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Naval Research Laboratory %A

Washington, DC 20375-5000 -SNRL Memorandum Report 6204

00N Design, Test and Evaluation of a Pair of

Bootlace Lenses

P. D. STILWELL, JR, M. G. PARENT, H. P. COLEMAN AND B. D. WRIGHT

0 Electromagnetics Branch SRadar Division

July 6, 1988 D T ICfELECTE

AUG- 0 1988

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Approved for public release; distribution unlimited. ".'i

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NRL Memorandum Report 6204

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SWarfare Systems CommandI

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11. TITLE (Include Security Classification)Design, Test and Evaluation of a Pair of Bootlace Lenses

12. PERSONAL AUTHOR(S)

Stilwell, P.D. Jr., Parent, M.G., Coleman, H.P. and Wright, B.D.

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Final FROM_ TO 1988 July 6 76

16 SUPPLEMENTARY NOTATION

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FIELD GROUP SUB-GROUP .... jri/iig," err,,py ac,1g"'o '" -"Bdamforming, Arra at ing - - .,.

Bootlace lens/ Rotman lens. . -&,-

;' .*'- ^V^ Qa r, f .,'( S' i)L a~.tS.

19 ABSTRACT (Continue on reverse if necessary and identify by block number)

This report details the design, test, and evaluation of two 3.2 GHz bootlace lenses. They were designedto be used to provide time delay beamforming for a 33 element linear array. The lenses were fabricatedusing a parallel plane medium with coaxial probes lining the entire perimeter. In this manner a true timedelay lens performance was achieved displaying good impedance matching over 200 MHz and excellent beammatch over +450 . Extensive performance results are given as measured with an HP-8510 Network Analyzerfor both the individual lenses and for their back-to-back configuration.

Or

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CONTENTS

I. INTRODUCTION .................................................. I

II. BACKGROUND ............................................................................... 1I

mII. BASIC LENS CONSIDERATIONS ............................................................. 3

IV. DESIGN PROCEDURES ....................................................................... 5

V. TEST AND EVALUATION .................................................................... 7

VI. CONCLUSIONS ............................................................................... 9

VII. REFERENCES ................................................................................ 10 I'

V.

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6

DESIGN, TEST AND EVALUATION OF A PAIR OF BOOTLACE LENSES

I\ INTRODUCTION S

This report concerns the development of a microwave lens of the

bootlace type for use as a beamformer for linear, phased array antennas.Such devices prove to be a practical implementation of the type of timedelay beamformer required in ECCM systemsidentified by Gabriel and others[1,2,3]. '-They constitute hardware which maps from a sampled (elementalantenna) space to beamspace, where beamspace denotes one of the many dis-crete sets of directional antenna patterns possible, e.g., a Fouriertransform of the antenna samples.

Successful implementation of a wide angle, wideband lens placesstrong conditions on impedance match over frequency and scan direction. rFurther, operation in beamspace implies the existence of a significant.number of beam ports and a commensurate number of antenna elements.! Of 7the numerous types of beamforming circuitry (Blass I4], Butler [5], Gent[6], Ruze [7], Rotman-Turner [8], etc., [9, 10]) none display the exactfeatures desired. It was decided that a generic bootlace lens using aparallel plane medium designed with an emphasis on channel matchingoffered the greatest potential for a high quality beamformer with amoderate number of beams. A key ingredient in obtaining the requisitematch is a uniform spacing of the probes feeding the parallel plateregion. This uniform spacing although compromising the independence ofadjacent beams, allows a common probe element pattern to be used andmaintains good match to large scanning angles. In spite of the intrinsicadvantages of a stripline design, it was felt that a beamformer withapproximately 30 beams using an air filled parallel plane medium connected w.

to coaxial probes would offer experimental convenience and be moreamenable to modification and fine tuning. The use of two such lenseswould allow a laboratory evaluation of performance in a back-to-back

arrangement while avoiding the necessity of operating with an array on anantenna range during the development of the lenses.

