Convergence of Radio with Fiber

8/13/2019 Convergence of Radio with Fiber

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL. 41, NO. 6/7,JUNWJULY 1993 1126

Electromagnetic Model of a PlanarRadial-Waveguide Divider/CombinerIncorporating ProbesMarek E. Bialkowski, Senior Member, IEEE, and Vesa P. Waris, Student Member, IEEE

Abstract-A field matching technique is used to develop anelectromagnetic model for an M-way planar radial-waveguidedivider/combiner incorporating probes. Based on this model, abroadband operation of the radial divider/combiner is investi-gated. The applicationof the developed model is shown in a designexample of a 20-way power divider.I. INTRODUCTION

ICROWAVE power combiners/dividers are frequentlyM sed in microwave systems in which power divisionor combination is required. They play a vital role in thecompetition of solid-state power amplifiers with their coun-terparts-tube amplifiers. Many times in the past, waveguidetransmission-line combiners, including rectangular, coaxial,conical, and radial [1]-[6], have been used, but only a fewhave been modeled so far. Most of the developed models areof the qualitative type, as they give only a general ideal of thewaveguide combineddivider operation. Quantitative modelsbased on a full-wave analysis have been obtained only for rect-angular waveguide combiners of the Kurokawa type [2], [3].This paper reports on a fulJ wave analysis of a planar radial-waveguide power combineddivider which incorporates probes.Based on this analysis, an electromagnetic model of the deviceis obtained. This model is used to study the optimal dimensionsof the radial power divider for its broadband operation.

11. FORMULATIONFig. 1 shows the configuration of the analyzed radial powerdividerkombiner. The device consists of a cylindrical cavitywith one central probe and A4 equispaced identical peripheralprobes. The probes are formed by conducting posts, loadedwith discs at their ends. For symmetry reasons, peripheralprobes are assumed to be identical in shape and size. Thecentral probe dimensions may differ from those of the periph-eral probes. The probes are energized from gaps in the postswhich are located between the cavity floor and the discs.In practice, the probes may also be energized from coaxialentries, as shown in Fig. l(c), diagram (i). However, sincethere exists an equivalence between the excitation from thecoaxial entry and the gap in the post [12], there is noneed to consider two types of excitation separately. In theManuscript received March 3, 1992; revised October 16, 199 2.The authors are with the Department of Electrical Engineering, TheIEEE og Number 9209330.University of Queensland, Queensland 4072, Australia.

theoretical approach, the coaxial entry of Fig. l(c) (i) isreplaced by an equivalent gap of Fig. l(c ) (ii). Note thatthe power dividerkombiner described in the form above isregarded as a passive device. Active devices, if required,can be attached from the outside. To include active devices(Le., Impatt or Gunn diodes), the probe configuration needs

PROBE

RADIAL GUIDE CENTRAL PROBE(a)

i i ) i i i )( 4Fig. 1. Configuration of an M -way radial-waveguide combiner/divider in-corporating probes. (a) top view, @) side view (c) probe configurations:(i) probe energized from a coa xial line, (ii) probe energized from an equivalentgap in the post, (iii) probe suitable in the design of active power combiner.

0018-9480/93 03.00 1993 IEEE

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to be modified from the one shown in Fig. l(c) (i) to theone shown in Fig. l(c) (iii). From a theoretical point ofview, this modification is easy to accommodate. The requiredmodification is explained in further analysis while producingthe expressions for the fields in regions surrounding the probes.The ideal operation of the passive power combiner/dividercan be described as follows. In the power divider mode, thepower is fed to the central probe and is equally divided withoutany loss between the match-terminated peripheral probes. Inthe power combiner mode, the power is fed in-phase to theperipheral probes and is collected without any loss by thematch-terminated central probe. It is apparent that the idealoperation calls for the impedance match of the central andperipheral probes. This match can be obtained by choosingproper dimensions of the central and peripheral probes, andof the cavity.To investigate the broadband match conditions, a full-wave analysis of this device is performed. A n alternativeanalysis, which includes approximations of the sectorial guidecontaining the peripheral probe by a rectangular waveguide,is described in [13].The present analysis is confined to the cases when theperipheral probes are fed in-phase or terminated in the sameloads. To analyze the power divider/combiner, the admit-tance- rather than the scattering-matrix approach is chosen(no need for specifying characteristic impedances). However,once the admittance matrix parameters are known, conversionto the scattering parameters is straightforward.For the case when the peripheral probes are fed in thesame way or are terminated in identical loads, the admittancematrix parameters of the device are defined by the followingequations

