national radio astronomy observatory green bank, west virginia
Contents
1. plotp 1 1 YlPydbl yl 40 yh60 yilO zl degrees z2 dB gt f g vi Display the plot Either mod f g or hp7550 f g The display will appear on the graphics screen or the HP plotter 24 APPENDIX B WARNING CONCERNING THE NEC USE OF APERTURE INTEGRATION AND THE GEOMETRICAL THEORY OF DIFFRACTION The Numerical Electromagnetic Code nec is being used for this analysis It uses a combination of Aperture Integration and Geometrical Theory of Diffraction For large scan angles 3 or better there exists a significant difference between the AI and GTD calculations At some limit O switchover occurs and the code changes from GTD calculations result there be discontinuities on the plots of far field patterns It is my understanding that GTD will not give useful information of a scanned beam and so I have now forced the program to use only AI in its calculations The switchover angle AI GTD can be set using the TO command in the NEC code The code can be set to do AI or GTD only The switchover angle is set at al 1 Vba 4 89 for D 300 66 6 cm i e 450 MHz Since we hope to scan to 8 if we do not increase 0 or over ride the GTD calculation the main beam will be calculated by GTD All field calculations have been forced to use AI X X X X X X X X X 25 REFERENCES Phased Array Theory 1 Rudge A W et al Ed The Handbook of Antenna2. 77 Calling BeamAngles Calling BeamPhase Preparing data for cut 4 1 Preparing data for cut 2 Preparing data for cut 3 Preparing data for cut 4 Preparing data for cut 5 Preparing data for cut 6 Preparing data for cut 7 Preparing data for cut 8 Preparing data for cut 9 Preparing data for cut 10 Preparing data for cut 11 Preparing data for cut 12 Preparing data for cut 13 Preparing data for cut 14 Preparing data for cut 15 Offset 6 20 feet Aperture Coordinates Phase Errors Beam Angle x y Patherr PathPhase LSQ fit Prim Coma All Coma 1 49 96 0 00 121 93 4 79 788 87 40 56 225 75 183 48 2 33 15 0 00 79 60 3 47 570 36 33 82 62 82 57 20 3 19 16 0 00 46 93 2 13 349 83 39 37 12 87 12 45 4 6 28 0 00 17 99 0 78 127 75 17 56 0 72 0 72 5 6 28 0 00 9 91 0 58 95 57 12 75 0 12 0 12 6 19 16 0 00 38 86 1 94 320 06 36 88 7 31 7 14 7 33 15 0 00 71 70 3 32 545 95 35 54 45 91 42 52 8 49 96 0 00 114 81 4 70 773 77 34 99 188 50 156 52 Note phasings opposite sign from the phase errors 20 FIGURE 4 Calculated Far Field Patterns for the 300 ft Telescope Scanned with an Array Feed O QO Q Qao o wo 6 2 feet b Feed displacement 0 0 feet a Feed displacement 23 0 feet d Feed displacement 15 0 feet c Feed displacement The feed pa
3. 9 9 9 O 19 4 Calculated Far Field Patterns for the 300 ft Telescope Scanned with an Array Feed 20 APPENDICIES A Running the NEC Program and Displaying Results 21 B Warning concerning the NEC Use of Aperture Integration and the Geometrical Theory of Diffraction 0 0 0 0 9 9 24 i ANALYSIS OF AN ARRAY FEED DESIGN FOR THE 300 FT TELESCOPE Peter R Lawson Introduction The 300 ft telescope is a transit instrument therefore its motion is restricted to a rotation in the north south direction In order for a particular observation to be made the telesoope must wait for the object of interest to approach the meridian and then attempt to track the object as it enters and leaves the telesoope s field of view Up until now the tracking has been accomplished by moving a single feed from the focal point This offset steers the far field beam in the opposite direction As the offset is increased the gain of the far field pattern is reduced and the levels of the nearest sidelobes significantly increased Sucha development may be seen in Figure 1 As a result the telescope can only steer the beam over a limited region If it were possible to correct the beam at wider scan angles and consequently to increase the tracking time then observations of weak sources would be Substantially improved
4. Design Volume I Publisher Peter Peregrinus Ltd London 1982 pp 48 49 435 438 2 Jasik ed Antenna Engineering Handbook McGraw Hill first edition New York 1961 pp 5 10 3 Hansen R C Microwave Scanning Antennas Vol II Array Theory and Practice Academic Press New York 1966 Lateral Feed Displacement 5 Ruze John Lateral Feed Displacement in a Paraboloid IEEE Trans AP Vol AP 13 pp 660 665 September 1965 5 Lo Y T On the Beam Deviation Factor of a Parabolio Reflector IRE Trans Antennas amp Propagation pp 347 349 May 1960 The Butler Matrix 6 Jordan E C ed Reference Data for Engineers Radio Electronics Computer and Communications Seventh Edition Howard W Sams amp 1985 pp 32 51 55 32 39 11 T Hansen R C Microwave Scanning Antennas Vol III Array Systems Academic Press New York 1966 258 263 8 Cochran W T Cooley J W et al What is the Fast Fourier Transform Proc IEEE Vol 55 No 10 October 1967 pp 1665 1673 9 Shelton J P Fast Fourier Transforms and Butler Matrices Proc IEEE March 1968 p 350 10 Shelton J P Multiple Beams from Linear Arrays IRE Trans Antennas amp Propagation March 1961 pp 154 161 The Numerical Electromagnetic Code 11 Rudduck R C and Chang Y C Numerical Electromagnetic Code Reflector Antenna Code NEC REF Version 2 Part I User s Manual Ohio State Univ
