A systematic method to design single-patch broadband microstrip patch antennas

6. S.D. Gedney and R. Mittra, Analysis of the electromagnetic scattering by thick gratings using a combined FEMrMM solution, IEEE Trans Antennas Propagat 39 Ž1991., 1605᎐1614. 7. H.A. Kalhor, Electromagnetic scattering by an array of conducting strips by an integral equation technique, Comput Elect Eng 5 Ž1978., 159᎐165. 8. C.W. Lee and Y.K. Cho, Periodically slotted dielectrically field parallel-plate waveguide as a leaky wave antenna for infinite and finite periodic structures, Proc URSI Int Symp Electromag Theory, St. Petersburg, Russia, 1995, pp. 314᎐316. 9. Y.K. Cho, U.H. Cho, and J.H. Ko, TM-polarized electromagnetic scattering from a periodic strip array on a grounded dielectric, Microwave Opt Technol Lett 11 Ž1996., 41᎐45. 10. J.I. Lee, U.H. Cho, and Y.K. Cho, Analysis for a dielectrically filled parallel-plate waveguide with finite number of periodic slots in its upper wall as a leaky-wave antenna, IEEE Trans Antennas Propagat 47 Ž1999., 701᎐706. 䊚 2001 John Wiley & Sons, Inc.

A SYSTEMATIC METHOD TO DESIGN SINGLE-PATCH BROADBAND MICROSTRIP PATCH ANTENNAS Jaume Anguera,1 Carles Puente,1 Carmen Borja,1 Gisela Font,1 and Jordi Soler 1 1 Technology Department Fractus, S.A. 08190, Sant Cugat del Valles, ` Barcelona, Spain Recei¨ ed 18 May 2001 ABSTRACT: A simple electrical network for a single-layer microstrip patch antenna (SLMPA) and the feeding structure (coaxial probe and compensating capacitor) is proposed to predict the input impedance. The mathematical analysis allows us to design an optimum feed that enhances the impedance bandwidth (BW). 䊚 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 185᎐188, 2001. Key words: microstrip antenna design; enhancing bandwidth techniques 1. INTRODUCTION

One of the simple techniques to improve the bandwidth Ž BW . of an SLMPA is to increase the substrate height w1x. When the antenna is fed through a coaxial probe, an additional inductance that tends to mismatch the antenna is introduced. A series capacitor may cancel this inductance, and as a result, the inherent BW of the antenna is obtained. Technologically, the capacitor can be etched on the same patch, as shown in Figure 1. This technique results in a compact feeding structure w2x. In this paper, a method to compute the optimum value of the inductance, the compensating capacitor, as well as the feeding point is presented. This first-order feeding circuit results in a BW improvement, although, due to the simplicity of the circuit, the improvement is about one half of Fano’s limit w3x. A simple-to-use design chart is introduced. Although commercially available computer design codes can be used in the design of this kind of antenna, the design chart offers an intuitive way to modify the original design to achieve an optimized solution.

Figure 1

Geometry of the single-layer microstrip patch antenna

as a consequence, the RLC network is a valid model of the input impedance w4x. A series inductor and capacitor can model the coaxial probe and the etched capacitor, respectively ŽFig. 2.. In the standard design procedure, the height of the patch is chosen for a given BW. Once this height h is fixed, and for a given diameter of the feeding probe, a series inductive reactance X L f is introduced. A series capacitive reactance XC f is then introduced by the etched capacitor, so X L f q XC f s 0. This standard compensation only ensures the recuperation of the inherent BWo . A deeper analysis of the RLC q L f C f circuit shows that there is a condition that enables an optimization of the antenna bandwidth. First of all, consider the input impedance as a function of frequency for a particular RLC resonator and feed L f C f : Zin Ž f . s Zin R LC Ž f . q j2␲ fL f y

Zin R LC Ž f . s

R 1 q jQ¨

;¨ s

f f0

y

f0 f

j

Ž1.

2␲ fC f

; f0 s

1 2␲'LC

Ž2.

where L f , in practice, for a given height h, can be calculated from w5x as . q 0.577x X f s y60khw ln Ž kd 4

Ž3.

where d is the diameter of the feed probe, k s 2␲r␭, Q in the RLC quality factor. By properly choosing the values of R, L f , and C f , it is possible that Zin from Eq. Ž1. presents three resonant frequencies. The three resonant frequencies Ž f 0 , f 1, and f 2 . can be calculated by equating the imaginary part of Eq. Ž1. to zero. One solution is f s f 0 , the resonant frequency of the SLMPA for a given L and h ŽFig. 1., resulting in the

2. ELECTRICAL MODEL FOR THE SLMPA

The input impedance of an SLMPA shows a parallel RLC resonator characteristic for frequencies near the resonance; Contract grant sponsor: Fractus, S.A.