Io = YOOVO + (Yo1+ * + Y0M)VlI = YlOVO + (Yll + . + Y1M)Vl (la)

which can be rewritten in the form10= Yoovo + MYoiViI = YlOVO + YY,lVl (1b)

where Vo is the voltage applied in the gap O (in the centralprobe), VI is the voltage applied in the gap 1 (in the periph-eral probes), and IO, are the resulting currents in gaps Oand l.Note that YYIl in ( lb ) is given as the sum of, Y11,Y12, a , Y ~ M . quations (la) and (lb) show that in order toobtain the admittance matrix for the symmetric radial powercombiner/divider for the case when the peripheral probes areloaded or energized identically, two field problems have to besolved: 1)when the central probe is energized by voltage Vand the peripheral probes are short-circuited; and 2) when theperipheral probes are energized by the same voltage VI andthe central probe is short-circuited.Assuming that the parameters YOO,Y10 Yol, and YY11 arefound, the input admittance seen at the central probe can bedetermined by using standard circuit analysis.The problem becomes more complicated when the pe-ripheral probes are energized or terminated arbitrarily. In

this case, all the individual admittance matrix elements Y11,Y12,. ,Y ~ Mn (la), rather than their sum YY11, have to bedetermined. This can be accomplished by solving the fieldproblem for the situation when probe 1 is energized byvoltage VI and all the remaining probes inside the cavity areshort-circuited. Since expressions describing the interactionsbetween the individual probes are derived in the Appendixfor an arbitrary location and excitation, the extension of thepresent theory to this general case should be straightfor-ward. The only new complication is the increased numberof unknowns (namely, the number of expansion coefficientsdescribing the local fields surrounding the peripheral probes) tobe determined. This complication can, however, be overcomeby solving M problems exhibiting M-fold axial symmetryfor which the number of unknowns can be reduced. Theseproblems are defined by the conditions that the central probeis short-circuited and the peripheral probes k = 1, . .,M areexcited by voltages Vkp = exp(i&(k - l) p - l ) ) ,whereo = 360 deg/M and p = 1, . ,M. Note that the sum ofVkp versus p divided by M is equal to 1 only for k = 1 andotherwise is equal to 0. It is apparent that the superpositionof the solutions to the new problems is equivalent to the

solution of the initial problem with only one peripheral probeexcited. The extension of the present theory to this case isnot considered here but is a subject of further investigationsin [14], [16].For the peripheral probes terminated in identical loadscharacterized by the admittance YL, the input admittance atthe central probe Yin s given by

Having determined the input admittance, the input reflectioncoefficient at the central probe, with respect to an arbitrarycharacteristic admittance Ycl, can easily be determined and isgiven byTin = - E n - Ycl)/(Xn +Ycl) * (3)From the earlier discussion of the ideal operation of thepower combiner/divider, it is apparent that for the perfectcombineddivider, Tin has to be zero for the case whenthe peripheral probes are terminated in their characteristicadmittances Yc2.