5. corresponds to positive y values It is in this plane that the beam peak of the hybrid antenna will lie since the scan is along the y direction 14 Results Software was developed to describe the array feed and three different phasings were examined The best results were obtained with phasings derived from residuals of a least square fit to the phase errors A trial run of the program is given in Figure 3 Far field patterns for this phasing method used at various offsets are shown in Figure 4 These patterns should be compared with the single feed patterns in Figure 1 We would like to describe the operation of the phased array feed as the offset of the feed is increased The far field pattern becomes unacceptable once the nearest Sidelobes rise above a level of 15 dB measured with respect to the peak This analysis does not take into account the effects of aperture blockage and strut reflection They would complicate the analysis and have been therefore neglected Using the phased array the 300 ft telescope produces a main beam identical to that produced using a single feed The gain of the antenna is calculated to be 51 6 dB with respect to an isotropic antenna The near sidelobe structure is different but the highest sidelobes are more than 20 dB down from the main beam peak and the pattern as a whole is quite acceptable There are no phase errors to correct for and thus all phasings are identical At an offset of
6. r 2 f 2f 2f x primary coma arises out of the second term in the series The first term is linear in r can causes beam shift but does not distort the beam 1 If we wish to include all coma terms but remove the linear term then we should write 1 7 27 f iii These expresssions are all theoretical and yet we know the phase errors from the path error calculated by our ray tracing program It has been mentioned that a linear phase progression across the aperture will not adversely affect the beam shape Therefore what we would like to do is correct for errors that occur over and above a linear shift Since we have sampled the phase errors at the beam locations we can fit a line to those points The array beams lie along the y axis and a plane fit is therefore unnecessary This line is a least squares approximation described in 20 The phase errors with respect to this line are found at the beam locations and the beams are phased by the negative of these errors Although not yet attempted a better fit would be found if the points were weighted by the amplitude of the element pattern Evaluating the Performance of Hybrid Antennas A Possible approaches using the NEC reflector program The analysis is performed by attempting to produce the far field pattern of the hybrid antenna This will give us information not only about the gain but also about the sidelobe levels and the beam shape The far field pattern may
7. rotation of the parabola From this source a plane wave is received at a parabolic reflector antenna The wave passes through the aperture and is reflected and imaged in the focal plane A focal plane array attempts to reproduce in transmission the complex conjugate of the fields that were set up by the source If this is possible then an ideal beam shape would be obtained in the 9 direction The success of the array in producing the desired beam is dependent upon the complexity of the field produced by the imaginary source and how well it is sampled by the placement of array elements It may be noted that for plane waves arriving along the axis of rotation of the reflector the shape of the fields in the focal plane is given by an Airy function containing a sharp This field is sampled well using a single feed that produces a spherical phase front However when large scan angles 0 are considered the focal plane fields become more complicated and are inadequately sampled by a Single feed A loss in gain and an increase in sidelobe levels is the result If low sidelobe levels and higher gain is desired it is necessary to increase the sampling of the fields and therefore to set up an array feed An antenna with the combination of array feed and reflector is called a hybrid antenna Most authors who build hybrid antennas use a large number of elements and build planar arrays This is seen frequently in satellite feed desig
8. to read Set the program i e 1 05 p m today
