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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 49, NO. 1, JANUARY 2001 45

The Dependence of the Input Impedance on FeedPosition of Probe and Microstrip Line-Fed Patch

AntennasLorena I. Basilio , Student Member, IEEE , Michael A. Khayat , Student Member, IEEE ,

Jeffery T. Williams , Senior Member, IEEE , and Stuart A. Long , Fellow, IEEE

Abstract The impedance of a rectangular patch antenna fed byan inset microstrip transmission linewas measuredfor various feedpositions. The dependence found was then compared to theoreticalpredictions both for this geometry and for the similar case of aninset coaxial probe feed.

Index Terms Impedance, inset feed, microstrip antennas, reso-nant frequency.

I. INTRODUCTION

R ECTANGULAR microstrip patch antennas have receivedmuch attention because of their low cost, low profile, andlightweight properties. Microstrip patch antennas can, for manyapplications, be fed using a simple coaxial probe feed. This typeof feed can be advantageous because of the ease of fabrication.However, in array applications, a microstrip line feed may oftentimes be more appropriate. It hasbeen typicallyassumed that theinput resistance of a conventional rectangular microstrip patchantenna has the same dependence on the feed position for boththe probe feed and the inset microstrip feed [ 1][3]. The inputresistance that is consistent with thecavity model fora probe-fedrectangular microstrip patch is proportional to a cosine-squared

type distribution as the feed position is varied from the edge intoward the center of the radiator.

In this paper, an experimental characterization of the inputresistance as a function of feed position for an inset microstripfeed is undertaken. The measurement techniques are firstdemonstrated by characterizing the input resistance behavior asa function of feed position for the probe-fed patch, confirmingthe predicted cosine squared behavior.

II. MEASUREMENT TECHNIQUES

Probe-fed and microstrip line-fed rectangular patches, suchas the ones shown in Fig. 1, were used to perform the mea-

surements. A copper clad Duroid substrate with a thickness of cm and an approximate dielectric constant of was used. Several patches were fabricated with widths of

cm and resonant lengths of cm, whichproduced radiators that were resonant near 2.3 GHz. This ge-ometry is illustrated in Fig. 2, where the microstrip line widthwas chosen to be cm to provide a 50- characteristicimpedance on this substrate. Although it has been shown that

Manuscript received August 5, 1999.The authors are with the Departmentof Electrical andComputer Engineering,

University of Houston, Houston, TX 77204-4793 USA.Publisher Item Identifier S 0018-926X(01)02288-8.

Fig. 1. Probe and microstrip line-fed rectangular patch antennas.

Fig. 2. Geometry of inset microstrip fed patches.

the input resistance is a function of the spacing between the lineand the patch conductor, a common design of one microstripline width spacing on both sides of the inset feed was adopted.Thus, the spacing cm was chosen for all cases.

The input impedance measurement of the probe-fed patch re-quired that theouterand inner conductorof theprobewere prop-

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46 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 49, NO. 1, JANUARY 2001

Fig. 3. Measured impedance of probe-fed patch versus feed position withcurve of normalized at .

erly secured to theground plane andthepatchconductor, respec-tively. In order to obtain the input impedance measurements forthe inset fed patch, a fixed length line to the feed position on thepatch was used. By experimentally characterizing the character-istic impedance of the microstrip line along with the transitionbetween thecoaxial feed and themicrostrip line, it was then pos-

sible to extract theinputimpedance of thepatchat thejunctionof the microstrip line and the patch. It was experimentally verifiedthat the spacing between the microstrip line and the patch wassufficiently large as to not alter the characteristic impedance andpropagation characteristics of the feed line.

Throughout this investigation, the resonant frequency of theantenna was defined as the frequency at which the maximuminput resistance occurred. Results for the input impedance werethen taken at this frequency. For the purposes of minimizingexperimental error, measurements were made on two antennas,which were fabricated to be as identical as possible. The resultsgiven here for both the probe-fed and microstrip line-fed an-tennas reflect the average of the two measurements (typical dif-

ference between the two values was less than 1%).

III. RESULTS AND DISCUSSION

To begin the investigation, a set of experimental measure-ments was made for the probe-fed patch. These results areshown in Fig. 3, where the resistance and reactance are plottedversus a normalized feed position. This position is chosen suchthat the full range of the graph represents feed positions fromthe edge to the center of the patch .The functional behavior of the resistance is evident when theseresults are compared to the curve on the samegraph. This curve is normalized at , where the

measurements are quite stable. The only minor discrepancyoccurs for the data point at the edge, which is expected sincethe cavity model tends to break down there, and hence theimpedance at this position is always more difficult to predict.The results for the reactance are also shown and are seen to berelatively independent of feed position.

