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User's manual of the Mode-Matching 3D software package

1. e 2 integer numbers M and N gt the indices of a TE mode that is accounted for e 1 real number Ref freq gt reference frequency 38 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE Plot the 1 parameter magnitude and phase for the TEmyn mode the magnitude being scaled down by the one corresponding to the frequency Ref_freq PLOT S_11 TM_MN Parameters e 2 integer numbers M and N gt the indices of a TM mode that is accounted for Plot the S parameter magnitude and phase for the TM my mode PLOT SCALED S_11 TM_MN Parameters e 2 integer numbers M and N the indices of a TM mode that is accounted for e 1 real number Ref_freq gt reference frequency Plot the S parameter magnitude and phase for the TMmyn mode the magnitude being scaled down by the one corresponding to the frequency Ref_freq PLOT VSWR TE_10 No parameters Plot the voltage standing wave ratio VSWR for the TEj9 mode PLOT SCALED VSWR TE_10 Parameter e 1 real number Ref freq gt reference frequency Plot the VSWR for the TEi mode scaled down by the one corresponding to the fre quency Ref_freq PLOT VSWR TE_MN Parameters e 2 integer numbers M and N gt the indices of a TE mode that is accounted for Plot the VSWR for the TEmyn mode PLOT SCALED VSWR TE_MN Parameters e 2 integer numbers M and N gt the indices of a TE mode that is acc
2. gt flag that controls the displaying of the colorbar in filled contour type plots generated by means of the the MATLAB conturf function NOTE The following values of Display_colorbar are accepted e 0 do not display the colorbar e 1 gt display the colorbars default Invalid values are converted to the default one 1 FONT SIZES Parameters e 2 integers FontSize and NotationFontSize gt the font sizes in points to be used in all kind of plots FontSize is used for rendering the titles and the axes labels and NotationFontSize is used for rendering the axes notations Invalid values i e negative ones are converted to the default font sizes 10 pt APERTURE DISTRIBUTION STEP RATIO Parameter e 1 real Step_ratio gt the ratio at which the steps of the non uniform grids employed for generating plots are increased NOTE By default two and pseudo three dimensional plots are generated using a uniform mesh Nevertheless it is often convenient to generate these plots for a non uniform grid having a maximum density in the vicinity of the edges of the waveguide s aperture and being increasingly coarser when moving away from them The accepted values of the Step_ratio parameter are Step_ratio gt 1 and invalid values Step_ratio lt 1 are converted to the default one 1 Note that experience has shown that the aspect of the generated plots tends to deteriorate significantly w
3. Brin k E kemm 142 denotes the propagation coefficient in the waveguide with k w Eq m being the wave number in the waveguide note that in view of ensuring the causality R Bmn gt 0 and S Gnn lt 0 Correspondingly the transverse components of H in the waveguide follow as A D ba ea ACTE km cos km cos kn y i 0 j 0 OO exp iBnnz VCP a g gt D e AGN kn COS Km x cos kn y i 0 j l VM exp j mnz PEM explj mnz X 5 Piy pee ACE kn sin km sin kn y i 0 j 0 VE exp iBhan2 VATE expliBnnn2 25 gt ESAD AGI km sin km 2 sin Fn y OMD exp j mnz PEM expli nnz 6 I E LAGER USER S MANUAL OF THE Mode_Matching_3D SOFTWARE PACKAGE 5 8g where the longitudinal wave impedances ve m 1 3 5 and n 0 2 4 and neee m 1 3 5 and n 2 4 have the expressions YAE Bran wm 7 Ae we1 Bmn 8 As for the longitudinal components of the field quantities and H 1 are concerned they follow directly by employing the strategy indicated in 6 pp 3 10 3 2 Aperture continuity requirements and boundary conditions at the flanges The continuity of the tangential components of the electric and of the magnetic field strengths at the aperture requires lim Base lim z for x lt a 2 and y lt 6 2 9 lim ry lim Boxy for x lt a 2 and y lt b 2 10 lim Ha lim Hx for x lt a 2 and y lt b
4. Eby y and S y z linear representation ax e 3 n z and arg Fay linear representation max e 4 o A o linear representation and o loga F max P max rithmic representation Mult_lambda_x Aemb Mult_lambda_z Aemp Mult_lambda_x Aemb Mult_lambda _z Aemp Figure 13 The dimensions of the plotted area in the case of near field type plots H plane 30 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE NEAR FIELD E_Y LIGHTED SURFACE B W Same as NEAR FIELD E_Y LIGHTED SURFACE black and white version NEAR FIELD E_Y SURFACE Same as NEAR FIELD E_Y LIGHTED SURFACE shaded surface three dimensional plots 11 colour version NEAR FIELD E_Y SURFACE B W Same as NEAR FIELD E_Y SURFACE black and white version NEAR FIELD E_Y CONTOURF Same as NEAR FIELD E_Y LIGHTED SURFACE filled contour pseudo three dimen sional plots conturf 11 colour version NEAR FIELD E_Y CONTOURF B W Same as NEAR FIELD E_Y CONTOURF black and white version By replacing in the definitions above E_Y by E Z H_X or H Z similar types of plots for the field quantities Ho a z Ho x z or Ho z x z respectively can be generated APERTURE E_Y LIGHTED SURFACE Lighted surface three dimensional plots of the field quantities E 0 y z E plane and E 0 z H plane in the vicinity of the radiating aper
5. the integrals is concerned it is noted that in view of the relevant integrands presenting a high convergence rate for large values of the integration variables the numerical integration schemes can be stopped at acceptably low values of these variables without a detrimental effect on the accuracy of the computed integrals 4 General description of the software package The mode matching technique for the analysis of dielectric filled flanged waveguide antennas described in Section 3 was implemented in a software package named Mode_matching_3D The configuration examined by the software package was illustrated in Fig 1 The main compo nent of the package is the stand alone executable Microsoft Windows compatible program Mode_matching_3D The computational engine of the package is implemented in C 9 The graphical post processing options employ the MATLAB engine 10 and a collection of M files 10 that need being available on the computer on which the program runs The executable can run independently as well in which case the graphical post processing are disabled Note that for taking advantage of all currently implemented post processing options MATLAB version 6 0 is required Nevertheless most graphical post processing modules will also run under MATLAB version 5 3 4 1 Installation of the software package The present implementation of the Mode_matching_3D software package assumes for the in stallation of the program the m
6. the rotation angle see Section 2 in degrees e 1 integer Density the number of points per 90 where the far field is computed e 1 real number Increment gt the minimum level in deciBells which is represented in the case of the logarithmic plot No checking of the input values is carried out Generates the co and cross polar radiation patterns for 0 0 90 and for a specified rotation angle y Phi at both a linear and a logarithmic scale POLARISATION PATTERN DB Parameters e 1 real number Phi gt the rotation angle see Section 2 in degrees e 1 integer Density gt the number of points per 90 where the far field is computed e 1 real number Increment gt the minimum level in deciBells which is represented No checking of the input values is carried out Generates the co and cross polar radiation patterns for 0 0 90 and for a specified rotation angle y Phi at a logarithmic scale I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 27 POLARISATION PATTERN LINEAR Parameters e 1 real number Phi gt the rotation angle see Section 2 in degrees e 1 integer Density gt the number of points per 90 where the far field is computed No checking of the input values is carried out Generates the co and cross polar radiation patterns for 0 0 90 and for a specified rotation angle y Phi at a linear
7. three dimensional plots 11 of the field quantities E gt 0 y z E plane and o 2 0 z H plane in the vicinity of the radiating aperture outside the waveguide only colour version For simplicity the subsequent definitions refer to the H plane only the definitions pertaining to the E plane following by swapping x and y Note that in the following Aemb denotes the wavelength in the unbounded right hand half space the embedding for the prescribed frequency of the fundamental mode Parameters I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 29 e 2 real numbers Mult_lambda_z and Div_lambda_z gt the width of the plotted area see Fig 13 in multiples of Aemb and the size of the mini mum discretisation mesh step in the Oz direction in quo tients of Aemb e 2 real numbers Mult_lambda_x and Div_lambda_x gt the height of the plotted area see Fig 13 in multiples of Aemb and the minimum size of the discretisation mesh step in the Ox direction in quo tients of Aemb e 1 integer Which_Type gt parameter indicating which type of plot must be gener ated NOTES The ploted area is symmetrical with respect to the Ox axis the ploted area corresponds to the rectangle Mult_lambda_x emp Mult_lambda_x Aemb X 0 Multlambda_z Aemp and y 0 The following values of Which_Type are accepted e 1 R Eby and y linear representation e 2 R