9. 6 2 feet the phased array shows a marked improvement in comparison with the single feed Main beam shape remains identical to the focus single feed but the gain is now reduced to 49 0 dB a loss in gain of 2 6 dB The nearest sidelobe is about 17 dB down from the peak At this offset the use of a single feed gives a broader beam and higher sidelobes The sidelobes for a single feed are only 11 5 dB down from the peak The beam is now scanned to 2 3 degrees With a 10 ft offset the main beam shape is still retained but the gain is again decreased and the nearest sidelobe has risen The gain is now reduced to 47 3 and the nearest sidelobe appears at 15 1 dB down The beam is now scanned 3 65 degrees off axis For further offsets the beamshape broadenes and the sidelobes rise very rapidly This can be seen on the plot of Figure 4 For further offsets only marginal improvements if any are evident when a comparison is made to the single feed 15 Discussion For the method of phasing used the beam of the 300 ft telescope is significantly improved up to feed offsets of about 10 ft This corresponds to a total scan angle of 2 x 3 65 anda total tracking time of 29 minutes If the sidelobe level was not crucial the offset could be extended perhaps two or three feet and the tracking time could thus be extended by about 6 minutes Using this method of phasing no appreciable increase in gain is seen However the beam shape of the focused singl
10. Check the time date v Set the program to run in the near future at 1305 timer i e 1 30 p m today vi Log off and get on with other things 22 In about a half hour check to see if the file timeout test has a second time in it If it has your program has ended and the output is contained in patout test If for some reason your program has bombed due to tampering with necdata f the diagnostics however few will appear in the file visual test which contains all printing that would have gone to the screen had you not used the at command Transfer the files to the MassComp You need to transfer the file back to the MassComp You could do this through VTRANS using a PC but Unix has its own transfer routines which often work much quicker Those routines are UUCP i ii iii Using UUCP to transfer times from Convex to MassComp You need to set up a subdirectory in an area to which UUCP can deliver your files That directory name I will call lawson On the MassComp type the following od usr spool uucppublic receive mkdir lawson chmod 777 usr spool uucppublic receive lawson This directory exists as of June 1986 If it still exists you can use it If it doesn t set up your own Note The last line made the directory read write accessible to everyone This is necessary for the delivery of your files Go back to the Convex and go to the directory which contains the files that you want to tran
11. It has been suggested that an array feed mounted in the focal plane of the 300 ft would improve the telescope s performance It is the purpose of this report to examine and discuss an array feed design intended for use with the 300 ft telescope I would like to outline the present problem discuss the theory behind the operation of the feed give an intuitive understanding of how it functions and detail the steps necessary for its analysis Extensive use has been made of the Numerical Electromagnetic Code 11 The code now installed on the Convex computer at NRAO Charlottesville was used to produce far field patterns of the hybrid antenna A separate program was used to desoribe the radiation pattern of the array feed The software which describes the feed pattern and produces data for the analysis will be described Included as well are several notes on file transfers between the Convex and the MassComp computers Although the analysis was carried out on the Convex in Charlottesville VA the display of data was done on the MassComp in Green Bank WV Such notes are useful if further analysis is to be done of this design The following work was carried out during the summer months of 1986 under the direction of Jim Coe at the National Radio Astronomy Observatory in Green Bank West Virginia Focal Plane Arrays for Hybrid Antennas Consider a point source an infinite distance away at an angle 0 measured with respect to the axis of
12. NATIONAL RADIO ASTRONOMY OBSERVATORY GREEN BANK WEST VIRGINIA ELECTRONICS DIVISION INTERNAL REPORT No 264 ANALYSIS OF AN ARRAY FEED DESIGN FOR THE 300 FT TELESCOPE PETER D LAWSON 1986 SUMMER STUDENT NOVEMBER 1986 NUMBER OF CoPIES 150 ANALYSIS OF AN ARRAY FEED DESIGN FOR THE 300 FT TELESCOPE Peter R Lawson TABLE OF CONTENTS Page be REPO GUC TION UR ae RV a 1 2 Focal Plane Arrays for Hybrid Antennas 2 Se Why use a Butler Matrix Nue Whe GSS ee owe 3 te The Butler Matrix cscs ce 39 993a ovi Sw NUR RC he S Sas 3 5 JTBulldling the Array 424549999 3 4 9 909 ad Sew eae 5 6 Phasing the Element Beams T T Evaluating the Performance of Hybrid Antennas 10 8 Describing the Feed Pattern for the Numerical Electromagnetic Code 12 05 RESULTS usui kn aC cs arp et ew OO TRES REC ie 14 10 DISOUSSIOD 1324949959 309 aa Se ee 15 LJ us OE wie NUN US RR 25 LIST OF FIGURES 1 Calculated Far Field Patters for the 300 ft Telescope Scanned with a Single Feed 17 2 The Element Feed Pattern 4 46593 994 4 4 9 99 OR We Seater 18 3 The Trial Run of Program necdata f to Produce the Field Pattern of a Phased Array Phased by a Butler Matrix 9 9 9 9 9