Fig. 4 shows the measured resonant frequency for each po-sition of the probe feed. This frequency was defined as the fre-quency for which the resistance was a maximum, and its valueremained quite constant over the entire range of feed positions,varying less than 1% from 2.295 to 2.316 GHz.

Next, the impedance was measured for the inset microstripfed patches, and the experimental results are shown in Fig. 5. As

Fig. 4. Measured resonant frequency of probe-fed patch versus feed position.

Fig. 5. Measured impedance of microstrip line-fed patch versus feed insetdistance.

with the probe-fed case, the maximum input resistance occursat the edge of the patch and decreases as the inset distance is in-creased toward the center of the radiator, while the reactance re-mains reasonably constant. However, the rate at which the resis-tance decreases with changing feed position is seen to be muchmore rapid, and the resistance is also seen to rise slightly as the

inset approaches the center of the patch. The latter behavior is incontrast to the probe-fed case, where the resistance became es-sentially zero near the center. For comparison purposes, a curveof normalized at is also shown andis seen to accurately model the behavior except near the centerwhere the measured resistance begins to rise again. Empirically,this seems to be the best fit for the experimental data, but thereis no real theoretical justification.

Most early derivations of the input resistance as a functionof feed position depended on the cavity model and assumed aprobe feed. As the inset microstrip line feed was developed, itwas always assumed that thebehaviorcouldcontinue to be mod-eled as a cosine-squared type function. Modern textbooks rou-

tinely assume that this is the case [ 4]. Some very early measure-ments by Weinschel [ 5] could have given a hint that the inset mi-crostrip feed produced a more rapid decrease in the resistance,but no other actual measurements seem to have been made. Theresistance measurements are shown again in Fig. 6 along withWeinschels data and both and curves normalized at

. Weinschels measurements show a more rapiddecline than the cosine squared function, but less than the co-sine to the fourth power. Since his data cover only a small rangeof inset distances, no definite behavior can be necessarily con-firmed.

The resonant frequency for the microstrip fed patch is shownin Fig. 7 and was found to vary between 2.253 and 2.282 GHz

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BASILIO et al. : DEPENDENCE OF INPUT IMPEDANCE ON FEED POSITION 47

Fig. 6. Measured resonant resistances with comparison to different powers of .

Fig. 7. Measured resonant frequency of microstrip fed patch versus feed insetdistance.

if the single measurement very near the center of the patch isneglected. Without this data point, the range of resonant fre-quencies is about the same as that for the probe-fed case (about1.2%).

IV. CONCLUSION

An experimental investigation has shown that the depen-dence of the input resistance on the feed position of a patchantenna differs when using a probe or a microstrip line feed.Although the measured input resistance for the probe-fedstructure demonstrated the familiar cosine squared behavior,the input resistance for the microstrip line-fed patch was foundto decrease at a more rapid rate. If a model is normalized tothe measured input resistance at a point between the edge andthe center of the radiator, it is found that a cosine to the fourthdependence best represents the experimental data.

REFERENCES

[1] K. R. Carver and J. W. Mink, Microstrip antenna technology, IEEE Trans. Antennas Propagat. , vol. AP-29, pp. 224, Jan. 1981.

[2] D. M. Pozar, Input impedance and mutual coupling of rectangular mi-crostrip antennas, IEEE Trans. Antennas Propagat. , vol. AP-30, pp.11911196, Nov. 1982.

[3] D. H. Schaubert, A review of some microstrip antenna characteristics,in Microstrip Antennas , D. M. Pozar and D. H. Schaubert, Eds. NewYork: IEEE Press, 1995, ch. 2, pp. 5967.

[4] C. A. Balanis, Antenna Theory: Analysis and Design . New York:Wiley, 1997.

[5] H. D. Weinschel, Measurements of various microstrip parameters, inProc. Workshop Printed Circuit Antenna Tech. , Las Cruces, Oct. 1979,pp. 2/12/15.

Lorena I. Basilio (S00) was born in Pasadana,TX, on June 22, 1970. She received the B.S. degree(magna cum laude) and the M.S. degree in electricalengineering from the University of Houston, TX,in 1996 and 1998, respectively. She is currentlyworking toward the Ph.D. degree at the sameuniversity.

