User Guide for Q-par PO reflector analysis software (QPORAS)
Contents
1. lt p lt p lt p m ko k za k i Zio ke 2j3 2 42 EP a EP 5 E 2 Q par QPORAS TR PO1 0 2 Page 9 of 44 Finally the surface normals f must be computed There is a possible sign ambiguity that must be resolved since we require the surface normals always to be pointed in the outward direction remembering that the surface interface represents the surface of a solid region of conductor We define this such that k lt 0 for all points on the scattering surface Note that transition regions where there may be a required change in sign of n k are ruled out by our assumption that no self shadowing of the reflector is permitted We therefore define a Zig 4 X Lig Lip 2 43 Ziz a X Lig 22 and c n dina lt 0 fi L7 2 44 i M ifalr gt 0 n Q par QPORAS TR PO1 0 2 Page 10 of 44 2 4 The incident fields In the previous section it was assumed that the incident fields E x and H r are available at the coordinates specifying the triangular nodes The software has various feed options which calculate or estimate these fields in different manners An electric dipole may be specified using the DIPOLE key word or a plane wave using the PLANEWAVE key word which provide an analytic determination of these fields More generally however no analytic formulation is available A rectangular horn or a user specified apertur2. There also exists a separate coordinate system which defines how the feed is orientated This is not relevant to an incident plane wave which is specified in the global coordinate system The feed coordinate system is specified by the coordinates x y and z such that the feed aperture is normal to the local z axis The nominal phase centre of the feed is assumed to lie on the origin of the primed coordinate system The orientation of the feed coordinate system with respect to the global coordinate system is controlled by user specified Euler angles 05 df and wv This is illustrated in figure 3 2 The illustration of the Euler angles Q par QPORAS TR PO1 0 2 Page 15 of 44 scan direction geen Figure 3 1 Main reflector global coordinate system x eed aperture x Figure 3 2 The feed coordinate system and Euler angles Q par QPORAS TR PO1 0 2 Page 16 of 44 is a little difficult we define them as in 2 If 2 and 2 are unit vectors in direction of increasing x y and z and similarly j and 2 are unit vectors in direction of increasing x y and z we have sin dy sin wy cos0 cos df cos p cos sin Ys cos 0p sin df cos Ws 7 sin 0y cos q i sin dy cos wy cos 6 cos df sin vy 3 1 cos cos Ys cos Of sin dy sin v tj sin 6 sin 72 sin Os cos ds sin Of sin s cos052 If a point in the global coordinate system is specified by r
3. Q par QPORAS TR PO1 0 2 Abstract This guide provides a technical overview and description of the use of the Q par Physical Optics Reflector Analysis Software QPORAS The software uses a meshed representation of a general reflector under illumination by a plane wave or feed to provide gain and radiation patterns It is based on the use of Physical Optics applied to a triangulated regular meshed reflector of arbitrary shape Q par QPORAS TR PO1 0 2 V List of contents Document changes record Abstract List of contents List of figures 1 Introduction 1 1 Background 1 2 Overview of the physical model 2 The mathematical formulation 2 1 The scattered far field 2 2 Scattered field directions and definitions 2 5 The Physical Optics integration 2 4 The incident fields 2 5 The scattered near field 2 6 Blockage effects 3 Use of the software 3 1 Introduction 3 2 The CALCOPTS key word 3 3 The FILENAME key word 3 4 The PLOTFILE key word 3 5 The ANGLES key word 3 6 The ANGLECUT key word 3 7 The FREQS key word 3 8 The FEEDCEN key word 3 9 The FEEDROT key word 3 10 The PLANEWAVE key word 3 11 The DIPOLE key word 3 12 The RECTHORN key word 3 13 The GEOMFILE key word 3 14 The SURFACE key word 3 15 The BOUNDARY key word 3 16 The BLOCKAGE key word Q par QPORAS TR PO1 0 2 iv vi Vili KS fi o Ot CW w 11 13 14 15 15 18 19 20 21 22 22 23 23 24 25 25 28 30 35 37 vi 3 17 3 18 3
4. x y z and in the feed coordinate system by r z y z then the transformation between the two is given by Xo y y AR v 3 2 Z Z9 Zz where rg 20 Yo zo is the position of the phase centre of the feed and the Euler rotation matrix R has coefficients with rows given by the row terms in 3 1 A typical script file might take the form CALCOPTS 1 ANGLES 90 0 0 0 1 0 0 0 25 361 FREQS 77000 0 0 0 1 FILENAME test out junk out FEEDCEN 0 0 0 15 0 0 AAFEEDROT 0 000 0 000 0 0 AARECTHORN 0 012 0 012 0 0300 0 0300 Y 0 10 PLANEWAVE 90 0 45 0 0 0 0 0 PLOTFILE junk ps 90 00 45 0 180 0 0 40 20 0TFFF SURFACE SPLINE1D splinei dat BOUNDARY ellipse 0 106 0 075 0 0 0 00 00 0 0 001 GEOMFILE qqq pj dat RW where we have assumed illumination by a plane wave The instructions to define a rectan gular feed horn and its Euler rotation angles have been commented out A definition of all the instructions now follows Q par QPORAS TR PO1 0 2 Page 17 of 44 3 2 The CALCOPTS key word Description Defines one of several types of calculation options in the method of evaluation of the incident fields at the reflector Currently version 0 0 12 there are just two options Option 1 uses both the incident electric and magnetic fields at each point on the reflector to determine the apparent direction of incidence using the Poynting vector method as described earlier Option 2 uses only the incident electric fie
5. S 1 1 where f r is an outward pointing surface normal and r is the incident magnetic field INC This physical optics PO assumption is an approximation which is generally considered accurate if These requirements are not necessarily independent and may sometimes be relaxed under special conditions Here they should be considered as rules of thumb It is Q par QPORAS TR PO1 0 2 Page 1 of 44 1 The radius of curvature of the surface is everywhere large compared to a wavelength except possibly over a region which is small compared to the rest of the structure 2 Every point of the surface is under direct illumination of the source without self shadowing of one part of the structure by another 3 The incident field is locally planar 4 The angle of incidence made between a locally planar wave and the surface normal should not be close to grazing incidence except possibly over a region which is small compared to the rest of the structure 5 The surface should be much larger than a wavelength in fact extremely difficult to obtain precise conditions that determine the accuracy of the physical optics method and under what conditions To our knowledge this remains an open question in mathematical physics In the discussion to date shadowing refers to a purely geometrical effect This is properly defined in the high frequency limit in terms of ray tracing If a source is represented by a wavefront which is model
6. This is required explicitly as a check since the Q par QPORAS TR PO1 0 2 Page 42 of 44 CST file does not specify the frequency at which the data is generated If the frequency is not correct the program terminates Parameters 4 5 and 5 6 are only used for illustration purposes for use by PLOTFILE This is because the aperture file is read in after the information is defined for generating the POSTSCRIPT files and so the aperture coordinates available here cannot easily be used for this purpose It is logically preferred to use different illustration parameters until or unless the software is significantly changed 3 21 The FARPOL key word Introduced in version 1 003 of the software this permits a rotation of the polarisation base of the far field and defines a value for the polarisation rotation angle The key word is optional but if present must occur only once If not present is is assumed that 0 The list below summarises the use of this command Number of parameters 1 Number of occurrences 0 or 1 File location Anywhere within input file Parameter 1 Real number This is the angle is degrees Q par QPORAS TR PO1 0 2 Page 43 of 44 4 References 1 TICRA report ed K Pontoppidan Technical description of GRASP 8 version 8 2 5 TICRA March 2002 2 J Synge B Griffith Principles of Mechanics McGraw Hill 1970 3 W H Press W T Vetterling S A Teukolsky B P Flannery Numerical Recipes in For