13. adiation pattern weighted by the array factor the inclination of the main beam to the array normalis dependent upon the interelement phase difference If signals are applied at all input ports a set of simultaneous orthogonal beams are generated since they are orthogonal the amplitudes and phases of the individual beams may be controlled independently The Butler matrix phases a linear array and thus all the orthogonal beams are linear array patterns The angular locations of the orthogonal beam peaks are important in determining the proper phase to apply to the input ports of the Butler matrix The beams produced by the Butler matrix are said to be orthogonal They are separated spatially so that their main lobes do not overlap above the half power points If a linear array fed by a Butler matrix is used as a feed then the beams will each be imaged onto separate but adjacent regions of the reflector aperture The angular position of the beams may be used to determine the center of the regions where the beans are imaged The phase distribution in those regions may be adjusted by controlling the phasing of the beams In this way aperture phase aberrations due to lateral feed displacement may be reduced Bs Linear Arrays The field pattern of an array of non isotropic antenna elements is the product of an Array factor and an Element factor The array factor is dependent upon the geometry of the array The element factor repres
14. array at an offset distance 2 Map the element beams onto the aperture through raytracing The location of the array center defines the origin of the ray to be traced The origin of the ray is located with respect to the vertex of the main reflector and is given by X Y Z where 0 Y Ay and Z f Ay is the offset distance from the focal point and f is the focal Length of the parabolio main reflector The direction of the ray is given by the beam angle In the convention used by the raytracing program that vector would be 0 sin Op cos Op This may be thought of as a vector originating at the intersection of the ray and main reflector and pointing towards the feed center A call to the subroutine trace yields the aperture coordinates x y and the path error measured with respect to the optical path length f D 2 4f 3 Phase the beams to correct for aberrations There are three ways which have been tried to correct for phase errors i primary coma ii all coma terms and iii residual phase errors after a least square fit i Primary coma is described by Ruze 4 and is given by 3 a s coso 4 3 where and are aperture coordinates f the focal length Ay is the offset of the feed and A is the wavelength ii The above equation comes from a more general expression 4 written as follows DUM where 2 sing a m d eee 1
15. be determined by the NEC reflector code 11 12 This program uses a combination of Aperture Integration and the Geometrical Theory of Diffraction to calculate beam patterns It will accept any feed pattern with a well determined phase center and is able to account for aperture blockage and strut scattering It assumes that a parabolic reflector is used and that the feed is located near the focus See item iii in the discussion We could use this code in two different ways 1 If we are able to determine the complex excitations of the array elements then each element may be examined separately in combinations with the reflector to produce a far field beam The total far field beam is then the sum of all far field beams produced by the element reflector combinations 2 If the reflector is in the far field of the array then as viewed from the reflector the array has a well defined phase center The far field pattern of the array therefore may be used as a feed pattern B Which method to use In order to use the first method the complex element phasings must be determined This would involve working through the Butler matrix to determine the phasings contributed from each input port The contributions from each port must then be summed at each element Each element is then used separately with the NEC code to obtain a far field pattern The total field is obtained only after all feeds have been treated This method is lengthy and re
16. center of the coordinate System is located at the center of the array Variables for the feed description What follows is a brief description of the array feed pattern as it is presented to the NEC program The program requires numerous input variables to be defined These variables are indicated here Although the array factor is rotationally symmetrio about the y axis the product of array and element factor is only symmetrio by reflection about the y z plane A piecewise linear feed pattern is to be used the feed is linearly polarized the output is in dB and as noted before the symmetry is about the y z plane y axis The polarization angle of the pattern relative to the x axis is 45 LLFD TRUE LCP FALSE LDB TRUE ISYM 3 TAU 45 0 The feed pattern is sampled and in general the feed is not located at the focus NHORN 0 LFOCUS FALSE 13 The offset of the feed is along the y axis and in the focal plane DXS 1 0 DXS 2 Ay DXS 3 0 The input pattern is described in planes of constant For y axis symmetry 905 590 all that is required 15 planes is all that the program allows and so 15 are used here NPHI 15 In each plane of constant the field is described at up to TT locations amplitude and phase 08685180 for all symmetrics TT points are used here with 005909 N2 T77 The output patterns of most interest lie in the 909 plane This lies along the y axis and here positive 0
