broad-band antenna array with application to radio astronomy

4
COMbTUNICATIONS 697 from which i t follows that for normal zero-mean e Then (17) becomes Similarly it may be found that Since sin (Ice) and e cos (k) are odd functions of e, their mean is zero. It follows that E(.$ - slh) = --nW(y) exp (-kz$(e)) E(s$ - S~S) 0 E(sls4 - ~$3) = n2W(e) exp (-k*uz(e)). Then the mean of (14) is EP”(0,e) = - (2kz)[$(y) - o“(e)]exp [-k%Q(e)]. For uz(e) << u2(y) as is here assumed, EP”(0,e) = -Zk%*(y) exp [-kZu2(e)] (15) for practical purposes. Comparison wit,h (6) shows that t.he effect of the errors is to multiply the second derivative P”(0) by a random factor whose meanisexp [-lz‘u*(e)]. The argument that led to (10) shows that the beamwidt-h is inversely proportional to the square root of P“(0). The effect of the errors is t.herefore approx- imately to multiply the beamwidth by a random factor whose mean is where .‘(e) is the variance of the error in estimating the coordinate of the element positions along the beam direction. The factor (16) has the values 1.05 for u(e)/k = 0.05, 1.22 for u(e)/k = 0.10, and 2.20 for u(e)/h = 0.20. The steering error remains to be discussed. The direction of the beam is defined to be the direction of maximum P(+,e), as a func- t.ion of + for any given e. As in (14), primes denote differentiation Bith respect to +. The direction of the beam with e = 0 is again t,aken to be along the z axis, so that P‘(0,O) = 0. The quest.ion is: For what +* near zero is P’(+,e) = O? +* is a random variable. By symmetry its mean must, be zero. Its variance $(+*) is computed in the following. For small e and small 4, approximately. Since P’(+,e) is zero for + = 4*, the steering error due to e is approximately. P”(0,O) is given by (6). If the partial derivative of is taken with respect to ei and the result evaluated for e = 0 it is found that where (6) has been used. The variance of t,he steering error is for thevariance of the steering error, where n is the number of array elements and 9(y) mas defined in (7). REFEREKCES YE,” IRE Trans. . 1962. xl arram.” IEEE .. randomly locatEd elemen%s.” IEEE TI AP-20, pp. 129-135, R.12 w. 1972. ‘alas. Aniennm Propciqat., VOC Broad-Band Antenna Array with Application to Radio Astronomy CLIFFORD L, RUFENACH, W . hI. CRONYN, AKD K. L. NEAL Abstract-A broad-band antenna element and beam-forming matrix have been developed for reception of signals at 25-100 MHz. The element is a zig-zag log-periodic antenna with a nominal im- pedance of 430 fi and a VSWR of less than 1.9. The matrix utilizes time-delay gradients to obtain frequency-independent beam posi- tions and also allows several different beam positions to be moni- tored simultaneously. Observations of natural radio sources using a 16-element array have verified its usefulness. - I. INTRODUCTION Large radio telescopes are generally characterized by narrow bandwidths and poor steerability at frequencies less than 100 MHz. A broad-band array hasbeen designed and built for use with a time- delay (frequency-independent) beam-forming matrix. The matrix coupling capacitors and open-wire linesallowversatileoperation, including multiple frequency and mult.iple beams. These features should have numerous applications in radio andradar receiving systems. work was supported in part by the Advanced Research l?roject,s Agency Manuscript received November 7 1972: revised March 26. 1973. This under ARPA Order 1361. Oceanic and Atmospheric Administration. Environmental’ Research The authors are m6h the Space Environment Laboratory hTational Laboratories, U.S. Department of Commerce,Boulder, Colo. 80302.

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COMbTUNICATIONS 697

from which i t follows that for normal zero-mean e Then (17) becomes

Similarly it may be found that

Since sin (Ice) and e cos ( k ) are odd functions of e, their mean is zero. It follows that

E(.$ - slh) = --nW(y) exp ( - k z $ ( e ) )

E ( s $ - S ~ S ) 0

E(sls4 - ~ $ 3 ) = n 2 W ( e ) exp ( -k*uz(e) ) .

