A Matrix fed Circular Array for Continuous Scanning
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A matrix-fed circular array for continuous scanning
Sheleg, B.
رسالہ:
Proceedings of the IEEE
DOI:
10.1109/PROC.1968.6778
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2016 PROCEEDINGS IEEE, OF THE VOL. 56, NO. 1 1 , NOVEMBER 1968 Scanning of the antenna beam is accomplished in an inSYSTEM APPLICATION AND PERFORMANCE cremental manner. A totalof 39 steps are required to move The electronically scanned antenna array is utilized in an the beam through the 100" angular range. Each step corairborne microwave radiometer imaging system. As shown responds to a half-power beamwidth interval. The time rein the block diagram of Fig. 8, this system consists of four quired for a complete scan is adjustableto one or two basic parts: 1) the antenna with its associated drive and seconds. This includes the time required to reposition the control network, 2) the Dicke switching network, including of the 39 positions and the dwell, or integrabeam to each the calibration and control subsystem, 3) the receiver, and tion, time at each position. 4) the data processing and display system. Typical of the data that have been obtained with this sysElectromagnetic energy emitted from the surface of the tem by the NASA Goddard Space Flight Center are those earth is received by the array antenna. The magnitude of shown in Fig. 9. This radiometric map of the Southern this energy is proportional to the radiometric temperature California coastal area was obtained from an altitude of observed. By comparing this energy with that emitted by a 37 OOO feet. The black to white span on the grey level scale known calibration standard, normally a hot and/or cold represents a temperature range of 228°K to 290°K. reference load, it is possible to determine the radiometric temperature of the body seen by the antenna.A twodimensional map of the radiometric temperature of the CONCLUSIONS earth is therefore generated when the antenna beamis A 19.35-GHz electronically scanned two-dimensional scanned as the vehicle moves. phased array has been described in detail. It has been shown The radiometer receiver is a solid-state superheterodyne that this configuration is compatible with the overall airdouble sideband re; ceiver. Included in this receiver are a borne microwave radiometer system requirements. The balanced mixer, solid-state local oscillator and multiplier, phased array described here has a high beam efficiency, can synchronously tuned I F amplifier, square law detector, be scanned rapidly, is volumetrically compact and light in preamplifier, and synchronous detector. The overall noise weight, consumes little power, and can be flush-mounted. figure of the receiver ranges between 6.0 and 7.0 dB. The The performanceof the array, as well as that of the radiommeasurement accuracy and sensitivity of the receiver are eter system in which it is used, has also been discussed. 2.O"K and 0.7"K, respectively. Data processing is performed by a digital data acquistion ACKNOWLEDGMENT system which produces a computercompatible tape output. A real-time grey level display, an analog readout, and a Appreciation is extended to R. Bowers whoassisted in the digital printoutare also generated simultaneously. The collection of a large portion of the data presented herein. tape output can be processed to give either a grey level dis- Acknowledgment is also made of the efforts of the many play or a color presentation, the latter offering almost a others who have designedand assembled the overall radiomsixfold increase in display resolution. eter system. A Matrix-Fed Circular Array for Continuous Scanning BORIS SHELEG Abstract-TheButler-matrix-fedcirculararray w l l i form a f d and calculated patterns Finally, a synthesis procedure is described for deradiation pattern when the proper current distributiw is established w the termining the matrix inpat currents repaired to attain a prescribed current inpas to the matrix.Further, this beam ean be scanned through 360" by distribution 011 the array. changingonly~phasesoftbematrivinputcorrea~jlstaswithalioenr array scannhg is accomplished by varying the phases of the element currents. Tbis operation was experimentallydemoostrnted with a 32dipole INTRODUCTION circular array and reasooable agreement was obtained between the measured A NTENNAS consisting of radiating elements arrayed on a circle have been studied and have been used Manuscript received April 1, 1968; revised July 31, 1968. for many years, but recent developments in switchThe authoris with the Microwave Antennas and Components Branch, ing and phase shifting have led to a renewed interest in Electronics Division, NavalResearchLaboratory,Washington, D. C. them. The