111. ANALYSISCurrents o and 11 ecessary to determine circuit parameters&, and therefore the value of Tin n (3), can be obtained byusing the relationship between the surface currents and themagnetic fields surrounding the probes. IO and 11 are relatedto the magnetic field tangential components at the surfaces

enclosing gaps O and 1 and are given by expressions [7]


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BlALKOWSKI AN D W ARIS: ELECTROMAGNETIC MODEL OF PLANAR RADIAL-WAVEGUIDEDIVIDEIUCOMBINER 1129

Expressions for the fields in volumes I11 and IV can beobtained by introducing the following substitutions in expres-sions 5) :Bi B3, B2 B4, 6 4 , c + 4 go 91

h0 --t hl I IC1 --t k 3 , IC2 -- IC47 2 1 2 3 , 2 2 -) 24,2 -+IC ,C )+ IC ),ill + r;), ri2)-,El, -+ E3,, D1, - D3,, 02, -+ 04,.The above-derived expressions for the field components arevalid for the case when the probes are of type (ii) [Fig. l(c)]with empty regions above the discs. These expressions, how-ever, can easily be extended for the case of probe type(iii) [Fig. l(c)] with the post above the disc. The requiredmodifications are straightforward. To include the post in theregion above the disc, the functions J J and JJP describingthe y-component of the electric field and the $-component ofthe magnetic field in regions I1 and IV have to be replaced byfunctions H J and H JP, respectively.

B. Field Expansions-External RegionTo determine the external tangential field components at the

interfaces r = 6 and r1 = a, expressions for the electric andmagnetic fields due to a single, arbitrarily positioned probein a radial cavity, derived in the Appendix, can be used.Now, those expressions have to be extended to the case ofM symmetrically positioned peripheral probes and one centralprobe. To simplify derivations, it is assumed that one of theperipheral probes is positioned at T = TO = 0. In this case,the combineddivider configuration becomes symmetric withrespect to 4 = 0, and for the assumed type of excitation thefields become even functions of . As a result, the exponentialterms exp(-j ) in the azimuthal expansions for the electricmagnetic field components (A6), (A7) are replaced by cos(p4)terms.The other modification comes from the M-fold symmetryof the dividedcombiner. Because of the M-fold symmetry ofthe device and its excitation, all the azimuthal harmonics inexpressions for the electric and magnetic fields inside the radialcavity which do not exhibit the M-fold symmetry disappear.This implies that in the term Qn,which appears in expressions(A8)-(All), only harmonics of the order p = 0, M, 2 M , etc.,have to be retained.Having exploited all the symmetries of the radialcombineddivider, derivations for the expressions for they-component of the electric field and the $-component of themagnetic field at the cylindrical boundaries r = 6 and T I = abecome straightforward.For the central probe (at T = b),m

EY = A,uu ~)C ~ V V ( ~ ) ]os(kyny)Bn=O

the probes. The remaining symbols are defined as follows:

nrr: = k2 - IC; C -B For the peripheral probe (at T I = a ,E y = AnTT(n) cnQQ(n)]os(kynY)

n=O

(7)

where Q,, defined in the Appendix, is now modified to thefollowing form:M

m=2m

p=O M ZMwhere rml is the distance between the middle positions of the1st probe and the mth probe.C . Field MatchingThe remaining goal in the field matching procedure isthe determination of the field expansion coefficients. Forthis purpose, continuity conditions for the tangential fieldcomponents are used. These conditions can be stated by thefollowing equations.

At r = 6EY* O I y 5 B i

E y ( e r t ) = 0 for B1 I 5 B - B2{ EyII B - B2 5 ?/ 5 BH i = H+(,,t)

H y = H+(e,t)for 0 I Y I Bi ,

for B - B2 5 y I . (8)Similarly, at T I = a,

HFI = H+(e,t)Hiv= H+qeZt)

for 0 I 5 B3for B - B4 5 y 5 B

EyIIEyIv

0 5 y 5 B3for B3 5 y I - B4B - B4 5 y 5 B . 9)

6)where IC 2 are the wave number and intrinsic impedance forthe cavity region outside the cylindrical volumes containing


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1130 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHMQUES OL. 41, NO. 6/7, JUNE/JULY 1993

Equations (8) and (9) are in the functional form and aretherefore unsuitable for computations.In order to convert (8) and (9) into algebraic equations,which can be handled by a computer, the following integra-tions are performed.At T = b,

m = 0,1, *

* COS( kg) - B- Bz))dy

At T I = a, the required integrations are analogous to those atT = 6, shown in (10). The necessary changes are obtained byreplacing indices 1,2 in (lo), corresponding to volumes I, 11,with new indices 3, 4 corresponding to volumes 11, IV.

