w xused in 3 , and compare the results with that of the first-orderBayliss]Turkel boundary condition, which is widely applied in

w xcylindrical coordinates 1 , and has the same number of nodesŽ .in space and time as that of the TDMEI in Eq. 2 . Compared

with the MoM results, accurate results are obtained both inthe TM and TE cases as depicted in Figure 5, where thenumber of meshes between the truncated boundary and theobject surface is only ten.

4. CONCLUSION

A conformable time-domain truncated boundary conditionbased on the MEI concept is discussed in this paper. Afterthe MEI coefficients have been determined accurately, theTDMEI can be used to truncate the FDTD mesh close to theobject surface and with the same shape of the object surface.This novel boundary condition provides an efficient way toimprove the conformability of the FDTD method.

REFERENCES

1. A. Taflove, Computational electrodynamics: The finite-differencetime-domain method, Artech House, Boston, MA, London, 1995.

2. T.G. Jurgens, A. Taflove, K. Umashankar, and T.G. Moor, Fi-nite-difference time-domain modeling of curved surface, IEEE

Ž .Trans Antennas Propagat 40 1992 , 357]365.3. M. Fusco, FDTD algorithm in curvilinear coordinates, IEEE

Ž .Trans Antennas Propagat 38 1990 , 76]89.4. E.A. Navarro, C. Wu, P.Y. Chung, and J. Litva, Application of

PML super-absorbing boundary condition to nonorthogonalŽ .FDTD method, Electron Lett 30 1994 , 1654]1655.

5. J.A. Roden and S.D. Gedney, Efficient implementation of theuniaxial-based PML media in three-dimensional nonorthogonalcoordinates with the use of the FDTD techniques, Microwave

Ž .Opt Tech Lett 14 1997 , 71]75.6. F.L. Texiera and C. Chew, PML-FDTD in cylindrical and spheri-

Ž .cal grids, IEEE Microwave Guided Wave Lett 7 1997 , 285]287.7. D.B. Meade, G.W. Slade, A.F. Peterson, and K.J. Webb, Com-

parison of local radiation boundary conditions for the scalarHelmholtz equation with general boundary shapes, IEEE Trans

Ž .Antennas Propagat 43 1995 , 6]10.8. K.K. Mei and Y.W. Liu, On time domain measured equation of

invariance, USRI Meeting, Seattle, WA, June 1995.9. W.C. Chew, Waves and fields in inhomogeneous media, Van

Nostrand Reinhold, New York, 1990.10. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery,

Numerical recipes in Fortran: The art of scientific computing,Cambridge University Press, Cambridge, England, 1992, 2nd ed.

Q 1999 John Wiley & Sons, Inc.CCC 0895-2477r99

FREQUENCY-DISCRIMINATOR-STABILIZED OSCILLATORS WITHCOMMON RESONATORSStefan Andersson11 Microwave Electronics LaboratoryChalmers University of TechnologyS-412 96 Goteborg, Sweden¨

Recei ed 5 January 1999

ABSTRACT: Topologies for frequency-discriminator-stabilized oscilla-tors where the resonator is a part of both the oscillator and the frequencydiscriminator is presented. Using one of the topologies on a 4.6 GHzmicrostrip MESFET oscillator, the phase noise is reduced by 10 dB to

y52 dBc r Hz at 1 kHz off carrier. Q 1999 John Wiley & Sons, Inc.Microwave Opt Technol Lett 21: 417]423, 1999.

Key words: phase noise; microwa e oscillator; frequency discriminator

INTRODUCTION

Phase noise is the limiting factor in almost all microwavesystems today. The phase noise causes decreased resolutionin radar systems, symbol interference in transmission links,and more. The need for low-phase-noise oscillators is obvi-ous.

If a resonator in an oscillator operates slightly off reso-nance, the phase-noise performance will very quickly be

w xdegenerated 1 . The situation appears if the resonator’sresonant frequency is not identical to the oscillator’s fre-quency of oscillation. The discrepancy is sometimes referredto as a phase error, and can arise from manufacturing toler-ances. Also, the always present low-frequency noise modu-lates voltage-dependent reactances, and thereby alters the

w xfrequency of oscillation 2, 3 .The use of a frequency discriminator is a well-known

technique for reducing these phase errors, and thereby im-proving the phase-noise performance of oscillators. Someestablished frequency-discriminator topologies suffer from

Žthe difficulty of synchronizing two resonators or a delay line.and a resonator , while more recent topologies exhibit struc-

tures with a common resonator where the problem of syn-chronization has been eliminated.