Then the mean of (14) is

E P ” ( 0 , e ) = - (2kz)[$(y) - o“(e) ]exp [ -k%Q(e)] .

For uz(e ) << u2(y) as is here assumed,

E P ” ( 0 , e ) = -Zk%*(y) exp [ -kZu2(e ) ] (15)

for practical purposes. Comparison wit,h ( 6 ) shows that t.he effect of the errors is to multiply the second derivative P”(0) by a random factor whose mean is exp [-lz‘u*(e)]. The argument that led to (10) shows that the beamwidt-h is inversely proportional to the square root of P“(0). The effect of the errors is t.herefore approx- imately to multiply the beamwidth by a random factor whose mean is

where .‘(e) is the variance of the error in estimating the coordinate of the element positions along the beam direction. The factor (16) has the values 1.05 for u ( e ) / k = 0.05, 1.22 for u ( e ) / k = 0.10, and 2.20 for u ( e ) / h = 0.20.

The steering error remains to be discussed. The direction of the beam is defined to be the direction of maximum P ( + , e ) , as a func- t.ion of + for any given e. As in (14), primes denote differentiation Bith respect to +. The direction of the beam with e = 0 is again t,aken to be along the z axis, so that

P‘(0,O) = 0.

The quest.ion is: For what +* near zero is P’(+,e) = O? +* is a random variable. By symmetry its mean must, be zero. Its variance $(+*) is computed in the following.

For small e and small 4,

approximately. Since P’(+,e) is zero for + = 4*, the steering error due to e is

approximately. P”(0,O) is given by (6). If the partial derivative of

is taken with respect to e i and the result evaluated for e = 0 i t is found that

where (6) has been used. The variance of t,he steering error is

for the variance of the steering error, where n is the number of array elements and 9 ( y ) mas defined in (7) .

REFEREKCES YE,” IRE Trans. . 1962. xl arram.” IEEE

. . randomly locatEd elemen%s.” I E E E TI AP-20, pp. 129-135, R.12 w. 1972.

‘alas. Aniennm Propciqat., VOC

Broad-Band Antenna Array with Application to Radio Astronomy

CLIFFORD L, RUFENACH, W. hI. CRONYN, AKD

K. L. NEAL

Abstract-A broad-band antenna element and beam-forming matrix have been developed for reception of signals at 25-100 MHz. The element is a zig-zag log-periodic antenna with a nominal im- pedance of 430 fi and a VSWR of less than 1.9. The matrix utilizes time-delay gradients to obtain frequency-independent beam posi- tions and also allows several different beam positions to be moni- tored simultaneously. Observations of natural radio sources using a 16-element array have verified its usefulness. -

I. INTRODUCTION Large radio telescopes are generally characterized by narrow

bandwidths and poor steerability a t frequencies less than 100 MHz. A broad-band array has been designed and built for use with a time- delay (frequency-independent) beam-forming matrix. The matrix coupling capacitors and open-wire lines allow versatile operation, including multiple frequency and mult.iple beams. These features should have numerous applications in radio and radar receiving systems.

work was supported in part by the Advanced Research l?roject,s Agency Manuscript received November 7 1972: revised March 26. 1973. This

under ARPA Order 1361.

Oceanic and Atmospheric Administration. Environmental’ Research The authors are m6h the Space Environment Laboratory hTational

Laboratories, U.S. Department of Commerce, Boulder, Colo. 80302.

698 IEEE TRANSACTIONS OK ANTJGNNAS AND PROPAGATION, SEPTE3dBER 1973

r =

- -

Y =

Fig. 1. Simplified diagram of zig-zag log-periodic antenna element. located between two wire planes (dashed and solid lines). Loops (ex- Element is symmetrical with respect to transmission line which is

tenor to soldered intersection points) were found usefu! in minimizing VSWR. Scale factor r = Uk/LTl;+?, and relative loop size y = L'k/Lk are deflned for I; = 1,2.3. . ..

