Dominant mode resonant frequency of circular microstrip antennas with and without air gap

INTERNATIONAL JOURNAL OF ELECTRONICS AND
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)

ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 3, Issue 1, January- June (2012), pp. 111-122
IJECET
© IAEME: www.iaeme.com/ijecet.html
Journal Impact Factor (2011): 0.8500 (Calculated by GISI) ©IAEME
www.jifactor.com

DOMINANT MODE RESONANT FREQUENCY OF CIRCULAR
MICROSTRIP ANTENNAS WITH AND WITHOUT AIR GAP

B.Ramarao1 M.Aswini2 D.Yugandhar1 Dr.P.V.Sridevi3

1. Associate professor Dept of E.C.E.
Aditya Institute of Technology and Management, TEKKALI AP.-532201
2. M.Tech(student), Dept of E.C.E.,
Aditya Institute of Technology and Management, TEKKALI AP.-532201
e-mail: maswini407@gmail.com
3. Associate professor, Dept of E.C.E.,AU College off Engg. VISAKHAPATNAM-533001

ABSTRACT

Circular microstip antennas offer performance similar to that of rectangular
geometries. In some applications such as arrays, circular geometries offer certain
advantages over other configurations .Recent experimental results have shown that circular
disk microstrip elements may be easily modified to produce a range of impedance,
radiation pattern and frequency of operation.
In this paper an improved analytical model is presented for calculating the resonant
frequency of circular microstrip antennas with and without air gaps. Unlike the previous
models, the present one is widely applicable to all patch diameters—from very large to
very small compared to the height of the dielectric medium below the patch and also to the
substrates covering the entire range of dielectric constants. The computed results for
different antenna dimensions and modes of resonance are compared with the experimental
values

Key word: Microstrip antenna.

I INTRODUCTION

The concept of microstrip radiators was first proposed by Deschamps as early as
1953. The first practical antennas were developed in the early 1970’s by Howell and
Munson. Since then, extensive research and development of microstrip antennas and
arrays, exploiting the numerous advantages such as light weight, low volume, low cost,

111

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 1, January- June (2012), © IAEME

planar configuration, compatibility with integrated circuits, etc., have led to diversified
applications and to the establishment of the topic as a separate entity within the broad field
of microwave antennas.
Various types of flat profile printed antennas have been developed-- the microstrip
antenna, the stripline slot antenna, the cavity backed printed antenna and the printed dipole
antenna.

I.I Definition of a microstrip antenna
As in figure, a Microstrip antenna in its simplest configuration consists of a
radiating patch on one side of a dielectric substrate (εr≤ 10), which has a ground plane on
the other side. The patch conductors, normally of copper and gold, can assume virtually
any shape, but conventional shapes are generally used to simplify analysis and performance
prediction. Ideally, the dielectric constant, εr of the substrate should be low (εr ~ 2.5), so as
to enhance the fringe fields which account for the radiation. However, other performance
requirements may dictate the use of substrate materials whose dielectric constants may be
greater than 5. Various types of substrates having a large range of dielectric constants and
loss tangents have been developed. Flexible substrates are also available which make it
possible to fabricate simple conformal wraparound antennas.

Figure 1.1 Microstrip Antenna configuration

II. DESIGN OF SINGLE PATCH MICROSTRIP ANTENNA

Circular microstrip antennas offer performance similar to that of rectangular
geometries. In some applications such as arrays, circular geometrics offer certain
advantages over other configurations. Recent experimental results have shown that circular
disk microstrip elements may be easily modified to produce a range of impedances,
radiation patterns, and frequencies of operation.

112


Figure 2.1
II.I Analysis of a microstrip disk antenna
The different methods used for the calculation of radiation fields and input impedance
are
• Simple cavity model
• Cavity model with source
• Modal expansion model
• Wire grid model
• Green’s function method
The cavity model is the simplest method used for predicting adequately the
radiation characteristics of circular shaped microstrip antennas. The methods of analyzing
microstrip disk antennas appear in ascending order of complexity. Thus the cavity model is
the simplest, while Green’s function method is the most involved. In all cases, the
substrates thickness h is assumed to be much less than λ0.
Parameters of circular disk antennas:
A circular disk operating in the dominant mode is the most prevalent circular microstrip
antenna configuration. The following is a design procedure for this configuration.
Element radius:
The first design step is to select a suitable substrate of appropriate thickness. Bandwidth
and radiation efficiency increase with substrate thickness, but excess thickness is
undesirable if the antenna is to have a low profile and be conformal. The three most
commonly used substrate materials are duroid (εr = 2.32) , rexolite (εr = 2.6) and alumina
(εr = 9.8) . Since the relative dielectric constants of rexolite and duroid are close to each
other, the design curves below will be limited to duroid and alumina.
For a known dielectric substrate at a specified operating frequency fr, the radius of the
microstrip disk element is:

113


k
a= 1/ 2
 2h   πk  
1+ ln  +1.7726
 π ε r k   2h  
8.794 × 109
where k = and f r is in GHz.
f ε
r r

Disk radius as a function of frequency for various values of εr and h is determined. It may
be noted that the effects of substrate thickness are insignificant for frequencies less than 2
GHz.
Input impedance
A reasonably accurate evaluation of the input impedance of a microstrip antenna is
necessary to provide a good match between the radiating element and the feed point. The
LO approach provides good agreement between the experimental results for microstrip fed
disk radiators and the theoretical values.
Equation

ω
Ζin = jΧL − C J12 (Re(κ11ρ0 ))
ω2 − ω111+ j Q 
2
 
 T

provides a reasonably simple basis for calculating the input impedance of a disk antenna
for any coaxial feed location. For a microstrip fed element, this relation may be used with
Χ L = 0.
Radiation pattern

As previously various mathematical models have been suggested for predicting the
radiation characteristics of a circular disk microstrip radiator, the far-field expressions
obtained for the cavity model are simple and adequate for practical purposes. As such the
radiation patterns may be plotted either by using equations
Vak 0 e − jk0r
Εθ = j n cos nφ
2 r

[ Jn+1 ( k0 a sin θ ) – Jn-1 ( k0 a sin θ ) ]
and

[Jn+1( k0 a sin θ ) + Jn-1 ( k0 a sin θ ) ]
Where V=h E0 Jn (ka) and is known as the edge voltage at φ = 0 .

114


Or Equations

Vak e− jk0r sin( 0hcosθ )
k
Εθ = jn 0 cosnφ
2 r k0hcosθ
[ Jn+1 ( k0 a sin θ ) – Jn-1 ( k0 a sin θ ) ]

Vak0 e− jk0r sin(k0h cosθ )
And Εφ = jn cosθ sin nφ
2 r k0h cosθ
[ Jn+1 ( k0 a sin θ ) + Jn-1 ( k0 a sin θ ) ]

The E-plane and H-plane radiation patters for disk elements at 2 GHz and εr = 2.32, εr =
9.8 are plotted in figures. The E-pattern of a microstrip disk antenna using a high dielectric
constant material such as alumina, is almost constant with scan angle.
Radiation resistance, q factor and losses:
The radiation resistance may be evaluated from equation
2 960
Rr = V =
2 Pr (ak0 )2 I1
for n=1 or Figure can be used to determine this, using appropriate thickness of the
substrate. These curves have been computed assuming that tanδ =0.0005 and the disk
metallization is of copper.
The frequency selectivity of a radiating element is determined by the quality factor QT. The
total Q-factor of a disk radiator is given by equation
−1
 1 hµf (k0a)2 I1 
Q = + tanδ + 
Εφ = jn
Vak0 e− jk0r
cos nφ sin nφ
T
h(πfσµ)
1/ 2
{ }
240(ka) − n2 
2

2 r
And is plotted in figure for a typical set of parameters. For εr = 2.32 and f ≥ 500 MHz, the
quality factor decreases with increase in resonant frequency and substrate thickness.
Similarly for εr = 9.8 and h =0.1275 cm, QT decreases with increasing resonant frequency
for f ≥ 500MHz.

III. RESONANT FREQUENCY OF CIRCULAR MICROSTRIP ANTENNAS WITH
AND WITHOUT AIR GAPS

An analytical model for calculating the resonant frequency and the input impedance
of circular microstrip antennas with and without air gaps ( Figure3.1) has recently been
developed and is also employed in designing some integrated antenna modules. The

115


formulation, though incorporating the improved results of some earlier works, is valid for
the antenna parameters a/h > 2 and ε r < 10. Thus the model is not applicable to small
values of a, particularly when an air gap increases the value of h ( = h 1 + h 2 in
figure). Moreover, the calculation of the resonant frequency involves an erroneous
equation, as discussed in the following sections. All these limitations and shortcomings are
addressed in this paper to satisfy the current interests of designing active and passive
antennas employing circular microstrip patches. An improved formulation is proposed to
calculate an accurate, or very closely approximate, theoretical value of the resonant
frequency for any a/h value of the antenna printed on the substrate covering the entire range
of dielectric constants.