A former topology for a frequency-discriminator-stabilizedtransmission mode oscillator with a common resonator in-

w xcludes a circulator 4]7 ; see Figure 1. Another former topol-ogy for a frequency-discriminator-stabilized oscillator with a

wcommon resonator is based on a reflection-mode oscillator 8,x9 ; see Figure 2.

Figure 1 Topology for a frequency-discriminator-stabilized trans-mission-mode oscillator including a circulator

Figure 2 Topology for a frequency-discriminator-stabilized reflec-tion-mode oscillator with common resonator

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 21, No. 6, June 20 1999 417

Figure 3 Resonator scattering parametersFigure 4 Frequency-discriminator-stabilized transmission-mode os-cillator with common resonator

Figure 5 Table of oscillator topologies

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 21, No. 6, June 20 1999418

This work presents a set of topologies for frequency-dis-criminator-stabilized oscillators with common resonators forboth reflection-mode and transmission-mode oscillators thatdoes not include any circulators.

TOPOLOGIES AND PRINCIPLE OF OPERATION

Consider the frequency-discriminator-stabilized reflection-mode oscillator with a common resonator as depicted in

w xFigure 2 8, 9 . Some of the reflected wave from the res-onator, labeled Q, and some of the transmitted wave passingthrough the resonator are sampled with couplers, and theirphases are compared. The phases of the resonator’s scatter-ing parameters S and S are presented in Figure 3. The11 21phase difference between S and S is zero at the res-11 21onator’s resonant frequency, and is proportional to the fre-quency in the vicinity of the resonator’s resonant frequency.The phase-compared voltage is therefore a frequency-dis-criminator output voltage. The voltage is then fed back viasome baseband control loop amplifying and filtering to anelectronically controlled phase shifter labeled f which con-trols the frequency of oscillation. In this way, the frequencyof oscillation is regulated to the resonator’s resonant fre-quency.

If the resonator in Figure 2 were completely matched atthe input port, there would be no reflected wave. In such asituation, one could sample some of the incident wave in-stead. A 908 phase shift would also be required to compen-sate for the wave passing through both couplers. In this way,

Ža transmission-mode oscillator could be realized see Fig. 4

w x. Ž w x.10, 11 without the use of any circulators as in Fig. 1 4]7 .w xThe idea is extended into a set of topologies in Figure 5 11 .

INITIAL SIMULATION RESULTS

The frequency discriminator part, including the resonator,surrounded by the broken line square in Figure 4 was simu-

w xlated using a commercial microwave simulator 12 . Inputdata are shown in Figure 6, and the simulation results inFigure 7 clearly show the characteristic frequency-discrimina-tor output voltage and the equally characteristic phase shiftof a resonator.

DESIGN

Using this topology, a circuit was designed in microstriptechnology on a 15 mil RT Duroid 5870 substrate; see Fig-ure 8.

For the microwave amplifier, to the left in Figure 8, anNEC 76084 GaAs MESFET transistor was used. The phaseshifter, at the top of Figure 8, consisted of a 3 dB branch linecoupler and two MA46H071-1088 GaAs hyperabrupt varac-tors.

The phase detector, at the lower right-hand corner of thelayout part in Figure 8, consisted of a 3 dB branch linecoupler and two amplitude detectors. For the detectors, bi-ased MA4E2054A-287 silicon Schottky diodes were used.

The resonator is placed approximately at the center ofFigure 8. Due to the resonator loss, the power level at theoutput port is approximately 6 dB lower than the power levelat the input port. To get approximately the same power level

Figure 6 Circuit diagram used as input data

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 21, No. 6, June 20 1999 419

Figure 7 Phase-shift and discriminator output voltage for the single-resonator frequency discriminator

Figure 8 Circuit

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 21, No. 6, June 20 1999420

at the two ports entering the phase detector, the coupler atthe resonator’s input port has approximately 6 dB less cou-pling compared to the coupler at the output port. Due tomanufacturing tolerances, at the etching process, it was de-cided to implement the output port coupler as a branch linecoupler and the input port coupler as a coupled line couplerto achieve the approximately 6 dB difference in coupling.

The control loop utilizing PI control characteristics hadlow-noise operational amplifiers OP37 and OP27. The OP37was used as a differential amplifier, and the OP27 was usedas a PI amplifier with adjustable gain.

MEASURED RESULTS

The circuit and some identical separate subparts of it wereetched and assembled. Measurements of the microwave am-plifier part are presented in Figure 9. It is well matched, andprovides 10 dB gain over a reasonable bandwidth.

The frequency-discriminator part, including the resonator,was also manufactured as a separate block. Measurementresults showing its transmission phase slope and detectoroutput voltage are presented in Figure 10. Some unimportantunbalance resulting in a small nonzero frequency-discrimina-tor output voltage at the steepest phase to the frequencyderivative can be observed. The measurement results shownin Figure 10 are quite similar to the simulation results inFigure 7.

