# Analysis and Design of Gap-Coupled Annular Ring Microstrip Antenna

Authors: Binod Kumar Kanaujia; Anil Kumar Singh
Journal: International Journal of Antennas and Propagation
 (2008)

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## Abstract

Theoretical investigation conducted on gap-coupled annular ring microstrip antenna is found to exhibit frequency tunability with the gap. The various parameters of the antenna such as input impedance, VSWR, return loss, and radiation pattern have been investigated as a function of gap length and feed point. It is found that the various parameters of gap-coupled microstrip antenna depend heavily on the gap length and feed points.


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## Body

## 1. Introduction

The annular ring microstrip antenna
(ARMSA) has been studied for a long time by a number of investigators [1, 2] because of
larger bandwidth as compared to the other conventional microstrip patch
antennas [1]. The interest in designing of such microstrip antenna has increased
because of light weight, easier to fabrication, conformability, and so forth.
The inner and outer radii of the ARMSA control the mode separation.In the present work, the authors have
endeavored to design a gap-coupled concentric ARMSA on the basis of equivalent
circuit model. The inner ring is a feed, and the outer ring is a parasitic
element. The effect of mutual coupling is also taken into account along with
variation of feed point and gap between the rings. The gap-coupled ARMSA can be
used for dual band operation and especially in mobile communication. The main focus
is on the effect of the gap length and feed point on the radiation pattern of
the gap-coupled ARMSA.


## 2. Theoretical Considerations

In the concentric ARMSA, the structure having physical
gap is shown in Figure1(a). The inner ring is fed coaxially, while the outer
ring is a parasitic element. Now, this can also be shown as a parallel gap-coupled
radiator using planar waveguide mode for inner ring and outer ring as shown in Figure
1(b) [3]. The characteristic impedance of the two-gap-coupled concentric ARMSA
radiator can be analyzed by applying the theory of coupled microstrip lines [4, 5] and coupled
microstrip antenna [6].(a) Concentric annular ring microstrip antenna. (b) Parallel
gap-coupled microstrip lines.
(a)(b)The input impedance characteristics
of the gap-coupled ARMSA can be analyzed. Figure1(a) which shows two-gap-coupled
annular ring antennas in which inner one is fed at point (x,0) by a coaxial cable (a1<x<b1),
where a1 and b1 are inner and outer radii of the inner
ring and outer ring, respectively. The thickness of the substrate h is small as compared to the difference
between the inner and outer radii of the inner ring.


### 2.1. Even and Odd Mode Capacitances

Two concentric annular ring antenna
having widthW1=b1−a1 and W2=b2−a2 of Figure 1(a) can be shown, as a gap-coupled microstrip line of Figure 1(b), by
using planer waveguide model. The inner ring of annular ring antenna of Figure 1(b) is excited in TM12 mode. Total line capacitance is taken up as a
parallel plate capacitance (Cp) and two fringing capacitances (Cf)
as shown in Figures 2(a) and 2(b) for even and odd modes, respectively. The
even mode capacitance is the capacitance between two parallel running conductors
with respect to ground. From Figure 2(b), it is given as Ceven=Cp+Cf+Cf′,
where Cp=εrε0(w/h) is the parallel plate
capacitance between the strip and ground plane, and Cf is the fringing capacitance due to edge
conductor [6]: (1)Cf=12[εeffcZc−Cp], where c=3×108 m/s and Zc are the characteristic impedance of the line and εeff is the
effective dielectric constant of substrate [7]. Since there is another line due
to the presence of parasitic element, there is some modification in fringe
capacitance as [6] (2)Cf′=Cf[1+A(hs)tanh(10sh)]−1(εrεeff)1/2, where A=exp(−0.1exp(2.33−2.53w/h)).(a) Odd mode capacitances of coupled microstrip lines geometry.
(b) Even mode capacitances of coupled microstrip lines
geometry.
(a)(b)The odd mode capacitance is as shown in Figure2(a) and given
by Codd=Cp+Cf+Cgd+Cga, where Cgd is the
capacitance between two strip lines through dielectric region, and Cga is the capacitance between two strip lines through air.The gap capacitance(3)Cga=12K(k′)ε0K(k), where K(k) and K(k′) are elliptic functions. Reference [5] defined as (4)k=s/h(s/h)+2(w/h),k′=1−k2,K(k′)K(k)={1πln[21+k′1−k′],0≤k≤0.5,πln[2((1+k)/(1−k))],0≤k≤1.    Since the two strips have the electric flux between the air
dielectric region so capacitance (5)Cgd=(ε0εrπ)ln{cothπs4h}+0.65Cf[0.02(s/h)εr+1−1εr2].


