Theory and experiment on microstripantennas with airgaps

J.S. Dahele, Ph.D.. C.Eng.. M.I.E.E., Sen.Mem.I.E.E.E., and Prof. K.F. Lee.M.Sc. Ph.D.. C.Eng., F.I.E.E.. Sen.Mem.I.E.E.E.

Indexing term: Antennas (Microstrip)

Abstract: In a microstrip antenna, the resonant frequency of a particular mode is determined by the shape andsize of the conducting patch, the relative permittivity of the substrate and, to some extent, the thickness of thesubstrate. If the resonant frequency is to be changed, a new antenna is usually needed. Recently, Lee and Dahelehave shown that the resonant frequencies of microstrip antennas can be changed by introducing an adjustableairgap between the substrate and the ground plane. In addition to providing a means for tuning the resonantfrequencies, the airgap also has the effect of increasing the bandwidth of the antenna. The purpose of the paperis to present a comprehensive report on our research on microstrip antennas with airgaps. First, experimentalresults obtained by introducing an airgap in (i) circular-discs, (ii) annular-rings and (iii) dual-frequency stacked-disc microstrip antennas are presented. Secondly, the theories that have been developed are described. Thirdly,comparison between theoretical and experimental results is given.

1 Introduction

The progress in microwave integrated circuits in the lastdecade or so has created a demand for compact antennaswhich are compatible with integrated electronics. Micro-strip antennas appear to be particularly suitable for thispurpose. The geometry of a microstrip antennas is shownin Fig. 1. A conducting patch is printed on the top of asubstrate, which is backed by a ground plane. The shape ofthe patch can, in principle, be arbitrary. In practice, therectangular, the circular and the annular ring are commonshapes. The antenna can be fed either by fabricating a stripline to the patch or by means of a coaxial arrangementshown in Fig. 1. One can visualise the flow of electromag-netic energy in the following way. Waves are guided alongthe coaxial line to the feed point. The energy then spreadsout into the region under the patch, some of which crossesthe boundary of the patch and radiates into the halfspaceabove the patch. Besides compatibility with integrated cir-cuitry, microstrip antennas offer other advantages such asthin profile, light weight, low cost and conformability to ashaped surface. These features make the microstripantenna very attractive for use in high-speed vehicles, suchas missiles, rockets and satellites, where wind resistanceand payload are major considerations.

The microstrip antenna also possesses a number of dis-advantages, the principal ones being narrow bandwidth,low efficiency, low power-handling capacity and toleranceproblems associated with the substrate properties. Thenarrow bandwidth (typically 1%) is a particularly seriouslimitation, and a considerable amount of effort has recent-ly been devoted to this problem. (For the purposes of thispaper, the bandwidth will be taken to be the widthbetween the frequencies at which the input resistances are1/2 of the value at resonance; i.e. VSWR ^ 2.) A relatedeffort is devoted to increasing the frequency agility of theantenna. One line of approach is to consider methodswhereby the operating frequency of the antenna can betuned over a range of values so that the same antenna can

Paper 4077H (Ell), first received 14th December 1984 and in revised form 20thMay 1985

Dr. Dahele is with the School of Electrical Engineering and Science, Royal MilitaryCollege of Science, Shrivenham, Swindon, Wilts SN6 8LA, United Kingdom. Prof.Lee is with the Department of Electrical Engineering, University of Akron, Akron,Ohio 44325 USA

substrate

ground plane

conductingpatch

Fig. 1 Geometry of a microstrip antenna

a side viewb top view

be used for several channels. The development of tunablemicrostrip antennas, particularly those utilising an adjust-able airgap in the structure, has been one of the researchareas of the present authors. As most of the results werepresented at meetings [1-3] and not published in archivejournals, we feel that it is appropriate to give a com-prehensive report on our research to date on this topic.This is the objective of the present paper.

In Section 2, the air gap idea is described qualitatively.In Section 3, experimental results obtained by introducingan airgap are presented for several types of microstripantennas, namely, the circular disc, the annular ring andthe dual-frequency stacked discs. In Section 4, the theoriesthat have been developed for these antennas are described.Comparison between theory and experiment is given inSection 5. Section 6 contains some concluding remarks.