The resonator in the complete oscillator circuit neededsome tuning for the oscillation to start. The resonant fre-quency was slightly lowered to about 4.6 GHz from theoriginally intended 5 GHz due to insufficient modelingof the microstrip resonator and the microwave transistor.After the tuning, the oscillator circuit performance was mea-sured. The phase noise was measured using the discriminatormethod with and without closing the phase-noise reductioncontrol loop. Figure 11 shows the phase noise with thecontrol loop broken, and Figure 12 shows the phase noisewith the control loop activated. A 10 dB improvement isobserved.

The resulting phase-noise level is remarkably low. It ismeasured to be approximately y52 dBcrHz at 1 kHz ofcarrier. Multiplying the oscillator output into a 15 GHz

Ž .oscillator using the q20 ? log n expression and calculatingthe phase noise at 100 kHz off carrier assuming a 30 dB

Ž .sloperdecade equals y52 q 20 ? log 15r4.63 y 2 ? 30 s

Figure 9 Microwave amplifier performance

y101.8 dBcrHz. A carefully designed MESFET microstriposcillator at 15 GHz is reported to have a phase-noise level of

w xapproximately y100 dBcrHz at 100 kHz off carrier 13 , anexceptionally low value for this type of oscillator.

DISCUSSION

The new frequency-discriminator-stabilized oscillators withcommon resonator topologies work. They provide a meansfor low-phase-noise oscillator designs. The principle is ex-pected to be scalable to higher frequencies.

In a VCO, the frequency of oscillation is indirectly con-trolled by electronically tuning the resonator’s resonantfrequency with, for example, a varactor or YIG sphere.However, the frequency of oscillation and the resonator’sresonant frequency will most likely differ at much of theVCO’s complete tuning bandwidth. This difference results inpoor phase-noise performance. The problem gets worse asthe VCO’s bandwidth get wider. The new topologies pre-sented in this work prevent this difference since they lock thefrequency of oscillation to the resonator’s resonant fre-quency, and thereby lower the phase noise.

The drawbacks are a more bulky design at lower frequen-cies due to the many branch line couplers. Also, an increased

Ž .number of RF devices varactors and detector diodes impliesa higher cost.

ACKNOWLEDGMENT

This work was supported by Chalmers Centre for High SpeedTechnology. The author would like to express his thanks to

Figure 10 Resonator]frequency discriminator measurements

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 21, No. 6, June 20 1999 421

Figure 11 Phase noise with control loop broken

Figure 12 Phase noise with control loop activated

Prof. Iltcho Angelov, Prof. Erik Kollberg, and Prof. HerbertZirath for their valuable comments on this work.

REFERENCES

1. K.K.M. Cheng and J.K.A. Everard, Noise performance degrada-tion in feedback oscillators with nonzero phase error, Microwave

Ž .Opt Technol Lett 4 1991 , 64]66.2. E.C. Westenhaven, A general procedure for low noise feedback

oscillator design, Proc RF Technol Expo, 1987, pp. 39]45.

3. T.E. Parker, Characteristics and sources of phase noise in stableoscillators, 41st Annu Frequency Control Symp, 1987, pp. 99]110.

4. M.J. Bianchini, J.B. Cole, R. DiBiase, Z. Galani, R.W. Laton,and R.C. Waterman, Jr., A single-resonator GaAs FET oscillatorwith noise degeneration, IEEE MTT-S Int Microwave Symp Dig,1984, pp. 270]273.

5. Z.G. Galani, M.J. Bianchini, R.C. Waterman, Jr., R. Dibiase,R.W. Laton, and J.B. Cole, Analysis and design of a single-reso-nator GaAs FET oscillator with noise degeneration, IEEE Trans

Ž .Microwave Theory Tech MTT-32 1984 , 1556]1565.

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 21, No. 6, June 20 1999422

6. Z. Galani, M.J. Bianchini, and J.R.C. Waterman, Tunable oscilla-tor with noise degeneration, U.S. patent 5032800.

7. E.N. Ivanov, M.E. Tobar, and R.A. Woode, Ultra-low-noise mi-crowave oscillator with advanced phase noise suppression system,

Ž .IEEE Microwave Guided Wave Lett 6 1996 , 312]314.8. C. Buoli, G. Mora, and T. Turillo, Microwave dielectric resonator

discriminator oscillator, 22nd European Microwave Conf, 1992,pp. 137]142.

9. C. Buoli, G. Mora, and T. Turillo, Microwave oscillator withimproved phase noise characteristic, U.S. patent 5463360.

10. S. Andersson, Cooperating oscillator and frequency discriminatorwith common resonator or delay unit, Swedish patent application9800648-9.