8. TE mode the funadamen tal mode When Frequency lt 0 the frequency of the funadamental mode is chosen such that the wavelength o corresponding to this mode satisfies the condition a frequency Ao with a denoting the necessarily prescribed width of the waveguide see Fig 1 WIDTH Parameter e 1 real number Width gt the width a of the waveguide see Fig 1 When Width lt 0 the width of the waveguide is chosen such that a Width Ao with Xo denoting the wavelength corresponding to the necessarily prescribed frequency of the fundamental mode NOTE Width and frequency cannot be negative at the same time The value of at least one of them must be prescribed by the user HEIGHT Parameter e 1 real number Height gt the height b of the waveguide see Fig 1 the dimension Height must be positive FILLING Parameters e 1 real number mu r 1 gt the relative permeability of the medium in the waveguide Hi r see section 2 e 1 real number eps r 1 gt the relative primitivity of the medium in the waveguide 1 see section 2 No checking of the input values is carried out 22 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE EMBEDDING Parameters e 1 real number mu_r_2 the relative permeability of the medium in the un bounded right half space 12 see section 2 e 1 real number eps_r_2 gt the relative primitivity of the medium i
9. analysed frequency range and the distribution of the sampling fre quencies over that range e The names of the files in which output data are saved Since the code performs the check on the consistency of the input data only after the complete set of parameters defining the problem at hand have been read the sequence in which the various parameters are input is arbitrary Note that there is a number of parameters that are of relevance for the spectral analysis of the open waveguide only see Section 4 6 The Mode_matching_3D program can operate in four different runtime modes The choice between these modes is done by means of a control variable denoted as Run_Type that can have any of the following values 10 GENERAL DESCRIPTION OF THE SOFTWARE PACKAGE Run_Type 1 default value The program is run for solving a new problem and no post processing tasks are executed this case is hereafter referred to as the solving a new problem only mode Run_Type 2 The program is run for solving a new problem and post processing the computed data this case is hereafter referred to as the solving a new problem and post processing mode Run_Type 3 The program is run for post processing the computed data pertaining to a previously solved problem this case is hereafter referred to as the post processing only mode Run_Type 4 The program displays the complete list of TE and TM modes that are a
10. following choice of modes is employed for expressing the transverse components of e TE and TM modes displaying an odd odd xz gt y symmetry in the case of the Bie component and e TE and TM modes displaying an even even x y symmetry in the case of the Big component With these choices the relevant components read ropes D Age kn sin km x sin kn y i 0 j 0 VEY ep VCP a se S Ag km sin km x sin kn y VEM exp j mnz EM explj mnz 1 Ey S ASD km cos km 2 cos kn y ll wR ll sae exp jBmnz ye exp i3inn2 2 Me Me ll a II a Tog kn cos km x cos kn y OSMD exp j mn2 VIM expli nnz 2 4 THE MODE MATCHING TECHNIQUE where m 2i 1 and n 29 i j 0 1 km mn a m 1 3 5 and kn nT b n 0 2 4 denote the transverse modal wave numbers AGE m 1 3 5 and n 0 2 4 and AM m 1 3 5 and n 2 4 denote some constants having the expressions A TE lt 2 ab T Ravan for n 0 3 o 4 ab Remi otherwise ALCTM 4 ab Y kemn a with kemn k2 k2 lie being the cutoff wave number yor and Vie m 1 3 5 and n 0 2 4 denote the modal amplitudes of the incident and reflected T7E modes respectively vim and yo m 1 3 5 and n 2 4 denote the modal amplitudes of the incident and reflected TM modes respectively and
11. into this directory The user may choose to modify the contents of this file in accor dance with her or his requirements or write her or his own input data files Recall that in the case when user written input data files are employed the name of these files must be specified on the command line The following data can be prescribed by the user e The number of excited TE and TM modes and their complex amplitude values In the case when no such information is explicitly provided the program assumes the standard excitation namely by means of a TEj mode of unit amplitude Note that attempting to excite the configuration by means of an evanescent mode will be signaled as an error e The frequency of the first prescribed TE mode the TE10 mode in the case of the default excitation hereafter referred to as the fundamental mode of operation e The width a and the height b of the waveguide see Fig 1 I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 9 B FFHETHEFHLF ATH TE ALE ETAL ETE ETAT ET EET ETHEL EEE HTE TPES EFTPS ttt ett PROBLEM DATA a EHEHEHE HEHEHEHE EHEHEHEH HEHHEHE single frequency analysis spectral analysis he choice for modes to be evaluated the minimum number of evaluated modes Define the data for the spectral analysis the lower limit of the highest cutoff frequency in the modal analysis low_frequency high_frequency the number of frequencies where
12. request Lager I de Hoop A T User s manual of the Mode Matching software package Inter national Research Centre for Telecommunications transmission and Radar Faculty of Infor mation Technology and Systems Delft University of Technology Scientific report IRCTR S 011 02 May 2002 available upon request Blok H van den Berg P M Electromagnetic Waves An Introductory Course Delft Uni versity Press 1999 Balanis C A Antenna Theory Analysis and Design second edition John Wiley amp Sons Inc New York 1997 Conciauro G Gugliemi M Sorrentino R Advanced Modal Analysis CAD Techniques for Waveguide Components and Techniques John Wiley amp Sons Ltd Chichester 1999 De Hoop A T Handbook of Radiation and Scattering of Waves Academic Press London 1995 Gonzalez de Aza M A Encinar J A Zapata J Lambea M Full wave analysis of cavity backed and probe fed microstrip patch arrays by a hybrid mode matching generalized scattering matrix and finite element method in IEEE Transactions on Antennas and Propagation Vol 46 No 2 pp 234 242 1998 Stroustrup B The C Programming Language third edition Addison Wesley Reading Massachusetts 1997 MATLAB The Language of Technical Computing Using MATLAB Version 5 The Math Works Inc 1996 MatLaB The Language of Technical Computing Using MATLAB Graphics Version 5 The MathWorks Inc 1996
13. that allows the three dimensional modelling of the radiating apertures of dielectric filled flanged waveguides The current version of the package provides a full range of new post processing options specifically designed for the three dimensional analysis that is aimed at as well as supplementary modules for the spectral analysis of the properties of the waveguide antennas Like its previous two dimensional version see 3 the Mode_matching_3D code was devel oped with an eye on the software being potentially employed as an educational tool For meeting the speed and versatility requirements imposed by educational applications the computational engine of the Mode_matching_3D package was implemented in C while the graphic post processing modules were implemented in MATLAB Furthermore new options for generating materials for presentations e g movies were added to the package The theoretical background of the implemented method will be firstly sketched Subse quently some general information concerning the installation and the use of the software code as well as some examples demonstrating its new post processing features will be provided This 2 THE ANALYSED CONFIGURATIONS report is completed with a quick reference containing the complete list of functions that are implemented in the present version of the package For suggestions concerning the employing of the package in educational activities the user is refer