IV. RESULTSBased on the theory described above a computer algorithmin MICROSOFT Fortran for an IBM PC for the analysis ofan M-way radial waveguide dividerbmbiner was developed.

This algorithm was aimed at calculating the input admittance(2) as observed at the central probe for the case when theperipheral probes were loaded identically. In calculations, in-finite expansions describing the fields in individual volumes I11,111,and IV and the cavity region were truncated.To evaluate0th and 1st-order Bessel and Neumann functions, polynomialapproximations [111were used. Higher order Bessel and Neu-mann functions were evaluated by using recursion formulas[ll]. or Bessel functions, the backward recursion formulawas used. For Neumann functions, the forward recursionformula was applied.In order to test the developed theory, and especially thevalidity of the approximation that the actual fields in regions I,11, 111, and IV surrounding the probes are axially symmetricfields, a two-probe divider was built. The device includeda radial cavity with one central probe and one peripheralprobe. For this device, a comparison between experimental andtheoretical results for the scattering parameters So0 (reflectioncoefficient of the central probe) and SI, (reflection coefficientof the peripheral probe) could be performed.Fig. 2 shows a comparison between theoretical and ex-perimental values for So0 and 511 in the frequency bandfrom 8 to 12 GHz. Experimental results were obtained byusing probes (type (i) of Fig. l(c)] fed from 50 R coaxiallines. The reference plane for measurements was chosen at

Fig. 2. Comparison between theoretical and experimental results for thescattering parameters So0 and Sll of the two-probe divider. Dimensions:radial cavity R = 19 .5 mm B = 6 . 7 5 mm, central probe d = 0 . 6 5 mm,b = 2.3 mm, B1 = 1 . 6 5 mm, B2 = 1.10 mm, go = BI ho = B1/2,e-ripheral probe c = 0 . 6 5 mm, Q = 2.2 mm, B3 = 2.00 mm, E4 = l 6 0 mm,g1 = B3, hl = B3/2, r , = 1 3 . 5 mm. Coaxial probe outer conductor radius2.1 mm. SOO:heory - experiment - - -,S11: theory - .- .- ,experiment. . . . . .

the junction between the coaxial line and the radial cavity.A Hewlett-Packard vector network analyzer HP 8510 B wasused in the measurements. Numerical results were obtainedby using the equivalent gap approach [see Fig. l(c) (ii)].In the latter case, results for So0 and S11 were referencedto the cylindrical surface enclosing the gap. Although goodagreement was obtained between the measured and calculatedreflection coefficient for both the central and the peripheralprobe, the numerical results for the central probe seem to bein slightly better agreement with experimental data. This canbe explained by the fact that the region which surrounds thecentral probe exhibits a better axial symmetry than the onewhich surrounds the peripheral probe.In the next step, the developed algorithm was applied tothe design of a 20-way radial divider. By using the developedalgorithm, a search for the devices optimal dimensions wasinitiated to produce the maximum value of the return loss forthe central probe, in the 10-18 GHz band. In the search, theinitial dimensions were chosen as follows. In order to obtainthe dominant mode propagation (uniform with height radialwaves), the waveguide height was chosen to be less thana half-wavelength, at 18GHz. Distances between adjacentperipheral probes were chosen approximately equal to half-free-space wavelength, at the middle frequency of 14 GHz.The distance between the peripheral probe and the cavity wallwas chosen approximately equal to a quarter-wavelength, atthe middle frequency of 14 GHz. It is worthwhile to mentionthat to produce 20 frequency points for the input impedanceof the central probe, it took only several seconds of CPU timeof 486DW33MHz PC.In order to validate the theoretical result, the actual model ofthe 20-way radial combineddivider was built. This model in-corporated coaxial probes which were energized from coaxialentries.Figure 3 shows the final dimensions of the radialdividerkombiner and a comparison between theoretical and