### 2.2. ARMSA Analysis

The gap-coupled ARMSA can be represented as the two
parallel microstrip lines. The equivalent circuit for ARMSA can be expressed as
the parallel combination ofY1, L1, C1 and Y2, L2, C2, where the subscript 1 represents for inner ring and
2 for the outer parasitic ring. The value of Y1, L1, C1 can be written as [8] (6)L1=μhπk12[n,m][Jn(k1c)Yn′(k1ae)−Yn(k1c)Jn′(k1ae)]2, where (7)[n,m]=12k12[(k12b12−1){Jn(k1b1e)Yn′(k1a1e)−Yn′(k1b1e)Jn′(k1a1e)}2−4π2k12a1e(k12a1e2−1)],C1=με0εrL1k12,Y1=πh[(EaEb)2g(a,a)+(EbEc)2g(b,b)−2EaEbEc2y(a,b)].   The values of L2, C2, and Y2
are obtained for the outer
parasitic ring using (6),  (7) for the inner ring of the antenna. The
equivalent circuit for gap-coupled ARMSA can be given as in Figures 3(a) and 3(b) for even and odd mode cases.(a) Modified equivalent circuit of gap-coupled ARMSA for odd
mode. (b) Modified equivalent circuit of gap-coupled ARMSA for even
mode.
(a)(b)


### 2.3. Impedance of Gap-Coupled ARMSA

Due to the presence of the parasitic ARMSA, the input impedance
of gap-coupled ARMSA differs from the impedance of single ARMSA. The effective
dielectric constant is due to the fringing and various other factors which can
be calculated for even modeεree and odd mode εre0 using even and odd mode capacitances [8] as (8)εree=CeCea,εre0=C0C0a, where Cea and C0a are the
even and odd mode capacitances for the gap-coupled ARMSA with air as
dielectric. With the help of these dielectric constants and the equivalent
circuit model (Figures 3(a) and 3(b)), input impedance for even mode, Zin(e), and for odd mode, Zin(0),
are calculated separately by putting even and odd mode relative permittivity
(given in (8), respectively. The input impedance of gap-coupled ARMSA is now written
as [6] Zin=Zin(e)+Zin(0).The return loss can be calculated as(9)R=20log(|Γ|).


### 2.4. Radiation Patterns

The radiation pattern of the ARMSA is due to the
superposition of the fields radiated by all the apertures. The radiation
patterns of theN apertures are [9] 12aEθ=[∑m=1NamEamJ1′(k0amsinθ)−∑m=1NbmEbmJ1′(k0bmsinθ)]cosϕ,Eϕ=[∑m=1NEamJ1(k0amsinθ)−∑m=1NEbmJ1(k0bmsinθ)]cotθsinϕ,  where Eam
and Ebm are the electric
field at the inner and outer peripheries of the mth ring, respectively. We are considering only two rings,
therefore, the radiation pattern of the ARMSA is obtained by putting m=1 and 2
in the above equations.


