tion capacitance model can be used to describe this process:

mŽ .C s 5nramp Ž .1 y Vrf

where m and n are constants which can be determined byusing the continuity conditions for the beginning and end ofthis process, i.e.,

C s C , when V s Vramp 1 1

Ž .C s C , when V s V . 6ramp 2 2

Ž . Ž .Using Eqs. 5 and 6 , we obtain

C1log nž / VC 221 Ž .n s and m s C 1 y . 72 ž /f y V f2

log ž /f y V1

Ž . Ž . Ž .Combining Eqs. 2 , 3 , and 5 , we obtain the complete C]Vmodel of the SRD as

C¡ 0, V F Vg 1Ž .1 y Vrf

m~ , V - V - V Ž .nC s 81 2Ž .1 y Vrf

qVC exp , V G V .f 0 2¢ ž /hkT

V. DISCUSSION

Through the measured C]V result, we have modeled theŽ .SRD using Eq. 8 . This model can be easily implemented in

a circuit simulator. The R ]V characteristic is more compli-scated. Just before conduction of the diode starts, R firstsdecreases, then in the transition region rapidly increases,reaching a peak value, and finally drops again. However, Rsdoes not vary much with the voltage. So, the values of Rsextracted through dc measurements may still be used tomodel the diode.

VI. CONCLUSION

This paper has presented a fast and accurate technique forthe characterization of microwave step recovery diodes. Asimple transmission line test fixture is designed for the char-acterization of SRD chips. Two SRD chips are measured byusing this technique. Based on the measured results, a moreaccurate model of the step recovery diode has been devel-oped.

REFERENCES

1. J. L. Moll and S. A. Hamilton, ‘‘Physical Modeling of the StepRecovery Diode for Pulse and Harmonic Generation Circuits,’’Proc. IEEE, Vol. 57, July 1969, pp. 1250]1259.

2. S. Hamilton and R. Hall, ‘‘Shunt Mode Harmonic Genera-tion Using Step Recovery Diodes,’’ Microwa e J., Apr. 1967,pp. 69]78.

3. J. Zhang and A. V. Raisanen, ‘‘A New Model of Step Recovery¨ ¨Diodes for CAD,’’ 1995 Int. IEEE MTT-S Symp. Dig., Orlando,FL, May 1995, pp. 1459]1462.

4. W. Konrath and H. Brauns, ‘‘First Fully CAD of a K-BandSampling Phase Detector Using Periodic Steady State Analysisand Sophisticated SRD-Modeling,’’ 26th European Microwa eConf., Prague, Czech Republic, Sept. 1996, pp. 973]976.

5. J. Zhang and A. V. Raisanen, ‘‘Computer-Aided Design of Step¨ ¨Recovery Diode Frequency Multipliers,’’ IEEE Trans. Microwa eTheory Tech., Vol. 44, Dec. 1996, pp. 2612]2616.

6. O. Boric, T. J. Tolmunen, E. Kollberg, and M. A. Frerking,‘‘Anomalous Capacitance of Quantum Well Double-BarrierDiodes,’’ Int. J. Infrared Millimeter Wa¨es, Vol. 13, No. 6, 1992, pp.799]814.

7. W. M. Sharpless, ‘‘Gallium Arsenide Point-Contact Diodes,’’ IRETrans. Microwa e Theory Tech., Vol. MTT-9, No. 1, 1961,pp. 6]10.

8. WILTRON Product Catalog.9. S. Lidholm, ‘‘Low-Noise Mixers for 80]120 GHz,’’ Res. Rep. 129,

Research Lab. of Electronics, Chalmers Univ. of Sweden, 1977,139 pp.

10. M. T. Faber, J. Chramiec, and M. E. Adamski, Microwa e andMillimeter-Wa e Diode Frequency Multipliers, Artech House, Nor-wood, MA, 1995.

Ž .11. ‘‘Appendix A}Using Symbolically-Defined Devices SDDs ,’’ HPMDS Designer’s Task Reference, Vol. 2}Creating Circuits asSchematics, 1995.

