vol 44 no 6 pp 792 798 June 1996 132 M Chevalier and R Luebbers FDTD Subgrid with Material Traverse IEEE AP S International Symposium and URSI Radio Science Meeting Baltimore MD July 21 26 1996 J Schuster R Luebbers and H Riazi FDTD Predictions and Measurements of Car Effects on Portable Telephone Received Signal Levels IEEE AP S International Symposium and URSI Radio Science Meeting Baltimore MD July 21 26 1996 R Luebbers Thirty Years After Kane Yee and FDTD IEEE AP S International Symposium and URSI Radio Science Meeting Baltimore MD July 21 26 1996 J Schuster R Luebbers Comparison of Site Specific Radio Propagation Path Loss Predictions to Measurements in an Urban Area IEEE AP S International Symposium and URSI Radio Science Meeting Baltimore MD July 21 26 1996 J Schuster R Luebbers FDTD for Three Dimensional Propagation in a Magnetized Ferrite IEEE AP S International Symposium and URSI Radio Science Meeting Baltimore MD July 21 26 1996 D Kelley R Luebbers Calculation of Dispersion Errors for the Piecewise Linear Rec
166. ursive Convolution Method IEEE AP S International Symposium and URSI Radio Science Meeting Baltimore MD July 21 26 1996 R Luebbers R Baurle FDTD Predictions of Electromagnetic Field in and near Human Bodies using Visible Human Project Anatomical Scans IEEE AP S International Symposium and URSI Radio Science Meeting Baltimore MD July 21 26 1996 R Luebbers and H S Langdon A Simple Feed Model that Reduces Time Steps Needed for FDTD Antenna and Microstrip Calculations IEEE Transactions on Antennas and Propagation vol 44 no 7 pp 1000 1005 July 1996 J W Schuster and R Luebbers Finite difference time domain analysis of arbitrarily biased magnetized ferrites Radio Science vol 34 no 4 pp 923 930 July August 1996 M Chevalier R Luebbers and V Cable FDTD Local grid with Material Traverse IEEE Transactions on Antennas and Propagation vol 45 no 3 pp 411 421 March 1997 133
167. ute aU 43 V37 349 Sphere S ossa sem ae CARE eae iHd dde aes 43 T f3 7 Spiral antena lt 2 2 x eot x eS DEP EXE tss 43 72753 8 WIO oo eee bitu etre et on e et ve e en as m ons 44 Jer puzzy Cells sus e sam aM edis d di MELLE 44 7 8 Spatial Increment s s t etes Sos eus pte fervor teu Sep ee 45 7 9 POC D al Grid Ase bese cs tet ee See ee SEE Ee B ee ee ee I EE 45 PATO PIelorBlI BS cue rut cue Turo wee TID TUS T Vu hula TIN geret 46 muneri mo E ER 48 8 1 The View Menu in Windows XFDTD essere 48 8 2 The View Menu in Unix XFDTD leeseeeeellll eee 48 S Edit R n Parameters sore dor erai or E teo Gero or ser e ae 50 91 SUMUINS lt 3 chee ease ee eee eee ee Le ee eee ae EAE BOSE 50 9 1 1 Sources Loads S Parameter Port Setup 50 9 1 1 1 Setting the Feed Port Location 51 9 1 1 2 Feed Port Parameters sullsus 52 9 1 1 3 Modifying Feed Port Parameters 53 9 1 1 4 Multiple Voltage and or Current Sources 53 9 1 1 5 S Parameter Calculations 54 9 12 Patio Wave veces esconde s vie irs Sy oie reor 54 9 1 3 TEM Excitation Plane i siib teeter ee ets fs 55 9 1 4 Specifying the Source Waveform 0000005 56 9 1 5 Number of Time Steps 200 c ee eee eee eee 60 9 1 6 Far Zone Transformation for a Sinusoidal Source 60 9 2 Sample Near Zone Data 0 0 eee 61
168. veform is as follows the first line must be an integer which is the number of time steps in the waveform additional timesteps will be zero padded The format of the rest of the file depends upon whether a voltage source or incident plane wave calculation is being 59 made For a voltage source excitation each following line one for each time step contains two floating point number representing the voltage and its time derivative at the feed at that timestep For an incident plane wave calculation each following line one for each time step contains two floating point numbers The first number on each line is the electric field value in Volts meter at each time step and the second is the time derivative of the electric field of the incident plane wave 9 1 5 Number of Time Steps For each of the different types of Stimulus a number of time steps for the FDTD calculation must be specified This number must be chosen with care since a low number will terminate the calculation before convergence of the results is obtained A high number will cause unnecessary calculations to be performed but will not result in errors XFDTD will display an error message if the number of timesteps entered is too small to include the input waveform but this number is far lower than the actual number of timesteps required by the calculation For a transient calculation the number of timesteps should be large enough for all fields to decay to zero This