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BIALKOWSKIAND WARIS: ELECTROMAGNETIC MODEL OF PLANAR RADIAL-WAVEGUIDE DIVIDEWCOMBINER

0 1 I

v)330

4010 12 14 16 18FREQUENCY [GHz]

Fig. 3. Com parison between theoretical and experimental results for thereturn loss (referenced to 50 R) of the central probe in the 20-way redialdivider. Radial cavity dimensions: B = 5.5 mm, R = 39 mm. Central probedimensions: c = 0 . 6 5 mm, b = 1.8 mm, E1 = 1 . 4 5 mm, Bz = 1 . 2 0 mm,go = B1 ho = B1/2. Peripheral probe dimensions: d = 0 . 6 5 mm,a = 1 . 8 mm, B3 = 2 . 1 mm B4 = 1 . 5 0 mm, g1 = B3, h l = & / 2 .Peripheral probe position P,, = 3 4 . 1 mm.Theory: peripheral probes terminated with 50 R loads -, peripheralprobes terminated with 43 R loads - - -,Experiment: o - -0 -0.experimental results for the values of the return loss observedat the central probe (for the case when the peripheralprobes were terminated in 50 R loads). Both theoretical andexperimental results show a reasonably good quality match,corresponding to the return loss of not worse than 17 dBthroughout the entire band from 10 to 18 GHz.The discrepancy between theoretical and experimental re-sults can be explained by different reasons, such as approxima-tions used in the theory or the difference in probe excitations.It was, however, felt that the more obvious reason would bethe use of nonideal SMA match loads which terminated theperipheral probes during measurements.To confirm this hypothesis, a separate set of measurementson SMA terminations was performed. These measurementsshowed that the return loss for individual SMA terminationsranged from 20 to 30 dB in the entire 10-18 GHz frequencyband. In order to investigate the influence of nonideal matchterminations, another set of calculations was performed. Fig. 3shows the return loss observed at the central probe when theSMA loads are modeled by constant admittances of 43 R (thiscorresponds to 22.5 dB return loss).It can be seen that, in the last case, the maximum valueof the return loss did not change and was about 1 7 dB.However, the shape of the curve representing the return lossfor the central probe had changed significantly. This simulationshowed that indeed nonideal terminations are likely to beresponsible for slight discrepancies between theoretical andexperimental results for the return loss of the central probe.

In order to further test the design of the 20-way divider,isolation measurements in the 10-18 GHz band between se-lected probes were performed. Fig. 4 shows the experimentalresults for the isolation between the 20th and l st , 2nd, 5th, and10th probe, respectively. It can be seen that, on average, theisolation is better than 10 dB. The best isolation seems to bebetween the 20th and the 2nd probe (for the probes which are

40

1131

18010 12 14 16FREQUENCY [GHz]

Fig. 4. Measured isolation in the 20-way radial divider. Isolation betweenprobes: 20th and 1st -, 20th and 2nd - - - ,0th and 5th , 0thand 10th - - * - - * - -*.

interleaved by one probe). The worst isolation is between the20th and the 10th probe, (the probes located on the oppositesides of the divider).V. CONCLUSIONS

A field matching technique for the analysis of a planarradial-waveguide power combineddivider has been presented.Based on this analysis, a computer algorithm for determin-ing the admittance matrix parameters of the radial com-bineddivider has been developed.This algorithm was tested on the example of a two-probedevice. Good agreement between theoretical and experimentalresults for the reflection coefficient of the central and theperipheral probe was noted. In the next step, the algorithm wasused to determine the optimal dimensions of the 20-way powerdivider for its operation in the 10-18 GHz frequency band.The theoretical design was verified experimentally by buildingthe physical model of the 20-way radial combineddivider.Comparison of the results has shown good agreement be-tween the developed theory and experiment. The analysis andcomputer algorithm described here should prove useful to thedesigners of radial-waveguide combineddividers in the future.