TT. BACKGROUND

A bootlace beamformer is an M input port device with N output ports,see Fig. II-1. The N output ports can be attached to at, N alement arraywith a linear spacing, a circularily disposed set of elemental antennas orsome other type of array. The attachment of a source to any of the Minput ports will create an antenna beam in the mth diTcLion. 1 1, R7"lacing" between the input and output ports constitutes the body of thelens and therefore dominates the RF performance of the device. The lnsmedium can either be stripline or space between parallel planes, in either Icase, probes provide the coupling to and from the lens. There is strong

Manusmp approved March 26. 1988.>.0

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coupling between adjacent probes since each is embedded in an array con-si6ting of all nearby probes. This may cause severe problems in caseswhere non-uniform probe spacing is used to make each of the M beams inter-sect adjacent beams at the 4 dB points. A non-uniform feed probe spacinggreatly complicates the matching of each probe to its transmission lineimpedance and simultaneously to the 2D modes in the parallel plane medium.

Total matching of the input ports of a multiport lens involves twodistinct matching conditions. The first is the impedance transformationfrom the transmission line to that of the parallel plane medium. Thesecond is the match or coupling to different propagation directions in theparallel plane region, especially when a close spaced array of probes isused. Thus, depending on the pattern of a single driven probe as seen inthe two dimensional region, the array could be properly matched to thetransmission line yet not to the 2D modes. Total matching of the lensinvolves a simultaneous meeting of boundary conditions on both sides ofthe probe. A heuristic argument (based on a requirement for perfectabsorption of plane waves falling at an arbitrary angle on an array) isconvincing that a cose behavior of the pattern for each element isrequired. (This is the pattern of an aperture of a blackbody radiator orthe albedo of a perfectly absorbing material.) Following this logic, itis then impossible to obtain simultaneous total matching of a parallelplane lens and beam "orthogonality" where orthogonality implies overlap atthe 3 or 4 dB points.

In addition to being used to excite wavefronts from a linear array,two lenses can be used in series (with the element planes attached one toone) to provide a laboratory approximation of an antenna range. Figure11-2 diagrams the concept. A signal attached to one of the input portscouples uniformly to output elements of that lens. These are directlyattached to the elements of the second lens. Finally, the space propaga-tion in the second lens excites the output probes and can approximate asinc(x) distribution. (The sinc function is sampled only at the pointswhere probes exist so only a line spectral approximation to the sincfunction will be observed.) In this way, one can obtain a beam combiningsystem for a discrete set of sources which has a time delay behavior.

The rather strong resemblance of Fig. 11-2, 3 to the multiplicationof matrices is not coincidental. In the back-to-back case the mathemati-cal model would involve the product of an MxN matrix, MI , times an NxMmatrix, M2 , which is mindful of a generalized inverse of M i . Thus, if theinput excitation vector had a 1 in the mth position, at some frequency ofoperation the output vector would have a single I in the m th position andzeros elsewhere. At other frequencies the same excitation vector mightyield an output which peaked at the proper place but show non-zerocoupling to the other beams. Only at one excitation frequency will theoutput probe array have the proper periodicity to sample the sinc function::actiy at sidelobe nulls.

it wa2 aecided to build a set if lenses using a parallel plane airfilled medium since this should be relatively easy to build. High die-lectric constant material could be used to significantly reduce thephysical size of the lens but would probably cause a considerable amountof bulk scattering from inhomogeneities in the dielectric material. A

2

?-A 71

goal of a port VSWR of better than 2:1 over a 200 MHz band centered at 3.2GHz was selected. At this match the return loss is sufficient to diminish

resonances to an ignorable level and eliminate effects of multiple delaysof the signals through the circuit. The feeds were tn be chosen to scanto ± 300 from broadside to the effective linear array with good beam,quality and to ± 450 with degraded performance.