Figure 2

Electrical model for the SLMPA

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185

feeding L f C f given by Ž7. and the single BWo w1x as

equation Cf s

1

␻ 02 L f

.

Ž4.

Substituting Eq. Ž4. into the imaginary and real parts of Eq. Ž1. gives

T  Zin 4 s y R Zin 4 s

RQ¨ 1 q Ž Q¨ . R

1 q Ž Q¨ .

2

2

q 2␲ fL f y

Ž 2␲ f 0 . 2 L f 2␲ f

.

Ž 5a .

Ž 5b .

To optimize the antenna BW, it is necessary that the impedance locus in the complex plane be inscribed inside a circle of VSWR s S. This objective is met by the following condition: R Zin Ž f 0 .4 s S ⭈ Z0 Z0

Ž 6b .

S

T  Zin Ž f 1 .4 s T  Zin Ž f 2 .4 s 0.

Ž 6c .

Graphically, the condition of Eq. Ž6. is represented in Figure 3. From Ž5b. and Ž6a., R s S ⭈ Z o . This condition can be satisfied by controlling the position of the feed probe Ž x in Fig. 1.. Applying the condition of Eqs. Ž6. to Eqs. Ž5a., Ž5b., and after some symbolic manipulations, the solutions f 1, f 2 can be found to calculate the improved BWf with respect to the original BWo as f2 y f1 f0

s

'S 2 y 1 Q

.

BWo

Ž 'S 2 y 1 rQ .

s

Ž S y 1 . r Ž Q'S .

s

'S 3 y S Sy1

.

Ž8.

For typical values of S s 1.5 or 2, the BWo can be improved with an optimum feeding up to a factor of 2.7 and 2.4, respectively. On the other hand, with an ideal matching network following Fano’s criteria, the enhancement factor is 4.8 and 4 for S s 1.5 and 2, respectively w3x ŽFig. 4.. Figure 4 compares the enhancing bandwidth factor of Eq. Ž8. with the ideal enhancing bandwidth factor of an infinite reactive matching network after Fano’s theory. The F for the LC network is obviously smaller because it is a truncation of the ideal matching network. Finally, the value of optimum L f can be calculated from Ž5a., Ž6a. ᎐ Ž6c. SZ o Q¨ 1

Lopt f s

Ž ¨1 s

2 1 q Ž Q¨ 1 .

f1 f0

f1 s f0

ž

2␲ f 1 y 2␲

f1

Ž 9a .

/

f0

y

'S

.

f 02

Ž 9b .

f1 2

y 1 q 4Q 2 y 'S 2 y 1 2Q

.

Ž 9c .

The value of the optimum inductance only depends on the antenna quality factor and the desired VSWR. As a conclusion, for a given Q and resonant frequency f 0 of an SLMPA, the inherent bandwidth BWo can be enhanced to BWf by a factor F if 1. the feeding point is chosen to satisfy Eq. Ž6a. 2. the feed probe inductance satisfies Eq. Ž9a. 3. the etched capacitor satisfies Eq. Ž4..

Ž7.

The enhancement factor F can be evaluated as the relationship between the BWf of the SLMPA plus the optimum

Figure 3 The input impedance of an RLC parallel circuit follows a constant admittance circle. The RLC᎐LC following condition Ž6. has a loop that allows a BW enhancement

186

BWf

Ž 6a .

R Zin Ž f 1 .4 s R Zin Ž f 2 .4 s

BWf Ž VSWR s S . s

Fs

3. DESIGN EXAMPLE

In this design example, a synthesis problem is presented: for a given f 0 and desired BWf , what are the necessary values of

Figure 4 Enhancing bandwidth factor for an ideal reactive network and LC network

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 31, No. 3, November 5 2001

the feed probe inductance, etched capacitor, and feeding point? To systematize the whole design process in a more compact form, a design chart is proposed and depicted in Figure 5. The design process is illustrated by the next example. Following the specifications of f 0 s 1.8 GHz and BWf Ž25%, S s 1.3., using the design chart ŽFig. 5., kd s 0.037 and hr␭ o f 0.08, so the necessary height is h s 14 mm and d s 1 mm. The inductance corresponding to these values of h and d is Lopt f s 11.2 nH. C f and its dimensions are calculated through Eq. Ž4. and w6x, resulting in C f s 0.7 pF, R s 4 mm, r s 2.7 mm, and the feeding point is placed at x s 15 mm as a first approximation ŽFig. 1. and can be adjusted to place the input impedance locus at the center of the Smith chart. The patch dimensions easily are calculated by w1x, resulting in L s 60 mm and W s 70 mm ŽFig. 1.. The measured BW is 15%, and is centered at 1.8 GHz as designed. The plot of the impedance in the Smith chart shows that the impedance locus is inscribed inside the cir-