appeal of the circular array is that, because ofits 20390 SHELEG: MATRIX-FEDCIRCULARARRAYFORCONTINUOUSSCANNING 201 7 symmetry, it can be used to scan a beam in discrete steps 3 through a full 360" without the variations in gain and pattern shape that occurwhen four linear arrays areused, each scanning through a single quadrant. The purpose of this study was to determine some of the possibilities and also the limitations of scanningwith circular arrays and, in particular, to demonstrate the use of the Butler matrix in feeding the elements of the array. The idea of using a Butler matrix for this purpose is due to Shelton [l], who showed that it permitted the formation of a narrow radiated beam that could then be scanned essentially like the beam from a linear array, by the operation of phase shifters alone. Theoperation of a Butler-matrix-fed circular array (multimode array)is fist described heuristically in terms of "modes" and then, more satisfactorily, by considering the distribution of currents impressed on theradiating elements by the matrix. In addition,calculations were made to show how the radiation patternof the multimode arrayvaries as it is scanned continuously, rather than in discrete steps. Fig. 1. Coordinates for a continuous cylindrical sheet of vertical current elements. The experimental portionof this program was performed at L-band with acircular array of 32 dipoles around a con- antennas of interest (e.g., dipoles approximately oneducting cylinder. Sidelobe level control was shown by using quarter wavelength over a reflecting cylinder) all the modes different amplitude tapers over the illuminated portion of make contributionsin the plane of the array. the array. Equations (1) and (2) demonstrate that a change in relative amplitude and phase of each current mode results in a OF OPERATION THEORY corresponding change in the corresponding pattern. mode The principles involved in scanning a multimode array (this can be done by controlling In). This is nearly identical are mosteasily seenby considering not an array, but a conto the formulation for linear arrays. A linear array of tinuous distribution of current. When this distribution is 2N 1 isotropic elements with interelement spacing a has expressed as a Fourier series, in general idnite, each term a radiation pattern given by represents a current mode uniform in amplitude but having N a phasevarying linearly with angle.The radiation pattern of E(u) = And" n= - N each mode has the same formas the current mode itself, and these pattern modes are the Fourier components of the where u = ka sin 4, 4 is the angle off-broadside, and A, is radiation pattern of the original distribution. The expres- the current on the nth element. Equations (1) and ( 3 ) show sion of the radiation pattern as the sum of modes of this the similarity of the patterns of the circular current sheet form is then seen to be analogous to the summation of the and the linear array, with the role of the current mode in contribution made to the pattern of a linear array by its the circular array taken by the element in the linear array. be exelements, so the operation of a multimode array can One difference is that for the circular array the argument plained by referring to an equivalent linear array. is 4, and for the linear array it iska sin 4. A second difference Referring to Fig. 1, consider a current .distribution I ( a ) is that equally excited elements in a linear array makeconto be the sum of a finite number of continuous current tributions of equal magnitude to the radiation pattern, with - N I ~I N . The radiation pattern for modes Z,@ but equally excited current modes donotcontribute 8 = x / 2 , is then given by equally, because their elevation patterns are not identical. N This results in differences in their strength of contribution in the plane of the antenna. For example, if in the antenna n= - N being considered (Fig. 1) it is desired that the pattern modes where the C , are complex constants given by be equal in magnitude and be in phase at 4 = 0, the excitations of the current modes must be [from (2)] + 2 1 with K a constant [2]. There is a one-to-one correspondence between the current modes F and the far-field pattern modes d*, but note that their relative phasesarenot necessarily the same. Another property peculiar to circular Its radiation pattern is then given by arrays with isotropic radiators is that some modes can be N made to give zero contribution in the plane of the circle by E(4) = &*, the selection of a proper diameter. However, for practical n= - N 1 2018 PROCEEDINGS OF THE IEEE, NOVEMBER 1968 which may be summed to give the pattern characteristic of a uniform array sin' LENGTHS , 2 The beam can be scanned (in