## 2.1. Even and Odd Mode Capacitances

Two concentric annular ring antenna
having widthW1=b1−a1 and W2=b2−a2 of Figure 1(a) can be shown, as a gap-coupled microstrip line of Figure 1(b), by
using planer waveguide model. The inner ring of annular ring antenna of Figure 1(b) is excited in TM12 mode. Total line capacitance is taken up as a
parallel plate capacitance (Cp) and two fringing capacitances (Cf)
as shown in Figures 2(a) and 2(b) for even and odd modes, respectively. The
even mode capacitance is the capacitance between two parallel running conductors
with respect to ground. From Figure 2(b), it is given as Ceven=Cp+Cf+Cf′,
where Cp=εrε0(w/h) is the parallel plate
capacitance between the strip and ground plane, and Cf is the fringing capacitance due to edge
conductor [6]: (1)Cf=12[εeffcZc−Cp], where c=3×108 m/s and Zc are the characteristic impedance of the line and εeff is the
effective dielectric constant of substrate [7]. Since there is another line due
to the presence of parasitic element, there is some modification in fringe
capacitance as [6] (2)Cf′=Cf[1+A(hs)tanh(10sh)]−1(εrεeff)1/2, where A=exp(−0.1exp(2.33−2.53w/h)).(a) Odd mode capacitances of coupled microstrip lines geometry.
(b) Even mode capacitances of coupled microstrip lines
geometry.
(a)(b)The odd mode capacitance is as shown in Figure2(a) and given
by Codd=Cp+Cf+Cgd+Cga, where Cgd is the
capacitance between two strip lines through dielectric region, and Cga is the capacitance between two strip lines through air.The gap capacitance(3)Cga=12K(k′)ε0K(k), where K(k) and K(k′) are elliptic functions. Reference [5] defined as (4)k=s/h(s/h)+2(w/h),k′=1−k2,K(k′)K(k)={1πln[21+k′1−k′],0≤k≤0.5,πln[2((1+k)/(1−k))],0≤k≤1.    Since the two strips have the electric flux between the air
dielectric region so capacitance (5)Cgd=(ε0εrπ)ln{cothπs4h}+0.65Cf[0.02(s/h)εr+1−1εr2].


## 2.2. ARMSA Analysis

The gap-coupled ARMSA can be represented as the two
parallel microstrip lines. The equivalent circuit for ARMSA can be expressed as
the parallel combination ofY1, L1, C1 and Y2, L2, C2, where the subscript 1 represents for inner ring and
2 for the outer parasitic ring. The value of Y1, L1, C1 can be written as [8] (6)L1=μhπk12[n,m][Jn(k1c)Yn′(k1ae)−Yn(k1c)Jn′(k1ae)]2, where (7)[n,m]=12k12[(k12b12−1){Jn(k1b1e)Yn′(k1a1e)−Yn′(k1b1e)Jn′(k1a1e)}2−4π2k12a1e(k12a1e2−1)],C1=με0εrL1k12,Y1=πh[(EaEb)2g(a,a)+(EbEc)2g(b,b)−2EaEbEc2y(a,b)].   The values of L2, C2, and Y2
are obtained for the outer
parasitic ring using (6),  (7) for the inner ring of the antenna. The
equivalent circuit for gap-coupled ARMSA can be given as in Figures 3(a) and 3(b) for even and odd mode cases.(a) Modified equivalent circuit of gap-coupled ARMSA for odd
mode. (b) Modified equivalent circuit of gap-coupled ARMSA for even
mode.
(a)(b)


## 2.3. Impedance of Gap-Coupled ARMSA

Due to the presence of the parasitic ARMSA, the input impedance
of gap-coupled ARMSA differs from the impedance of single ARMSA. The effective
dielectric constant is due to the fringing and various other factors which can
be calculated for even modeεree and odd mode εre0 using even and odd mode capacitances [8] as (8)εree=CeCea,εre0=C0C0a, where Cea and C0a are the
even and odd mode capacitances for the gap-coupled ARMSA with air as
dielectric. With the help of these dielectric constants and the equivalent
circuit model (Figures 3(a) and 3(b)), input impedance for even mode, Zin(e), and for odd mode, Zin(0),
are calculated separately by putting even and odd mode relative permittivity
(given in (8), respectively. The input impedance of gap-coupled ARMSA is now written
as [6] Zin=Zin(e)+Zin(0).The return loss can be calculated as(9)R=20log(|Γ|).


## 2.4. Radiation Patterns

The radiation pattern of the ARMSA is due to the
superposition of the fields radiated by all the apertures. The radiation
patterns of theN apertures are [9] 12aEθ=[∑m=1NamEamJ1′(k0amsinθ)−∑m=1NbmEbmJ1′(k0bmsinθ)]cosϕ,Eϕ=[∑m=1NEamJ1(k0amsinθ)−∑m=1NEbmJ1(k0bmsinθ)]cotθsinϕ,  where Eam
and Ebm are the electric
field at the inner and outer peripheries of the mth ring, respectively. We are considering only two rings,
therefore, the radiation pattern of the ARMSA is obtained by putting m=1 and 2
in the above equations.