17. e feed is preserved up to an off axis scan of about 3 7 and the sidelobes due to coma and other aberrations are suppressed to lower than 15 dB down from the main beam Beyond a scan of 5 the beam shape has already severely deteriorated and this method of phasing only worsens the beam I believe that better results may be obtained if an alternate method of phasing is adopted for larger scan angles The success of this array design is wholly dependent upon the phasings chosen and it is quite possible that a better method of phasing may be developed for large scans These results represent only one method of phasing 16 Why does the array not work better i If the reflector is not truly in the far field of the array then the far field patterns as derived here do not accurately represent the hybrid antenna performance The reflector is not clearly in the far field by an order of magnitude and this may affect the results ii The NEC program perhaps does not accurately represent the far field pattern for large scans The program allows for an offset feed and yet suggests that the feed be near the focal point If this is the case then we may have underestimated the antenna performance at large scan angles iii The focal plane field distribution set up by a point source an infinite distance away at a large scan angle is perhaps insufficiently sampled by a linear array It may be that a planar array is needed for proper com
18. ents the far field pattern of a Single element in that array The Array factor The Array factor of a linear array of N equally spaced elements is 1 joo jv 12 j N 1 E E e l e e T e 1 where a is arbitrary phase reference is the magnitude of the field at each element assumed equal and y is a geometrical pathlength dependent upon the element separation d and the element phasings 8 I 27 _ 2 D d sind sino a 2 Equation 1 ean be rewritten in the following manner jo j N 1 y 2 e 0 sin Ny 2 E 3 sin y 2 Since a is an arbitrary phase reference it may be set to N 1 y 2 The resulting array factor is E Sin Ny 2 sin y 2 4 For antenna gain calculations the magnitude of the field is of no consequence if more power is radiated the gain will not change and therefore the E term has been dropped The Element factor An analytical function has been chosen to represent the Element factor It is given as follows l 5 BE 2 xc 1 0 where A and n are parameters which shape the function This was chosen to approximate the pattern of a cavity backed crossed dipole A 0 78 n 5 0 A comparison between this function and an averaged E and H plane field patterns of the actual element is shown in Figure 2 The actual element is a cavity backed crossed dipole designed for use at 400 MHz B Linear Arrays Fed By a Butler Matrix As the a
19. ersity ElectroScience Laboratory Columbus Ohio December 1982 Available through S Srikanth at Green Bank WV 26 12 Chang Y C Analysis of Reflector Antennas with Array Feeds using Multi Point GTD and Extended Aperture Integration Technical Report 715559 3 March 1984 Contract No NAS1 17450 NASA Langley Available throughS Srikanth Hybrid Antenna Design 13 Rudge A W and Withers M J New Technique for Beam Steering with Fixed Parabolic Reflectors IEE Reflector Antennas ed Love Vol 118 pp 857 863 July 1971 14 Browning Adatia and Rudge An Aperture Phase Compensation Technique IEE or IEEE conference proceedings 15 O Brien Shore Paraboloid Scanning by Array Feeds IEEE APS 1322 467 16 Assaly Ricardi A theoretical Study of aMulti Element Scanning Feed System for a Parabolic Cylinder IEEE Trans Antennas and Propagation Vol 14 No 5 September 19660 trs Hung Chadwick Corrected Off Axis Beams for Parabolic Reflectors 1979 IEEE International Symposium Digesta Antennas and Propagation Vol 1 18 Mrstik A V Smith P G Scanning Capabilities of Large Parabolic Cylinder Reflector Antennas with Phased Array Feeds IEEE Trans on Antennas amp Propagation Vol AP 29 No 3 May 1991 19 Hung C C Mittra R Secondary Pattern and Focal Region Distribution of Reflector Antennas Under Wides Angle Scanning IEEE Trans Antennas amp Propagat