III. BASIC LENS CONSIDERATIONS

Figure II-1 illustrated the basic structure of a bootlace lens. The

goal of the design is to determine the loci f(x) and e( ) which yield aplane waves from the element ports e, see Fig. III-1. The symbol e. isused to denote the j element o the linear array which would- beconnected to the output ports of the lens. Each of the transmission linesconnecting the jth port to the actual linear array would have identicallengths. The M input ports to the system are labeled fi and occur at aheight f i above the axis of symmetry. This figure strongly resembles a

cross section of an eye. The similarity holds further in that the rightsolid curve constitutes the actual lens and the left one the receptors(transmitters?). It will be assumed herein that an axis of symmetry isrequired to permit scanning to equal angles from the broadside of theassumed linear array. Peculiar scanning requirements might be devised forwhich this is not so but such cases will not be discussed in thisreport. Likewise the output ports are coupled to the parallel plane

medium at heights e Since the transmission lines L(f i ) and L(e.) arenot constrained to a plane these lengths may be varied at will withoutaltering the geometry indicated in the figure, where E denotes thedielectric constant of the parallel plane medium. The total phase lengthfrom feed point f to element point e is given by

(f,e) - (21/A)[L(f) + eD(f,e) + L(e)] III-la

with

D(f,e) - SQRT {(E _ x) + (e - f)2}. III-Ib

For the lens to perform ideally a uniform phase gradient shouldexist between element probes. The magnitude of the gradient is governedby the selection of f. In equation form this is

ai/De = F(f) and 3F/3e = 0. 111-2

To be realistic, the function F will not be an exact constant overthe entire range of e. Therefore the more appropriate approach would beto minimize the expression

VAR (;/3e)with

ABS(e) < e II -3

It will be noted that there is no hint of the existence of probes inFig. III-1, only loci. The loci must be measured with respect to thecenter of phase of the probes. This is a very important aspect of thelens and must be accurately determined. Anticipating results to beobtained later, the central feed probe phase center must lie exactly at

oba3e Iaete eta

the center of the circular arc e(E). Isolated probes in front of a ground

plane exhibit a center of phase at the groundplane since this is thecenter of symmetry for the probe and its image. As additional probes are

placed near the test probe the same distance from the groundplane the Wphase center will migrate away from the wall due to phase shifts intro-

duced by the mutual coupling with nearby probes. In lieu of solving adifficult set of boundary conditions to determine the effective phase

center of a probe embedded in a non-uniform array, a direct method is to

make the array uniform so that each probe will display an identical shiftof phase center. Thus an experimental measurement can determine this

shift and the loci can be located at this point relative to the probe

itself, i.e., the loci to be determined relate to the phase center, notthe wall nor the probes. Non-uniform spacing of probes could be expected

to yield differing phase centers and a shift of up to 900 may result.

Now that the technique for the determination of the phase center of

a probe embedded in a uniform array has been clarified, we can proceedwith the determination of the loci associated with the inputs (feeds) and

outputs (elements) of a lens. This entails a determination of the

functions f(x) and e( ) either from equation 111-2 or from 111-3. it will

be assumed that the L(f i ) and L(ej) are constants as is the dielectric

constant, e. Then we can work only with D(f,e) rather than with the more

involved (f,e). ol ih ,

To start, we will investigate the information available from the

derivatives of the phase along the locus of e( ). Denoting partial deriva-tives by subscripts one can write

D = SQRT((f-e)2 . (x-) 2 ) III-lb

and

D= (1/D) {(&-x) e + (e-f)} III-4

Continuing by taking the second derivative, Dee, and equating to zero

allows one to deduce the conditions necessary to obtain zero phase error

for any feed point f over the entire range of the element ports e. Due t)

the algebraic complexity (and also the fact that D,, cannot be identically

zero over the entire range of e) we will assume e() to be the functionwhich by inspection minimizes the dependence of De on e yet maintains a

dependence on f. Rewriting III-4 as

DD e +e) -xS -f II-5

allows us to see that the term in parenthesis can be made identically zero

by the choice & --e/ , which happens to be the differential equation for a

circle centered at e-0, =0. From the geometry of the problem the radiusof that circle is o the separation between the feed and element postions

on the axis of symmetry. With that geometry the remaining dependence

is linear in f as desired but with an error term xe/s. This error term

is to be small and it will be insofar as x and e are small relative to

o" Continuing then

D ee= 11 + (e/&)2}x/ D - lexi/& f12 /D 3 111-6

4

This can be cast in the form

f2 + (2e/&)fx + (e2/&2)x2 +(- &+3)x = 0 111-7

with D E. This is a canonical form for a rotated ellipse of shifted

origin but centered on the x axis. Ignoring the rotation term yields anellipse with a major axis of .56 & and a minor axis of .44 . Thiscurve was graphed and fitted with a circle of radius .63 for f up to .5(measured in terms of & ). Alternately this can be approached by approxi-mating the equation by