1EE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985 455

2 Idea of an air gap in a microstrip antenna

Let us return to the geometry of Fig. 1. As mentioned pre-viously, the electromagnetic energy is first guided along thecoaxial line to the feed point, then spreads out into theregion under the patch. Some of the energy crosses theboundary of the patch and radiates into space. If the fieldsin the exit region can be determined, they can be represent-ed by equivalent sources, from which the radiation fieldcan be calculated. One of the methods of determining thefields in the exit region is known as the cavity model [4].In this method, the region between the patch and theground plane is considered as a cavity bounded by electricwalls on the top and the bottom, and by a magnetic wall(to simulate the open-circuit condition) on the sides. Theresonant frequency of a particular mode is determined bythe permittivity of the substrate, the shape and size of thepatch, and, to some extent, by the thickness of the sub-strate. Consequently, if the resonant frequency is to bechanged, either to that of an adjacent channel or for thepurpose of compensating for the tolerances associated withthe substrate properties and etching process, it is necessaryto design a new antenna or to incorporate some tuningelements such as varactor diodes in the structure [5]. Thelatter requires the provision of a biasing network, with theresult that the simplicity of a microstrip antenna is lost.For these reasons, it is desirable that simple methods fortuning the resonant frequencies are available. One suchmethod is to introduce an adjustable airgap between thesubstrate and the ground plane. Let us explore this idea indetail.

The geometry of a microstrip antenna with an airgap isshown in Fig. 2. Consider the cavity under the conducting

substrate conduct inpatch

A airgap

spacer

Fig. 2 Geometry of a microstrip antenna with airgap

patch. It is now made of two layers, a substrate of thick-ness t and an air region of thickness A. Compared to thecase without an airgap, the effective permittivity of thecavity is evidently smaller. As a result, the resonant fre-quencies of the various modes will increase. As the effectivepermittivity decreases as A increases, tending towards thefree-space value e0 as A—• oo, it follows that the resonantfrequencies can be tuned by adjusting the airgap width A.Moreover, the airgap is expected to have the effect ofincreasing the impedance bandwidth of the antenna. Thisis partly due to the increase of the effective height of thedielectric medium and partly because the effective permit-tivity is smaller.

It is obvious that the airgap idea is a general one in thesense that it can be applied to patches of arbitrary shape.It can also be applied to dual-frequency stacked antennasas well as arrays of identical elements. The method is parti-cularly attractive for arrays, as the resonant frequencies ofall of the elements, and therefore of the array, can be tuned

by a single adjustment of A. As far as we are aware, theairgap idea was first proposed in the context of microstripantennas by the present authors in 1982 [1].

In the next Section, experimental results supporting thisidea are presented for several types of practical antennaconfigurations.

3 Experimental results

3.1 Circular discThe first antenna configuration we studied experimentallywas the circular-disc microstrip antenna. A circular patchof radius 5 cm was fabricated on RT/Duroid 5870 materialof thickness 0.157 cm and relative permittivity 2.32. Thewidth of the airgap is controlled by using spacers betweenthe substrate and the ground plane. In our experiment,0.5 mm and 1.0 mm spacers were used. The antenna isprovided with a coaxial feed near the edge of the disc at adistance d = 4.75 cm from the centre. This feed position ischosen as it is well known that it yields a larger resistanceat resonance compared to a feed which is closer to thecentre. The resonant frequencies and input impedanceswere measured with a HP8010A network analyser. Theresults are summarised in Table 1. For the lowest mode,

Table 1: Measured resonant frequencies and impedancebandwidths of the first few modes of a 5 cm radius circular-disc microstrip antenna with er = 2.32, f = 0.159 cm, fed at4.75 cm from the centre, for three values of the airgap widthA

TM2 1

TM31

A = 0

'nm

112818792596

MHzMHzMHz

BW

0.890.850.77

A = 0.