14. 2 11 lim Hay lim Hayy for x lt a 2 and y lt b 2 12 The boundary conditions at the perfectly conducting flanges are lim Pose 0 for z gt a 2 and y gt 6 2 13 lim Bary 0 for x gt a 2 and y gt 6 2 14 3 3 Field quantities in the right half space Integral representations of the field quantities A first possibility of expressing the field quantities in the right half space is by employing their Helmholtz integral representations in terms of the values of the electric field strength s compo nents and at the aperture see 5 7 The relevant expressions are amenable to a direct numerical evaluation thus providing the values of all the components of the field quantities in the right half space Fourier representations of the field quantities For the computation of the modal expansion coefficients an alternative more adequate repre sentation of the field quantities based on a spatial Fourier representation will be employed For the derivation of the relevant representations of the field quantities it is firstly observed that the field in the right half space corresponds to a field propagating in an unbounded domain Based on the odd odd x y symmetry of the Pies component inside the waveguide the quantity Eo is expressed in terms of the inverse Fourier transform of a yet to be determined 6 THE MODE MATCHING TECHNIQUE function 911 a 3 the function B3 4 a 8 showing an o
15. AGE 23 END No parameters The end of the input data file NOTE This keyword is recognised by the parsers of the post processing part of the input data file as well A 3 Post processing keywords The post processing keywords are used for selecting the post processing options The use of all keywords listed in this section is optional Keywords employed for console output COMPUTE GAIN 0 No parameters Compute the gain of the aperture for 0 0 see Section 2 COMPUTE GAIN Parameters e 2 real numbers Theta and Phi gt the direction angles 0 and see Section 2 in degrees Compute the gain of the aperture for the direction defined by 0 Theta and y Phi COMPUTE DIRECTIVITY 0 No parameters Compute the directivity of the aperture for 6 0 see Section 2 COMPUTE DIRECTIVITY Parameters e 2 real numbers Theta and Phi gt the direction angles 0 and see Section 2 in degrees Compute the directivity of the aperture for the direction defined by 9 Theta and y Phi COMPUTE TL PARAMETERS TE_10 No parameters Compute the tramsmission line parameters of the aperture i e the S11 parameter mag nitude and phase and the VSWR for the TE 9 mode 24 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE COMPUTE TL PARAMETERS TE MODE Parameters e 2 integer numbers M and N gt the indices of a TE mode that is accounted for C
16. D SOFTWARE PACKAGE The complete list of keywords together with their pertaining parameters is presented here after For reasons of consistency the keywords are given in uppercase only Recall however that the parsers are case insensitive As a general rule the valid input lines have the format KeyWord first line of parameter s second line of parameter s line of parameter s Note that parameters listed in this quick reference on one line must appear in the input data file on the same line A 2 Pre processing keywords The pre processing keywords are used for defining the data concerning a new problem All parameters that are prescribed by means of valid input described in this section have default values and hence the use of all these keywords is optional However most default values concern a trivial problem and hence these parameters should be explicitly defined by the user for any practical application Keywords employed for problem definition MINIMUM NO OF MODES Parameter e 1 integer Minimum_No_Of_Modes gt the minimum number of TE modes to be accounted for MINIMUM HIGHEST CUTOFF Parameter e 1 integer Minimum_Highest_Cutoff gt the minimum limit of the maximum cut off frequency of the TE modes to be ac counted for NOTES The program effectively employs as number of TE modes the larger value be tween the one that is specified by means of the MINIMUM NO OF MODES comm
17. User s manual of the Mode Matching_3D software package IRCTR S 016 03 Scientific report 2 July 2003 Ioan E Lager User s manual of the Mode_Matching_3D software package Ioan E Lager International Research Centre for Telecommunications Transmission and Radar Faculty of Information Technology and Systems Delft University of Technology Mekelweg 4 2628 CD Delft The Netherlands Abstract A software package for the analysis and design of dielectric filled flanged parallel plate waveg uide antennas is presented For the computation of the electromagnetic field quantities the package employs an efficient semi analytic method the mode matching technique The fea tures of the package and the presently available post processing capabilities are described The possibilities for employing the software package as an educational tool are discussed 1 Introduction The use of the semi analytic mode matching technique for the analysis of dielectric filled flanged parallel plate waveguide antennas was discussed in 1 2 3 The theoretical foundations of this method were presented in 1 and 2 for the cases of the E and H polarisations 4 p 172 respectively The method was initially implemented for the two polarisations separately 1 2 and subsequently in a computer code for their simultaneous analysis 3 The present contribution focuses on the new version of the Mode_matching code denoted as Mode_matching_3D
18. _Y LIGHTED SURFACE B W Same as APERTURE E_Y LIGHTED SURFACE black and white version APERTURE E_Y SURFACE Same as APERTURE E_Y LIGHTED SURFACE shaded surface three dimensional plots colour version APERTURE E_Y SURFACE B W Same as APERTURE E_Y SURFACE black and white version APERTURE E_Y CONTOURF Same as APERTURE E_Y LIGHTED SURFACE filled contour pseudo three dimen sional plots colour version APERTURE E_Y CONTOURF B W Same as APERTURE E_Y CONTOURF black and white version 32 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE By replacing in the definitions above E_Y by E Z H_X or H Z similar types of plots for the field quantities x z H x z or H x z respectively can be generated SLICE LIGHTED SURFACE Lighted surface three dimensional plots of the field quantities Ex a Y 20 E a Y 20 E x y 20 Hx x y 20 Hy x y 20 or Hz x y 2 for a plane z zo that is parallel to the aperture s plane z slice plots Parameters e 1 integer Which_Quantity gt parameter indicating which field quantity must be represented e 2 real numbers Mult_WGdims and Div_ WGdims gt the dimensions of the plotted area in multiples of the waveg uide s width a and height b and the size of the minimum rep resentation mesh step in the Ox and Oy directions in quotients of a and b respectively e 1 real Z_shift gt the value of the co
19. ampled at constant steps INCREASING SAMPLING STEPS No parameters Flag indicating that the frequency range is sampled at logarithmically increasing steps 36 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE SPECTRAL SOLUTION FILE NAME Parameter e string s_a_Solution_File Name gt the name of the file without the full path and the extension where the solution of the problem is saved NOTE The program fills in automatically the full path to the directory where the Mode_matching_3D output data files are located and the default extension sol Keywords employed for the overall program management The program management keywords indicate the beginning of a sequence of post processing commands that are specific to the spectral analysis module Recall that these keywords may appear after the POST PROCESSING keyword only POST PROCESS SPECTRAL ANALYSIS No parameters Activates the search for spectral analysis module related post processing commands NOTE After this keyword spectral analysis module related post processing commands may appear only END No parameters The end of input data file NOTE This keyword is recognised by the parser of the post processing part of the input data file as well Keywords employed for selecting the post processing options The post processing keywords are used for selecting the post processing options The use of all keywords listed in this sec
20. and and that that follows from the condition given by the MINIMUM HIGHEST CUTOFF command For example for the configuration indicated in Fig 3 specifying a Minimum_Highest_Cutoff 200 GHz will require a number of 75 TE modes that is larger than the specified Minimum_No_Of_Modes 6 Consequently the program will employ a number of 75 T E modes The number of TM modes is automatically determined from the condition that the highest cutoff frequency of a TM mode should not exceed the highest cutoff frequency of any TE mode that is accounted for Due to the 7T M modes having a higher minimum cutoff frequency than that of the TE modes the program will always account for less TM modes I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 21 EXCITED MODES Parameters e 1 integer N EXCITED_Modes gt the number of excited modes fatal error when N_EXCITED_Modes exceeds the total TE amp TM modes fatal error when the amplitude of an evanescent mode is prescribed e N_EXCITED_Modes doublets of real numbers each on a separate line gt the ampli tude values of the excited modes ordered according to their increasing cutoff fre quency in the case TE and TM modes with the same frequency are prescribed the amplitude of the TE mode must be prescribed firstly No consistency check is carried out FREQUENCY Parameter e 1 real number Frequency gt the frequency of the first