7. are all options within the software Q par QPORAS TR PO1 0 2 Page 2 of 44 2 The mathematical formulation 2 1 The scattered far field The radiation pattern and gain are determined from the scattered far field We define the far field electric field scattering coefficient by E where E lim kore E r 2 1 where ko is the free space wave number r r r is a point in space and E r is the electric field at r The coordinate origin is assumed at the reflector and we may use a standard definition for E e g 1 given by B ji Je Lef E E 4 ke ds Lex ut k ds 2 2 where Zo is the free space impedance r rf is the observation vector and r is a point in the surface S over which the integration is performed J is the equivalent electric current and J is the equivalent magnetic current on the surface defined by Jr n x Hine Hrer Hae 2 3 UNC and Jie x E F E Eran 2 4 where is the outward pointing surface normal at ds point r see figure 2 1 H is the incident magnetic field in the absence of the scatterer H is the scattered magnetic field just off the scatter in the direction of positive and Han is the transmitted magnetic field non zero only if the surface represents an interface between two regions of dielectric Similar definitions apply to the electric field terms Under the PO approximation for a perfect conductor so far our purpose we may
8. 2 Parameter 3 Parameter 4 Parameter 5 Parameter 6 Parameter 7 Parameter 8 Parameter 9 to N 8 lf Parameter 1 Parameter 2 Q par QPORAS TR VARIPARAB1 then Real number Defines fj the focal length of unmodi fied parabola y x z in metres Real number Defines the x component of the focal point of y x z in metres Real number Defines the y component of the focal point of y x z in metres Real number Defines the z component of the focal point of y x z in metres Integer gt 0 The number N of additional a param eters for 1 i N Real number The exponential decay parameter 5 in 75 Real number The first mandatory dimensionless pa rameter o Real numbers These are the values a in units of m If N 0 these parameters are not specified SPLINE1D then Character string containing no separators This de fines the name of the input file specifying the cubic spline control points as defined previously PO1 0 2 Page 34 of 44 3 15 The BOUNDARY key word Description This is mandatory if the reflector geometry is not defined by the GEOMFILE command If present it must also be accompanied by the SURFACE command The first parameter defines the type of boundary Subsequent parameters depend on the type of boundary Currently version 0 0 12 there are two types of permitted surface a rectangular boundary RECTANGLE and an elliptical boundary ELLIPSE The bounda
9. 2 Page 11 of 44 In 2 45 and 2 46 the V gradient terms are interpreted as acting on r i e 1 e jkor Vy V e tjr i z f 2 51 and 3 J jkor LVV UAE Uko unciae Fko vn 2 52 where R E al p zs 2 PUR E Hcr 2 53 For a rectangular feed we assume a feed which flares from waveguide with dimensions d by d to an aperture of dimensions D by D over a length H where D gt d and D gt dy The flare introduces a phase distortion We assume operation in either the TEO1 or TE10 mode in which case the aperture field takes the approximate form E Bag cos TE exo jlal22 D 8 2u D 9 2 54 x or the alternative mode with interchange of x and y coordinates The values for and 68 may be approximated by Ro vri c D 2P rz koly ry Dy 2 ry 2 55 y where To S Try x H 2 56 The coefficient E is a normalisation constant which is adjusted so that the feed always radiates exactly 1 watt We assume that the admittance at the aperture is approximately that of free space in which case it can be shown that 2 1 A fe 2 2 57 v D Dy Ho The magnetic field and the electric field are related in a waveguide by the modal admittance At the aperture of a flared horn this relation is only approximate We have attemped to use numerical differentiation on the assumed electric field to generate a more consistent approximation but generally this seems to be
10. If this is F then no far fields are calculated using this method Character string with no separators This is the name of the near field file to be created Character string with no separators This is the name of the far field file to be created Page 39 of 44 3 18 The GRASPOUT key word Description This command is optional and constructs a geometry sfc file suitable for input into GRASP 1 The file only contains the reflector nodes with coordinates offset by the specified x y and z offsets ro yo zo defined here GRASP uses this scatter profile to generate its own curved surface through these points This file may only be used if a full version of GRASP is available for analysis Number of parameters 4 Key word requirement Optional Number of occurrences 1 or 0 File location Anywhere within input file Parameter 1 Character string containing no separators This defines the name of the GRASP sfc file Parameter 2 Offset coordinate ro in metres Parameter 3 Offset coordinate yo in metres Parameter 4 Offset coordinate zo in metres 3 19 The FILEREFL key word Description This command is optional and is intended mostly for diagnostics It provides the incident electric and magnetic field components evaluated at the nodal points of the reflector surface There are three coordinate options In the first designation CART REFL the fields are defined in the global cartesian coordinate system In the secon
11. there is a difference in the specified coordinates for the electric and magnetic field data an error is flagged In theory the use of both electric and magnetic fields should result in greater accuracy which is important for describing cross polar performance and side lobes However as of version 1 003 May 2010 we have not performed exacting validation to test this assertion The list below summarises the use of this command Number of parameters 5 or 6 Key word requirement Special Represents one of several types of feed One and only one feed type must be present Number of occurrences 1 or 0 File location Anywhere within input file Parameter 1 Integer This must be 1 or 2 If 1 then only the electric field is supplied If 2 then both electric and magnetic field files are required Parameter 2 Name of the required electric field data file CST for mat If parameter 1 1 then Parameter 3 Frequency in MHz Parameter 4 Display scaling distance in metres z direction Parameter 5 Display scaling distance in metres y direction If parameter 1 2 then Parameter 3 Name of the required magnetic field data file CST format Parameter 4 Frequency in MHz Parameter 5 Display scaling distance in metres z direction Parameter 6 Display scaling distance in metres y direction Parameter 3 4 must be the same as the frequency only a single frequency is permitted here specified by the FREQS command
12. 19 3 20 3 21 The NEARFIELD key word The GRASPOUT key word The FILEREFL key word The FEEDFILE key word The FARPOL key word References Q par QPORAS TR PO1 0 2 38 40 40 41 43 44 vii List of figures 2 1 Definition of surface normal 2 2 Arbitrary cuts on the surface of a sphere specified by ANGLECUT 3 1 Main reflector global coordinate system 3 2 The feed coordinate system and Euler angles 3 3 Aperture excitation types for a rectangular horn 3 4 Boundary rectangle and its projection 3 5 Near field region shadow masking and far field Q par QPORAS TR PO1 0 2 16 16 26 36 38 viii 1 Introduction 1 1 Background Although there are many powerful and efficient software packages available for the accurate analysis of reflector antennas these tend to be expensive commercial packages which are not readily affordable For example a full version of GRASP 1 often cited as an industry standard costs several tens of thousands of pounds Unfortunately free software is generally not available to analyse general shaped reflectors with standard feeds This report documents our own in house software which in this report we will call QPO RAS intended for this purpose This is not intended to compete with GRASP or similar general purpose analysis software but it is adaptable and can be added and modified as and when desired It is written in FORTRAN for use on a Linux platform but may be ported to other systems s
13. 5 0 19028E 13 16 0 00000E 00 0 41190E 04 0 00000E 00 Number of facet elements Q par QPORAS TR PO1 0 2 Page 28 of 44 20 Element reference list 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 11 17 12 18 13 19 14 20 15 15 11 11 11 12 12 13 13 14 14 15 15 FON oO WwW 16 16 16 16 16 The first list defines the node coordinates of the reflector in metres and assigns a node number to each point The second list defines the triangles by reference to the node such thate each triangle is defined by three nodes The list below summarises the command use Number of parameters Key word requirement Number of occurrences File location Parameter 1 Parameter 2 Q par QPORAS TR PO1 0 2 2 Mandatory 1 Anywhere within input file Character string containing no separators Defines the name of the points and joins file Character string Defines the permission This must be either RO or RW Page 29 of 44 3 14 The SURFACE key word Description This is mandatory if the reflector geometry is not defined by the GEOMFILE command If present it must also be accompanied by the BOUNDARY command The first parameter defines the type of surface Subsequent parameters depend on the type of surface Currently version 0 1 02 there are five types of permitted surface a plane surface PLANE a parabolic surface PARABOLOID a distorted parabolic su