fnm

128621362951

5 mm

MHzMHzMHz

BW

121

.48

.15

.63

A = 1

fnm

135022563106

.0 mm

MHzMHzMHz

BW

2.072.612.02

T M U , there is a tuning range of about 20% in frequencyand a more than twofold increase in the bandwidth asA goes from 0 to 1.0 mm. Similar behaviour is recordedfor the other modes. The measured input impedances ofthe TMj! mode as a function of frequency are shown in

600

•o 200a

K 0

-200

y'\

A=0.5mm = 1.0mm

1100 1150 1250 1350 K001300f.MHz

Fig. 3 Measured input impedance of the T M j , mode of a 5 cm circular-disc microstrip antenna, for three values of the airgap width Aer = 2.32, t = 0.159 cm

Fig. 3. The upward shift in the resonant frequency and thewidening of the bandwidth are clearly seen. We have alsomeasured the radiation pattern and found that the airgapdoes not have a significant effect on the pattern.

3.2 Annular ringThe second antenna on which we have done some work isthe annular-ring microstrip antenna, the geometry ofwhich is shown in Fig. 4. For some time it was thoughtthat the annular-ring geometry did not offer anything sig-nificantly different from the circular disc. However, it is

456 IEE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985

now known that, although this is true for the lowest T M n

mode, the TM1 2 mode of the annular ring does have some

coaxial feed

A airgap

conductingpatch

Fig. 4 Geometry of an annular-ring microstrip antenna with airgap

a side viewb top view

attractive features. Like the T M n mode, the radiation isstrongest in the broadside direction. However, it has animpedance bandwidth which is substantially larger thanboth the T M n mode of the ring and the T M n mode ofthe circular disc. Unlike the TMX1 mode, whose inputimpedance is very large and is insensitive to the feed posi-tion, the input impedance of the TM1 2 mode is very sensi-tive to the feed position and can attain a convenient valueof about 60-70 Q when fed at the inner edge of the ring.Theoretically, these results were predicted by Ali et al. [6]and Chew [7] in 1982 and verified experimentally by thepresent authors in the same year [8].

The experimental results showing the effect on these twomodes when an airgap is introduced are summarised inTable 2. The annular ring has b = 7.0 cm, a = 3.5 cm, fab-ricated on RT/Duroid 5870 material of thickness 0.159 cm,

Table 2: Measured resonant frequencies and impedancebandwidths of the T M , , and TM 1 2 modes of an annular-ringmicrostrip antenna with inner radius 3.5 cm, outer radius 7.0cm, ep m 2.32, t = 0.159 cm, for three values of the air gapwidth A. The feed is placed at dja — 1.05 where d is the dis-tance from the centre

TM, ,TM1 2

A = 0

'nm

6262757

MHzMHz

%BW

0.64.0

A = 0.5 mm

fnm

720 MHz3040 MHz

%BW

0.78.0

A = 1

fnm

7783240

.0 mm

MHzMHz

%BW

0.88.6

and relative permittivity 2.32. As in the circular disc, thereis an upward shift in the resonant frequencies and a widen-ing of the bandwidths. It is significant that, for the TM1 2

mode, the bandwidth attains a value of 8.6% when A isequal to 1.0 mm.

3.3 Dual- frequency stacked discsThe next microstrip-antenna configuration to which wehave applied the airgap idea is the dual-frequency stacked-disc antenna shown in Fig. 5. This antenna was proposedby Long and Walton in 1979 [9]. It is clear from Fig. 5

conductingpatch

ground plane —coaxialfeed

Fig. 5 Nontunable dual-frequency stacked microstrip antenna

that the structure contains two coupled cavities, one undereach patch. Because the fringing fields are different for thetwo cavities, they resonate at two different frequencies,even if the disc radii and substrate thickness are the same.The input impedance therefore shows two resonant peaks.However, in the original arrangement, the two resonantfrequencies are fixed and not tunable. A tunable version ofthis antenna can be obtained by applying the airgap idea,as illustrated in Fig. 6 [1]. Some of our experimental

conducting patch

A 2 airgap

A, airgap

spacers

ground plane

Fig. 6 Tunable dual-frequency stacked microstrip antenna utilising theairgap idea

results, performed on a tunable structure with two stackeddiscs of 7 cm radius each, are shown in Figs. 7 and 8. Fig.7 shows that the upper airgap has the effect of altering theresonant frequency of the upper resonance. The effect ofthe lower airgap, as shown in Fig. 8, is more complicated.