21. case of the configuration analysed in Section 4 5 Microsoft Windows oriented displaying of numerical results Unlike the previous versions of this software the Mode_matching_3D package uses a Microsoft Windows compatible message box system for displaying numerical data as directivity gain etc see Fig 6 In this manner situations when these data are lost due to the scrolling of the console window are prevented 16 GENERAL DESCRIPTION OF THE SOFTWARE PACKAGE S Ho Hay A m 2 1 5 0 5 Y 0 0 0 005 x aa TON ae Figure 9 The distribution of the z Poy and a quantities in the plane z 2 2 107 fm Evaluation of the transmission line parameters of waveguide antennas The Mode matching 3D package implements for the first time facilities for computing some transmission line parameters of waveguide antennas such as the S parameters and the voltage standing wave ratio VSWR 5 These parameters can be computed both for single frequency and for spectral analyses an example for the latter case being provided in Fig 7 Analysis of the field quantities at z constant planes The previous versions of the Mode matching package offered facilities for generating plots of the field quantities along the symmetry planes of the waveguide antenna only Apart from this type of plots the Mode_matching_3D package provides the possibility to generate plots of these quantities at planes that are parall
22. ccounted for with their pertaining cutoff frequencies no processing of the input data is performed this case is hereafter referred to as the mode displaying only mode b HHEEHEHEHEEHHE EHEHEHEH HH HHEHEHEHHH EHEHEHEH HHH HHHHHHH HEEHH H HHH H H H H H H POST PROCESSING b EHEHEHEH EHEHEH EHEHEHEH HEHEHEH EHEHEHEH H H HHEH HEHEHEH HEH H H H H H H H POST PROCESSING plot angle 1 shading type 1 font sizes 18 14 display text 0 aperture distribution step ratio Compute directivity 00 Compute TL parameters TE_10 Figure 4 Example of an input data file post processing part I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 11 By default the Mode_matching_3D program runs in the post processing only mode The user can override this default setting by giving the Run_Type parameter a value in the input data file see Appendix A Mode matching three dimensional analysis c 2003 by Delft University of Technology Output generated on Tue Jun 24 2003 at 15 55 03 The problem s definition The problem s data is read from the file D Lager cpp Mode_matchi ng_3D input Mode_matching_man dat EVALUATED MODES Modal indices cutoff frequency 7 813 GHZ propagating mode 440 GHZ evanescent mode i 744 GHZ evanescent 7 067 GHZ evanescent 4 284 GHZ evanescent 7 380 GHZ evanescent Modal indices cutoff frequency 30 744 GHZ evanescent mode 36 284 GHZ eva
23. data to be used for the generation of movies NOTE This keyword may be skipped if the movie declaration is ended by the keyword END the end of input data The Mode_matching_3D package offers the possibility to save a generated movie into an ex ternal mat file 10 that can be subsequently loaded into the MATLAB environment and played back In the case when MATLAB version 6 0 or higher is available the generated movie can be saved into an external Audio visual interleaved avi file as well The user is prompted to indi cate which of the generated movies should be saved in what format Subsequently the name of the output file without extension the required extension being appended by the program must be provided The movie files are saved in the lt home_directory gt Matlabmovies di rectory see section 4 1 The user may indicate the path to subdirectories of this directory providing that these subdirectories exist For playing back of a movie saved as a mat file it is recommended to use the MATLAB module play_saved_movie m that is provided with the package It should be taken into account that the saved movie files are often extremely large typically tens of megabytes From this point of view saving a movie as an avi file represents a considerably more convenient solution In this manner a compression factor of 20 or larger is often obtained with a negligible loss of
24. dd odd symmetry as well The representation is then written as o 5f Il 83a 2 sin ax sin 8y exp jf da dp 15 where k3 a B ue denotes the propagation coefficient with k2 w e202 a the wave number in the right half space Note that in view of ensuring the causality RT gt and S T lt 0 Similarily based on the even even xz gt y symmetry of the i bee inside the waveguide the quantity y is expressed in terms of the inverse Fourier transform of a yet to be determined function B a 3 showing an even even symmetry A Ezy is if Bs a p cos az cos Gy exp jf da df 16 By using the formalism described in 5 p 623 15 and 16 yield the values of the magnetic field strength in the right half space that read f A eia even ap Dodd haz ff te L bgla 8 Bs oa cos az cos By exp jh da d8 17 a Dodd ap Deven Hoy whe n2 f Je 2 see a p T ap sin az sin Gy exp itz da d8 18 3 4 Computation of the modal expansion coefficients For determining the modal expansion coefficients 1 and 2 are firstly equated to 15 and 16 respectively by means of the interface boundary conditions in 9 and 10 and of the boundary conditions at the perfectly conducting flanges in 13 and 14 A direct Fourier transform of the thus obtained equations then yields the expressions of the functions 299 a 3 and BS a 3 These exp
25. dowed with a spectral analysis module This module repeatedly solves a problem concerning a specified configuration at a number of user defined frequencies of the fundamental mode For carrying out such an analysis the user is required to specify a frequency range and a number of samples that need being evaluated The samples can be either equally spaced along the indicated frequency range default choice or can be chosen at an increasing or decreasing logarithmic division of that range the minimum step being in this case specified by the user The computed data are then saved in an output file that can be subsequently used as input for various post processing tasks Since the implementation of the spectral analysis part is based on reusing the standard mod ules of the Mode_matching_3D code the format of the required input and output data is similar to that discussed in Sections 4 3 and 4 4 For activating this module it is sufficient to include a number of specific commands see Section A 4 in any valid Mode_matching_3D compliant input data file For example by un commenting the command Do spectral analysis in the input file illustrated in Fig 3 the spectral analysis will be activated in the solving a new prob lem and post processing mode The investigated configuration will be identical In view of reducing the computation time a lower accuracy for the evaluation of the infinite integrals can be prescribed in this case with n
26. e open waveguide In this manner the input data file can be reused for carrying out a spectral analysis by simply un commenting the commands that switch the program over to the relevant mode Firstly the program reads the input data file and the successfully read data are echoed to the system s console see Fig 6 In the case when all data have been successfully read the program proceeds to solving the new problem note that Run_Type 2 After the completion of the computation the elapsed time is displayed and the computed data are saved in the user specified file Subsequently since the program was instructed to run in the solving a new problem and post processing mode the computed data are post processed The input data file presented in Fig 4 contains console oriented post processing commands only the relevant output being illustrated in Fig 6 For the various types of plots that can be generated by means of the Mode_matching_3D package the reader is referred to the quick reference included in Appendix A Note that a wide variety of examples of this kind of plots can be found in 1 2 3 Additionally examples demonstrating the new post processing features implemented in the Mode_matching_3D package are provided in Section 4 7 4 6 Spectral analysis of the radiation properties of the open waveguide For investigating the frequency behaviour of some of the open waveguide s parameters the Mode_matching_3D was en