Q 1998 John Wiley & Sons, Inc.CCC 0895-2477r98

DIELECTRIC-RESONATOR-LOADEDMICROSTRIP ANTENNA FORENHANCED IMPEDANCE BANDWIDTHAND EFFICIENCYJacob George,1 C. K. Aanandan,1 P. Mohanan,1 K. G. Nair,1

H. Sreemoolanathan,2 and M. T. Sebastian21 Department of ElectronicsCochin University of Science and TechnologyCochin 682 022, Kerala, India2 Regional Research LaboratoryTrivandrum, Kerala, India

Recei ed 10 September 1997

ABSTRACT: A new method for enhancing the 2:1 VSWR impedancebandwidth of microstrip antennas is presented. Bandwidth enhancementis achie ed by loading the microstrip antenna by a ceramic microwa¨e

( )dielectric resonator DR . The ¨alidity of this technique has been estab-lished using rectangular and circular radiating geometries. This methodimpro¨es the bandwidth of a rectangular microstrip antenna to more

(than 10% f 5 times that of a con¨entional rectangular microstrip)antenna with an enhanced gain of 1 dB. Q 1998 John Wiley & Sons,

Inc. Microwave Opt Technol Lett 17: 205]207, 1998.

Key words: antennas; microstrip antenna; bandwidth; dielectricresonator

INTRODUCTION

Microstrip antennas find far-reaching applications in the cur-rent communication scenario due to their unique propertieslike light weight, ease of fabrication, low production cost, lowprofile, etc. The fields of application of these antennas aremainly limited by their inherent disadvantage of low-imped-ance bandwidth. Two commonly used microstrip radiatinggeometries are rectangular and circular. Techniques areavailable in the literature for improving the impedance band-

w xwidth of microstrip antennas 1]4 . However, these methodswill increase the complexity of the system or, in most of thecases, reduce the antenna gain.

In this letter, a method for improving the impedancebandwidth of a microstrip antenna using a dielectric res-

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 17, No. 3, February 20 1998 205

onator attached on the surface of the patch is proposed. Thistechnique improves the impedance bandwidth, to more than10% for a rectangular microstrip antenna.

DESIGN AND EXPERIMENTAL DETAILS

The schematic diagram of a typical antenna configuration isŽshown in Figure 1 a magnified view of the cylindrical DR

.used is also shown . The configuration consists of a rectangu-lar patch of length L and width W on a substrate of thicknessh and dielectric constant e . The antenna is loaded with arcylindrical dielectric resonator of diameter d, height H, anddielectric constant e . The patch is fed by a probe at thedr

Ž .position X , Y . The operating frequency of the antenna isp pselected to be close to the TE mode resonant frequency of01d

the dielectric resonator.A rectangular microstrip antenna resonating at 2.70 GHz

Ž .L s 2.58 cm, W s 3.35 cm, h s 0.16 cm, e s 4.5 is de-rw xsigned for optimum radiation performance 5 . A cylindrical

Ž .DR H s 0.9 cm, d s 1.4 cm, e s 58 having TE modedr 01d

frequency close to the resonating frequency of the aboveantenna is suitably positioned on the patch surface. Thepatch width, position of the DR on the patch, and the feedpoint are optimized experimentally for maximum impedancebandwidth, and the DR is pasted at this position using a thinlayer of conducting epoxy. This typical configuration gives amaximum bandwidth of 274 MHz at 2.63 GHz when L s 2.58cm, W s 2.94 cm, X s 1.98 cm, Y s 0.0 cm, and the DR isp pplaced at the middle of the nonradiating edge in such a waythat its surface just grazes the radiating patch edge as shownin Figure 1. The variation of percentage bandwidth with feed

Žlocation is shown in Table 1. When the patch is fed at 2.58,.0 , the system was not at all matched. But on loading with

DR, the antenna is found to be matched, and provides animpedance bandwidth of more than 8%. This shows that thistechnique can be used for the impedance tuning of microstripantennas.

The experiment is repeated on a circular microstrip an-Žtenna resonating at 4.01 GHz radius s 1.42 cm, e s 2.2,r

. Žh s 0.08 cm with a DR H s 0.565 cm, d s 0.979 cm, e sdr.63, TE mode frequency 4.0 GHz . Here, the position of01d

the DR on the patch surface and the feed point are experi-mentally optimized for maximum bandwidth. The configura-tion gives a maximum bandwidth of 239 MHz at 3.92 GHzwhen the feed point is at a distance of 1.00 cm and the DRcenter is at a distance of 1.21 cm from the patch center. Thesector angle formed between two radial vectors, one passing

Figure 1 Schematic diagram of a typical antenna configuration

TABLE 1 Variation of Impedance Bandwidth with Respectto Feed Location for the Experimentally TunedRectangular Microstrip Antenna Configuration

% BandwidthFeed PointŽ .X , Y s 0p p Before DR After DR

Ž . Ž . Ž .X cm Loading % Loading %p

a2.58 8.90a2.43 8.15a2.28 8.10a2.13 10.10

1.98 2.2 10.411.83 2.2 8.201.68 3.3 7.211.53 3.3 6.84

a Not matched.