11. S. Andersson, Low phase noise voltage controlled micro- andmillimeter wave oscillators, Dep. of Microelectronics, ChalmersUniversity of Technology, Goteborg, Sweden, Licentiate thesis¨ISBN 91-7197-743-0, 1998.

12. Hewlett-Packard, Microwave design system, 1998, 6th ed.13. W. Anzill, O. von Stryk, R. Burlirsch, and P. Russer, Phase noise

minimization of microwave oscillators by optimal design, IEEEMTT-S Int Microwave Symp Dig, 1995, pp. 1565]1568.

Q 1999 John Wiley & Sons, Inc.CCC 0895-2477r99

COMPACT BROADBAND CIRCULARLYPOLARIZED SQUARE MICROSTRIPANTENNAJian-Yi Wu,1 Chih-Yu Huang,2 and Kin-Lu Wong11 Department of Electrical EngineeringNational Sun Yat-Sen UniversityKaohsiung, Taiwan, R.O.C.2 Department of Electronic EngineeringYung-Ta College of Technology and CommercePingtung, Taiwan, R.O.C.

Recei ed 2 December 1998

ABSTRACT: A new design for achie ing compact broadband circular( )polarization CP radiation of a square microstrip antenna is presented.

The compactness of the microstrip antenna is easily obtained by insertingfour slits of equal lengths at the patch edges, and broadband CPradiation is achie ed simply by loading a chip resistor at a properposition in the patch. The present proposed CP design has been imple-mented with an increase of about 50% in CP bandwidth as compared tothe compact CP design using inserted slits of unequal lengths. Details ofthe antenna design and experimental results are presented and discussed.Q 1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21:423]425, 1999.

Key words: circular polarization; broadband microstrip antenna

1. INTRODUCTION

Recently, a compact circularly polarized square microstripantenna with two pairs of narrow slits of unequal lengths has

w xbeen reported 1 . In such a design, the narrow slits areinserted at the centers of the patch edges, which lengthensthe equivalent excited patch surface current path of thefundamental resonant mode. This behavior results in a lower-ing of the fundamental resonant frequency of the squaremicrostrip patch. And by carefully adjusting the inserted slitsto have unequal lengths in orthogonal directions, the funda-mental mode can be split into two near-degenerate orthogo-nal resonant modes of equal amplitudes and 908 phase dif-ference, making possible a compact CP radiation. However,

when CP radiation with a larger antenna size reduction isrequired, the length difference of the inserted slits in orthog-onal directions needs to be small, which makes such a com-pact CP design very sensitive to possible fabrication errors inpractical applications. To overcome this problem, we proposein this paper a design using inserted slits of equal lengths inthe square patch for antenna size reduction, and CP ra-diation is achieved by applying a chip-resistor loading, thefundamental resonant mode can also be split into two near-degenerate resonant modes for CP radiation. And most im-portantly, the smaller CP bandwidth associated with thereduction in antenna size for a given operating frequency canbe significantly improved, owing to the chip-resistor loadingthat produces excited resonant modes with a low Q charac-

w xteristic 3 . That is, compact CP radiation with an enhancedoperating bandwidth can be achieved for the present pro-posed design. Details of the proposed antenna are described,and performances of the obtained CP operation are analyzed.

2. ANTENNA DESIGN

The proposed compact broadband CP design is depicted inFigure 1. The square patch has a side length of L, and isprinted on a substrate of thickness h and relative permittivity« . A single probe feed at point C is for right-hand CPrexcitation, and point D is for left-hand CP radiation. At thecenter of each patch edge, a narrow slit of length lr2 and

Ž .width w w < lr2 is inserted. Note that the four insertedslits are of equal lengths, and the total slit lengths in the x-and y-directions are of the same length l. A chip resistor ofresistance R is loaded along the positive y-axis with a dis-tance S away from the patch center. In this case, the resonantfrequency of the y-directed mode will be slightly larger thanˆ

w xthat of the x-directed mode 3 . And by adjusting the distanceˆof S, these two orthogonal resonant modes can be excitedwith equal amplitudes, but with 908 phase difference. Withthe present proposed arrangement, compact broadband CPoperation can be obtained.

3. EXPERIMENTAL RESULTS AND DISCUSSION

The proposed antenna has been successfully implemented.Figures 2 and 3 show, respectively, typical results of themeasured input impedance and return loss against frequencyfor the proposed antenna with R s 4.7 V and l s 19 mm.Two near-degenerate resonant modes are clearly seen to be

Figure 1 Geometry of the proposed compact broadband CP designof a square microstrip antenna

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 21, No. 6, June 20 1999 423