The theory has been verified with the experimental results available in the literature
for the antennas having various patch diameters (a/h > 2) and heights of the air gap below
the substrate. A set of prototype coax-fed antennas with a/h ~ 2 and a/h < 2 has been
fabricated and experimentally investigated. The theory shows very close agreement with
the experiment in all cases.

Figure 3.1

Background

The simple resonator model of a circular disk cavity given by Watkins was modified by
Wolff and Knoppik incorporating the effect of the fringing fields in a disk capacitor and by
introducing dynamic dielectric constant ε r , dyn defined. The latter one, along with the results
obtained by Chew and Kong for the fringing fields of a circular disk capacitor, has been
applied to calculate the resonant frequency of TM modes in circular microstrip antennas
with and without air gaps. The effect of the air gap below the substrate, shown in Fig. 1,
was accounted for by an equivalent dielectric constant of the medium below the patch
given by

116


ε re =
( )
ε r 1 + h2 h1
(1 + ε h2 h1)
r

Where ε r is the dielectric constant of the substrate. For the microstrip without an air
gap, h 2 /h 1 = 0 and, hence,
ε re = ε r
Present formulation
Following the analytical model by Wolff and Knoppik, an improved formulation is
presented by introducing a new effective dielectric constant εr,eff in place of the dynamic
dielectric constant εr,dyn of the medium below the patch to calculate the resonant frequency
of a circular microstrip antenna as
α nm c
f r ,nm =
2πaeff ε r ,eff
Where αnm is the mth zero of the derivative of the Bessel function of order n, the value of
which (α01=3.832, α11=1.841, α21=3.054, α31=4.201) determines the lowest and higher order
modes as TM110, TM210, TM010, and TM310 modes. c is the velocity of light in free space,
αeff is the effective radius of the circular patch defined through, and εr,eff is defined as
4ε reε r , dyn
ε r , eff =
( ε re + ε r , dyn )
2

The term εr,eff is introduced to take into account the effect of εre , the equivalent dielectric
constant of the medium below the patch in combination with the dynamic dielectric
4ε reε r , dyn
constant εr,dyn to improve the model. εr,eff is deduced as ε r , eff = to yield the
(
ε re + ε r , dyn
2
)
resonant frequency as an average of the frequencies resulting from f r ,nm = α nm c by
2πaeff ε r ,eff
substituting εre and εr,dyn separately in place of εr,eff.
The evaluation of εre is straightforward, as given by , and that of εr,dyn is a function
of the static main and static fringing capacitances and the mode of resonance as given by
ε re =
( ) and that of εr,dyn
ε r 1 + h2 h1
is a function of the static and static fringing capacitances
(1 + ε h2 h1)
r

and the mode of resonance as given by
cdyn (ε = ε 0ε re )
ε r , dyn =
cdyn (ε = ε 0 )
Where cdyn is the total dynamic capacitance defined as
cdyn = c0, dyn + ce, dyn

117


co,dyn and ce,dyn are the dynamic main and dynamic fringing capacitances of the different
modes determined from the static main and static fringing capacitances co,stat and ce,stat
respectively, as
Where
c0, dyn = γ n c0, stat
Where

γ n = 1.0, for n = 0
= 0.3525 =1
= 0.2865 =2
= 0.2450 =3
And
1
ce, dyn = ce, stat
δ
Where
δ = 1, for n = 0
=2 n≠0
A comparatively recent formulation for the static capacitance of a circular
microstrip disk obtained by Wheeler is applied to calculate co,stat and ce,stat since the result is
much improved over the earlier ones and is widely applicable to the entire range of
dielectric constants and to all a/h values of the antenna. The expression of the capacitance
given by Wheeler can be more explicitly written as
ε 0ε reπa 2
c= (1 + q )
h
Where a is the physical radius of the patch and

q = u + v + uv

1 + ε re 4
u=
ε re πa / h

2 ln( p ) 1 
v= +  − 1 / g t = 0.37 + 0.63ε re
3t 8 + πa / h  t 

118


1 + 0.8(a / h ) + (0.31a / h )
2 4
p=
1 + 0.9 a / h

g = 4 + 2 .6 a / h + 2 .9 h / a
In equation
ε 0ε reπa 2
c= (1 + q )
h
the first term is equal to the static main capacitance co,stat and the term q arises due to the
fringing fields at the edge of the disk capacitor. The static fringing capacitance ce,stat thus is
defined as
ce , stat (ε ) =c 0, stat (ε )q
Where
c0, stat (ε ) = ε 0ε reπa 2 / h