27. eafter presented e radiation patterns for the co polar component of the electric field s strength in the E and H planes see Fig 10 e radiation patterns for both the co and the cross polar components of the electric field s strength 5 p 66 in the E and H planes see Fig and e radiation plots illustrating the three dimensional distribution of the co and cross polar components of the electric field s strength for the complete radiation hemisphere 0 0 7 2 and y E 0 277 see Fig 12 Acknowledgement The theoretical foundations of the reported results were laid during a four year cooperation with PROF DR IR ADRIANUS T DE Hoop His constant support received during the development and testing of the software package is gratefully acknowledged Acknowledgement is also due to ING CRISTIAN COMAN for providing implementation solutions to some of the post processing and user interface features of the code 18 GENERAL DESCRIPTION OF THE SOFTWARE PACKAGE ESS E pol E 90 1 ross pol pol max 120 60 B Vie R 0 8 0 6 150 30 0 4 0 2 180 0 210 330 240 300 270 Figure 11 Radiation patterns for the co and cross polar components of the electric field s strength in a plane rotated at an angle y 24 4 corresponding to one of the diagonal planes of the aperture the scale is linear co pol co pol max Eo pol co pol max Ez Ez 0 Ez 0 10 20 30 40 a b F
28. ed that after entering a sequence of spectral analysis related post processing commands the single frequency specific post processing keywords are not recognised anymore Consequently it is the user s responsibility to close the relevant sequence with an END command or by the end of the file thus stopping the execution of the program The three classes of keywords recognised by the parsers of the spectral analysis module are hereafter examined separately Keywords employed for describing the problem at hand These keywords are used for defining the data concerning a new problem All parameters that are prescribed by means of valid input described in this section have default values and hence the use of the keywords listed in this section is optional However most default values concern a trivial problem and hence for all practical applications these parameters should be explicitly defined by the user SPECTRAL FREQUENCY RANGE Parameters e 2 real numbers low frequency and high frequency gt the lower and upper bounds of the frequency range to be investigated SPECTRAL SAMPLING FREQUENCIES Parameter e 1 real number N tot_f the number of frequency samples along the frequency range to be investigated DECREASING SAMPLING STEPS No parameters Flag indicating that the frequency range is sampled at logarithmically decreasing steps CONSTANT SAMPLING STEPS No parameters Flag indicating that the frequency range is s
29. egligible influence on the accuracy of the computed results To this end the line 1e 6 pertaining to the command Truncation error at infinity should be commented out and the subsequent line reading 5e 6 should be un commented The specific frequency behaviour parameters are provided by the commands spectral frequency range 7 51e9 40e9 spectral sampling frequencies 200 constant sampling steps I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 15 indicating that the spectral analysis will be performed for the frequency range 7 51 40 GHz sampled at 200 equally spaced frequencies The console output for a run in which a new problem is solved as well as the pertaining computed results are presented in Fig 7 S Exe R Eau V m V m 0 075 1 5 0 05 0 025 0 0 025 0 05 0 075 1 0 0 0 005 T ben TORDO a Figure 8 The distribution of the a z Ey and a quantities in the plane z 2 2 1074m v 4 7 New post processing features of the Mode_matching_3D package Since the Mode_matching_3D package was developed for the three dimensional analysis of the radiation properties of the waveguide antennas the range of graphic post processing features implemented in the previous versions of the code needed being augmented with ones specifically designed for the new class of investigated problems A number of examples of the use of these new features are hereafter given for the
30. el to the aperture s plane hereafter referred to as z slice plots Note that these plots can also be employed for generating movies For illustrating this feature all three components of the quantities and H are represented in Figs 8 and 9 respectively for the plane z 2 21074m 7 331074 9 with o denoting the wavelength in free space corresponding to the exciting frequency 10GHz In these figures the singular behaviour of the field in the proximity of the aperture s edges is clearly visible Note that for being able to highlight this phenomenon a number of 75 TE and 70 TM modes were employed for expanding the field in the waveguide I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 17 a 90 120 60 120 60 0 8 0 8 0 6 0 6 150 30 150 30 0 4 0 4 0 2 0 2 180 180 0 210 330 210 330 240 300 240 300 270 270 a b Figure 10 Radiation patterns for the co polar component of the electric field s strength the scale is linear a E plane b H plane Co and cross polar radiation patterns and plots The previously available facilities for examining the propagation properties in the far field region were broadened in the Mode_matching_3D package by adding options for generating plots of the co and cross polar components of the electric field s strength 5 p 66 these components co pol being denoted as B52 and Io respectively The following types of plots are her
31. he relative material parameters outside the waveguide are the relative permeability 1 0000 the relative permittivity 1 0000 The problem s solution will be stored in the file D Lager cpp mMode_matching_3D output Demo_s_a_solution sol gt gt gt gt The input data describe a valid problem a U SPECTRAL ANALYSTS MODE ee solving a new problem The computed results are also post processed gt gt gt gt Total time required for solving the problem 50 3 seconds Post processing the spectral analysis numerical results gt gt gt gt Plot of the S_ 11 at theta 0 and phi 0 for the frequency range 7 510 40 000 GHz gt gt gt gt End of spectral analysis post processing Figure 7 The console output corresponding to the spectral analysis part included in the input data file presented in Figs 3 and 4 and the pertaining numerical results the magnitude and the phase of the S11 parameter in the case of the TEio mode The input data file corresponding to this configuration is presented in Figs 3 problem de scription part and 4 post processing part For the significance of the various input commands the user is referred to the quick reference included in Appendix A Note that this file also con 14 GENERAL DESCRIPTION OF THE SOFTWARE PACKAGE tains some commands employed for prescribing parameters that are of relevance for the spectral analysis of th
32. hen Step_ratio exceeds 1 2 1 3 Keywords employed for the analysis of propagation properties in the far field region RADIATION PATTERN or FAR FIELD PATTERN obsolete Parameters e 1 integer Density gt the number of points per 90 where the far field is computed e 1 real number Increment gt the minimum level in deciBells which is represented in the case of the logarithmic plot 26 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE No checking of the input values is carried out Generates the radiation patterns for 0 0 90 in the E and H planes at both a linear and a logarithmic scale RADIATION PATTERN DB or FAR FIELD PATTERN DB obsolete Parameters e 1 integer Density gt the number of points per 90 where the far field is computed e 1 real number Increment the minimum level in deciBells which is represented No checking of the input values is carried out Generates the radiation patterns for 0 0 90 in the E and H planes at a loga rithmic scale RADIATION PATTERN LINEAR or FAR FIELD PATTERN LINEAR obsolete Parameter e 1 integer Density the number of points per 90 where the far field is computed No checking of the input values is carried out Generates the radiation patterns for 0 0 90 in the E and H planes at a linear scale POLARISATION PATTERN Parameters e 1 real number Phi gt