She has been a Research Assistant at the Univer-sity of Houston since September 1996 and was an In-

structor in the summer of 1999. Her current researchinterests are in the areas of theoretical and appliedelectromagnetics, with a focus on frequency-tunable printed circuit antennas.

Michael A. Khayat (S00) was born in Houston, TX, in 1972. He received theB.S.E.E. andM.S.E.E. degrees from theUniversityof Houston, TX,in 1996 and1999, respectively. He is currently working toward the Ph.D. degree in electricalengineering at the same university.

During the summer of 2000, he was with Compaq Computer Corporationresearching wireless technologies for the Portable PC Division. His current in-terests include microstrip antenna design and computational electromagnetics.

Jeffery T. Williams (S85M87SM97) was born in Kula, Maui, HI, on July24, 1959.He receivedthe B.S., M.S., andPh.D. degrees in electricalengineeringfrom the University of Arizona, Tempe, in 1981, 1984, and 1987, respectively.

He joined the Department of Electrical and Computer Engineering, Univer-sity of Houston, Houston, TX, in 1987, where he is now an Associate Professor.Prior to that, he was a SchlumbergerDoll Research Fellow at the Universityof Arizona. He spent four summers (19831986) at the Schlumberger-Doll Re-search Center, Ridgefield, CT, as a Research Scientist. From 1981 to 1982, hewas a Design Engineer with Zonge Engineering and Research Organization,Tucson, AZ, and a Summer Engineer at the Lawrence Livermore National Lab-oratory, Livermore, CA. He is a past associate editor for Radio Science . Hisresearch interests include the design and numerical analysis of high-frequencyantennas, antenna measurements, the applicationof high-temperature supercon-ductors in antenna systems, and leaky-wave propagation.

Dr. Williams is a past Associate Editor for IEEE T RANSACTIONS ONANTENNAS AND PROPAGATION . He is a member of URSI Commission B.

Stuart A. Long (S65M74SM80F91) was born in Philadelphia, PA, onMarch 6, 1945. He received the B.A. (magna cum laude) and M.E.E. degreesin electrical engineering from Rice University, Houston, TX, in 1967 and 1968,respectively, and the Ph.D. degree in applied physics from Harvard University,Cambridge, MA, in 1974.

From 1968 to 1969, he was an Aerosystems Engineer in the Antenna De-sign Group of General Dynamics, Ft. Worth, TX. From 1970 to 1974, he wasa Teaching Fellow and Research Assistant in applied mathematics and appliedphysics at Harvard University. He was also a Research Assistant at Los AlamosScientific Laboratories, Los Alamos, NM, in 1970 and 1971. In 1974, he joinedthe Faculty at the University of Houston. He was Chairman of the Departmentof Electrical and Computer Engineering (1984 to 1995 and 1998 to 1999) andAssociate Dean of the College of Engineering (1995 to 1998). Presently, heis a Professor in the Department of Electrical and Computer Engineering. Heteaches a variety of undergraduate and graduate-level classes in applied electro-magnetics.

Dr. Long is a membera of Phi Beta Kappa, Tau Beta Pi, Sigma Xi, and Com-

mission B of URSI. He is a member of the Electromagnetics Academy and wasan IEEEAntennasand Propagation Society Distinguished Lecturer from1992 to1994. He is a registered Professional Engineer. He was a member of the Admin-istrative Committee (AdCom) of the IEEE Antennas and Propagation Society(AP-S) for a three-year term in 1981 and again in 1989. He was the Organizerand General Chairman of the 1983 IEEE AP-S/URSI International Symposium,Houston, TX, and presently is the National Meetings Coordinator of AP-S. HewasVice-President in 1995 andPresident in 1996 ofAP-S.He also servedon theIEEE Technical Activities Board (TAB), was TAB Magazines Chair, and was amember of the Periodicals Review Committee from 1997 to 1999. He presentlyis a Member-at-Large of the IEEE Publications Activities Board and is on theSpectrum Editorial Board. He received the Halliburton Award of Excellence asthe Outstanding Teacher in Engineering at the University of Houston in 1983,the UniversityTeaching ExcellenceAwardin 1991, the EngineeringAlumni As-sociations 1992 Distinguished Faculty Award, and the Senior Research Awardfrom the College of Engineering in 1995. He was chosen as the outstandingteacher in electrical engineering by the IEEE/HKN students in 1994.