Figure 5 Design chart. For a desired improved bandwidth BWf ŽSWR - S ., the optimum normalized height Ž hr␭ o . and normalized feed probe diameter Ž k ⭈ d . can be obtained. k s 2␲r␭ o , ␭ o is the free-space wavelength

cumference of SWR s 1.3 ŽFig. 6.. The enhancement factor F is 1.63, which is not as significant as the theoretic one, but at least, through this technique, a better BW can be obtained when patches are fed by a coaxial probe and a series capacitor.

Figure 6 Measured impedance locus. The impedance within the bandwidth is circumscribed inside the circumference of S s 1.3. Feed point x s 14 mm, height h s 14 mm

Figure 7 Electrical current distribution on the patch surface wColor figure can be viewed in the online issue, which is available at www.interscience.wiley.com.x

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4. CURRENT DISTRIBUTION AND RADIATION PATTERNS

Once the patch has been designed for a wide input impedance bandwidth, it is interesting to analyze if its radiation pattern over the whole input impedance bandwidth remains the same. Before measuring the radiation pattern, the current distribution over the patch surface is calculated through a commercial MoM code. The current distribution is depicted in Figure 7. From Figure 7, the TM 10 mode is observed, and how it degrades as the operating frequency increases. It seems that, when the frequency is increased, the well-known current pattern of the TM 10 mode predicted with the cavity method is no longer valid. At f s 1.95 GHz, the current degrades as the maximum current level is placed at the radiating edge near the feed probe. Following the cavity model, it is expected that the radiation pattern for a frequency of 1.95 GHz will present an asymmetry in the E-plane Ž ␸ s 90⬚.. The radiation patterns for the frequencies 1.55 and 1.75 GHz are expected to be similar because the current pattern is almost identical. No asymmetries are expected in the H-plane Ž ␸ s 0⬚. radiation pattern because the distribution is symmetrical in the x-axis for the three frequencies. To corroborate this

prediction, the radiation patterns are measured in an anechoic chamber, and are presented in Figure 8. In Figure 8, the main cuts Ž E- and H-plane. are represented. The E-plane, as mentioned before, is quite symmetrical for 1.55 and 1.75 GHz, but at 1.95 GHz, the direction of the maximum radiation is slightly tilted to ␪ f 5⬚. The Hplane is symmetrical, as expected. The cross-polar component is high for the H-plane, especially at ␪ s "40⬚. However, for the E-plane, the cross-polar component has a very low level compared with the copolar component. The polarization in the broadside direction is linear, with an axial ratio better than 25 dB. 5. CONCLUSIONS

In this paper, an optimum LC feeding mechanism has been proposed to increase the BW of the SLPMPA. The practical example case gives an enhancement factor F s 1.63 for an SWR around 1.3, which corroborates that an optimum design can improve the impedance bandwidth. This technique can be extrapolated to other feeding mechanisms, as presented in w7x. The figure of merit F of Eq. Ž8. is a theoretical limit. If the values of the feeding inductance L f and etched capacitor C f tend to satisfy Eqs. Ž9. Ž4., the input impedance will tend to reach the theoretical limit. The radiation pattern has been measured in the whole bandwidth, confirming the wideband performance of this kind of antenna. REFERENCES 1. I.J. Bahl and P. Bhartia, Microstrip antennas, Artech House, Norwood, MA, 1980. 2. P.S. Hall, Probe communication in thick microstrip patches, Electron Lett 23 Ž1987., 606᎐607. 3. R.M. Fano, Theoretical limitations on the broad-band matching of arbitrary impedances, J Franklin Inst 249 Ž1950., 57᎐83, 139᎐154. 4. H.F. Pues and A.R. Van de Capelle, An impedance-matching technique for increasing the bandwidth of microstrip antennas, IEEE Trans Antennas Propagat 37 Ž1989., 1345᎐1354. 5. C. Balanis, Antennas theory: Analysis and design, Wiley, New York, 1997, 2nd ed. 6. R. Bernard, R. Tchanguiz, and A. Papiernik, Capacitors provide input matching of microstrip antennas, Microwaves RF 33 Ž1994., 103᎐106. 7. K.M. Luk, C.L. Mak, Y.L. Chow, and K.F. Lee, Broadband microstrip patch antenna, Electron Lett 34 Ž1998., 1442᎐1443. 䊚 2001 John Wiley & Sons, Inc.

Figure 8 Measured radiation main cuts. Ground-plane dimensions 180 = 210 mm

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