20. f to produce the field pattern of a phased array phased by a Butler Matrix Qe de de e de k e k de de e e dee de he dee He He de dede dece dede kok He cke He de dede k R R Ro kO R K RR k k k kk he dede e de kR oko k dede fe debe dex NECdataMaker C Ck de dese debe dee dede dese dee e de hk ke k R dee R KO ee he KOK e de KO k K de dede dee S k k ee fe k k e de kk k dee de dede de ek dede This program is used to set up a feed pattern for the NEC reflector program The feed pattern describes an eight element phased array which is phased to correct for aperture phase errors arising from lateral feed offsets The output is a file DIN which is used by the NEC program to calculate the far field pattern of this Hybrid Antenna This program has been set up for use with the 300 ft telescope at Green Bank The focal length of the main reflector is 127 000 feet The Diameter of the reflector is 300 000 feet The wavelength used is 66 667 centimeters The corresponding frequency is 0 450 Ghz Do you wish to prepare data for 1 NEC program or 2 PLOTP routines Input the offset from the focal point feet 2 Do you want to consider 1 A single Element feed or 2 An Array feed Do you want to include the effect of non isotropic array elements y 1 n 0 Do you wish to correct for 1 All Abberations or 2 Coma 3 Residuals of a Least Squares fit to the Phase errors in the Aperture 3 How many points do you want along a cut
21. ion Vol AP 31 No 5 Sept 1983 Miscellaneous 20 Taylor J R An Introduction to Error Analysis Univerisity Science Books Mill Valley California 1982 pp 153 157 21 Rudge Electronically Controllable Profile Error Compen sation Proc IEE Vol 117 No 2 Feb 1970 22 NRAO Engineering Memo 144 Patrick Crane October 1981 23 Forsythe G E Malcolm M A Moler C B Computer Methods for Mathematical Computations Prentice Hall Inc Englewood Cliffs New Jersey 1977 pp 182 187 Title page Page 2 Page 7 Page Page Page Page Page 8 10 12 14 21 ERRATA to Electronics Division Internal Report No 264 ANALYSIS OF AN ARRAY FEED DESIGN FOR THE 300 FT TELESCOPE Peter R Lawson 3e Name is Peter R Lawson Second paragraph last sentence change to read lt beam shape could be transmitted in the 9 direction Fourth paragraph add word and If we are given the origin of the ray and the unit vector ii change can to and as follows The first term is linear in and causes Second paragraph sentence in parentheses change iii to ii as follows See item ii in the discussion Fifth paragraph remove y axis Sentence would then read A piecewise linear feed is about the y z plane Third fourth and fifth paragraphs should be one paragraph Second line from bottom of page Remove the comma Appendix A 3 v change
22. l loss and would present a significantly larger aperture blockage The total array of 8 elements would be 7 spacings long or 2 66 meters from the centers of the furthest elements Using eight elements the beam directions as produced by the Butler matrix are shown in the following table Beam n Angle Beam Directions 4 49 969 5332199 2 19 16 uu 6 28 1 6 28 2 19 16 3 33 19 H H9 96 We have now described the array and the fields it produces In order for it to work as part of a hybrid antenna we must determine the phasings at the input ports to correct for lateral feed displacement Phasing the Element Beams Since we have decided not to amplitude weight the inputs we have only the eight input port phasings to contend with If the reflector lies in the far field of the array then we may make some simplifications 12 The far field begins D J away from the array D is the largest dimension of the array 47 and A is the wavelength in use 66 ems The far field thus begins about 10 meters from the feed or about 30 feet Since the focal length 127 ft of the reflector is more than four times that distance it is safe to say that the reflector is in the far field The array thus has as viewed from the reflector a well defined phase center It may be moved as if it were a single feed and the element beams appear to originate from the center of the array If an analytio expression is t
23. mplitudes and phases of each beam may be controlled independently we have as a total pattern N 2 jo D a e n sin Ny 2 n 0 e sin y 2 N N 2 where a and are respectively the applied amplitude and phase weights The peaks of the individual beams appear at 9 sin 2 ie Aly 255 EN 2 P n 2nd Building the Array Feed Rudge suggests that a good choice of element spacing is 21 where sin 6 and 6 is the angle subtended by the by the reflector rim observed from the focus and measured from the axis This choice of spacing excludes the formation of grating lobes over the angular spectrum subtended by the reflector from the focus Rudge lists other benefits as well The 300 ft antenna has a focal length of 1525 inches 22 and a diameter one would guess of 300 00 ft The depth of the reflector is thus with z r Hf 44 26 feet We now can find 61 19 and 2sine 1 75 So without any loss of accuracy we may write that d 7 The phased array feed is to be designed for operation in the region of 400 500 MHz This would give us at 450 MHz a wavelength of approximately 66 67 ems array element spacings for this would then be 38 10 cms An eight element linear array was chosen If a Butler matrix is to be used the number of elements must be a power of 2 Butler matrices with 16 elements the next possible are much more difficult to build incur more signa