theory) by a linear variation of the phases of the mode excitations, just asthe beam from a linear array is scanned by a linear variation of the element phases. If the phase difference between adjacent modes is q50 radians [multiplying I, of (4) by e - j & O ] , the resultant pattern is expressed as I BUTLERMATRIX I RIABLE PHASE 0 Fig. 2. Schematic diagram of a scanning multimode array. which is the original pat.tern scanned $o radians. Although the foregoing analysis was based on the particular example of a cylindrical sheet of infinitesimal current elements, the same reasoning applies to any circular antennahaving similar pattern modes. The only difference in the analysis would bethe particular relationship between the phases and and their respective current amplitudes of the pattern modes modes. Various antennashave made use of the multimode principle in their operation [3]-[5] but, as has been mentioned, Shelton discovered that it waspossible to excite simultaneously and independently all the modes, both positive and negative, from zero to N/2 by connecting asingle ringof N elements to the outputs of a Butler matrix. That this is true is evident from the definition of the Butler matrix [6]. This matrix is a lossless, passive network having N inputs and N outputs, where N usually is some power of 2. The inputs are isolated from one another, and asignal into any input results in currents of equal amplitude on all the outputs with phasevarying linearly across the eIements. Specifically, if N iseven and the Kth input port is energized (K=O, k 1, +2, . , f( N - 2)/2,N/2), the difference in phase between adjacent ports is 2xK/N and the total phase variation around a circular array connected to the Butler matrix would be 2xK, which is the Kth mode. Hence, with the Butler matrix we may establish on the array the N current modes corresponding to K=O, l , . . . , _+ (N-2)/2, N/2, and, because the input ports are isolated, the modes are independent. It should be noted here that there are Butler matrices that do not satisfy the definition given above and that cannotbe used unmodifiedin a multimode array. These networks establish, across their outputs, linear phase progressions whose total variations are odd multiples of x radians. A matrix of this type can be changed to one having the proper modes by adding fixed phase shifts to all the output ports; if the N outputs are labeled J = 1, 2, . . , N , the phase shift applied to the Jth output is Jn/N. A schematic diagram of a scanning multimode array is -- * shown in Fig. 2. The desired phase and amplitudedistribution is established over the inputs to the Butler matrix by fixed phase shifters and a corporate structure. Once the pencil beam pattern is formed at some azimuth angle, it is scanned just as in a linear array; the mode amplitudes are held fixed, and a linear phase progression is set up on the mode inputs by operating the variable phase shifters. PATTERN CALCULATION Thus far, the explanation of a multimode arrayhas been of the form based on the summation of pattern modes dK4.The summation couldbe exactly acheved with a continuous current sheet, or it could be approximated arbitrarily well with a ring array having a sufficient number of elements. For arrays fed from a Butler matrix, as many current modes can be established as there are elements, and it is not obvious how many of these modes have farfield patterns that fit the e''+ form sufficientlywell. For example, in an N-element array the highest order mode (K=N/2) has an element-to-element phase variation of x radians. By symmetry, its pattern mustbe scalloped, with N nulls and N peaks; therefore, it obviously cannot be used as a uniform mode. To determine the quality of the modesestablished by the Butler matrix, a series of calculations was made, both of mode patterns and of pencilbeam patterns obtained by summing different numbers of modes. The array consisted of 32 elements, and the interelement spacingwas varied from 0.4 to 0.61. Two different element patterns were used, one was an approximation to the measured pattern of the elements that were actually used (dipoles around acylinder) and the other was the exact pattern of an infinitesimal vertical current element in front of a conducting cylinder [7].' Also, for a more detailed description, see R. H. DuHamel, "Pattern synthesis for antenna arrays on circular, elliptical, and spherical surfaces," Elec. Engrg. Research Lab., University of Illinois, Urbana, Contract N6-ORI-71: Task 15, Tech. Rept. 16, May 1952. FOR CONTINUOUSSCANNING SHELEG:MATRIX-FEDCIRCULARARRAY O - 1 -&, . CILCU.TED ,a.i , , WRlTUDE W A S CVCULaTED W I S E i; ;z "----.,., ~ 2019 -10 I 1 0 0 1 2 0 '. I 80 -20 I20 140 140 160 I60 a. 163 -30 0 I 2 3 4 5 6 7 8 9 10llH25 -3 0m 0 _I /2 3 4 5 6 7 8 910111125 163 -30 0 I 2 3 (a) Modes 0 through 8 (b) Mode 9 4 5 6 7 8 9 Wllll25 ( c ) Mode 10 -1OV'i .mL 140 160 180 -30 0 I 2 3 4 5 6 7 8 9 w111125 (d) Mode 1 1 -30 0 I 2 3 4 5 6 7 8 9 10llll.23 AZIMUTHAL ANGLE(OEGQEES1 -30 0 I 2 3 4 5 6 7 8 9 01111.23 -30 0 I 2 3 4 5 6 7 8 9 Wllll25 (e) Mode 12 ( f ) Mode 1 3 0 I 2 3 4 5 6 7 8 9 W111125 0 I 2 3 4 5 6 7 8 9 1011ll25 AZIMUTHAL ANGLE'(DEGREES1 AZIMUTHAL ANGLE(DEGREES) (g) Mode 14 (h) Mode 15 ( i ) Mode 16 Fig. 3. Calculated mode patterns for a 32dipole circular array compared with the ideal mode patterns. The approximate patternof the dipole in front of a cylinder is given by 4 4 ) = 81 + cos 4J), (8) where the phase was assumed constant in azimuth when referred to a point one-third the distance from the cylinder to the dipole. This assumption is reasonably good, at least in the unshadowed region. Mode patterns andpencil beam patterns computed using (8) were in good agreement with those obtained using the exact pattern of the vertical current element, and no results for the latter have been included. Consider, .as in Fig. 1, a circular array of radius R with N elementsequally spaced at aJ = J27c/N, where J = 1,2, . . . , N . Referred to the center of the circle, the relative space phase of the J t h element is (2aRli) cos (+-aJ), where only the plane of the array is considered. If the element pattern is A ( + - a J ) andthe current on the elementis the radiation pattern of the array is given by E(#,) = N 1 A,@JA(+ - a J ) 8 ( 2 n R / ~ ) c o s ( + - ~* v ) J= 1 (9) Mode patterns were calculated from this equation with the element pattern given by(8) and, for the Kth mode, acurrent are distribution given by A,= 1, +,=27cKJ/N.Results shown for a 32element array, forwhich the modes correspond to K=O, +1, +2, ..., f15, 16. The phase and amplitude of computedmodepatterns for a 32-element circular array (0.5Rspacing) are comparedwith ideal modes in Fig. 3. It is seen that all modes up to 10 are in sub- + PROCEEDINGS OF THE IEEE, NOVEMBER 1968 2020 TABLE I THERELATIVE GAINSAND PHASES OF THE PATTERN MODESOF A JZ-ELEMENT A R R A Y 1 Mode 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 I i ~ I Relative Gain (dB) 0.0 0.2 0.1 0.2 0.2 0.0 0.5 0.2 - 0.5 0.8 I I I ~ Relative Phase at 4 = 0 (degrees) I I I -0.5 0.7 3.5 5.1 5.6 5.6 0.00 0.74 7.51 14.63 29.27 44.63 63.06 91.93 115.35 144.56 - 168.45 - 128.07 - 105.74 -35.18 20.91 120.92 - 172.05 This current distribution may then be substituted into (9) to give the radiation pattern expressed as E(4)= N 1 [X B J=l K 1 &BK&'JK(~~IN) K . A(C#J- u J ) & ' ( 2 W A ) cm(4-a~) (12) It is perhaps evident from the symmetry of the multimode array that the pattern shape doesnot change if the beam is scanned by some multiple of27r/N, the anglebetween elements. If for example,the beam isto be scanned M(27r/N) radians, where M is an integer, the mode amplitudes B K are held constant but there must be a mode-to-mode phase difference of M ( 2 4 N ) ;hence, the phase of the Kth mode becomes j l K + KM(27rIN). When thisis substituted into (1 l),the current on the Jth radiating element is found to be A ,$*J 1 =- 1B f i K &'BK&'(M+J K(277IN) 7 K (13) showingthat the original current distribution has been moved, intact, M elements around the array. To show the formation of the radiation patterns as the modes are superimposed, patterns of a 32-element array with 0.54 spacing were computedfrom (12)using the cardioid element pattern of (8). With uniform excitation of the Butler-matrix inputs (all B K = 1) and with phases corresponding to those in Table I, the modeswere successively excited and at each stage the radiation pattern was calculated, giving the series of patterns shownin Fig. 4. It can be seen that the beam narrows as more modes are added and that, until modes &- 11 are reached, the far-out sidelobes decrease as theywould if the modes were perfect. This improvement ceases as the higher modes are added; when all the modes but the 16th are included, the pattern is noticeably worse than when just the modes up to 10 are used. The two patterns using modes up to 10 and up to& 15 are compared in Fig. 5 with the patterns thatwould result if the corresponding numbers of ideal modes were summed. The agreement, when allthe modes areused, is particularly poor in the region of the far-out lobes; when the less uniform modes (1 1 x 15) were not used, the patterns for the discrete and continuous cases agreed everywhere to within 0.5 dB. It is interesting to note that about 95 percent of the total power is radiated by the 13 elements nearest the direction of the beam and that the currents on 11 of these differed in phase from the cophasal condition by less than 20". The sidelobes from alinear array canbe