APPENDIX

Cylindrical Cavity with a Single ProbeFig. 5 shows the top view of a radial cavity of radius Rand height B containing two cylindrical regions of differentradii a and b and of equal height B. Inside the cavity, thereis a probe which energizes the entire structure. The probe islocated inside a cylinder of radius a, which is positioned at

T = TO q = 40. It is assumed that the shape of the probeand the form of excitation are such that the probe supports anaxially symmetric current having a y-component, possibly aradial q-component, and no 41-component.From the theory of cavities [lo], [15], it is known that underthe above-specified conditions, the field existing in the cavityis described in terms of radial TM (to the y-direction) waves.


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BlALKOWSKl AND WARIS: LECTROMAGNETIC MODEL OF PLANAR RADIALWAVEGUIDE D IVIDEWCOMBINER 1133

Averages of the Electric and MagneticFields Over Cylindrical Surfaces

In the analysis of the radial power dividerkombiner, itis required to extract from expressions (A6) and (A7) theaxially symmetric terms of the y-component of the electricfield and the 41- nd 42-components of the magnetic fieldat two cylindrical surfaces: r1 = a and r 2 = b, respectively(Fig. 5).The required axially symmetric terms can be obtained byapplying the addition theorem to the cylindrical functions in(A6), (A7) and by retaining only symmetric (constant with4) terms in infinite expansions. By using this procedure, thefollowing approximations of the fields are obtained.For the cylindrical volume r1 5 a, inside which the probeis located, Ell is approximated by

where

Note that in the expression (A8), the singular nature of thefield is represented by the Hankel function

For F < 0, radial waves produced by the peripheral probesdecay with distance and therefore the expression for Qn canbe approximated by

where rli is the distance between the middle position of theprobe and its fist image against the side cavity wall.The 41-component of the magnetic field for points insidethe cylinder 7-1 5 a can be approximated by

The axially symmetric terms for the y-component of theelectric field and the 42-component of the magnetic field at thecylindrical surface r 2 = b can be obtained by using a similarprocedure to that which used to obtain (A8) and AS). Note,however, that as opposed to volume r1 5 a, the cylindricalvolume 7-2 5 b is source free, and therefore the fields in thisvolume are nonsingular.It can be shown that the axially symmetric term of they-component of the electric field at 7-2 b is given by

Ey(r2 2+b) = CnQnJ0(I,r2) cos(k,,y) (A10)Bn=Owhere Qn is now given by

and the axially symmetric term of the &-component of themagnetic field at r2 E b is given by

ACKNOWLEDGMENTThe authors wish to thank Dr. J. Ness, Dr. P. Allen, andother technical staff from MITEC Ltd., Australia, for makingavailable the manufacturing and testing facilities required foraccomplishment of the work presented in this paper.