2f . x 111-80

which is an equation for a parabola. Using the Gaussian curvature

1/R = f"(x)/[1 + (f"(x)) 2 ]3 /2 111-9

the radius of curvature at the axis is R = .5& . This is the expectedfeed locus for a lens which, without error, feeds a cylindrical array. Inconclusion, an examiniation of the derivatives of D(f,e) directly elicitsthe property that e(&) should be a circle of large radius of curvature.The curve f(x) cannot so easily be determined but is found to be an ellip-tical shape.

IV. DESIGN PROCEDURES

Two major questions remain to be answered in the design of the lens.

a. what is the phase center of the probes, and

b. what are the feed and element probe positions?

To resolve the first question we built a "D" lens for which the finallayout is shown in Fig. IV-1. There were 3 major goals of thisexperimental effort, namely, what are the probe dimensions that yield agood transmission line match, what is the array element pattern, and whereis the phase center. An additional factor was whether either the elementpattern or the phase center varied if the array were linear or mildlycurvilinear. The "D" shape was selected since it bracketed the curvaturesexpected for the final lens, i.e., the linear side had less curvature andthe arc had greater curvature. The experimental assembly used two largesheets of aluminum spaced by sections of X-band waveguide, one suchsection functioning as the wall for the linear array of input probes.Absorber was placed in an arc away from this wall and a single probeinserted. Access holes in the top plate of the lens provided a means ofinserting a field probe to determine field strength. The plan was tomeasure match and pattern. Once a probe was transmission line matched itwould be embedded in a larger array of identical probes. The centralprobe would then be altered for improved match and all probes modified tothat design. This iterative procedure with ever increasing array sizeshould eventually terminate in that no modification of the probe would berequired on increasing the number of elements in the array. Finally theabsorber would be removed and replaced by a reflecting wall with a similararray of probes to terminate the entire region. Completely enclosing the

5 p

perimeter of the lens by the probe array was done primarily to avoid the

use of absorbing material within the parallel plane structure.

When the probe array was of size 7 it was determined that there were

too few design degrees of freedom available to simultaneously match theprobe to the transmission line and obtain a good cose element pattern. Toprovide another degree of freedom, a parasitic stub was placed in front ofeach probe away from the wall, see Fig. IV-2. A very considerableimprovement of the element pattern resulted, Fig. IV-3.

The phase center of a single driven probe embedded in an array wasmeasured by inserting a field probe through the top plate of the cavitythrough holes drilled in a circle with center at the central probe of thelinear side. Figure IV-4 shows the results. The radius of the circlewas approximately 3 wavelengths and the size of the array was also about 3wavelengths. Such near field probing, although providing for considerablephase center location accuracy, suffers from large relative angularchanges from the group of probes. Consequently, instead of obtaining avery smooth curve, indicated by the conceptualized curves labeled at walland 1/2 way in Fig. IV-4, the phase measurements show a growing oscilla-tory form away from the symmetry axis. This arises from the differencesin space attenuation and angle between elements of the array. Withparasitic stubs the oscillations seem to have a mean which is centered onthe horizontal axis, indicating that the phase center exists at the centerof the circle, i.e., exists at the on-axis probe itself. (Looking ahead,after testing of the final assembly this interpretation was confirmed, atleast to the accuracy possible in the above measurement. A very minordifference of about 4% closer to the wall was measured.)