400

300

C 200x•o 100o

K 0

-100

750 800 850f.MHz

900

Fig. 7 Measured input impedances of the TMn mode of a pair ofstacked circular-discs of 7 cm radius, for three values of the upper airgapd = 6.5 cm, A, = 0, er = 2.32, t = 0.159 cm

R valuesX values

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985 457

It shifts not only the lower but also the upper resonances.In addition, the bandwidth of the lower resonance is sub-stantially broadened by the presence of the lower airgap.

300

200

100

0

-100

750 800 850 900f .MHz

Fig. 8 Measured input impedances of the TMlx mode of the stackedcircular-discs of Fig. 9 for two values of the lower airgapd = 6.5 cm- • - • - • - • R A, = 0 ; A 2 = 0

- • - • - • X

x x x - x X A, = 0.55 mm; A2 = 0

Summarising the presentation up to this point, we haveexplained qualitatively how the airgap works in a micro-strip antenna and have presented experimental results forthree types of microstrip antennas. In the next Section,some theories that have been developed, based on thecavity model, will be described. So far, the theories dealwith the single-patch circular-disc and annular-ringantennas. The theory for the dual-frequency stacked dischas not yet been developed, even for the case when there isno airgap.

4 Cavity-model theory

4.1 IntroductionThe microstrip antenna with an airgap can be analysedusing the cavity model, suitably modified to account forthe fact that the cavity under consideration is now a two-layered cavity. The assumptions and method of analysis, aswell as the theoretical results obtained for the circular disc,have recently been reported in the literature [10]. In thisSection, the theoretical results for the annular ring aregiven.

In the interest of brevity, the derivations are omittedand only the formulas for the resonant and input imped-ance are given, as these are the quantities which dependsensitively on the airgap width A. Numerical results showthat the airgap does not affect the radiation fields signifi-cantly. For this reason, the formulas for the radiation fieldsare not given below.

4.2 Theoretical results for the annular ring(a) Resonant frequencies: Consider an annular-ring micro-strip antenna with outer radius b, inner radius a, substratethickness t and airgap thickness A. If it is assumed to bebounded by electric walls on the top and bottom and by amagnetic wall along the side, the resonant frequencies forTM modes are given by

knmc (t + Ae,)1'2

27l£r1 / 2 A)

i/2 (1)

where c is the velocity of light in free space, er is the sub-strate relative permittivity and knm are the roots of thecharacteristic equation

J'n(kb)Y'n(ka) - J'n(ka)Y'n(kb) = 0 (2)

In eqn. 2, J'n(x) and Y'n(x) are Bessel functions of the firstand second kind, order n, respectively, and the primedenotes derivatives with respect to kp.

To account for the fact that a small fraction of the fieldexists outside the dielectric, it is customary to use an effec-tive permittivity ee in place of er in eqn. 1. The formula foree as given by Schneider [12] is

10/ ~1/2

(3)

whereW = {b-a)h = t + A.

To account for the fringing fields along the curved edges ofthe ring, it has been suggested that the outer and innerradii be modified according to [13]

b' = b + {WJJ) - WO/2

a' = a- {WJJ) - WO/2

where

W(0) — W

WJ0) =120nh

2\ih

(4)

(5)

(6)

(V)

(8)

In eqns. 7 and 8, /J. is the permeability and Zo is the quasi-static characteristic impedance of a microstrip line ofwidth W.