14. E cos E 2 16 The default angle for 0 but may be changed using the input tag command FARPOL as given later Note that the sense of the angle for is chosen so that a positive angle is equivalent to a positive rotation of the feed by an angle v in an axisymmetric system Thus in a system where the reflector is axisymmetric and the feed lies on this axis choosing wr s implies that Ej and E5 remain invariant of s when 0 90 The key word ANGLES defines a block of required 0 and angles directly However it is also required to specify an arbitrary angular cut which cannot be achieved for constant 0 or constant This is accomplished using the ANGLECUT key word In this case we define a particular direction specified by 0 0 and o We then specify a scan direction angle ro made with respect to the direction I and vary the angle v along this cut This is illustrated in figure 2 2 below Q par QPORAS TR PO1 0 2 Page 5 of 44 le lg y A NN 89 Specification of the cut angle No and the cut plane defined by No and T 0 X spherical polar directions at the point 05 do I4 great circle through the origin in the plane of fg and n showing the scan angle v Figure 2 2 Arbitrary cuts on the surface of a sphere specified by ANGLECUT Q par QPORAS TR PO1 0 2 Page 6 of 44 The angle o at the point 05 9 defines the direction fj COS No Io sin np
15. User Guide for Q par PO reflector analysis software QPORAS Q par QPORAS TR PO1 0 2 Q par Angus Ltd v IDEAS ENGINEERED Cover viii 44 pages May 2010 Barons Cross Laboratories Leominster Herefordshire HR6 8RS UK Tel 44 0 1568 612138 Fax 44 0 1568 616373 Web www q par com E mail sales q par com Report Copyright 2010 Q par Angus Ltd U K Although the author has made every reasonable effort to ensure the accu racy of the contents of this document neither the author nor Q par Angus Ltd will be held liable for damages resulting from the use or application of the material contained to the extent permitted by international law This document may be distributed freely subject to the following conditions The document may not be changed or modified or the contents altered It must remain complete without selective removal of material It may not be sold or reproduced for commercial gain without the written approval of an authorised representative of Q par Angus Ltd UK Q par Angus Ltd Barons Cross Lodge Leominster Herefordshire HR6 8RS UK Q par QPORAS TR PO1 0 2 ii Author Date Issued by Q par QPORAS TR PO1 0 2 Dr A J Mackay May 2010 Q par Angus Ltd Barons Cross Laboratories Leominster Herefordshire HR6 HRS UK Document changes record Issue Date Change summary Issue 0 1 September 2008 In progress Issue 0 2 May 2010 Extended
16. We aim for a function such that a z is close to one for z gt 0 with progressive deviation for smaller z We choose a z 1 ap iz azz Je 3 5 where a is dimensionless and 3 a1 Q have units of m t We will assume a total of N such a parameters Q par QPORAS TR PO1 0 2 Page 30 of 44 The SPLINE1D surface This surface assumes a general reflector surface given by ys v z C x 3 6 which is independent of z and where C x is defined by a one dimensional cubic spline func tion whose control points are provided by an auxiliary input file We assume a natural cubic spline with control points that must span the range of values required by the BOUND A RY defined boundary The required input file name is a parameter and takes the format coordinates specified in metres itot z 1 y 1 z 2 w2 BHO tan where z 1 lt z 2 lt lt x itot The algorithm for defining C x is given in pp119 of 3 Such a surface may be regarded as an extrusion of a cubic curve along the z axis truncated by the BOUNDARY The list below summarises the command use Number of parameters At least 2 Key word requirement Special Mandatory if BOUNDARY command present Number of occurrences 1 or 0 File location Anywhere within input file Parameter 1 Character string This defines the surface type and must be ei ther PLANE PARABOLOID PARABDISTORT VARIPARAB1 or SPLINE1D Further parameters depend on the s
17. ampling interval lt 0 2 wavelengths and the rectangle must be large enough such that the fields outside the rectangle are small enough to ignore When no blockages are present this method of computing the far field is inferior to the main method The list below summarises the command use Number of parameters Key word requirement Number of occurrences File location Parameter 1 Parameter 2 Parameter 3 Parameter 4 Parameter 5 Parameter 6 Parameter 7 Parameter 8 Parameter 9 Parameter 10 Parameter 11 Q par QPORAS TR PO1 0 2 11 Optional 1 or 0 Anywhere within input file Real number This defines the position of evaluation plane yo in metres Real number Minimum x coordinate of near field region min in metres Real number Maximum x coordinate of near field region maz in metres Integer Number of evaluation points nz between min and za Real number Minimum z coordinate of near field region z in metres Real number Maximum z coordinate of near field region Zmar in metres Integer Number of evaluation points n between Zmin and Zmaz Character This represents the shadow mask flag If this is I then a blockage is assumed defined by the BLOCKAGE option If this is F no account is take of blockage effects Character This represents the far field flag If this is T then the far field is calculated from the near field region with or without masked fields
18. citly in the notation and 3 kolz 24 w 31 kolt 2 w 23 kolz 3 w 2 27 In the limit that one or more of the s terms tends to zero the expression 2 26 must be modified to permit computation To do this define 1 Po 5 f e dn 2 28 0 1 H P 6 nel dy 2 29 0 1 P 6 T re dy 2 30 0 which may be evaluated by l 56 zx e 1 for 6 Z 0 P J l 2 31 1 67 6 4 1 8 12 ford 0 e poeto Py 6 36 for 6 0 2 32 1 2 67 8 6 3 ford 0 e O Pye as 2P 6 j6 for 6 40 2 33 1 3 j6 4 for 6 0 Now for 531 0 Ig 2Aei tit 1 5531 2 Po 531 1 js31 Pi 521 3 531 2 P 521 2 34 For 53 4 0 we must consider the cases s23 0 and or s21 0 in which case 9 Aejkoz iw Ig 5 e 9 P 93 Po sa1 2 35 J 31 Q par QPORAS TR PO1 0 2 Page 8 of 44 The area of each triangle may be conveniantly evaluated using Heron s formula A A s s a s b s c 2 36 where a b c 5 and a e zo b z zil c z z 2 37 If a surface is represented by triangles which are in turn defined by nodes representing the triangle vertices there is a numerical dichotomy the fields and directions of waves are naturally defined at the nodes but they are required on the triangle surfaces where the surface normals are defined However since it is assumed that these quantities are slowly va
19. d designation SPH FEED the fields are defined in spherical coordinates in the coordinate system of the feed In the third designation CART FEED the fields are defined in cartesian coordinates in the coordinate system of the feed Number of parameters 4 Key word requirement Optional Number of occurrences 1 or 0 File location Anywhere within input file Parameter 1 Character string containing no separators Name of the electric field output file Parameter 2 Character string containing no separators Name of the magnetic field output file Parameter 3 Character string Coordinate options CART REFL SPH FEED or CART FEED Q par QPORAS TR PO1 0 2 Page 40 of 44 3 20 The FEEDFILE key word Description One of several methods to illuminate the reflector and is logically considered as a feed type This defines a user specified feed aperture distribution whose format is that of a CST 4 output file It is included as of version 0 0 13 of the software An aperture distribution is specified by a regular rectangular grid of points where the fields are specified There are two options either the electric field only is specified or both the electric and magnetic fields In both cases the z components of the fields perpendicular to the aperture are not required although they are specified in the input files for consistency with CST 4 format Let us assume the aperture lies in the x y plane of the feed coordinate system Wh