33. igure 12 The components of the electric field s strength for the complete radiation hemisphere the scale is logarithmic a co polar component b cross polar component 0 I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 19 A The list of functions implemented in the Mode_matching_3D software package As mentioned in section 4 3 all input data for describing a new problem and or for selecting the post processing options must be included in an input data file In this section a complete list of the keywords recognised by the current version of the Mode_matching_3D software package is given In this manner the user can familiarise her or himself with the capabilities of the present version of this package A 1 General structure of the input file The input data file is a standard ASCII file For processing this file appropriate data parsers have been incorporated in the Mode_matching_3D software package For reasons of enhancing the flexibility of the manner in which the input data file can be prepared the parsers are case insensitive Nevertheless for avoiding an excessive complication of the resulting code the correctness and consistency checks carried out by the parsers are minimal and hence the user is expected to fully comply to the indications given in this quick reference Note that most syntax errors will result in an unpredictable behaviour of the program However the parsers will a
34. inimal directory tree structure indicated in Fig 2 The location of the home directory can be chosen arbitrarily Note that the user may choose to add to the indicated tree structure additional directories she or he considers to be necessary but the minimal tree structure with the specified names is mandatory for a correct run of the program The following actions need being carried out during the installation of the package e the minimal directory tree structure must be created e the Mode matching 3D exe file must be copied into the directory lt home_directory gt bin and this directory must be added to the system s PATH variable e the MATLAB modules pertaining to the package must be copied into the directory lt home_directory gt Matlabmodules and e the default input data file see Section 4 3 Mode_matching dat must be copied into the directory lt home_directory gt input As for the directories lt home_directory gt output and lt home_directory gt Matlabmovies they are used by the program itself for saving output data and post processing files Note that all user written input data files must also be located in the directory lt home_directory gt input 8 GENERAL DESCRIPTION OF THE SOFTWARE PACKAGE lt home_directory gt bin Mode matching 3D exe input Mode matching 3D dat user written input data files Matlab_modules MATLAB M files Matlab_movies output movie files output ou
35. ional plots of the field quantities E 0 y zo E plane and E a 0 20 H plane for a specified fixed z coordinate colour version The employed mesh may be uniform or non uniform This type of plots are usually generated for analysing the field distribution in the vicinity of the radiating aperture Parameters e 2 real numbers Z_Shift and Div_lambda_z gt the fixed zo coordinate for which the plot is generated in multiples of the waveguide s width a see Fig 1 and the minimum size of the discretisa tion mesh step in the Oy direction E plane and in the Oz direction H plane in quotients of a e 1 integer Which_Type gt parameter indicating which type of plot must be gener ated NOTES The specified field quantity is plotted along the segments x 0 y 1 5a 1 5a z Z Shifta E plane and x 15a 15a y 0 z Z_Shifta H plane The following values of Which_Type are accepted e 1 R y and S linear representation linear representation max and SE fi e 2 R max e 3 and arg linear representation max By replacing in the definition above E_Y by E_Z H_X or H Z similar plots for the field quantities E x z Hz x z or H x z respectively can be generated Keywords employed for generating pseudo three dimensional plots NEAR FIELD E_Y LIGHTED SURFACE Lighted surface
36. lving a new problem The computed results are also post processed gt gt gt gt Total time required for solving the problem 0 6400 seconds Post processing the numerical results gt gt gt gt End of post processing Figure 6 The console output corresponding to the input data file presented in Figs 3 and 4 problem description post processing part and the pertaining numerical results 4 5 Example of using the package for a single frequency analysis The use of the Mode_matching_3D software for performing a single frequency analysis of a waveguide is demonstrated by solving a problem concerning a configuration having the following parameters the width a 22mm the height b 10mm the waveguide is taken to be empty and the prescribed frequency of the fundamental mode is 10 GHz I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 13 Mode matching three dimensional analysis c 2003 by Delft University of Technology The waveguide is excited by means of a TE_ 10 mode of unit amplitude The frequency range of the spectral analysis is 7 51 GHz 40 GHz sampled at 200 frequencies the frequences are sampled at equal frequency intervals The dimensions of the waveguide are the width a 22 0000 mm the height b 10 0000 mm The relative material parameters inside the waveguide are the relative permeability 1 0000 the relative permittivity 1 0000 T
37. lways check the syntax of the keywords the occurrence of a keyword that does not belong to the program s dictionary resulting in stopping the program with an error message The structure of the input data file consists of valid input lines and possibly comments as follows 1 Valid input lines contain keywords and parameters The keywords are grouped into two classes e keywords that are used for describing the problem at hand pre processing keywords and for overall program management e keywords that are used for selecting post processing options The sequence of the keywords that belong to the same class is arbitrary However since the input data file parsers for the two classes are separate keywords belonging to different classes may not be mixed 2 Any text that follows after a CHR 37 character is taken to be a comment and is not interpreted In view of enhancing the readability of the input data file some text formatting options are accepted by the software package s parsers 1 The file may contain completely blank lines Note that including blank lines and comments between keywords and their pertaining parameters is permitted 2 The valid input lines can be indented using BLANK CHR 32 characters Note that the use of TAB CHR 7 characters for indentation should be avoided as it can result in an unpredictable behaviour of the parsers 20 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3
38. n SLICE CONTOURF B W Same as SLICE CONTOURF black and white version Keywords employed for generating two and pseudo three dimensional movies For visualising transient phenomena the Mode_matching_3D software package contains an option for generating a sequence of frames snapshots of the distribution of the field quantities at successive instants that can subsequently be played back as a movie 11 For generating movies any of the plot types mentioned above may be employed MOVIE Generate the frames for a movie using one of the types of plots described above Parameters e 2 integers Time_Divisions and Repeat the number of intervals one period of the first prescribed mode is divided into and the number of times the sequence of frames is repeated during the movie 34 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE NOTE The movies are generated using any of the types of two and pseudo three dimensional plots mentioned above Consequently the declaration of the movie parameters must be followed by a valid definition of a two or pseudo three dimensional plot Any other post processing keyword will be ignored by the movie parser This will result most likely in a syntax error that will be detected at the first subsequent non comment input line MAKE THE MOVIE No parameters Keyword used for marking the end of the input
39. n the unbounded right half space E2 see section 2 No checking of the input values is carried out TRUNCATION ERROR AT INFINITY Parameter e 1 real number Inf_Truncation_Error gt the prescribed accuracy in the computation of the infinite integrals Inf_Truncation_Error must be larger than 1077 and it is typically chosen in the range 10 1076 SOLUTION FILE NAME Parameter e string Solution_File Name gt the name of the file without the full path and the extension where the solution of the problem is saved NOTE The program fills in automatically the full path to the directory where the Mode_matching_3D output data files are located and the default extension sol Keywords employed for the overall program management RUN TYPE Parameter e 1 integer Run_Type gt parameter controlling the runtime operating mode of the program see section 4 3 DO SPECTRAL ANALYSIS No parameters The execution is switched over to the spectral analysis mode POST PROCESSING No parameters Beginning of the part of the input data file containing the data for post processing NOTE This keyword commutes the processing of the input data file to the parsers of the post processing part that do not recognise any problem definition pre processing keywords As a consequence no such keywords may occur after the POST PROCESSING keyword I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACK
40. nescent mode 45 380 GHZ evanescent mode Figure 5 The console output corresponding to the input data file presented in Figs 3 and 4 information concerning the evaluated modes part 4 4 Output data The output of the program consists of e numerical data that are directly displayed at the system s console or in Results type windows see Fig 6 e various types of MATLAB plots and or movies 11 12 GENERAL DESCRIPTION OF THE SOFTWARE PACKAGE Results x The directivity of the radiating aperture at theta 0 and phi 0 is 6 4 dB Results x The transmission line parameters corresponding to the propagating TE_ 1 0 mode have the values abs S_ 11 12dB The waveguide is excited by means of a TE_ 10 mode eS ry of unit amplitude VSWR 1 6 The frequency of the fundamental mode is 10 0000 GHz The dimensions of the waveguide are the width a 22 0000 mm 0 7338 wavelength the height b 10 0000 mm 0 3336 wavelength The relative material parameters inside the waveguide are the relative permeability 1 0000 the relative permittivity 1 0000 The relative material parameters outside the waveguide are the relative permeability 1 0000 the relative permittivity 1 0000 The problem s solution will be stored in the file D Lager Cpp Mode_matching_3D output Demo_solution sol gt gt gt gt The input data describe a valid problem So
41. nstant zo parameter in multiples of a e 1 integer Which_Type gt parameter indicating which type of plot must be gener ated NOTES The ploted area is symmetrical with respect to the Ox and Oy axes the ploted area corresponds to the rectangle Mult_WGdims a Mult WGdims a x Mult_WGdims b Mult_WGdims b The following values of Which_Type are accepted La E y 20 e 2 E x y z0 3 E x y 20 ell H y 20 e 12 H x y zo e 13 H 2 y 2 Attempting to prescribe a different value of the Which Type parameter will be signaled as an error and will result in the command being ignored I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 33 The following values of Which_Type are accepted e1 F and S y linear representation e 2 RI y and S linear representation max max e 3 y and arg linear representation max A 2 mic representation linear representation and logarith max SLICE LIGHTED SURFACE B W Same as SLICE LIGHTED SURFACE black and white version SLICE SURFACE Same as SLICE LIGHTED SURFACE shaded surface three dimensional plots colour version SLICE SURFACE B W Same as SLICE SURFACE black and white version SLICE CONTOURF Same as SLICE LIGHTED SURFACE filled contour pseudo three dimensional plots colour versio
42. ompute the tramsmission line parameters of the aperture i e the S11 parameter mag nitude and phase and the VSWR for the TEmyn mode COMPUTE TL PARAMETERS TM MODE Parameters e 2 integer numbers M and N the indices of a TM mode that is accounted for Compute the tramsmission line parameters of the aperture i e the S11 parameter mag nitude and phase and the VSWR for the TMi n mode Keywords employed for setting aspect parameters of the generated plots PLOT ANGLE Parameter e 1 integer Angle gt the viewing angle to be used in the case of lighted surface plots in multiples of 90 No checking of the input values is carried out SHADING TYPE Parameter e 1 integer Shading_Type gt flag that controls the shading type to be used in the case of lighted surface plots NOTE The following values of Shading_Type are accepted e 0 gt shading flat e 1 gt shading facetted default Invalid values are converted to the default one 1 DISPLAY TEXT Parameter e 1 integer Display_text gt flag that controls the displaying of the titles in all kind of plots NOTE The following values of Display_text are accepted e 0 do not display titles e 1 display titles default Invalid values are converted to the default one 1 I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 25 DISPLAY COLORBAR Parameter e 1 integer Display_colorbar
43. ounted for e 1 real number Ref_freq gt reference frequency Plot the VSWR for the TEmn mode scaled down by the one corresponding to the frequency Ref_freq I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 39 PLOT VSWR TM_MN Parameters e 2 integer numbers M and N the indices of a TM mode that is accounted for Plot the VSWR for the TMayn mode PLOT SCALED VSWR TM_MN Parameters e 2 integer numbers M and N gt the indices of a TM mode that is accounted for e 1 real number Ref_freq gt reference frequency Plot the VSWR for the TMmyn mode scaled down by the one corresponding to the frequency Ref_freq 40 REFERENCES References 1 Lager I de Hoop A T The Mode matching software package for dielectric filled wave 10 11 Anie guides analysis International Research Centre for Telecommunications transmission and Radar Faculty of Information Technology and Systems Delft University of Technology Scientific report IRCTR S 036 00 December 2000 available upon request Lager I de Hoop A T The Mode Matching software package for dielectric filled flanged parallel plate waveguide antennas H polarisation International Research Cen tre for Telecommunications transmission and Radar Faculty of Information Technology and Systems Delft University of Technology Scientific report IRCTR S 001 02 January 2002 available upon
44. picture quality The generated avi files can then be played back with any standard Microsoft Windows software such as Microsoft Media Player and are amenable to be included in Microsoft Power Point presentations A 4 Spectral analysis keywords The keywords pertaining to the spectral analysis module of the Mode_matching_3D code are grouped into three classes e keywords that are used for describing the problem at hand pre processing keywords e keywords that are used for overall program management activation of the spectral analysis module itself and of the pertaining post processing options e keywords that are used for selecting post processing options Except for the keywords in the second class the sequence of the keywords that belong to the same class is arbitrary Since the input data file parsers for the three classes are separate keywords I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 35 belonging to different classes may not be mized In view of ensuring the consistency of the input referring to this module with that employed by the single frequency one the keywords in the second and the third classes may appear after the POST PROCESSING command only On the other hand the keywords in the first class are accepted by the pre processing parser even in the single frequency operating mode When encountered their pertaining parameters are simply ignored without causing any error The user is warn
45. red to 3 infinite flange dielectric filling E1 H1 gt e free space E2 H2 Figure 1 Dielectric filled flanged rectangular waveguide antenna 2 The analysed configurations The Mode_matching_3D software package analyses the behaviour and the performances of a dielectric filled flanged rectangular waveguide antenna see Fig 1 In this configuration po sition is specified by the coordinates in a Cartesian reference frame Oxyz For being able to express the field quantities in the far field region where the electromagnetic field propagates practically as spherical waves a polar reference frame Ordy is employed as well Following the usual conventions 5 p 47 the angle 0 measures the tilting of an arbitrary direction with respect to the Oz axis while the angle y measures the rotation around Oz with the Oz axis being taken as a reference The sub domain in the interior of the waveguide a 2 lt a lt a 2 b 2 lt y lt b 2 w lt z lt 0 with a and b being the width and the height of the waveguide respectively is filled with a homogeneous isotropic dielectric medium with permittivity and permeability 41 The open waveguide radiates into the right half space 00 lt lt oo lt y lt oo 0 lt z lt oo where the medium is taken to be homogeneous and isotropic and it is characterised by the permittivity 2 and the permeability u2 The perfectly conductive flange extends to infini