A pair of empirical formulas for the modified radii isalso available. It is given by [14]

d = a-\h (9)

b' = b + lh (10)

{b) Input impedance: The input impedance of the annular-ring microstrip antenna with an airgap, with the coaxialfeed located at distance d from the centre (modelled by auniform current ribbon of effective width w), is given by

sinZ = — icou ) >

V J. m V nw J 2

Vn(knmd)Y'n(knma') - J'n(knma')Y'n(knmdY

(

J'n2(knmb')Y k 2 b ' 2 J V

(t _ p (11)

where deff is the effective loss tangent. Assuming thatsurface-wave loss is negligible, deff is given by

eff = Jt + A)(fi0

(12)

458

In eqn. 12, S is the loss tangent of the substrate, a is theconductivity of the patch and the ground plane, and thequantities Dnm and /, are given by

1EE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985

JniKm 0 ) k2 h'- 1 -

k2 a'Knma

(13)

' sin 9) - j;(/c0 a' sin 6>)1

+ n2 cos2 9J'n(knma') J'n(kob'sin 9)

J'n(Kmb') kob' sin 9

k0 a sin 9(14)

For the annular-ring antenna of Section 3, 5eff is about0.004 for the T M n mode and ~0.04 for the TM1 2 mode.

5 Comparison between theory and experiment

In this Section, we compare the measured and calculatedvalues of the resonant frequencies and input impedances ofthe circular-disc and the annular-ring microstrip antennaswith airgaps. The dimensions, substrate material and feedpositions of these antennas are the same as those given inSection 3. It should be mentioned that measurements ofthe radiation patterns have also been made, and the resultsshow that they are not significantly affected by the airgap,which is consistent with theoretical predictions. In theinterest of brevity, the measured and calculated patternsare not shown here.

Table 3 shows the calculated and measured resonant

Table 3: Comparison of calculated and measured resonantfrequencies for the circular-disc and the annular-ring micro-strip antennas(a) Circular disc

A = 0

Calc.(MHz)

TM, , 1127TM21 1869TM31 2571

r = 5.0cm, t = 0.

(b) Annular ring

A = 0

Calc.(MHz)

TM, , 622TM1 2 2820

Meas.(MHz)

112818792596

159 cm,

Meas.(MHz)

6262757

A = 0.5

Calc.(MHz)

127621172911

</ = 4.75

A = 0.5

Calc.(MHz)

7143123

mm

Meas.(MHz)

128621362951

cm, tr =

mm

Meas.(MHz)

7203040

A = 1.0

Calc.(MHz)

135122413082

2.32

A = 1.0

Calc.(MHz)

7633210

mm

Meas.(MHz)

135022563106

mm

Meas.(MHz)

7783240

b = 7.0 cm, a = 3.5 cm, d = 3.6 cm, e, = 2.32

frequencies of the circular disc of 5 cm radius and theannular ring of 7 cm outer radius and 3.5 cm inner radius.It is seen that the agreement between theory and experi-ment is good. In the majority of cases, the discrepanciesare within 1%, whereas, for the worst case, the discrepancyis about 2.5%. These differences can be due to a variety offactors, e.g. the tolerances associated with the value of thedielectric constant and the fact that the formulas for themodified physical radii are approximate rather than exact.It should be pointed out that the frequencies in Table 3bdiffer from those listed in Table 4 of Reference 3. This isbecause Reference 3 did not take into account the modifiedradii in the theory, which resulted in an incorrect identifi-cation between the theoretical and experimental resonantfrequencies. In Fig. 9, the input impedances of the TMX1

modes of the annular ring as a function of frequency(plotted in terms of deviations from the resonant

A=0

500

-500

A= 1.0mm

-20 -10 •10

Fig. 9 Theoretical and measured input impedances of the TM,, mode ofan annular-ring microstrip antenna with a = 3.5 cm, b = 7.0 cm, r.r = 2.32,t = 0.159 cm, fed near the inner edge, for three values of the airgap width A.The calculated and measured resonant frequencies are given in Table 3

a = 3.5 cm, b = 7.0 cm, cr = 2.32, / =0.159 cm, d/a = 1.05theory experiment

frequency) are shown for A = 0, 0.5 mm and 1.0 mm. Theexperimental values were obtained with a HP8010Anetwork analyser, and the calculated values were obtainedusing eqn. 11. The effective feed width w was chosen suchthat the calculated results provide the best fit with experi-ment. The theoretical curves shown in Fig. 9 are bothobtained using w = n/10. It is seen that the agreementbetween theory and experiment is good. It should be notedthat the calculated impedances are not very sensitive to thevalue of w. For example, if w is changed to n/20, the valuesof Z at resonance differ from those corresponding tow = 7t/10 by only 2%. A similarly good agreement wasalso obtained for the T M n mode of the circular disc [10].