20. d through the blockage on to the y yo plane These are the rays previously discussed when defining the effect of the blockage Now however all the currents are evaluated on the reflector including the ones which in the basic method are taken as non contributory if the respective facets were taken as being in shadow In this option it is the plane y yo plane which defines the existence of shadow Thus if any shadowing rays intersect the plane y yo for which min lt lt Emar and Zmin X Z X Zmaz then the fields there are assumed zero Given a possibly masked near field region the far field may then be computed This is performed if the far field flag is set True Figure 3 5 shows the near field region and the effect of shadowing on the far field using this alternative method masked region of near field set to zero field blockage far field computed from fields evaluated on near field plane gt near field plane reflector Figure 3 5 Near field region shadow masking and far field The method of near to far field transformation is similar to the one employed for evaluating the far field from the aperture of a feed The method uses 2 2 where J nx H r e EY Ja x Er 3 12 m Q par QPORAS TR PO1 0 2 Page 38 of 44 where H r and E r are the near fields evaluated on the plane y yo Note that the sampling must be sufficiently fine over the rectangular region typically with a s
21. e distribution may be provided too The latter allows either the electric field or both the electric and the magnetic field to be given on a plane in space Once these aperture fields are specified the far fields E r and H x may be determined by integration The basic formulas for the E and H radiated fields evaluated at a point R in terms of the aperture fields E and H are given by Silver section 5 11 of 5 1 E R J ax LY ax B STI wen x E x VW ds 2 45 P 4mjw o JA and HU LL Rax E ax E V VY jon x H x V ds 2 46 a An juHo Ja where the surface integral is over the aperture plane A and E x and H z are evaluated on this plane and n z is the outward pointing surface normal in the direction of the radiating field taken as a constant unit vector for this application eg and uo are the permittivity and permeability of free space V is defined by V R ERE 4T f 2 Rapz 2 47 where r R 2 2 48 Notice that only the transverse fields with components in the plane normal to n are required in the formulation Without loss of generality assume n 2 where 2 is the unit vector normal to the plane surface and we have nx ZOE 2 49 and nxH 2xH 2 50 where E and H are the tangential field components of the electric and magnetic fields Specification of E and H depends on the feed method as outlined shortly Q par QPORAS TR PO1 0
22. e given on the plane z 0 The next three specify the x y and z components of the real part of the electric field electric field file or magnetic field magnetic field file The next three specify the x y and z components of the imaginary parts of the fields This is consistent with CST output files 2Note that the units of mm are for compatibility with CST export files where for microwave applications units are specified in mm This is in contrast with the units of distance elsewhere in the software which are specified in metres Q par QPORAS TR PO1 0 2 Page 41 of 44 When using an exported CST output file employ a text txt export format and ensure distance units are in milimetres this is the CST default condition Also ensure that the plane on which the fields are specified is transverse to the CST z axis for consistency with the above feed coordinate system Finally remove delete the header lines in the text file containing the ascii description of the numbers There are CST versions 6 to 10 two such header lines When only the electric field file is supplied scaling of the electric field components is unim portant since the program will re normalise to assume 1 Watt is radiated When both field files are supplied there can be an arbitrary common scaling factor but this must be common to both files A regular grid is assumed If the program detects the specified coordinates do not form a regular grid or
23. ed horn is defined by the widths of the aperture in the 2 and directions as well as offset phase distances that define the distance of the phase centre to the aperture associated with and 9g directions Also required is a meshing interval in fractions of a wavelength and a type designator to define the manner of polarisation of the horn Since the phase centre of the source may not exist at a single point in space i e if the offset phase distances are different and since the local phase centre of the aperture field may not coincide with the apparent phase centre as seen by the reflector in the intermediate or far field of the horn it is generally best to assume the physical location of the phase centre defined by FEEDCEN lies close to the centre of the aperture of the horn The offset phase distances required here are principally required to accurately define the aperture field distribution from which the field at the reflector is calculated The meshing interval should typically lie between a value of 0 2 and 0 01 depending on the accuracy required and the computation time penalty We have usually found that a sampling value of 0 1 is quite adequate The type designator is a character X Y LCP or RCP X implies the elctric field on the aperture is aligned in the direction Y implies the elctric field on the aperture is aligned in the g direction LCP and RCP imply that t
24. eference point for which the phase is zero and defines a front back reference to the reflector surface normal For other feeds it defines the phase centre of the feed The list below summarises its use Number of parameters 3 Key word requirement Mandatory Number of occurrences 1 File location Anywhere within input file Parameter 1 Real number Defines the x coordinate of phase centre in metres in global coordinate system Parameter 2 Real number Defines the y coordinate of phase centre in metres in global coordinate system Parameter 3 Real number Defines the z coordinate of phase centre in metres in global coordinate system 3 9 The FEEDROT key word Description This is mandatory if a real feed is used such as a dipole or horn It must not be present if an incident plane wave is employed in order to avoid possible confusion since a plane wave is defined with respect to the global coordinate system For a feed this defines the Euler rotation angles of the feed 05 and vy See earlier notes for a definition of these The list below summarises its use Number of parameters 3 Key word requirement Special Mandatory if a real feed is employed other wise must not be present Number of occurrences 1 or 0 File location Anywhere within input file Parameter 1 Real number Defines the Euler rotation angle 0 in degrees Parameter 2 Real number Defines the Euler rotation angle o in degrees Parameter 3 Rea
25. en only the transverse electric field is specified The transverse magnetic field is approximated from the tangential electric fields E E via H e H amp Hy 3 13 where H foZo E Hy foZo Es 3 14 where fp is a power scaling factor taken to ensure that the power radiated by the aperture is unity This approximation is valid if the fields are locally planar and is usually considered good in the apertures of horns provided the flair angle is not too large If both the transverse electric and magnetic fields are available this approximation is not required though we still calculate the component of the real part of the Poynting vector normal to the aperture to normalise total power radiated by the aperture to unity The component of the reactive part of the Poynting vector is also computed as a diagnostic If only the transverse electric field is available this component is estimated as exactly zero If both electric and magnetic fields are available it will in general be non zero If so the reactive component should be small compared to the radiated part or else the program will issue a warning and the supplied aperture fields should be considered as poor The specified aperture files take the same format This consists of a list of rows where the first three entries in a row specify the z y and z coordinates in milimetres the 2 coordinates are not used except for diagnostics i e the field is assumed to b