11. DESCRIPTIOX OF RADIO TELESCOPE

A . Antenna Element The prototype element is a 2-plane wire zig-zag log-periodic

antenna [l], [2] positioned apex up. It has a nominal driving-point impedance from 300-600 $2 allowing impedance-matched direct- coupling onto open-wire transmission line (OWL). The element design parameters were varied experimentally to minimize the VSWR and physical size of a full-scale element. The design param- ters include the scale factor 7, wire size, separation distance betxeen planes d, and the relative loop size y (see Fig. 1). The element VSWR was measured on an inner element of the 16-element array (see Section 111). Impedance measurements a t the end of a 40-m OWL =ere transformed back to t.he terminals of the element at the apex. In t he final design the VSWR was less than 1.9 about an impedance 2 = 430 Q over t.he frequency range 25-100 MHz. The base of the element was terminated in 430 Q, and the final design parameters were T = 0.84, y = 0.95.5, and d = 4 cm.

Experimental probing of the element indicated that the active, or radiating, portion was centered around a region approximately X/3 in horizontal width (see Fig. 1). Physically, the element was constructed of no. 18 copperweld mire attached to a m-ooden frame in the shape of a right. isosceles triangle.

B. Beam-Forming Matr ix

Beam-forming matrices combine signals from individual elements to form an array beam. Broad-band beam-forming mat.rices were first proposed by Blass [a]. More recently a variety of geometries and coupling techniques have been suggested with some application at microw-ave frequencies [4], [j]. In the present work, a beam-forming matrix was constructed for radio astronomical observations at lower frequencies using a novel combination of capacitive coupling and OWL, as fist suggested by one of us (Cronyn).

The broad-band matrix consist,s of coupled columns and rows (nonorthogonal) at each intersection point, as illustrated in Fig. 2. For each row, the individual element signals are combined in a unique real-time gradient to obtain frequency-independent beam positions. In the example of Fig. 2, two rows, or equivalently, the two different. timedelay gradients produce two beams, one beam in the zenith direction and another beam 30" off the zenith direc- tion. The beam direction from the zenith eo is given in terms of the column angle (r and t.he matrix angle 8,

sin eo = sin a [sec j - tan 61 cos a. (1)

Phpically, the rows and columns were built of OWL using no. 18 copperweld spaced to give a characteristic impedance 20 = 430 0.

Fig. 2. Simplified diagram of beam-forming matrix for 4element array. a is angle between element phase centers and columns, 6 is angle between an individual row and line normal to columns.

Receiver Input Termmatton

M' G A

Reslstlve Terminotlon

I&

Fig. 3.. Schemati? diagram cleft) aqd equivalent Grcuit (right) of indmdua! matnx coupler. GR IS raslstive termmation equal to row charactenstic conductance or input conductance of broad-band balun. VA and VR are antenna voltage and matrix out.put voltage, respectively.

Each column is terminated at one end in a 4304 resistor and at the other end in the individual element of nominal impedance 430 Q. Similarly, each row is terminated at one end in a 4 3 0 4 resistor and at the other end in either a 4304 resistor or a broad-band balun for impedmce matching to the receiver.

The signal from each individual element is coupled a t each inter- section point through identical capacitors equally spaced along the row. The capacitors were selected to provide light coupling at the highest desired frequency. The coupling is light if less than about 7.3 percent of t.he power coupled onto the row is dissipated in the receiver [SI.