lowered bytapering the amplitude distribution over the array, and,by analogy, the same shouldbe true for a circular array if the mode amplitude-distribution is tapered. With the phases again as 1 A~@J B &'BK&'KJ(~WN). (10) in Table I, a cosine taper was applied to the mode inputs f i K [i.e., B K = cos (Kn/32)], and the patterns were computed as If many input ports are simultaneously excited, the output modes were added successively. Fig. 6 is a comparisonof the currents may be added to give final pattern, when all the modes were used, with the pattern that would result if the modes were ideal. This shows A,&'J - 1 BK & ' S K & ' K J ( ~ ~ I N ) . (11) that the sidelobe level has indeedbeen reducedbut not to the f i K level that would be obtained with perfect modes. In this stantial agreementwith the ideal patterns, having at most a f 0 . 2 5 d B difference from a uniform pattern, with a maximum phase error of 3". Modes 14, 15, and 16 are poor approximations.Modepatterns were also computed for arrays withelement spacings of0.4 and 0.62. With 0.42 element spacing, modes up to f12 are close to ideal, and modes 15 deviate about as much as did modes f 14 for the array with 0.5-1spacing. For 0.6-2 spacing, modesup to *9 are good, and mode 12 corresponds to mode 14for 0.54 spacing. Table Ilists the relative gains of all the pattern modes for 0.5-2 spacing and also their relative phases at 4 =0 when the current modes are in phase at u,= 0 (i.e., at element 32). To form a narrow beam with its peak at C#J = 0, the pattern modesmustbeinphasein thatdirection; therefore, the phase differences between the modes must be accounted for, as shown in Fig. 2, by fixed phase shifts at the inputs tothe Butler matrix. The analysis of a circular array in terms of ideal modes is adequate for a qualitative description of its operation and does predict reasonably well the position and shape of the main lobe but not the structure of the sidelobes. For a more accurate estimate, the current distribution on the array must be determined, and the pattern must then be calcuthe N-elementButler lated from (9). Firstassumethat matrix has all the current modes in phase at the Nth element if the mode inputs are fed in phase; this means that for the Kth mode the Jth element has phase 27rKJIN. Then, if BKBBRis the current applied to the Kth input port, the resultant A Jd*Jon the Jth radiating element is given by * * * 1 * * FOR CONTINUOUSSCANNING SHELEG:MATRIX-FEDCIRCULARARRAY 0 . ' " ' ' 1 -I -10 L 20 L 202 1 iy,,,y , -30 L , - (b) 1 through + I w 01 ( c ) -2 through +2 I '/'\' ' , I I I (d) - 3 through $ 3 t ' -13 I w -a -30 -40 ( e ) - 4 through t4 - o (g) -6 through t6 Y ( f ) - 5 through +5 - r-7T--7 (h) - 7 through t7 L ( j ) -9 through +9 (i) - 8 through +8 .n O r - 7 T - 7 7 (k)-10 through +IO (1) - 1 1 through +ll I " ' ' ' A ' I ' "1 -13 -20 .30 -40 (m) -12 through +12 (n)-13 through +13 A " " ' 1 (0)-14 through t14 (p) -15 through + I 5 Fig. 4. Mode-by-mode buildup of the pattern of a 32-element array with uniform excitation of the modes. case more than95 percent of the total poweris radiated from the 9 elements closest to the beam andon these elementsthe currents differ from cophasalby at most 5". One of the distributions used in the experimental program was B, = cos2 (zK/40),which provided a 17-dB taper over the 31-mode inputs. To indicate how much the pattern shape couldbe expectedto change as the beam wasscanned, patterns were computed for various beam positions. Fig. 7 shows three patterns, one phased so that its peak is in the direction of element 32 ($J=O), the other two having the same amplitudedistribution over the modes but phased to scan the beam one quarter and one half, respectively, of the angle between elements. It may be seenthat, at least for this distribution, the pattern changes only slightly as the beam is scanned. Patterns were also calculated for different element spacings, elementpatterns,andamplitude distributions, but those shown satisfactorily illustrate the beam formation PROCEEDINGS O F THE IEEE, NOVEMBER 1%8 2022 0 -0 - -m 0 5 -M $ W t 2 -33 -40 -120- 1 8 0 -?a -150 -60 -30 AZIMUTHANGLE 0 ?o 60 ?a 180 (DEGREES) (a) S u m of modes -10 through t10 0 -10 -40 - 1 5 0 -?a -120 - 1 m -60 -30 0 30 60 IBO AZIMUTH ANGLE (DEGREES) (b) S u m of modes -15 through t15 Fig. 5 . Comparison of the patterns of a 32element array andof a continuous current sheet using 21 and then 31 uniformly excited modes. 