26. eral types of feed One and only one feed type must be present 1 or 0 Anywhere within input file Real number Defines the aperture width in x direc tion in metres Real number Defines the aperture width in y direc tion in metres Real number Defines the distance to the local phase centre for the TEO1 type Y mode Real number Defines the distance to the local phase centre for the TE10 type X mode Character string Defines the type designator as de scribed above Real number Defines the aperture sampling interval as a wavelength fraction Character string Optional If present defines the name of an output file defining the aperture electric field on the sampling grid Character string Optional Must be present if pa rameter 7 is present If present defines the name of an output file defining the aperture magnetic field on the sampling grid for example be used in tests of the FEEDFILE command Q par QPORAS TR PO1 0 2 Page 27 of 44 3 13 The GEOMFILE key word Description This key word defines the name of a secondary file required by the program and is mandatory There are two uses of this command The first parameter defines the name of a points and joins file The second defines a permission and the mode of operation This takes the form of a two character string either RO or RW In RO mode the defined file can only be read In RW mode
27. fication as well as some logical flags to switch on and off various features The list below summarises its use Number of parameters 11 Key word requirement Optional Number of occurrences Any number File location Anywhere within input file Parameter 1 Character string containing no spaces or separators Name of output POSTSCRIPT file Parameter 2 Real number 0 The 0 view rotation angle in global coordinate system specified in degrees Parameter 3 Real number The view rotation angle in global coordinate system specified in degrees Parameter 4 Real number v The w view rotation angle in global coordinate system specified in degrees Parameter 5 Real number magnification scale factor Parameter 6 Real number x ccordinate display offset in meters Parameter 7 Real number y ccordinate display offset in meters Parameter 8 Logical T or F If T displays reflector Parameter 9 Logical T or F If T displays shadow structure when there is a blockage Parameter 10 Logical T or F If I displays incident wave direc tions on each facet of reflector Parameter 11 Logical T or F If T displays reflected wave direc tions on each facet of reflector Q par QPORAS TR PO1 0 2 Page 20 of 44 3 5 The ANGLES key word Description This is mandatory and defines the angular range at which the far field gain is required This defines a uniformly sam
28. he feed is left or right circularly Q par QPORAS TR PO1 0 2 Page 25 of 44 polarised Note that the main reflector reverses the sense of circularity of the polarisation of the radiated field It is assumed here that only a TE01 and a TE10 mode can be excited When either one or the other is present but not both the type is designated by Y or X respectively The LCP and RCP types involve a suitably phased linear combination of both Figure 3 3 shows the excitation type with respect to the local feed coordinate system y y x x TEO1 mode TE10 mode type Y type X Figure 3 3 Aperture excitation types for a rectangular horn When the PLOTFILE command is used the 2 direction of the feed and its aperture are illustrated The list below summarises its use Q par QPORAS TR PO1 0 2 Page 26 of 44 Number of parameters Key word requirement Number of occurrences File location Parameter 1 Parameter 2 Parameter 3 Parameter 4 Parameter 5 Parameter 6 Parameter 7 Parameter 8 Note that parameters 7 and 8 included as of version 0 0 14 are optional If present they should contain no separators and define the name of output files containing the transverse electric and magnetic fields on the aperture The components of the field perpendicular to the aperture are defined as zero This file is in the same format as a CST file 4 and may 6 or 8 Special Represents one of sev
29. ields at other than the main reflector In outline we as sume a general blocking surface either specified by another triangulated surface represented as a user specified points and joins file or that the feed aperture is blocking the reflected wave This latter option is relevant only to certain feed types i e it is not relevant to an infinitesimally small dipole or incident plane wave The primary method follows This is one of the simplest and fastest algorithms to establish the effects of blockage It is probably also one of the least accurate and must be treated with care until we are able to establish the level of accuracy that may be expected A second method is also implemented which requires the computation of the near field This is described in more detail in the user section on the NEARFIELD command Q par QPORAS TR PO1 0 2 Page 14 of 44 Determine the incident wave direction at the centroid of each facet Determine the reflected wave direction at the centroid of each facet Trace a ray from the centroid of each facet with wave direction k Determine whether any such reflected ray intersects any part of the blocking surface 5 If such a ray does intersect mark the facet on the reflector from which the ray originates as shadowed It is assumed that the energy associated with this ray is totally absorbedi i e that the blocking structure is black 6 Assume any shadowed facet does not contribute t
30. ignore the second integral term in 2 2 It may be shown that the gain of the antenna in the direction f is given by x ec gt Dh Zo Pinc 2 7 where Pine is the incident power For a feed this may be defined as the power radiated by the feed For an incident plane wave this may be defined as the product of the projected area of the reflector in the direction of the incident plane wave and the intensity of the plane wave Q par QPORAS TR PO1 0 2 Page 3 of 44 Since we assume the source field from the feed does not contribute to the scattered far field we will also assume that Pinc is the radiated power from the feed radiated in all directions This definition is especially significant for a dipole feed source We now assume that the curved surface can be approximately represented by a polygonal surface consisting of contiguous non overlapping flat facets whose maximum deviation from the curved surface that they represent is small Over the i such flat facet n r fi is a constant In addition if we further assume that each such facet is small enough to lie in the far field of the source then the direction of incidence does not vary over the facet and H r may be approximated by tinc H plr H e 75 7 over the ij facet 2 8 cine where k kok is the direction of the incident wave on the i facet and H is the constant vector amplitude of the magnetic field over the tiin facet r Figure 2 1 Def
31. ince no system dependent calls are implemented 1 2 Overview of the physical model A general shaped curved reflecting surface is assumed topolgically open with no part shad owing any other part under a point illuminator or incident plane wave The surface can be described in several different ways either accepting a previously meshed structure or meshing the structure itself The mesh is regular and composed of triangular facets Unlike moment method or finite element analysis methods there are no hard restrictions on how large each facet may be compared to a wavelength The mesh size is primarily governed by geometrical requirements For example a flat rectangular plate reflector could be modelled by only two triangular facets with no loss of accuracy independent of the wavelength However any representation of a curved surface by a faceted polygonal surface involves a difference in its electromagnetic properties so in such cases the maximum departure of a flat triangle from the curved surface should be small compared to a wavelength It is still therefore a rule for a general curved surface that a triangle mesh cell should be small compared to a wavelength The main faceted reflector is assumed to be perfectly conducting as of version 0 0 12 modelled using the version of physical optics that assumes that the induced electric currents at a point r on the surface S J r is given by the approximation J a r 28 r x H r for r