The ratio of the row (array) temperature T R to the sky back- ground temperature Te (fraction of background temperature available at the row), based on light coupling and neglecting losses other than the termination losses (see Fig. 3 for equivalent circuit) 1s €Ap.

where APIPA is the power coupling ratio at each intersection, n is the total number of elements in array, B, is the coupling susceptance, wC, GA, and GR are the column and row termination conductivity, respectively. It may be shown that under lossless light coupling,

is the aperture efficiency if the receiver input is taken at the row output terminals [7], since light coupling approaches a uniform aperture illumination. The light coupling requirements are A P / P A '? 0.05 and cap 0.73 based on (2) , or in terms of the normalized parallel conductance, g $: 0.1 [6] where g is obtained from the equivalent circuit of anindividual coupler (see Fig. 3), g = $(Bc/GR)'. If GR = Gd, then g = ~ ( A P / P A ) since the power splits at each

COMMUNICATIONS 699

Frequency, MHz

Fig. 4. 16-element arrav near Sederland Cola. Elements are spaced Fig. 6 . YSWR of matrix row as function of frequency. BO = -5" row. at 4.5-m intervals along baseline azimuth of 70". Terminated ends of the rows (see Fig. 2) are at eastern-end of matrix.

Prohibited frequency range near 55 M H z .

and/or wide-band impedance matching at the coupling points would eliminate this problem.

2) The individual b e a m decrea5e in width as t.he frequency is increased while the beam posit.ions remain fixed. Therefore, inde- pendent multiple beams positioned for intersection at: say t.heir 3 d B points near the lowest. desired frequency, would not overlap at

Fig. 5. Sample strip ch.art recording of Cygnus A and Cassiopeia A at higher frequencies. 50 MHz. Earth's rotat.lon moved antenna pattern fist. through galactic canter. second through Cygnus A, and third through Cassiopeia A . Angular response of about. 5' indicates t.hat array elements are reason- ably uniformly illuminated. Rapid fluct.uations during source transit 111. OBSERVATIOSS are ionospheric scintillation.

intersection point. For the prototype array described in this paper, n e const,ructed a sixteen-element array, i.e., n = 16. Also, 4 p F mica coupling capacitors were selected based on APiP-4 N 0.04 and EAP 0.6 near 70 XHz allowing EAP to vary from 0.07 to 1.1, for the frequency range 23-100 MHz based on (2).

It. is inst,ructive t.o compare the beam-forming matrix with a conventional feed system in which each individual element is lightly coupled to a single traveling-wave line [SI. In terms of the matrix, the convent.iona1 feed is equivalent to a single row matrix where most of the energy received by each element is reflected at the coupling point and reradiat.ed through the element. In t.he beam- forming matrix essent,ially all t.he energy received by each element is coupled into t.he column. Part of the column energy is then coupled onto the first row; t,he remaining energy continues down the column and may be coupled ont,o several other rows with the remainder being dissipated in the column termination. Mutual interact.ion be- tween beams and beam orthogonality have been described else- where [5].

For application at microwave frequencies, aperture efficiency is important. since t.he sky background temperature is usually lower than the receiver noise temperature. Therefore, the efficiency must be as high as possible to maximize signal-to-noise ratio; efficiency may be increased by a factor of two b?; employing directional couplers rather than nondirectional couplers. In contrast-t: at frequencies 2 100 MHz, sky background temperatures are usually higher t,han typical receiver noke temperatures thereby allowing t.he use of nondirectional couplers and low coupling efficiencies, which simplify design and const,ruct.ion. In addition, capacitive coupling allows a nearly constant array background temperature over the frequency range of interest. since the coupling decreases 6 dB/octave based on light coupling while t.he sky background temperature usually in- creases 7 or 8 dB/octave.

Two aspects of the matrix which might be undesirable for some applications are as follows.

1) The VSWR rises to unaccept,ably high values near 'prohibited' frequencies a t which the coupling points along the row is spaced at an integral mult,iple of X72 (see Fig. 6). Directional coupling

A 16-element. array was constructed near Nederland, &lo., at the University of Colorado Radio Astronomy Field Site (see Fig. 4). The column angle a as chosen equal t.0 30" and three rows were constructed to give effective beam positions, BO = -3" f 20" including a correction for the slope of the land. Radio sources Cygnus A and Cassiopeia A were observed during the fall of 1971 at 34, 50, and 74 MHz. A sample strip-chart recording of the re- ceiver det.ector output is shown in Fig. 5 for the 00 = -5" row. The VSWR characterkt.ic for thi: row was measured and plot,ted in Fig. 6.