The second question which had to be answered was that concerning theideal loci and positions for the f and e probes. In lieu of actuallysolving the variational equations a numeric method was used to empiricallyestimate the desired functions. The numerical procedure has someadvantages since amplitudes could be used in computing the sum of thephasors which represents the far field from an array antenna attached one-to-one to the ports ei . Physically, at some angle from the broadside tothe antenna (dependent on the feed port fi) the phasor sum will reach amaximum. The maximum should have a value proportional to N2 but will bedegraded by phase errors. Thus the difference from N2 will be measure ofthe phase error. This could be a useful criterion in selecting the curvesf and e, assuming that the phase errors which occur are not periodic. Alens with a fixed separation of the axial intercept points was assumed anddifferent curves used to calculate the phasor sum, or gain. The curveparameters were altered in a multivariable gradient routine using max gainas a performance criterion. Ellipses were chosen for the curve form.

A second empirical approach was used based on the minimization ofthe variance from a linear dependence of D(e). This was motivated by theexamination of the derivatives in section III. A spreadsheet was preparedon an IBM PC which was programmed using a circle for e( ). A value of fwas chosen and a value of x iteratively entered to find a minimum in thedeviation of D(e,x) from a linear dependence on e. This very rapidlyyielded the shape of the desired curve f(x) and showed a form very closeto a circle for probes near the axis.

6

Both empirical approaches arrived at the same curve for the feedsover the desired interval in spite of the fact that the gain calculationused an amplitude weighting and the variance procedure used only the phaselength. In fact, the curve f(x) was not terribly sensitive to exactcontour and a circle of 10) yielded the best gain and minimum variancefor o=16X. The approximating circle was used in the construction of thefinal lenses. The two sets of points needed to locate the probes, (eFi)and (f.,x.), were calculated such that there was an element probe and a

e , and afeedprob e on axis and the chord length between adjacent probes wasexactly A/2. To blend these two curves together into a closed surface an

ad hoc spline curve was used which was both smooth and of a length whichwas a multiple of A/2. The final assembly blueprint is represented inFig. IV-5.

V. TEST AND EVALUATION

The T&E of the pair of lenses was conducted using an HP 8510 NetworkAnalyzer system. This system provides a very accurate measurement of thescattering matrix for a microwave circuit two ports at a time. Since eachof the lenses had more than 100 ports it was necessary to load all portsexcept the two for which the components of the >100x100 scattering matrixwas being evaluated. After each lens was characterized individually theywere connected in a back-to-back configuration and the combinationsimilarly characterized. For the back to back case of each transmissionline interconnecting element ports was phase trimmed to a standardlength. This was done by connecting the central input port and centraloutput port to the network analyzer, loading all other ports save two,connecting those two with a transmission line, and trimming that length ofline to a reference electrical phase length. The connecting cables hadpreviously been cut to very nearly the same length such that no 21 errorexisted. After the trimming that cable was disconnected, the ports loadedand another set of elements treated in the same way.

Figure V-i , 2 show the complex reflection coefficient for one of thelenses. The abscissa for these curves are labeled BOTTOM (UPPER) PORTNUMBER which refer to the lens input port, and element ports, respec-tively. In these Fig. 67 ports are measured for the input and 51 for theelements. The remaining ports occur in the "corners" of the lenses, inthe spline fit region, and are superfluous for this analysis even thoughthey are critical for the performance of the lens. Figure V-I shows themagnitude of the reflection coefficient at the top and the phase at thebottom. The critical region covers ±24 ports which corresponds to anoutput scan angle from a linear array attached directly to the elements(±16 ports) of ±450. It can be seen that the reflection coefficient isless than -20 dB over this region everywhere except for port 0, the on-axis port. This corresponds to VSWR of better than 1.2:1 almost every-where. The exception, port 0, is unique in that all the mismatch fromthe opposite surface returns in phase because it occurs on a circle withcenter at port 0. This peak is almost exactly 3 dB higher than that forthe adjacent ports. This implies that the reflection from a given portcomes primarily from reflections within the lens rather than from a simplemismatch of the transmission line at port 0. Since the reference phasewas that through the lens using input 0 and element 0 (involving theentire inphase reflection from the element surface) the reflection phase