6 Concluding remarks

In this paper, we have given a comprehensive report onour research on microstrip antennas with airgaps. We haveestablished conclusively that the introduction of an airgapin single or stacked patch antennas offers a simplermethod for tuning the resonant frequencies than othermethods which use varactor diodes or tuning elementssuch as stubs. The method described here is particularlyattractive for arrays, as the resonant frequencies of all ofthe elements, and therefore of the array, can be tuned by asingle adjustment of A.

As a byproduct, the airgap also increases the impedancebandwidth of the antenna. Although the increase isachieved at the expense of increasing the thickness of theantenna, it should be noted that a two-layered structure oftotal thickness h, consisting of a substrate of height t andan air layer of width A, has a larger bandwidth than asingle-layer structure of substrate thickness h, simplybecause the effective relative permittivity of the former isless than er. It should also be noted that the radiation effi-ciency of the former is higher than the latter, because thedielectric loss in the air layer is negligible.

Finally, it is appropriate to end this paper by pointingout two areas in which further investigation is necessary.The first is that, although we have used only discrete valuesof the airgap width A in our measurements so that itseffect can be illustrated easily, we see no practical difficultyin developing a scheme in which A is continuously vari-able. The development of such a scheme is of considerablepractical interest. The second area is theoretical in nature.As mentioned in Section 4, the theories for the stackedmicrostrip antenna are not available, both for the caseswith and without airgaps.

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985 459

7 References

1 DAHELE, J.S., and LEE, K.F.: 'A dual-frequency stacked microstripantenna'. IEEE/AP-S International Symposium Digest, 1982, pp.308-311

2 DAHELE, J.S., and LEE, K.F.: 'A dual-frequency circular disc micro-strip antenna with tunable characteristics'. European MicrowaveConference Proceedings, 1982, pp. 390-395

3 LEE, K.F., DAHELE, J.S., and HO, K.Y.: 'Annular-ring and circular-disc microstrip antennas with and without air gaps'. Ibid., 1983, pp.389-394

4 LO, Y.T., SOLOMON, D., and RICHARDS, W.F.: 'Theory andexperiment on microstrip antennas', IEEE Trans., 1981, AP-29, pp.38-46

5 BHARTIA, P., and BAHL, I.J.: 'A frequency agile microstripantenna'. IEEE/AP-S International Symposium Digest, 1982, pp.304-307

6 ALI, S.M., CHEW, W.C., and KONG, J.A.: 'Vector Hankel Trans-

form analysis of annular-ring microstrip antenna', IEEE Trans., 1982,AP-30, pp. 637-644

7 CHEW, W.C.: 'A broad-band annular-ring microstrip antenna', ibid.,1982, AP-30, pp. 637-644

8 DAHELE, J.S., and LEE, K.F.: 'Characteristics of annular-ringmicrostrip antenna', Electron. Lett., 1982,18, pp. 1051-1052

9 LONG, S.A., and WALTON, M.D.: 'A dual frequency stacked circu-lar disc antenna', IEEE Trans., 1979, AP-27, pp. 270-273

10 LEE, K.F., HO, K.Y., and DAHELE, J.S.: 'Circular-disk microstripantenna with an air gap', ibid., 1984, AP-32, pp. 880-884

11 BAHL, I.J., and BHARTIA, P.: 'Microstrip antennas' (Artech House,1980), Chap. 3

12 SCHNEIDER, M.V.: 'Microstrip lines for microwave integrated cir-cuits', Bell Syst. Tech. J., 1969, 48, pp. 1421-1444

13 OWENS, R.P.: 'Curvature effect in microstrip ring resonators', Elec-tron. Lett., 1976,12, pp. 356-357

14 WU, Y.S., and ROSENBAUM, F.J.: 'Mode chart for microstrip ringresonators', IEEE Trans., 1973, MTT-21, pp. 487-489

460 IEE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985