0 -10 -m - APPROXIMATED MODES IDEAL MODES rn -x) - B w $ d -33 - d n, -180 - 1 5 0 -lx) -90 -60 -33 0 33 60 90 1 1 2800 1 5 0 AZIMUTH ANGLE (DEGREES) Fig. 6 . Comparison of the patterns of a 32element array andof a continuous current sheet using cosine amplitude taper on 31 modes. SHELEG:MATRIX-FED CIRCULARARRAY FOR CONTINUOUSSCANNING 2023 AZIMUTH ANGLE (DEGREES1 (a) One-quarter way between dipoles 32 and 1 0 -10 m 0 E 3 -20 x Y > + J L -30 -40 - 1 8 0 -150 -120 -90 -60 -30 0 60 I 20 I M AZIMUTH ANGLE (DEGREES1 (b) Midway between dipoles 32 and 1 01 I I AZIMUTHANGLE(DEGREES1 (c) Dipole on 32 Fig. 7. Patterns and the corresponding current distributions on a 32-element array for beams at O', 5.625', and 2.813'. The amplitude taper on the modes is B,=cos2(xK/40) with K=O, + 1, +2, . . . , 15. + and scanning and also indicate how the pattern differs from one based on the existence of perfect pattern modes. SYNTHE~IS OF APERTURE DISTRIBUTIONS It should now be evident that the radiation pattern of a circular array computedon the assumption thatthe pattern modes are perfect is not the same as that computed from the actual current distribution, and that a certain amount of cut-and-try is involved in determining the number of modes to use and in adjusting the phases of the modes to form a beam in a particular direction. Instead of picking the mode excitations, only to find that the corresponding current dis- tribution results in a poor radiation pattern, it would be preferable first to pick a current distribution having an acceptable pattern and then find to the mode excitations which will give these currents. That this is always possible was discovered by Davies [SI, who showed that any prescribed output currents can be achieved with a Butler matrix by properly exciting the matrix inputs. Consider an N x N Butler matrix with input and output ports labeled K and J , respectively. If the prescribed currents AJej*J,where J = l , 2, . . . , N are to be set up on the array, the N currents that must be applied to the inputs of the matrix are PROCEEDINGS NOVEMBER OF THE IEEE, 2024 COPHASALDISTRIBUTION FOR T H E BFAM AT ON T H I A m TABLE I1 5.625' WITH REQUIRED INPUTCURRENT$AND y FOR B w SCANNED TO 8.438' A N D 11.25' THE 1968 CURRENTDISTRESJTION Beam Position Input to Modes Mode Amplitude Phase (rad) ~ ~ T 1 + Ele- 1 merit + Phase dB - 4 -2.98853 0.00000 1 -I5 0.05014 -2.80781 -0.51926 2 - 14 0.16982 -2.60148 3 - 1.43457 0.31358 -13 -2.37450 4 -2.84185 - 12 0.43767 -2.09735 0.51999 5 -4.93675 -I1 -8.17489 6 -10 1 0.59752 - 1.76797 7 -1.42198 -9 ! 0.68904 - 14.02687 8 - 110.95878 -8 I 0.73786 -110.29151 -7 1 0.70416 9 IO - 108.42737 -6 0.63277 -112.01176 -5 0.49759 0.68746 II -4 -111.17657 0.23592 I2 -107,88319 0.17912 -2.74105 13 -3 -117.77163 1.78156 14 0.25706 -2 15 - 112.87704 0.25264 0.54328 -1 16 -117.61885 0 0.25664 0.41310 0.35481 17 -118.16084 1 I 0.41310 18 - 11 1.86473 2 I 0.25264 0.24785 19 3 0.25706 -1.29069 - 122.53436 20 -107,81624 4 I 0.17912 I -2.05383 21 - 114.45265 5 0.23592 2.34765 6 1.76738 0.49759 22 1 -116.41499 7 1.35404 0.63277 23 i -109.30689 8 0.93386 0.70416 9 -113.92446 0.63030 0.73786 IO 0.68904 0.44333 - 14.02684 0.29369 11 12 13 -2.84186 14 - 1.43458 15 4.51925 32 -0.00002 16 j l- 7 8 9 10 11 12 13 14 15 16 17 18 i ~ ~ ~ i I 2 3 4 5 6 I I 1 _ _L -3- i II L TI dB ~ 4- 1 ;FI 1 ' Ele- c - .- I 1 One-Quarter Way Between Elements 1 and 32 On Element 1 ' ment I 4.41432 39.47402 108.24662 -151.91152 -24.83651 124.58780 I -69.38130 9.40060 i -127.37128 -80.12002 103.52423 -75.03709 - 119.27306 34.95047 65.89978 -131.95122 - 136.67705 60.67050 43.74770 I - 112.96098 -75.31601 94.23270 -95.61509 - 108.60654 8.94868 -69.38122 124.58789 -24.83631 -151.91129 108.24684 39.47413 4.41439 I ~ ~ I Between Elements 32 and 1 19 20 21 22 23 24 25 1 0.0 L Phase I + 0.00000 -2.01691 -1.10324 -2.07344 -5.79880 - 10.95202 - 13.44224 - 13.49060 - 19.78507 -22.97828 -25.16028 -26.75804 -27.94438 -28.80676 -29.39541 -29.73847 -29.85107 -29.73843 -29.39536 -28.80673 -27.94435 -26.75802 -25.16029 -22.97834 - 19.78514 - 13.49063 - 13.44226 - 10.95202 -5,79880 -2.07344 -1.10324 -2.01692 1.30606 17.80973 64.83482 160.91891 - 80. I3033 43.41646 164.97679 -44.26421 147.62327 -27.73955 154.81247 -23.60801 157.42682 -21.90153 158.52920 - 21.22499 158,85470 -21.22460 158.52921 -21.90223 157.42611 -23.60789 154.81323 -28.73901 147.62316 -44.26440 164.97683 43.41665 -80.13017 160.91905 64.83485 17.80984 :ophasal Deviations 1.3 0.2 5.0 6.4 11.4 3.0 10.9 62.2 - - - - - 62.2 10.9 3.O 11.4 6.4 5.0 0.2 Element I 2 3 4 5 6 7 8 9 10 dB 0.00000 - 1.64249 - 1.45862 -2.17622 - 5.09892 -10.31497 - 18.95701 - 18.54252 -23.49W -26.36628 -28.37765 -29.86092 -30.96016 -31.75041 -32.27577 -32.56037 -32.61636 - 32.44693 -32.04448 - 3 1.39070 -30,45327 -29.17439 -27.45203 -25.07565 - 21.47069 -12.17991 -9.45066 -7.73339 -5.12229 -2.07351 -0.76244 -1.35198 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Phase IC i :ophasal Deviations 1.98974 28.35642 83.40610 - 176.63541 -48.91991 94.83752 -132.54333 - 39.69405 149.10857 -26.97267 