The radio telescope operated as elrpected at 34, 30, and 74 MHz at the different beam positiom. The aperture efficiency ~~p was calculated from measured values of array background temperature T B and sky background temperature TB based on convolution of the antenna pattern with a contour map of sky brightness [8, Fig. 21. The increase in the array t.emperature during transit. of a discrete radio source is relat.ed to the effective aperture of the array s de- termined entirely by pattern A,, [7]

where Ts is the increase in array temperature due to source of flux-, S and k is the Boltzmann's constant.

In Table I, measured values of TR and T S and published values of TB and S are given yhich aere used to compute the effective aperture area of the array, or equivalent.ly, the collect.ing area for each individual element, i.e., A,,/16.

At 34 and 30 MHz, CAP E 0.06 and 0.09, respectively, and may be compared with CAP E 0.13 at 34 MHz based on (2). The difference is probably due to ohmic losses in the balun and mat.rix and t.he ap- proximations in (2). The collecting area per element is h2/4 - X2/3 and may be compared with the collecting area of a half-wave dipole a t a height X/4 above a ground plane, A., h'/3.

IV. COXCLUSIOSS

A broad-band array with multiple beams for operat.ion at 23-100 MHz can be built using coupling capacitors and open-wire line.

700 IEEE TRANSACTIOKS ON ANTENNAS AVD PROPAGATION, SEPTEMBER 1973

TABLE I PARA~TERS FOR ESTJXATION OF APERTURE EFFICIENCY

AND COLLECTINQ AREA

34 50 MHz MHz

Sky Background Temperature T,(K)l 14 000 5600 Measured Array Background Temperature TR(K) 820 520

csgnus A Cassiopeia A

34 50 34 50 MHz MHz M E h MHz ----

Source Flux AS(F.U.)~ 27 000 22 000 37 OOO 28 000 Measured Source Tempera-

ture, TdIO 230 140 220 190

BaBed on Tg = 70 000 K at 17.5 iMHz near 0200 sidereal time from [9] and a spectral index of 2.4.

Cmsiopeia A, refpectively, and the 38-MHz flux values in [lo]. Based on spectral indices of 0.6 and 0.7 for Cygnus A and

Cassiopeia A flux at 1971.8 corrected for 1.1 percent per year secular decrease.

The favorable results with a 16-element array indicate that these simple design and construction techniques could be suitable for use in large meter wavelength arrays.

ACEXOFTLEDGNEXT

The authors wish to thank C. A. Brink for help with the design, construction and operation of the radio telescope, and W. Klemperer and G. Lerfald for their encouragement and support. We also thank the referee for a number of helpful comments.

REFERENCES [ l ] 9 E Lee and K K Mei “Analysis of zig-zag antennas,” I E E E [ 2 ] H D. Pruett Design for log-periodic %M and TV antennas.”

Tra i s . Antenna:,kropagat.’, vol. AP-18, p 760-764, Nov. 1970.

[3] J. S l y , “Multldirectlonal antenna-a new approach to stacked Eiedron. 1Vorid. vol. 78, pp. 46-49, Dec. 1967.

[4] T C. Chest,on and J. Frank “Array antennas” in Radar Handbook. beams in 1960 I R E Int. Conv. Record, vol. 8. pt. 1, pp. 48-50.

SI‘. I . Skolnik, Ed. Kew kork: McGraw-Hill, 1970, Ch. 11, pp. 11-1-11-21.

[5 ] J L. Butler “Digit?l matrix and intermediate-fre uency scanning,” in Wcrotcade Scannmg Antennas, vol. 111, R. C. €?amen, Ed. New Tdrk: Academic Press, 1966, pp. 254-258.

[6] W. H. Kummer, “Feeding and phase scanning” in Microwace Scanning Antennas, vol. 111, R . C. Hansen, Ed. S e w York: Acadermc Press. 1966, pp. 26-29.

I i l J. D. Kraus. Radu, Astronomg. New York: McGraw-Hill. 1966.