24. n for broadcasting In such cases there exist optimal filtering algorithms 17 which will phase and amplitude weight the elements if the focal plane field is known for a given offset angle This approach however is impractical when only a small number of feeds are considered and the beam structure does not resemble a banana republic The design being considered will use a linear array of only eight elements to sample the aperture fields It has been assumed that since the off axis scan is in only one direction that a linear array in that direction would provide adequate sampling A Butler matrix is to be used to phase the array This takes advantage of the relationship discussed in a paper by Rudge and Withers 13 and greatly simplifies the control of the array Why use a Butler Matrix If the focal plane fields can be determined for an off axis source then in order to correct for aberrations a focal plane array must attempt to recreate the complex conjugate of those fields A Butler Matrix will simplify this procedure under the proper circumstances There exists a Fourier transform relationship between the aperture fields and the focal plane fields 13 14 The relationship is valid for aperture fields from off axis sources if the transform planes are suitably defined 13 The Butler Matrix operates as a microwave analog of a fast Fourier transform device 1 6 9 If the focal plane fields are sampled by an array of element
25. o be used for the phasings i e an expression for coma or if the correction is to be done by pathlength error from feed to aperture we need to know where in the focal plane the feed lies and where in the aperture the element beams are imaged If the wavelength is much smaller than the curvature of surface of the reflector then geometrical optics is applicable and we can use raytracing to map the beams Raytracing is hinted at in 14 and it is used here as the simplest manner of determining the phasings If we are given the origin of the ray the unit vector describing the ray s direction then a computer program can be used to reflect the ray from the main reflector map it onto the aperture and determine the pathlength of the ray TRACE is such a raytracing program TRACE is a simplified version of RAYTRACE RAYTRACE was written at the VLA by Peter Napier and was intended to study shaped subreflectors of Cassegrain antennas for the VLBA project I have removed RAYTRACE s amplitude calculation added my own intersection routine using FMIN 23 for a Golden Search method and removed the problem of ray s propagating in the y O plane have of course removed the subreflector entirely and calculations are performed for only a single ray TRACE is a subroutine The phasings of the input ports is the most crucial aspect in the design of this system The following is a description of how the phasings are determined 15 Position the
26. pensation beyond a certain scan angle iv The simplicity of the phasings with a Butler matrix may not be sufficient for large scans with a focal plane array The method of phasing and indeed the use of the Butler matrix was chosen because of the Fourier transform relationship between aperture and focal plane fields This focal plane must be redefined for large scans For large scans it no longer lies in the focal plane but is about one foot removed from it This may affect the usefulness of the phasings 17 FIGURE 1l Calculated Far Field Patterns for the 300 ft Telescope Scanned with a Single Feed TTT X 6 2 feet b Feed displacement 0 0 feet a Feed displacement 23 0 feet d Feed displacement 15 0 feet c Feed displacement The feed pattern is that of the single feed given in Figure 2 b 18 FIGURE 2 The Element Feed Pattern CAVITY BACKED CROSSED DIPOLE POWER PATTERN dB 90 00 80 60 40 20 0 Degrees a The cavity backed crossed dipole AVERAGED E AND H PLANE PATTERNS b A raised cosine approximation ELEMENT POWER PATTERN SITINI MAITIN ITTUN iiA 5 function dB e RAISED COSINE FUNCTION NOTE The two patterns are very closely matched out to the edge of the reflector at 61 At wider angles the raised cosine approxima tion is more tapered 19 FIGURE 3 A trial run of the program necdata