TABLE 2 Characteristics of the DR-Loaded Rectangularand Circular Microstrip Antenna Configurations

Rectangular CircularCharacteristic Patch Patch

Substrate dielectric constant 4.5 2.2Resonance frequency without DR 2.70 GHz 4.01 GHz

Ž .% bandwidth VSWR F 2 without DR 2.2% 1.1%Ž .% bandwidth VSWR F 2 with DR 10.41% 6.1%

Central frequency with DR 2.63 GHz 3.92 GHz

3 dB beamwidthE-plane 128.78 109.88

H-plane 71.28 79.58

Figure 2 Variation of VSWR with frequency for the two proposedŽ . Ž .antenna configurations. a Rectangular patch configuration. b Cir-

cular patch configuration

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 17, No. 3, February 20 1998206

through the DR center and the other through the feed point,is 1358.

The different characteristics for the above optimum an-tenna configurations are given in Table 2 for a comparativestudy.

The variation of VSWR with frequency for the two con-figurations is shown in Figure 2. The E-plane and H-planeradiation patterns of the antenna systems at the correspond-ing central frequencies are shown in Figure 3. In both cases,the E-plane patterns differ slightly from those of conven-

Figure 3 E-plane and H-plane radiation patterns of the two an-tenna configurations at the corresponding central frequencies. Solidline: rectangular patch configuration. Dashed line: circular patchconfiguration

Figure 4 Variation of S21 with frequency for the optimum rectan-gular patch configuration. Solid line: after DR loading. Dashed line:before DR loading

tional microstrip antennas. H-plane patterns are similar tothose of conventional ones. Figure 4 shows the variation ofS21 with frequency for the configuration shown in Figure 1.This figure shows that, compared to ordinary microstrip an-tennas, the present configuration gives an increased gain of) 1 dB. This may be due to the reradiation from the DR.

CONCLUSIONS

A new method for enhancing the impedance bandwidth ofmicrostrip antennas is proposed. This approach enhances thegain of the antenna, as well as enabling impedance tuning.

Ž . Ž .Optimum rectangular BW ) 10% and circular BW ) 6%antenna configurations are demonstrated. These configura-tions may find applications in wideband phased arrays.

ACKNOWLEDGMENT

One of the authors, Jacob George, wishes to acknowledge theŽ .Council of Scientific and Industrial Research CSIR , Gov-

ernment of India, for providing a research fellowship.

REFERENCES

1. H. Iwasaki and Y. Suzuki, ‘‘Electromagnetically CoupledCircular-Patch Antenna Consisting of Multilayered Configur-ation,’’ IEEE Trans. Antennas Propagat., Vol. 44, June 1996, pp.777]780.

2. C. K. Aanandan and K. G. Nair, ‘‘Compact Broadband MicrostripAntenna,’’ Electron. Lett., Vol. 22, Oct. 1986, pp. 1064]1065.

3. G. Kumar and K. C. Gupta, ‘‘Non-Radiating Eges and Four EdgesGap-Coupled Multiple Resonator Broad-Band Microstrip Anten-nas,’’ IEEE Trans. Antennas Propagat., Vol. AP-33, Feb. 1985,pp. 173]178.

4. S. Dey, C. K. Aanandan, P. Mohanan, and K. G. Nair, ‘‘A NewBroadband Circular Patch Antenna,’’ Microwa e Opt. Technol.Lett., Vol. 7, Sept. 1994, pp. 604]605.

5. I. J. Bahl and P. Bhartia, Microstrip Antennas, Artech House,Norwood, MA, 1981.

Q 1998 John Wiley & Sons, Inc.CCC 0895-2477r98

AIRCRAFT DOWN-RANGE PROFILESFORMED FROM SIMULATEDAND COMPACT-RANGERADAR BACKSCATTERE. C. Botha,1 J. W. Odendaal,1 and K. M. Geggus11 Department of Electrical and Electronic EngineeringUniversity of PretoriaPretoria 0002, South Africa

Recei ed 10 September 1997

ABSTRACT: Compact-range radar backscatter measurements are takenof aircraft scale models. In addition, computer software is used to predictthe RCS of the aircraft. Synthetic down-range profiles formed from thetwo sources of backscatter data are compared and ¨isualized in aninno¨ati e manner. Similar discrimination rates between the two aircraftare obtained on data from both sources. Q 1998 John Wiley & Sons, Inc.Microwave Opt Technol Lett 17: 207]213, 1998.

Key words: compact-range measurements; radar cross-sectionprediction; down-range profiles; noncooperati e target recognition

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 17, No. 3, February 20 1998 207