169. verview of the entire interface More detailed descriptions of the menu options are found in other chapters NOTE The Windows NT 95 98 version of XFDTD and the UNIX version of XFDTD have slightly different formats Whenever important differences exist between the versions mention will be made The term windows version will refer to the Windows NT 95 98 version of XFDTD while UNIX version will refer to XFDTD for any UNIX platform 4 1 Starting XFDTD 4 1 1 Starting XFDTD in Windows NT 95 98 In Windows NT or Windows 95 98 go to the Start Menu select Programs then REMCOM and finally XFDTD 5 0 4 1 2 Starting XFDTD in UNIX To start XFDTD from a Unix installation enter the command xfdtd504 Remember the XFDTD program files xfdtd504 calcfdtd504 xpostp50 and xpostpss50 must be in the PATH or in the current directory and all files must have execute permission It is best to make separate directories for each calculation Consequently it is best to start XFDTD from the desired output directory 4 2 The XFDTD User Interface Figure 2 below shows XFDTD running in Windows NT with an example geometry and project file already loaded A similar window for the UNIX version of XFDTD is shown in a later figure Initially the XFDTD main window will be empty with just the menu bar across the top When a project file is loaded both the geometry and the calculation parameters are loaded and displayed on the screen The important features of
170. y be performed as well The maximum EE El ERES 1 and or 10 gram average SAR id viol values and location will be located e 74 c p cuu and files of the averaged SAR will be created for viewing Figure 53 The SAR Statistics menu Note To compute the SAR statistics the SAR values must have been saved in All Planes in at least one direction xy yz or xz To compute the SAR statistics Figure 53 first choose the direction As mentioned above the SAR values must be saved in all planes in at least one direction Choose the direction as either XY YZ or XZ Select the desired output as either Max Whole body average which will only find the maximum and average SAR in the entire geometry or choose 1 10 or 1 and 10 gram averaging With all choices the maximum and whole body average SAR values will be computed If either the 1 or 10 gram averages are selected the geometry must contain at least enough mass to form a valid sample space If the entire geometry contains less than either 1 or 10 grams an error message will be displayed stating that no averaging could be performed f there is enough mass the calculation will proceed This averaging routine is computationally intensive and could take a significant amount of time depending on the speed of the computer the number of cells in the geometry and the density of the material The progress of the calculation will be displayed on the screen to provide some feedback The
171. y be edited simply by follow the procedure below 1 Select the feed from the list 2 Make the desired changes to the Feed Specifications While the changes are being made the selected feed will remain highlighted 3 Click on Modify Selected Feed to replace the selected feed with the new specifications 9 1 1 4 Multiple Voltage and or Current Sources For calculations with multiple voltage and or current sources such as antenna arrays or multi port S parameter calculations multiple feed points can be specified with the Sources Loads window For transient feeds each source function must have the same pulse width and amplitude or use the same user supplied file of voltage versus time The polarity can be adjusted by clicking the desired button This may be useful in controlling the sign of the phase terms in S parameter calculations For each feed independent source resistances may be specified For sinusoidal excitations each feed can be specified with a different magnitude and phase 53 For antenna calculations keep in mind that determining a good approximation to an actual antenna feed is not always simple Many antennas are fed with coaxial cable The simplest approach to simulating this is to locate a source in line with the center conductor of the coaxial cable where the cable is connected to the antenna This will result in an impedance at this point in the cable See the monopole antenna on conducting box example later in thi
172. y constructed subgrids can lead to instabilities especially when many timesteps are computed The subgrid implementation in XFDTD is extremely general One important feature is that perfect conductor and lossy dielectric materials can cross the subgrid main grid boundaries This allows a subgrid of finer resolution within a dielectric body However due to the interpolation of electromagnetic fields between main and subgrids there must be continuity of the materials in the normal direction to the boundary Any non free space materials must either continue through the boundary or be spaced at least 4 cells away from the boundary for a 1 3 cell grid and 6 cells away from the boundary for a 1 5 cell grid This spacing may need to be increased if stability problems occur or if the cell size is very small compared to the wavelength This applies whether or not the material is passing through the main grid subgrid boundary Although sources may be located within a subgrid the source must be located away from the boundary of the subgrid with the main grid by at least 4 cells for 1 3 ratio or 6 cells for 1 5 ratio Subgrid regions may not overlap and must be separated by at least 3 main grid cells A subgrid may not be located within 6 cells of the outer boundary The subgrid has the effect of overwriting any geometry in the main grid If free space cells in the subgrid overlap material in the main grid the main grid materials will be changed to free s

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