32. ining the distortion parameters distortfilename Currently version 1 02 only options are ndistort 0 where there is no distortion applied functionally equivalent to the use of Parameter 1 PARABOLOID or ndistort 1 When ndistort 1 the coordinates of the reflector surface are defined by Ys 2 Yx 2 d r 0 3 7 where x rcos d z rsinO 3 8 and d r 0 is a deviation function defined by d r 0 R r OG 0 3 9 with R r pir port py 3 10 O 0 ag a cos i0 b sin i6 3 11 i 1 for real coefficients p a and b Q par QPORAS TR PO1 0 2 Page 32 of 44 The named file distortfilename must be present or an error is flagged When present it must take the form comments optional M ao ay aM by PN comment Integer M gt 0 comment comment Last of the a coefficients comment comment Last of the b coefficients comment This must be a hash designator to separate file parts comment Integer N gt 1 comment comment Last of the p coefficients For example for a circular dish of radius rp we may employ N 2 specify p 1 r2 and py 1 its so that there is no deviation at the rim and maximum deviation when r 1o V2 With this special form R r is dimensionless and the coefficients a and b take units of distance All units of distance are specified in metres Q par QPORAS TR PO1 0 2 Page 33 of 44 lf Parameter 1 Parameter
33. inition of surface normal It then follows that DEMN j Zoko p jkor k k Jol E k E gt Ji a QU aS 2 9 where the projected current amplitude J p 2 is constant over each facet JO J J k Jk 2 10 where J 2h x H 2 11 and f is the scatter direction The sum over i is over all the flat facets 5 representing the surface Q par QPORAS TR PO1 0 2 Page 4 of 44 2 2 Scattered field directions and definitions The direction of the required scattered field is specified within the software using spherical polar coordinates 0 and These angles are illustrated in figure 3 1 The field directions are specified with respect to the directions of increasing 0 defined by the unit vector and the direction of increasing defined by the unit vector Expressed in cartesian coordinates cos cos 01 sin 9 cos Oy sin 02 sin cos oy 2 12 S gt ID Il We may write the components of the scattered electric field vector E k E19 Fad 2 13 The coefficients E and Es are the complex scattering amplitudes in these directions The program permits a rotation of this polarisation base by a constant angle so that final outputs may be expressed at an angle to the spherical angle directions i e in the directions 6 cos C sin 6 sin cosC 2 14 Writing A al al E k E18 E59 2 15 we therefore have Ej cos E sin E E sing
34. ious documentation concerning the definitions of angles here The list below summarises its use Number of parameters 5 Key word requirement Optional Number of occurrences Any number File location Anywhere within input file Parameter 1 Real number 05 defining the value for 0 of the centre point of the cut in degrees Parameter 2 Real number 9 defining the value for of the centre point of the cut in degrees Parameter 3 Real number no defining the angle of the cut in de grees with respect to the direction Bo Parameter 4 Real number Av defining the angular increment along the cut in degrees Parameter 5 Integer Defines the total number of increments such that the sweep is made nAv lt v lt nAv 3 7 The FREQS key word Description This is mandatory and defines the frequency range for which predictions are required Fre quencies are entered in MHz The list below summarises its use Number of parameters 3 Key word requirement Mandatory Number of occurrences 1 File location Anywhere within input file Parameter 1 Real number Defines the first value of frequency in MHz Parameter 2 Real number Defines the frequency increment in MHz Parameter 3 Integer Defines the total number of frequency values Q par QPORAS TR PO1 0 2 Page 22 of 44 3 8 The FEEDCEN key word Description This is mandatory and defines the phase centre origin of the excitation For a plane wave this defines the r
35. its projection If Parameter 1 ELLIPSE then Parameter 2 Parameter 3 Parameter 4 Parameter 5 Parameter 6 Parameter 7 Real number Ellipse semi major minor axis along x direction before rotation In metres Real number Ellipse semi major minor axis along z direction before rotation In metres Real number coordinate of ellipse centre e Real nember z coordinate of ellipse centre ze Real number Rotation angle 6 of ellipse about its centre rotated about a vector parallel to the y axis Defined in degrees Real number Target mesh size in metres Note that the target mesh size is used as a meshing criterion and is not prescisely met Meshing method is hard wired into the software This can be changed and other hard wired options used but the default method divides the ellipse into concentric shells together with a central core Each shell is uniformly divided into triangles to the target mesh size The final remaining core assumes a single node at the centre so that triangles here may be rather smaller Details of the method are not reported here Q par QPORAS TR PO1 0 2 Page 36 of 44 3 16 The BLOCKAGE key word Description This command is optional If present it must occur only once and describes the nature of a blockage to the main reflector Currently software version 0 0 12 it takes two forms The first form is where the feed is responsible for the blockage FEED designatio
36. l number Defines the Euler rotation angle v in degrees Q par QPORAS TR PO1 0 2 Page 23 of 44 3 10 The PLANEWAVE key word Description One of several methods to illuminate the reflector and is logically considered as a feed type This defines an incident plane wave of arbitrary polarisation and ellipticity One and only one feed type must be used A plane wave is specified by an incoming wave along the direction specified by 0 and with a polarisation defined by the angles Xa and xg The former defines the angle of the principal axis of the polarisation ellipse with respect to the elctric field vectors When yg 0 this refers to the polarisation angle of a linearly polarised wave When x4 45 degrees the two states of circular polarisation are defined when xe 90 degrees More generally the plane wave is elliptically polarised with the electric vector amplitude taking the form Eine 008 Xo eX sin Xa 9 3 3 When the PLOTFILE command is used the direction of the plane wave is represented by an arrow through the phase centre point specified by FEEDCEN The principal direction shown as cos xa 0 sin Xa is also illustrated through the phase centre point by an un arrowed line The list below summarises its use Number of parameters 5 Key word requirement Special Represents one of several types of feed One and only one feed type must be present Number of occurrences 1 or 0 File location Any
37. lds together with a knowledge of the phase centre or in the case of a plane wave the defined direction of incidence to determine the direction of incidence The list below summarises its use Number of parameters 1 Key word requirement Optional May occur anywhere in a composite If not present Option 1 is assumed Number of occurrences At most one File location Anywhere within input file Parameter 1 Integer Its value is 1 for option 1 and 2 for option 2 Q par QPORAS TR PO1 0 2 Page 18 of 44 3 3 The FILENAME key word Description Defines the name of the main output files Currently version 0 0 12 this takes two filenames though only the first is used The second is reserved for further software enhancements The first filename is the name of the output file containing the predicted far field gains The list below summarises its use Number of parameters 2 Key word requirement Mandatory Number of occurrences One File location Anywhere within input file Parameter 1 Character string containing no spaces or separators Name of output gain file Parameter 2 Character string containing no spaces or separators Currently unused Q par QPORAS TR PO1 0 2 Page 19 of 44 3 4 The PLOTFILE key word Description Defines the name of optional output POSTSCRIPT files showing the reflector and feed Intended for diagnostic purposes There may be any number of these The parameters control the Euler view angles and magni
38. led by a collection of ray bundles then if a given ray intersects the surface more than once the surface at the second intersection point is said to be in the shadow of the surface at the first intersection point Shadowing within physical optics can only be modelled by making secondary approximations Generally though not always this is accomplished by assuming an incident field that is defined by the value of the field within a ray bundle at the point of intersection with the surface Thus if a point of the surface is in shadow the incident field is there assumed to be zero In this approximation we assume sudden transitions of electric current i e the electric current on the surface varies continuously until a region of shadow where the induced electric current drops to zero Although theoretically admissable we always assume no self shadowing of the main reflector Shadowing is permissable only when considering blockage effects Various sources are permitted to illuminate the main reflector These may be placed at any position and orientation Currently version 0 0 12 feed types include a standard rectangular aperture horn a dipole source a plane wave illuminator The main purpose of the software is to compute radiation patterns in the far field of the antenna However there are applications where the near field is also required and if there is blockage a means to re compute the far field from the possibly blocked near field These