155.27371 -23.31109 157,62730 -21.77114 158.60405 -21.19276 158.85068 -21.26605 158.62071 -22.04947 157.20708 -23.93888 154.29411 -28.62743 145.78916 -51.94113 143.16679 1.07559 -118.84582 135.92040 51.05834 9.49976 L - ON DIPOLE ONE-OUARTER WAY BETWEEN TWO DIPOLES MIDWAY BETWEEN TWO DIPOLES -0 - - K I i i I -180 -60 -I20 -150 -90 -3J 0 190 50 i 120 I80 AZIMUTH ANGLE (DEGREES) Fig. 8. Pattern of the 32-element array with a synthesized cophasal distribution and the pattterns when scanned to 8.44" and 11.25' N These currents are conjugate to those that would appear at the inputs if currents AJe-j*J were fed into the outputs of the matrix. The correctness of (14) may be versed by substitution into (11). As has been shown previously, since the matrix has a zero mode (looking from input to output), the current distribution that has been set up can be moved, intact, M elements around the array by holding the ampli- tudes B, of the input currents k e d but changing their phases by applying alinear phase progression with a modeto-mode phasedifference of M(27r/N). It has been shown that the current distribution and the radiation pattern of a multimode array areinvariant (aside from rotation) if the beam is scanned in steps equal to the angle between elements. For any other angle of scan, the current distribution willbe changed. If, for example,all inputs are fed in phase with equal amplitude, only element N will be excited. If the linear phase progression e-jK(zziN) CONTINUOUS SCANNING SHELEG: FOR ARRAY MATRIX-FED CIRCULAR is then applied to the inputs, the excitation is switched to element 1. If, however, the linear phase progression were only half this (i.e., e-jKrIN),two elements, Nand 1, would be strongly excited, but there would be currents on all the elements of the array. As a practical example, consider a 32element array with a cophasal distribution on the 14-element sector which includes elements 2 6 7 . The desired amplitude distribution is cos [(K- 1/2)~/16],which is symmetrical about a point midway between elements 32 and 1, and the elements are to be phased to form a beam in this direction. All other elements are to be inert. To show how the current distribution varies as the beam is scanned in small steps, the input currents required to achieve this distribution are first determined from (14), then their phases are changed to scan the pattern and the new distribution on the array is computed from (1 1). Table I1 gves the original distribution, phased for a peak at 4 = 5.625", and the corresponding input currents tothe Butler matrix. Also in Table I1 is the distribution on the arraywhen the beam is scanned to 11.25' (the direction of element 1) and the distribution when the beam is scanned to the angle midway between the first two. It is seen that, forthe scanned beams, the currents are no longer confined to a sector; all elements are illuminated, with those on the rear of the array about 30 dB down. The stronger currents are on 15 or 16 elements, and over t h s sector there are only minor amplitude ripples with the currents differing from the cophasal condition by about 20". The two scanned patterns (Fig. 8) do not differ signficantly from the original one. Their beamwidths, near-in sidelobes, and the general level oftheir far-out lobes are comparable. If this distribution had been designed for very lowsidelobes, it is likelythat the pattern changes would have been more significant. EXPERIMENTAL PROGRAM The circular array used in the experimental program had 32 elements and was operated at 900 MHz. Various radiating elements were used: dipoles, short back-fire elements, and Yagis (the lattertwo to reduce the elevation beamwidth without increasing the height of the antenna), but the only array that will be described is a 32-element array of slot-fed dipoles, vertically polarized, spaced 0.53.apart and 0.251 from a conductingcylinder. This antennais shown in Fig. 9 and the associated beamforming and scanning network is shown in Fig. 10. Since 3-dB quadrature couplers were used in the matrix, it had no zero mode; therefore, the coaxial cables connecting the matrix to the dipoles had to be cut to the proper lengths to correct for this. Corporate structures made in triplate linewereused to establish the various amplitude distributionsover the inputs tothe Butler matrix. The measured mode patterns for this array (Fig. 11) do not comparefavorably with the computed patterns in Fig. 3. The deviations are attributable primarily to phase and amplitude errors in the matrix. All the current modes were fed so as to have the same phase at element 32, and the relative phases of the patternmodes were determined by comparing 2025 Fig. 9. Circular array of 32 dipoles ( i 2 spacing, 900 MHz). Fig. 