27. quires the the NEC code to be called numerous times for one total field calculation The second method is describedinareport concerning development work with the NEC program 12 If the reflector is located in the far field region of the array feed a straightforward two step procedure be used to calculate the reflector pattern with an array feed very efficiently The first step is to input the information associated with the array feed such as the element pattern and location then the far field patterns of the array feed are calculated and stored The second step uses these far field patterns as though it 11 was a single feed to calculate the radiation patterns of the reflector This two step procedure calculates the reflector patterns very efficiently because the algorithm is applied only once for each aperture point As it has been shown that the reflector is in the far field the second method would appear to be the most efficient It was therefore used in this work 12 Describing the feed pattern for the Numerical Electromagnetic Code If we are to use the two step procedure then we must calculate the far field pattern of the array The array pattern can be calculated once the phasings are known It is important to understand the geometry of the input array pattern to be sure that the output from the code is correct The geometry of the feed pattern is as follows 9 The array lies along the y axis the
28. s controlled by a Butler Matrix then the output from the matrix will resemble the fast Fourier transform of those fields The output from the Butler matrix therefore represents the twice Fourier transformed aperture field distribution A field distribution that is twice Fourier transformed will remain unchanged except for a sealing factor If the aperture fields had a uniform amplitude distribution then the fields as transformed by the matrix will also have a uniform amplitude distribution If a Butler Matrix is used then we do not need to amplitude weight the signals in order to achieve conjugate field matching in the focal plane All the control that is required is input port phasings to the Butler Matrix These phasings will then correct for offset feed displacement The Butler Matrix A very good description of the Butler matrix be found in the paper by Browning Adatia and Rudge 14 The Butler matrix is a passive and theoretically lossless orthogonal beam forming matrix whioh possesses 2 input and output ports and is capable of producting a set of 21 simultaneous orthogonal beams in space when coupled to a uniform array of feed elements In the transmit mode a signal applied at an input port produces a uniform amplitude distribution across the output ports but with an interelement phase difference which is dependent upon the particular input port This results in a far field beam which is composed of the elemental r
29. sfer The example here will transfer two files named filel file2 On the Convex uucp file file2 nraogba usr spool uucppublic receive lawson After a few minutes on a good day the files will appear on the MassComp Log into the MassComp and retrieve the files from the subdirectory you had set up mv usr spool uucppublic receive lawson filel users students plawson filet You are now ready to slice and dice the files in preparation for their plotting 23 Making Antenna Plots from PATOUT Files You now have a file PATOUT on the MassComp computer that contains the data describing the far field pattern of the antenna You would like to make a hardcopy of the pattern Go to room 232 of the Jansky Lab and sit down at a terminal The graphics terminal would be a good choice Get into a directory on the MassComp that contains your file renamed to anything other than PATOUT and an executable version of read f I will assume that all you have is a file named patout test and read f i Remove all files that rm PATOUT xx ydb f g would be created by this procedure ii Compile read f so that read f an executable version is available iii Copy the file of interest cp patout test PATOUT into the file PATOUT iv Run the read program a out Choose as an option 1 The Total field then 2 A 90 cut e The output is xx1 and ydb1 v Use the plotp routines to create the plot file
30. ttern is that of the array feed phased by a Butler Matrix 21 APPENDIX A RUNNING THE NEC PROGRAM AND DISPLAYING RESULTS You would like to produce an antenna pattern using the NEC reflector code and plot the data in a convenient manner The NEC code runs on the ConVex computer in Charlottesville and you are in Green Bank on the MassComp computer 1 You have an account on the Convex with an executable version of the NEC program and programs to produce input for it NECDATA F and TRACE F You also have an account on the MASSCOMP You have access to the Convex through a terminal attached to the Digital Data Switoh Create data for the NEC code by running an executable version of NECDATA F and TRACE F fo necdata f trace f a out The program in execution is somewhat self explanatory The output is named DIN An example run is given in Figure 3 Run the NEC code Although you may do this in interactive mode it is far faster 15 or 20 minutes if you use a command file and the at command i Move DIN to din test 4 mv DIN din test ii Set up the following command file using an editor and call it timer rm PATOUT DIN PATIN visual test patout test patin test timeout test cp din test DIN date timeout test date visual test nec visual test date visual test date timeout test rm DIN mv PATOUT patout test mv PATIN patin test iii Make it executable chmod x timer iv
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