46. ressions are subsequently filled in two equations relating 5 and 6 on one hand and 17 and 18 on the other hand by means of the interface boundary conditions in 11 and 12 Finally a Galerkin procedure is applied to these two equations that result into an infinitely dimensional linear mapping between the modal amplitudes corresponding to the incident and reflected waves For reasons of convenience the double indices mn of the TE and TM modes are reduced to one l by ordering the modes according to their increasing cutoff frequency 8 The field expansions in the waveguide are truncated to a finite number of modes Nmax a KEN this procedure translating the previously obtained mapping into a system of linear algebraic equations By assuming that the incident waves have known impressed amplitudes this system directly provides the values of the unknown reflected wave amplitudes I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 7 From a computational point of view the most expensive operation is the determining of the entries in the system s matrix the scattering matrix For obtaining the values of these coefficients double infinite integrals that contain an integrable singularity as well need being evaluated The difficulties arising from the presence of the integrable singularities are circumvented by applying a procedure that was described in 2 As for the infinite part of
47. scale RADIATION PLOT Parameters e 1 integer Density gt the number of points per 90 for both 0 and y where the far field is computed e 1 real number Increment gt the minimum level in deciBells which is represented in the case of the logarithmic plot No checking of the input values is carried out Generates the co and cross polar radiation patterns for the complete radiation hemisphere 0 0 90 and y 0 360 at both a linear and a logarithmic scale RADIATION PLOT DB Parameters e 1 integer Density gt the number of points per 90 for both 0 and y where the far field is computed e 1 real number Increment gt the minimum level in deciBells which is represented No checking of the input values is carried out Generates the co and cross polar radiation patterns for the complete radiation hemisphere 0 0 90 and y 0 360 at a logarithmic scale RADIATION PLOT LINEAR Parameter e 1 integer Density the number of points per 90 for both 0 and y where the far field is computed No checking of the input values is carried out Generates the co and cross polar radiation patterns for the complete radiation hemisphere 0 0 90 and y 0 360 at both a linear scale 28 THE LIST OF FUNCTIONS IMPLEMENTED IN THE Mode_matching_3D SOFTWARE PACKAGE Keywords employed for generating two dimensional plots LINE APERTURE E_Y Two dimens
48. the spectrum is sampled Minimum no of modes 6 the type of steps decreasing constant increasing default Minimum highest cutoff Define the data for the spectral analysis NOTE activated in the case of the spectral analysis only he dimensions of the waveguide spectral frequency range low_frequency high_frequency 7 51e9 40e9 spectral sampling frequencies 2 the number of samplig frequencies at which the spectrum is sampled constant sampling steps Validate the spectral analysis solution file name Demo_solution spectral solution file name Demo_s_a_solution The frequency of the fundamental excited mode TE_ 10 frequency 10e9 Figure 3 Example of an input data file problem description part Note that the user has the option to prescribe either the width of the waveguide or the frequency and to instruct the code to compute the complementary parameter i e the frequency or the width respectively such that the width of the waveguide equals a user specified quotient from the wavelength of the fundamental mode e The material parameters of the medium inside the waveguide i e the relative permittivity E1 and the relative permeability 11 e The material parameters of the medium in the right hand half space i e the relative permittivity 2 r and the relative permeability p2 r e Parameters required for carrying out the spectral analysis for example the upper and lower bounds of the
49. tion is optional REVERT HARDCOPY No parameters Revert the plot during printout Note that most spectral analysis related plots have a dark background UNCHANGED HARDCOPY No parameters Leave the plot unchanged during printout I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 37 PLOT GAIN No parameters Plot the gain of the aperture for 0 0 see Section 2 PLOT SCALED GAIN Parameter e 1 real number Ref freq gt reference frequency Plot the gain of the aperture for 6 0 scaled down by the one corresponding to the frequency Ref_freq PLOT DIRECTIVITY No parameters Plot the directivity of the aperture for 0 0 PLOT SCALED DIRECTIVITY Parameter e 1 real number Ref_freq gt reference frequency Plot the directivity of the aperture for 6 0 scaled down by the one corresponding to the frequency Ref_freq PLOT S_11 TE_10 No parameters Plot the S parameter magnitude and phase for the TE19 mode PLOT SCALED S_11 TE_10 Parameter e 1 real number Ref freq gt reference frequency Plot the S11 parameter magnitude and phase for the TE10 mode the magnitude being scaled down by the one corresponding to the frequency Ref_freq PLOT S_11 TE_MN Parameters e 2 integer numbers M and N gt the indices of a TE mode that is accounted for Plot the S parameter magnitude and phase for the TEmy mode PLOT SCALED S_11 TE_MN Parameters
50. tput data files Figure 2 The required directory tree structure for the installation of the Mode_matching_3D software package 4 2 Utilisation of the software package The utilisation of the Mode_matching_3D software package is illustrated for the case when the program runs in a Microsoft Windows command window For starting the program the following command must be issued Mode_matching_3D File_Name The optional parameter FileName denotes the name of a user written input data file In the case when this parameter is not specified the default input data file Mode matching_3D dat will be employed Since the software package is designed to work in batch mode the input data file is processed by the package without requiring any further input on behalf of the user except possibly for some minimal keyboard input during the previewing of movies see below 4 3 Input data All input data required by the program are included in an input data file which is a stan dard ASCII file containing keywords parameters and possibly comments A complete list of the keywords recognised by the current version of the Mode_matching_3D software package together with the pertaining numerical parameters is provided in the quick reference in cluded in Appendix A The user written input data files must be located in the directory lt home_directory gt input At installation the default input data file Mode matching_3D dat is copied
51. ture both inside and outside the waveguide colour version For simplicity the subsequent definitions refer to the H plane only the definitions pertaining to the E plane following by swapping x and y Parameters e 2 real numbers Mult_Width_z and Div_Width gt the length of the represented do main inside the waveguide in mul tiples of its width a see Fig 14 and the size of the minimum rep resentation mesh step in both di rections in quotients of a e 1 integer Which_Type gt parameter indicating which type of plot must be gener ated NOTES The ploted area is symmetrical with respect to the Ox axis the ploted area corresponds to the rectangle 1 5a 1 5a x Multlambda_za 2a and y 0 the areas delimited by the surfaces of the perfectly conducting shield and flanges being clipped out I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 31 NOTES The following values of Which Type are accepted e 1 R Ey and S linear representation linear representation max e 2 R y and S max e 3 and arg linear representation max 4 A 2 mic representation linear representation and logarith 1 5a 2a l Z p Z 1 5a 2a Mult_lambda_z a Figure 14 The dimensions of the plotted area in the case of aperture type plots H plane APERTURE E
52. ty At any location in the investigated configuration the electromagnetic field s state is described in the time Laplace domain by the electric field strength E r jw and by the magnetic field strength H r jw with r ri yt zi denoting the position vector j I and w gt 0 denoting the angular frequency For simplifying the notation the explicit mentioning of the complex jw parameter is hereafter discarded The rectangular waveguide is excited by means of a TE g mode For the chosen excitation the electromagnetic field is characterised by an E polarisation 4 p 172 I E LAGER USER S MANUAL OF THE Mode_Matching_ 3D SOFTWARE PACKAGE 3 in the y 0 plane and an H polarisation in the x 0 plane Employing the terminology in 5 pp 29 31 the x 0 plane is referred to as the E plane while the y 0 plane is referred to as the H plane Assuming a spherical waves behaviour of the electromagnetic field in the far field region the electric field strength reads E Eg Ey with Eg Egito and Ey Eytg while the magnetic field strength reads H Hy Hy with Hg Apig and Hy Ayiy 3 The mode matching technique 3 1 Field quantities in the waveguide The electric field strength inside the waveguide is expressed as a superposition of an infinite number of incident and reflected TE and TM waves modes 6 In view of the excitation being an y component with an even even x y symmetry the

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