REFERENCESK. . Russel, Microwave power combining techniques, IEEE Trans.Microwave Theory Tech., vol. MlT -27 , pp. 472-478, May 1979.K. hang and C. Sun, M illimeter-wave power-com bining echniques,Trans. Microwave T heory Tech, vol. MTT-31, pp. 91-107, Feb. 1983.B. J. Sand ers, Radial com biner runs circles a round hybrids, Mi-S. J. Foti et aL, 60-way radial combiner uses no solators, MicrowavesN. Okubo et al., A 6 GHz 80-W GaAs FET amplifier with TM-mod ecavity power combiner, in 1983 IEEE Int. Microwave Symp. Dig.,June 1983, pp. 276-278.P. J. Allen and J. B. Ness, A hemispherical radial power-wav eguidedividerkombiner for high power amplifiers, in IREE Conv. Proc.,Sydney, 1987, pp. 102-104.M. E. B ialkowski, Analysis of disc-type resonator m ounts in parallelplate and rectangular waveguides, Archiv fur Elektronik und Ubertra-gungstechnik, AEU, vol. 38, no. 5, pp. 306-311, 1984.-, Analysis of a coaxial-to-waveguide adaptor incorporating adielectric-coated probe, IEEE M icrowave Guided Wave Lett., vol. 1,-, Modeling of a coaxial wa veguide power co mbining structure,IEEE Trans. Microw ave T heory Tech.,vol. MTT-34, pp. 937-942.1986.R. . Harrington, Time Harmonic Electromagnetic Field s. New YorkMcGraw-HIII, 1961, Ch. 5.M. Abram ovitz and I. A. Stegun, Handbook of Mathematical Functions.New York Dover, 1965.R.L. Eisenhart et al., A useful equivalence for a coaxial-waveguide junction, IEEE Trans. Microwave Theory Tech, vol. MIT -26, pp. 172-174, Mar. 1978.M. E. Bialkow ski and V. P.Waris, A systematic approach to the designof radial-waveguide dividers/combiners, in Proc. 1992 Asia-PacificMicrowave Conf., Adelaide, pp. 881 884.V. . Waris, postgraduate thesis, Univ. Qu eensland, to be submitted.M. E. Bialkowski, Electroma gnetic model of a radial-resonator diodemount with off-centered diodes, IEEE trans. Microwave Theory Tech.,M.E. Bialkowski, Analysis of a planar M-way radial waveguidecombiner/divider for the case of arbitrary excitation, in 199 3 SBMOInt. Microwave ConfJBrazil Proc., p. 213-218.

crowave~, p. 55-58, NOV. 1980.andRF, pp. 96-118, July 1984.

pp. 211-214, AUg. 1991.

VOI MTT-37, pp. 1603-1611, Oct. 1989.


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1134 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 41, NO. 617,JUNE/JULY 1993Marek E. Bialkowski (SM88) was born inSochaczew, Poland, in 1951. He received theM.Eng.Sc. degree in applied mathematics and thePh.D. degree in electrical engineering, both fromthe Warsaw Technical University, Warsaw, Poland,in 1974 and 1979, respectively.In 1977 he joined the Institute of Radioelec-tronics, Warsaw Technical University, and in 1979became an Assistant Professor there. In 1981 hewas awarded a Postdoctoral Research Fellowshipby the Irish Department of Education an d spent oneyear at the University College Dublin carrying out research in the area ofmicrowave circuits. In 1982 he won a Postdoctoral Research Fellowship fromthe University of Queensland, Brisbane, Australia. During his stay in Brisbanehe worked on the modeling of millimeter-wave guiding structures (particularlyon waveguide diode mounts). In 1984 he joined the Department of Electricaland Electronic Engineering, James Cook University, Townsville, Australia,as a Lecturer in the field of communications. In 1986 he was promotedto Senior.Lecturer. In 1988 he was a Visiting Lecturer in the Departmentof Electronics and Computer Science, University of Southampton, U.K. Hewas invited to lecture in the field of antenna theory and design. In 1989 heaccepted an appointment as Reader (Associate Professor) in Communicationsand Electronics in the Department of Electrical Engineering at the Universityof Queensland, Brisbane, Australia. At present he is the Leader of theMicrowave and Antenna Group there. His current research interests includesix-port techniques, quasi-optical power combining techniques, modeling

of electromagnetically cou pled microstrip patch antennas, antenn as formobile satellite communications, near-field/far-field antenna measurements,and industrial applications of microwaves.

Vesa P. Waris (S91) was born in Pello, Finland,in 1967. He received the B.E. degree from theUniversity of Queensland in 1988.Since 1989 he has w orked for MITEC Ltd. Aus-tralia on the L-band Radioastron receiver, phase-locked oscillators and synthesizers, and a 30-GHzreceiver using packaged HEMTs. He is currentlycompleting the Master of Engineering Science de-gree at the University of Queensland.

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