[9] A. H. Bridle, The’spectym of the radio background between 13 422-427. 31ay4?965

and 404 MHz,” Mon. i’fotzc. Roy. Astrm. SOC., vol. 136, pp. 219-

[lo] E. A. Parker Precise measurements of the flux dezsities of the 240. May 1966:‘ radlo sources ’cas A and Cyg A at metre wavelengths, 340% Nototic. Roy. Astroa. SOC., vol. 138, pp. 407-422, Mar. 1968.

Antenna Radiation-Pattern Measurement Using Model Aircraft

C. W. GLIDDON AD C . T. CARSON

Abstract-It is shown that model aircraft can provide a useful method of on site evaluation of antenna performance, with advan- tages of economy and speed over existing antenna measurement methods. Recommendations for further development of this tech- nique are also included.

Manuscript received Eovember 16,’19i2; revised February 20, 1973. C . W. Glipdon was mth the .Department of El+xxal Ewneermz.

Monash Timverslty, Clayton. VIC., Australla. He s now mth Andrew Antennas Reservoir Vic., Australia 3073.

University, Clayton, Vic., Australia 3168. C. T. Ckson is wit.h t.he Department of Electrical Engineering. JIonash

I. INTRODUIXION In situ measurement of antenna performance is necessary when the

effect of the environment on the antenna must be evaluated. Scale models of the antenna system and environment can be used in some circumstances, but often modeling of conductivity [l] presents dif& culties which necessitate full-scale antenna testing. A major problem in full-scale testing is locating a radio source around the antenna. Helicoptem [2], [3], light aircraft [4], and balloons [5] have been employed for this purpose, but a need exists for a more economic and flexible method, which could be satisfied by the use of model aircraft. This communication is a report on the use of model aircraft for in situ antenna measurements.

11. EXPERIMEXTAL TECHSIQUE

Fig. 1 shows a block diagram of the antenna-measurement system, which comprises a model aircraft used for carrying the source antenna and t.ransmitter around the antenna under test, an inter- ferometer tracking system to provide the coordinate angles of the aircraft, and field strength measuring equipment monitoring the signal from t.he antenna under test. The model aircraft can be radio controlled, or alternatively flonm on control lines. The latter control method was used for t,he initial investigation because it simplified the tracking system.

Control lines consist of a pair of steel or nylon lines that actuate the elevators of the aircraft when the control handle held by the operator is rotated. The lines are typically 20 m in length and provide a radial constraint on t,he flight path. An increase in &ght radius is possible but a faster model is required to mint.ain sufficient tension in the lines. A 3-ft wingspan model powered by a 2.5 cm3 diesel motor was employed in the tests, and carried a 100-mW t.ransmit,ter operating a t 460 MHz ahich fed a vertically polarized half-wave dipole mounted on the fuselage. The model had adequate lift to carry the half-pound payload represented by the transmitter, source antenna, and battery.

The 46@-MHz interferometer antenna comprises three-quarter- wavelength monopoles 1, 2, and 3, spaced one-wavelength apart on a ground plane at the vertices of a right triangle. The phase differenca $l?, $13 betxveen antenna 1 and antennas 2 and 3, respect,ively, are measured by a vector voltmeter which is time shared at a rate of 50 Hz between antennas 2 and 3 by a pi-n diode switch. Sample and hold circuits decode t.he time division multiplexed phase signal from the vector voltmeter into the phase signals $12 and $13 ahich are recorded on a magnetic tape instru- mentation recorder simultaneously with the output from the field st,rength meter.

111. DATA PROCESSISG Processing of t,he recorded data is accomplished on a small com-

puter with analogue to digital conversion facilities. In the absence of mutual coupling between t,he interferometer monopoles, and with the source infinitely distant, from the interferometer, the azimuth and coelevat.ion angles are found from t,he relations

tan = - +I3

Correction for mutual coupling is necessary and is obtained from the impedance matrix for the system comprising the interferometer antennas 1, 2, and 3, and the source antenna 4. The system equa- tion is