39. less reliable Our most robust approximation is simply to assume that at the aperture H t X E Zo 2 58 using the free space admittance More accurate field distributions require the export of aperture field distribution files e g from CST 4 using the FEEDFILE option Q par QPORAS TR PO1 0 2 Page 12 of 44 When importing aperture field distributions we have two options either we specify both the electric and magnetic fields in which case the approximation 2 58 is not made or we specify the E field and use 2 58 to estimate the H field on the aperture Finally we note that in the formulation 2 45 is not required to generate the electric field scattered by the reflector in 2 9 only 2 46 However we calculate both since the overhead in doing so is small and this allows us to determine Poynting vectors and local directions of incidence k the wave is assumed locally planar over a facet of the reflector when the phase centre of the source field is not defined 2 5 The scattered near field We assume that there are no dielectrics present between the perfectly conducting reflector and a required set of points where the scattered near field is required Let r be an observa tion point where the field is required and let S be the scatterer reflector The scattered electric field E r is given see e g 1 by om E zc ae ae Ze ER kph kp Re M E Sm RB a RR am ert od where R r r and R
40. n assuming that it is only the feed aperture that is responsible for the blockage The second form NEW designation requires the user to specify a file name containing a points and joins file with the same format as specified in defining the reflector This allows an arbitrary blockage to be defined The list below summarises the command use Number of parameters At least 1 Key word requirement Optional Number of occurrences 1 or 0 File location Anywhere within input file Parameter 1 Character string This defines the feed type and must be either FEED or NEW If Parameter 1 FEED then there are no further parameters If Parameter 1 NEW then Parameter 2 Character string containing no separators This is the file name of the points and joins file specifying the blockage Q par QPORAS TR PO1 0 2 Page 37 of 44 3 17 The NEARFIELD key word Description This command is optional If present it defines a rectangular region in space where the near fields are to be evaluated Various options are also provided to provide an alternative method to calculate the effect of the blockage to the far field and or to determine the far field from the calculated near field Firstly it is assumed that the near field is to be specified on the plane y yo on a rectangle defined by T min lt x lt maa and Zmin lt Z lt Zmar Secondly if the shadow mask option is flagged as True the geometric rays from the reflector are trace
41. o d where g cos bo Cos Ap sin Go cos 0o sin 0o So sin o cos do fj We also require the direction vector at 0o o defined by fy cos Go sin 0o sin Go sin 0o Y cos 0o The direction vector under the scan is now given by f cosvfg sin v fj but we also have f cos sin0 sin sin0 cos0 2 8 2 18 2 19 2 20 2 21 so equating terms we obtain expressions for 0 and in terms of 0o o no and v The cartesian components of f are given by Tolv cosy cos Qosin o sin v cos No cos Gp cos 0o sin v sin no sin do ry v cosvsin dp sin o sin v cos No sin o cos o sin v sin No cos do r v cosy cos o sin v cos no sin Ip SO cos r from which we may obtain 0 under the assumption 0 lt 0 lt 7 and arctang ry Te where the arctan function is the angle unambiguous arc tangent of the ratio r rz Q par QPORAS TR PO1 0 2 2 22 2 23 2 24 Page 7 of 44 2 3 The Physical Optics integration In evaluating the PO integrals we assume the facets are triangular in which case the integrals are of Gorden s generic form Taw f eFko w 2 dy 2 25 over a general triangle A with area A If the triangle is defined by the coordinates x x5 and x of the vertices then it can be shown after some algebra that fen Matt demi mon T J831 J 523 J 21 where the 7 subscripts are no longer shown expli
42. o the far field at any scatter angle or at any frequency Exclude shadowed facets from the PO sum over facets puces ber 3 Use of the software 3 1 Introduction The software is driven from an input script file using a command line console The name of the excutable is arbitrary so let us assume here it is called testpo The command would thus read testpo filename where filename is the name of the script file The program searches for recognised com mands designated by a key word followed by a list of parameters Unrecognised words are ignored but it is good practise to comment out any unused commands with a symbol such as Generally and as of version 0 0 12 of the software any commands may be entered in any order The commands specify the calculation options required frequencies and scan angles geome try designations coordinate rotations etc There are two coordinate systems used within the software The first is the global coordinate system in which the main reflector is defined and to which the scan angles are referenced Currently as of version 0 0 12 the commands that define standard reflector shapes and their boundaries assume a reflector that is pointing forwards in the direction of the y axis This is illustrated in figure 3 1 together with the definitions of elevation scan angle 0 and azimuth angle There are commands however to read in surfaces defined by an arbitrary list of coordinates
43. pled block of solid angle defined by a range of 0 and 9 The list below summarises its use Number of parameters 6 Key word requirement Mandatory Number of occurrences 1 File location Anywhere within input file Parameter 1 Real number Defines the first value of 0 in degrees Parameter 2 Real number Defines the 0 increment in degrees Parameter 3 Integer Defines the total number of 0 values Parameter 4 Real number Defines the first value of in degrees Parameter 5 Real number Defines the increment in degrees Parameter 6 Integer Defines the total number of values Note that we may set Parameter 3 and Parameter 6 to zero in which case ANGLES does not specify any requested directions Angles may also be requested using ANGLECUT any number of times see below If no angles are specified either by ANGLES or by ANGLECUT then the program will terminate with an error message Q par QPORAS TR PO1 0 2 Page 21 of 44 3 6 The ANGLECUT key word Description This is optional It may be used any number of times It defines a single cut angular sweep about any great plane of the direction sphere Data output from each ANGLECUT is appended sequentially to the output file in order of their appearance in the input file after the data generated by the ANGLES definition The output file as of version 1 004 of the software in which this tag is introduced contains a field position 10 which outputs the scan angle v See the prev
44. r r R Similarly the magnetic field is given by 1 jkoR _ amp f sete J x Rae e jFoRqs 2 60 Again under the PO approximation we assume J 2n r x HE for E ES 2 61 Using the same faceted representation of the surface as above we assume that each facet is small enough to be individually in the far field of a fictitious elemental dipole source at r We may then safely assume that R varies very little over any given facet and all terms other than the phase variation involving R may be taken outside the integral It may then be shown that Ah 0 2 Y uoto Va c FC RO 1 2 62 where d ed w R k 2 63 A SRR 2 64 Q par QPORAS TR PO1 0 2 Page 13 of 44 RO n 2 65 Hi esr eq 2 66 where Ig k ko and ro are defined in the previous section The vector coefficient Q is given by 1 c c 3 3 Q A d use usos RP RP Lg Gu e kofi ko Ri ja kj Ri ie kohi k R J kj Ri s 2 67 Similarly it may be shown that Ka ho R9 RO O HEN CDS ee 2 68 where the vector coefficient c 1 c pues Ol o cano 2 69 knoy jJ 2 6 Blockage effects There are a large number of logically and computationally different methods for approximat ing the effect of blockages under high frequency and or physical optics approximations In our implementation we employ a combination of ray tracing and PO on the main reflector avoiding the need to recompute far f