7

relates to the scattering from the second surface as seen from the inp;Lport). The 0 port is self conjugate, meaning that all the reflections V

combine in phase at the input port. All other ports have their inphasereflections combining at the conjugate port. In our enumeration of the S

ports the port conjugate to input port 1 would be input port -1, thatconjugate to port 10 is port -10, and so forth. V

Figure V-2 portrays the same information as Fig. V-I except that the

lens surface ports are used as "inputs" from the Network Analyzer. Again

the reflection coefficient is small over the range of interest, ±16 ports.In this case there is no exactly conjugate port corresponding to a giveninput and the reflections from the second surface nowhere add up entirelyinphase. Again, the phase curve shows mainly 3600 jumps which is oflittle importance practically.

Figure V-3 to V-28 shows the magnitude and phase behavior across thearray of element ports (labled "UPPER") with the feed (BOTTOM) port as aparameter. For the phase curves the li.iear trend and mean phase have beeneliminated by subtracting the most frequently occuring slope, the mode,

and then removing the mean value. The system was designed to be optimizedover 33 element ports although 51 ports are associated with that side (the 4.additional ports act as dummy ports to eliminate edge effects). The on-

axis ports are labled zero. Figure V-3 shows the data for all 51 portswith the input being BOTTOM port 0. It can be seen that beyond 16 oneither side (near the sharpest corners in Fig. IV-5) rather large

interference occurs. Within the design range, both the phase and I,

amplitude is well behaved, withing 0.5 dB, and of a cyclic nature. All inall the amplitude and phase variation is well behaved. There is even the

semblance of a cosine elemental pattern apparent in the magnitude plot. SThe fact that the MODE SLOPE of Fig. V-3 is not zero indicates that the

center of curvature of the UPPER or element ports is not exactly a' inputport (BOTTOM) 0. The 1.641 degree trend from port to port is indicativeof a center of curvature approximately A/14 to the negative side, toward

negative port numbers. This corresponds to a 7 mm wedge (over 33 ports)inserted in the two sections of the lens as it was joined together. Thislinear trend could be taken out when the lenses were configured in a back- 10to-back configuration although it is so small that it is probably not 1.0significant. If a linear array were attached directly to the element

ports it would cause the beam to be squinted by 0.50.

Figure V-29 to V-35 are samples of patterns in the back-to-bacK

configuration. The abscissa is output "feed" ports with input "feed" port

as a parameter, these are denoted BOTTOM and BOTTOM(1), respectively. it

should be remembered that the back-to-back configuration is very similarto a telescopic arrangement of optical lenses which have the same focallength. In essence the two lenses are positioned so that the back focalplane of the first is coincident with the front focal plane of thesecond. Ideally, a point source positioned in the front focal plane ofthe first lens (at the feed point) will focus all the energy to the %conjugate point, the inverted image, located in the back focal plano )fthe second lens (since the wavefronts are collimated between thelenses). The source radiates energy which is not captired by the firstlens (the element pattern in this case) so there is some loss in tnetransfer of energy from object to the image. For the bootlac- iens. s

8

q6

approximately half the energy is lost in passing through each lens for atotal of 6 dB loss. This loss is evident at the top of Fig. V-29. Theimpulse response function or pattern in this case should be mindful of asinc squared function modified slightly due to a cosine apertureweighting. Figure V-29 does resemble a sinc squared for the near in

sidelobes but deviates in the far out sidelobes as might be expected.

Figure V-30 shows a similar situation wherein input port -8 isexcited. Figure V-31 illustrates input +11, Fig. V-32 for port 16, andFig. V-33 for port -25. It will be noted that the main beam occurs at tneconjugate port in the back-to-back arrangement and second time aroundeffects which would occur at the proper port number are not strong.Figure V-34, 35 illustrate patterns when multiple ports are excited. The C.,first shows ports 8 and 9 equally driven. The second, Fig. V-35, excizesports 7, 9 and 11 with weights 0.5, 1.0, and 0.5. The latter caseapproximates a Taylor weighted beamformer for 45 dB far out sidelobes.