10. Beam-forming and scanning network for the 32dipole array. the phase of each mode with that of the zero'mode in the far field at 4=0. Fig. 12 shows the pattern of the array when a corporate structure was usedproviding currents of equal amplitude to all the mode inputs but number 16. For comparison, the corresponding calculated pattern (from Fig. 5) is shown solid. The two patterns agree reasonably well; both have beamwidths of about lo", the measured first sidelobes are 1.5 dB higher than those calculated, and the general level of the far-out sidelobes is about 21 dB down for both. The next series of patterns was taken with a tapered amplitude distribution over the modes. By dividing the outputs with tees, 31 modes were fed from a 16-element corporate structure. T h s resulted in a stepped distribution (since pairs of adjacent modes had equal amplitudes) with a 17dB taper. The measured beamwidth (1 1.5') and the first side- PROCEEDINGS OF THE IEEE. NOVEMBER 1968 2026 . : r = -x, (a) Mode 0 -0 (b) Modes i1 - 1- 0 -0 (m) Modes i 1 2 (n)Modes i 1 3 0 % o ~ o - m ~ - 9 0 - 6 0 - 3o0 30 60 90 eo ~ ~ O E O S O - O . B ) - ~ O o ~30Q -60Y )90 AD.uTHpNsLE(oEGREEs1 (0) ~ Modes i14 P H O l ~ eo 160 m l (p) Modes i 1 5 Fig. 1 1 . Measured mode patterns for the 32dipole array. -0 -m -10 CALCULATED 0 L ; Y -20 w ? t w a -30 -150 -40 ' -180 I -120 - 90 I - 60 -30 0 I I , 30 60 90 I I20 AZIMUTH A N G L (ED E G R E E S 1 Fig. 12. Measured and calculated patterns of the 32element array with uniformly excited modes. 150 I 180 SHELEG:MATRIX-FEDCIRCULARARRAYFORCONTINUOUSSCANNING 1 5 0 - 1 8 0 -150 -,x) -93 -m -30 0 30 2027 60 93 1 5 0 1 2 0 I80 -150 AZIMUTH ANGLE (DEGREES) Fig. 13. Scanned patterns for the 32-element array with a tapered stepped distribution on the modes. lobe (19 dB down) agree well with those calculated, but the level of the far-out lobes was somewhat worse than for the calculated pattern. The beam was then scanned by operating the phase shifters, and some of the patterns areshown in Fig. 13. It was found that the beamwidth and sidelobe level changed only slightly, and the gain varied by about 1 dB as the beam was scanned. CONCLUSIONS It has been shown that a Butler matrix can be used to feed a circular array to form a narrow pattern that can be scanned through 360" in azimuth by the operation of phase shifters alone. Oneexplanation of this, based on the assumption that the radiation pattern could be written as the sum of a finite number of uniform pattern modes, was found to work only qualitatively in that it could not beused to predict the structure of the sidelobes. A 32-element array of dipoles was used to demonstrate experimentally how a beam was formed by superposition of the pattern modes (even though imperfect) and how the scanning was performed. Finally, the synthesis procedure of Davies was described, andasan example, the inputs to the Butler matrix required to achieve a prescribed cophasal sector distribution on the array were determined and the change in the currentdistributionforother beam positions were shown. ACKNOWLEDGMENT The authoracknowledges the help given by R. M. Brown through numerous discussions and consultations, the contributions of F. W. Lashway, who was responsible for the mechanical design, and of R. J. Wiegand, who helped with the measurement program. In addition, the author expresses his gratitude to J. Tyszkiewicz of the Naval Air Systems Command, who sponsored and supported thls work. REFERENCES [I] G. C. Chadwick and J. C. Glass, "Investigation of a multiple beam scanning circular array," Scientific Rept. 1 to USAF Cambridge Research Lab., Cambridge, Mass., Contract AF19(628)367, December 31,1962. [2] W. R. LePage, C . S. Roys, and S. Seely, "Radiation from circular current sheets," Proc. IRE, vol. 38, pp. 1069-1072, September 1950. [3] R. C. Honey and E. M. T. Jones, "A versatile multiport biconical antenna," Proc. IRE, vol. 45, pp. 1374-1383, October 1957. [4] A.C. Schell and E. L. Bouche, "A concentric loop array," I R E WESCON Conr. Rec., vol. 2, pt. 1, pp. 2 12-2 15, August 1958. [5] C. P. Clasen, J. B. Rankin, and 0. M. Woodward, Jr., "A radialwaveguide antenna and multiple amplifier system for electronic scanning," RCA Rec., vol. 22, no. 3, pp. 543-554, 1961. [6] J. L. Butler, "Digtal, matrix, and intermediate-frequency scanning," in Micronace Scanning Antennas, vol. 3, R. C. Hansen, Ed. NewYork: Academic Press, 1966, ch. 3. [7] P. S. Carter, "Antenna arrays around cylinders," Proc. IRE, vol. 31, pp. 671693, December 1943. [8] D. E. N. Davies, "A transformation between the phasing techniques required for linear and circular aerial arrays," Proc. IEE (London), vol. 112, pp. 2041-2045, November 1965.
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