45. rface PARABDISTORT a shaped parabolic surface VARIPARAB1 and an extruded one dimension cubic spline surface SPLINE1D The boundary of all these surfaces is defined by the BOUNDARY command The PLANE surface This surface is a simple flat mirror whose normal is defined by the vector n Nz ny nz and a point p Px Py Pz in the plane The PARABOLOID surface This surface is a paraboloid of revolution It is defined by its focal length f and the coordinates of the focal point ry xy yy zy It is assumed that the paraboloid is always orientated such that its axis of revolution is parallel to the y axis The PARABDISTORT surface This surface is a paraboloid of revolution as above with an additive deviation function desig nated by a type specified by an integer and a filename containing the deviation parameters associated with the type The VARIPARAB 1 surface This surface represents a distorted paraboloid of revolution intended to permit a profiled beam in one angular direction e g an approximation to a cosec 0 distribution in the 0 direction while maintaining a narrow beam in the orthogonal direction There are any number of ways in which this can be done Here we will assume that the reflector surface function y z z is given by yen 2 a 2 up z 2 3 4 where yp x z is a paraboloid of revolution about the y axis as defined by the PARABOLOID option The function a z defines the distortion
46. ry command defines a uniformly meshed flat bounded rectangle or ellipse defined perpendicular to the y axis The triangles and nodes of this flat mesh are then projected along the y axis on to the surface defined by the SURFACE command The list below summarises the command use Number of parameters At least 2 Key word requirement Special Mandatory if SURFACE command present Number of occurrences 1 or 0 File location Anywhere within input file Parameter 1 Character string This defines the boundary type and must be either RECTANGLE or ELLIPSE Further parameters depend on the surface type If Parameter 1 RECTANGLE then Parameter 2 Real number The rectangle width w in metres de fined parallel to the x axis prior to rotation Parameter 3 Real number The rectangle height w in metres de fined parallel to the z axis prior to rotation Parameter 4 Real number z coordinate of rectangle centre e Parameter 5 Real nember z coordinate of rectangle centre Ze Parameter 6 Real number Rotation angle 6 of rectangle about its centre rotated about a vector parallel to the y axis Defined in degrees Parameter 7 Integer Number of meshing divisions ng along the x axis Parameter 8 Integer Number of meshing divisions n along the z axis See figure 3 4 below Q par QPORAS TR PO1 0 2 Page 35 of 44 centre coordinates Xoe Figure 3 4 Boundary rectangle and
47. rying using 2 8 we may take INc INC N l H 3 659 Hn eI H s eI H s 2 38 where Xij are the vertices Lx of the t n triangle The incident wave directions k must also be approximated We permit two ways of doing this within the software though in practise there is very little difference between them if our assumptions on slow variations are correct The first method assumes that the phase centre of the source is specified and that the field radiated by the source may be considered to radiate from this phase centre at all points over the reflector surface In this case if the phase centre is specified at the coordinates rg then the vector from the phase centre to the triangle centroid is given by 1 z Za Zio Liz T9 2 39 3 hence k kor rf 2 40 The second method makes no assumption on the position of the phase centre but assumes the wave direction is that of the Poynting vector This basically assumes that the field is locally planar with the E and H fields orthogonal and in phase The direction of the wave at a general point in space may be defined by i ae R E x x H x RCE ae x H x 2 41 which is required when E x E x and H x H x Evaluation of the incident fields at the nodal coordinates depends on the method employed see below Again since the fields are only available at the nodes we employ an average defined by
48. the designated file can be read and written to The effect of this command depends on whether the SURFACE and BOUNDARY commands are present SURFACE and BOUNDARY commands must either both be present or neither must be present If both are present the points and joins file will be written to if RW is designated or there is no effect if RO is designated i e this command is ignored In both cases the reflector geometry is defined by the SURFACE and BOUNDARY commands and not the points and joins file If neither SURFACE or BOUNDARY commands are present the software takes the reflector geometry defined by the points and joins file In this case the permission must be set to RO The required format of the points and joins file is shown in the following example note that the node coordinates are specified in metres Number of nodes 16 Node coordinates 1 0 80680E 01 0 99296E 04 0 48644E 01 2 0 34082E 01 0 69546E 04 0 71018E 01 3 0 20870E 01 0 24396E 04 0 73532E 01 4 0 79174E 01 0 13780E 02 0 49868E 01 5 0 10600E 00 0 30000E 02 0 41399E 05 6 0 80663E 01 0 15101E 02 0 48659E 01 7 0 31787E 01 0 19570E 03 0 71548E 01 8 0 25243E 01 0 46067E 05 0 72842E 01 9 0 80294E 01 0 10700E 03 0 48964E 01 10 0 10600E 00 0 22617E 03 0 43846E 13 11 0 15782E 01 0 48883E 04 0 30572E 01 12 0 35072E 01 0 80834E 04 0 21060E 01 13 0 34648E 01 0 88332E 04 0 21409E 01 14 0 15777E 01 0 48921E 04 0 30573E 01 15 0 46000E 01 0 45332E 0
49. tran Cambridge University Press 1986 4 CST EM simulation software See web site www cst com 5 S Silver Microwave antenna theory and design McGraw Hill 1949 Q par QPORAS TR PO1 0 2 Page 44 of 44
50. urface type If Parameter 1 PLANE then Parameter 2 Real number Defines the x component of the surface normal in metres Parameter 3 Real number Defines the y component of the surface normal in metres Parameter 4 Real number Defines the z component of the surface normal in metres Parameter 5 Real number Defines the x component py of a sur face point in metres Parameter 6 Real number Defines the y component p of a sur face point in metres Parameter 7 Real number Defines the z component p of a sur face point in metres Q par QPORAS TR PO1 0 2 Page 31 of 44 If Parameter 1 PARABOLOID then Parameter 2 Real number Defines f the focal length of parabola in metres Parameter 3 Real number Defines the x component of the focal point in metres Parameter 4 Real number Defines the y component of the focal point in metres Parameter 5 Real number Defines the z component of the focal point in metres If Parameter 1 PARABDISTORT then Parameter 2 Real number Defines f the focal length of parabola in metres Parameter 3 Real number Defines the x component of the focal point in metres Parameter 4 Real number Defines the y component of the focal point in metres Parameter 5 Real number Defines the z component of the focal point in metres Parameter 6 Integer number Specifies the distortion type ndistort Parameter 7 Character string Specifies the name of the file con ta
51. where within input file Parameter 1 Real number Defines the incidence angle 0 in de grees Parameter 2 Real number Defines the incidence angle in de grees Parameter 3 Real number Defines the polarisation angle x in degrees Parameter 4 Real number Defines the ellipticity angle xg in de grees Q par QPORAS TR PO1 0 2 Page 24 of 44 3 11 The DIPOLE key word Description One of several methods to illuminate the reflector and is logically considered as a feed type This defines an elementary perfect Hertzian electric dipole radiator situated at the phase centre point defined by FEEDCEN The electric dipole is assumed to lie in the 2 direction As of version 0 0 12 of the software this takes no parameters though it is planned to generalise this dipole at some later time When the PLOTFILE command is used the 2 direction of the dipole is represented by an arrow through the phase centre point specified by FEEDCEN The list below summarises its use Number of parameters 0 Key word requirement Special Represents one of several types of feed One and only one feed type must be present Number of occurrences 1 or 0 File location Anywhere within input file 3 12 The RECTHORN key word Description One of several methods to illuminate the reflector and is logically considered as a feed type This defines rectangular aperture horn with a cosine electric field distribution on the aperture The fe
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