The last two sets of figures, 36-44 and 45-53, display the frequencyresponse with feed and receive ports as parameters. The first nine areassociated with input or feed port 0 whereas the last nine relate to acommon feed port 8. These curves essentially illustrate how the peaks andnulls of the back-to-back combination of bootlace lenses change as thefrequency is altered. It is to be remembered that this system includes avirtual linear array between the lenses by the interconnecting cables.Although the arrangement is a pure time delay system which implies thatthe mainbeam direction will not deviate with frequency, the size of theaperture in terms of wavelenghts will change. This alters the sidelobeperiodicity. Because the frequency excursion is not great, only 200 MHz,there is less evidence of a frequency sensitivity for the sidelobes thanfor the nulls. Figure V-36, for example has a null within the frequencyrange and a near null elsewhere. The 1800 phase change as the frequency ,.

is swept through the null is apparent. For Fig. V-38 there are apparentlytwo nulls but the first is probably an artifact of the data (also V-47).It can be seen that there is obviously inconsistent data near 3.11 GHz,spikes, and nere is a high probability that some system malfunction,transient effect or data dropout introduced these artifacts. Figure V-42shows much the same type of behavior and should in fact be identical withFig. V-38, except for the lack of sharpness of the phase transition. Thislatter property points to both some coma and some spherical aberration inthe lens system. Figure V-44 illustrates the effect of spherical aberra-tion more strongly in decreasing the depth of the null at 3.215 GHz andmoderating the phase jump at that frequency. Figure 45-53 are similarexcept that the constant feed port is number 8. Now the sphericalaberration completely eliminates the formation of a deep null in thefrequency span.

VI. CONCLUSIONS

The main conclusion which can be drawn from this effort is that itis possible to obtain a reasonable quality beamformer using a parallelplane medium for the lens. This is true provided care is taken in thedesign of the probes so that a reasonable approximation to an idealPlement pattern can be achieved. The system being well matched impliesthat the element pattern even when embedded in the curvilinear arrays ised

9 '%

.... ... .. . .. ... .... - 7

P

(10A and 16 of curvature) is close to ideal although not perfect. Tnere

does not have to be severe resonances nor is it necessary to load the

medium with absorber to avoid unwanted modes. It was observed however,

that if even one of the ports were opened or shorted, severe degradation

of the beamforming resulted. This means that the system is quite unstable

to variations of the transmission line match.

VII. REFERENCES

1. W.F. Gabriel, "Adaptive Arrays-An Introduction," Proc. IEEE, Vol. 64,

pp. 239-272, Feb 1976.

2. W.F. Gabriel, "Using Spectral Estimation Techniques in AdaptiveProcessing Antenna Systems," IEEE-AP, AP-34, #3, pp 291-300, Mar 1986.

3. A.M. Vural, "Effects of Perturbations on the Performance of

Optimum/Adaptive Arrays," IEEE-AES, Vol. AES-15, #1, pp 76-87 Jan

1979.

4. J. Blass, "Multi-Directional Antenna-A New Approach to Stacked Beams,"

IRE Natl. Cony. Record, Pt. 1, pp 48-50, 1960.

5. J. Butler and R. Lowe, "Beamforming Matrix Simplifies Design of

Electronically Scanned Antennas," Electronic Design Vol. 9, pp 170-

173, 1961.

6. H. Gent, "The Bootlace Aerial," Ray. Radar Establishment J., pp 47-57,

Oct 1957.

7. J. Ruze, "Wide-Angle Metal-Plate Optics," Proc. IRE, Vol. 38, pp 53-

58, Jan 1950.

8. W. Rotman and R.F. Turner, "Wide-Angle Microwave Lens for Line Source

Applications," IEEE-AP, Vol. AP-11, #6, pp 623-632, Nov 1963. "

9. D. Archer, "Lens-Fed Multiple-Beam Arrays," Microwave J., Vol 18, #kO,pp 37-42, Oct 1975.

10. K. Takashi, S. Mano, and S. Sato, "An Improved Design Method of Rot-man

Lens Antennas," IEEE-AP, Vol AP-32, #5, PP 524-527, May 1984.

''p

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