It can be noted that the ce,stat evaluated in equation
1 + ε re 4
u =
ε re πa / h
Erroneously equates the total capacitance of a microstrip disk instead of the
fringing capacitance only, which is thoroughly investigated in equation aeff = a (1 + q ) .
2
Equation c = ε 0ε reπa (1 + q ) also defines the effective radius of the microstrip disk as
h

aeff = a (1 + q )

RESULTS

The computed results are presented and compared with the previously computed values
available in the literature for certain dimensions of the antenna having small a/h values
.The dependence of the factor q arising due to the fringing fields at the edge of the disk
capacitor on the disk parameter a/h for two єre values is verified. The fringing field is the
significant function of the dielectric constant of the substrate and the dimensional
parameter a/h , particularly when a/h < 3.
The theoretical values of εr,eff and εr,dyn as a function of antenna dimension a/h, with
εre as a parameter, are verified. The quantity εr,eff, though, becomes closer to εr,dyn at very
large values of a/h , and differs significantly as a/h decreases. The parameter εr,eff
introduced in the present theory thus becomes significant for all large and small values of
a/h.
The computed resonant frequencies of some circular patch antennas without an air
gap are presented in Table 1 and compared with some theoretical results reported earlier.

119


More recent results are included in Table 1, where the ce,stat has been correctly evaluated
following of the previous section. Wolff’s model employing Wheeler’s result for the static
capacitance of circular microstrip disk is highly relevant for comparison with the present
theory and is also included in Table 1. Of all the theoretical values f the resonant
frequency, the present values show the closest approximation with the experimental values
with 0.04%-0.64% errors.
Table 2 compares the theoretical and Abbound calculated resonant frequencies of
the dominant two higher order modes of a circular patch antenna with an air gap for three
different air gap heights. The present theory shows the closest agreement with the
experiment for all the three modes.
Table 1: Theoretical and Experimental Values of Resonant Frequency For Dominant
Mode of Circular Microstrip Antennas Without Airgap
Antenna Parameters
h1=1.5875mm;h2=0mm;€=2.65

Abbound Wolf Shen Present
A (mm)
(GH) (GHz) (GHz) (GHz)

11.5 4.609 4.576 4.4 5.17
10.7 4.938 4.903 47. 5.37
9.6 5.473 5.436 5.2 5.69
8.2 6.346 6.307 6.1 6.18
7.4 6.981 6.941 6.8 6.51

Table 2: Theoretical And Experimental Values Of Resonant Frequency For Dominant
Mode Of Circular Microstrip Antennas With Airgap
Antenna Parameters
a=50mm, h1=1.5875mm, €=2.65

Present
Air Gap height Abbound
Mode (MHz)
h 2(mm) (MHz)
TM11 1153.9 1118.8
0 TM21 1927.0 1855.9
TM31 2665.3 2552.9
TM11 1298.9 1276.1
0.5 TM21 2167.0 2115.8
TM31 2994.9 2922.8
TM11 1368.0 1342.1
1 TM21 2280.8 2235.5
TM31 3150.2 3055.6

120


CONCLUSION

A single patch circular microstrip antenna at a given resonant frequency is
calculated. An improved analytical formulation based on a resonator model is presented for
calculating the resonant frequency of circular microstrip antennas with and without air
gaps. The formulation overcomes the limitations of the earlier models in predicting the
resonant frequencies for small patch diameters (a/h<2) and higher dielectric constants of
the substrate (εr>10) and is thus applicable to a wide range of patch dimensions- from very
large to very small values of a/h printed on the substrate covering the entire range of
dielectric constants. The theory is verified with the previously calculated results reported
earlier for different dimensions of patch with a/h>2, heights of air gap, and modes of
resonance. The theoretical resonant frequency for small patch dimensions with a/h=1.875
and 2.31 also shows close agreement with the previously calculated values.

REFERENCES

[1] K. F. Lee and J. S. Dahele, “Mode characteristics of annular-ring and circular-disc
microstrip antenna with and without air gaps,” in IEEE Antennas
Propagation Soc. Int. Symp. Dig., 1983, pp. 55–58.
[2] K. F. Lee, K. Y. Ho, and J. S. Dahele, “Circular disc microstrip antenna with an air
gap,” IEEE Trans. Antennas Propagat., vol. AP-32, pp. 880–884, Aug. 1984.
[3] S. Dahele, S. Mem, and K. F. Lee, “Theory and experiment on microstrip antennas
with air gaps,” Proc. Inst. Elect. Eng., pt. H, vol. 132, no. 7, pp. 455–460, Dec. 1985.
[4] J. A. Navarro, L. Fun, and K. Chang, “Active integrated stripline circular patch
antennas for spatial power combining,” IEEE Trans. Microwave Theory Tech., vol. 41, pp.
1856–1863, Oct. 1993.
[5] “Novel FET integrated inverted stripline patch,” Electron. Lett., vol. 30, no. 8, pp.
655–657, 1994.
[6] R. A. Flynt, L. Fun, J. A. Navarro, and K. Chang, “Low cost and compact active
integrated antenna transceiver for system applications,” IEEE Trans. Microwave Theory
Tech., vol. 44, pp. 1642–1649, Oct. 1996.
[7] C. M. Montiel, L. Fun, and K. Chang, “A novel active antenna with selfmixing and
wideband varactor-tuning capabilities for communication and vehicle identification
applications,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 2421–2430, Dec. 1996.
[8] K. L.Wong and Y. F. Lin, “Circularly polarized microstrip antenna with a tuning stub,”
Electron. Lett., vol. 34, no. 9, pp. 831–832, 1998. [9] K. L. Wong and J. Y. Jan,
“Broadband circular microstrip antenna with embedded reactive loading,” Electron. Lett.,
vol. 34, no. 19, pp. 1804–1805, 1998.
[10] F. Abboud, J. P. Damiano, and A. Papiernik, “A new model for calculating the
impedance of coax-fed circular microstrip antennas with and without air gaps,” IEEE
Trans. Antennas Propagat., vol. 38, pp. 1882–1885, Nov. 1990.
[11] I. Wolff and N. Knoppik, “Rectangular and circular microstrip disk capacitors and
resonators,” IEEE Trans. Microwave Theory Tech., vol. MTT-22, pp. 857–864, Oct. 1974.
[12] W. C. Chew and J. A. Kong, “Effects of friging field on the cacapacitance of circular
microstrip disk,” IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp. 98–104, Feb.
1980.

121


[13] J. Watkins, “Circular resonant structures in microstrip,” Electron. Lett., vol. 5, pp.
524–525, Oct. 1969.
[14] H. A. Wheeler, “A simple formula for the capacitance of a disc on dielectric on a
plane,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 2050–2054, Nov. 1982.
[15] L. C. Shen, S. A. Long, M. R. Allerding, and M. D. Walton, “Resonant frequency of a
circular disc, printed-circuit antenna,” IEEE Trans. Antennas Propagat., vol. AP-25, pp.
595–596, July 1977.
[16] M. S. Leong et al., “Determination of circular microstrip disc by Noble’s variational
method,” Proc. Inst. Elec. Eng., vol. 128 H (M.O.A.), pp. 306–310, Dec. 1981.
[17] D. Guha, “Comment on ‘A new model for calculating the impedance of
coax-fed circular microstrip antennas with and without air gaps’,” IEEETrans. Antennas
Propagat., vol. 48, pp. 1010–1011, June 2000.
[18] T. Itoh and R. Mittra, “Analysis of microstrip disk resonator,” Arch. Eleck.
Übertragung, vol. 27, no. 11, pp. 456–458, 1973.

122

Dominant mode resonant frequency of circular microstrip antennas with and without air gap

Recommandé

Recommandé

Contenu connexe

Tendances

Tendances (16)

En vedette

En vedette (7)

Similaire à Dominant mode resonant frequency of circular microstrip antennas with and without air gap

Similaire à Dominant mode resonant frequency of circular microstrip antennas with and without air gap (20)

Plus de IAEME Publication

Plus de IAEME Publication (20)

Dominant mode resonant frequency of circular microstrip antennas with and without air gap