## 3. Design Parameters

The gap-coupled ARMSA is designed with the following specifications
as given in Table1.Table 1
Designing specification of annular ring microstripantenna.
ParametersValueSubstrate material usedRT Duroid 5870Effective relative
permittivityεeff  =  2.1936Relative permittivity of
the substrateεr  =  2.32Thickness of dielectric
substrateh  =  0.159 cmInner radius of the
inner ringa1  =  3 cmOuter radius of the
inner ringb1  =  6 cmFeed point of the inner
ringc  =  3.35 cmInner radius of outer
ringa2  =  6.05 cm.Outer radius of outer
ringb2  =  9.05 cm.


## 4. Discussion of Results

Figure4 shows the variation of
input impedance with frequency for different gap length for particular feed
location of 3.001 cm. It is observed that the lower band shows the different
resonant frequencies of 1.727 GHz and 1.778 GHz for different gap lengths of 0.095 cm. and 0.11 cm, however, for an upper band of gap-coupled ARMSA, the resonance
frequency is approximately the same for different gap length. This type of
characteristic can be used for different applications. It is also observed that
peak value of real part of the input impedance for lower patch increases with
increasing gap length. The variation of input impedance with frequency for
different feed location and gap length is also verified from Tables 2 and 3,
respectively.Table 2
Peak value of input impedance,
resonance frequency for upper and lower band for different feed locations.
Gap length→S  =  0.095 cmS  =  0.100 cmS  =  0.110 cmFeed point↓Plower* (ohms)Pupper**
(ohms)Flower#
(GHz)Fupper##
(GHz)Plower
(ohms)Pupper
(ohms)Flower
(GHz)Fupper
(GHz)Plower
(ohms)Pupper
(ohms)Flower
(GHz)Fupper
(GHz)c  =  3.001 cm39.4074.081.7271.89943.5873.931.7441.89953.0573.301.7781.900c  =  3.101 cm37.5572.151.7541.93443.6272.061.7711.93455.9071.751.8061.934c  =  3.201 cm36.5065.021.7881.97742.3564.161.8061.97753.2065.501.8421.977*Plower: The peak value of input impedance for lower band.**Pupper: The peak value of input impedance for lower band.#Flower: The resonance frequency for lower band.##Fupper: The resonance frequency for upper band.Table 3
Peak value of input impedance,
resonance frequency for upper and lower band for different gap lengths.
Feed point→c  =  3.001 cmc  =  3.101 cmc  =  3.201 cmGap length↓Plower
(ohms)Pupper
(ohms)Flower
(GHz)Fupper
(GHz)Plower
(ohms)Pupper
(ohms)Flower
(GHz)Fupper
(GHz)Plower
(ohms)Pupper
(ohms)Flower
(GHz)Fupper
(GHz)S  =  0.09 cm35.3974.311.7101.89934.8172.411.7361.933733.6165.331.7701.9771S  =  0.10 cm43.5873.931.7441.89943.6272.061.7711.933842.3564.161.8061.9771S  =  0.11 cm53.0573.301.7781.90055.9071.741.8061.934353.2065.491.8421.9774Figure 4
Variation of input impedance with frequency for different gap
length atC  =  3.001 cm.The return
loss of gap-coupled ARMSA is shown in Figures5(a)-5(b) for
different value of gap length and feed locations. Return loss of lower band
decreases with increasing the feed point, while it decreases with increasing
the feed point for upper band. It is also observed that the bandwidth of lower
band decreases with increasing the feed point, however, the bandwidth of upper
band increases with increasing the feed point for a different gap length.(a) Variation of return loss with frequency for different feed
location atS  =  0.095 cm. (b) Variation of return loss with
frequency for different feed location at S  =  0.11 cm.
(a)(b)The radiation pattern of the gap-coupled
annular ring microstrip antenna in the direction of elevation and azimuth plane
is shown in Figures6(a)-6(b), respectively. It is observed that the
beamwidth of gap-coupled annular patch is lower than the individual annular
patch but the side lobes of gap-coupled annular patch are higher than the
individual annular ring patch because enhancement in radiation power due to
parasitic element is not accompanied by an increase in ohmic loss of the system.(a) Variation of radiation patternEθ with angle for S  =  0.095 cm. (b) Variation of radiation pattern Eϕ with angle for
S  =  0.095 cm.
(a)(b)


## 5. Conclusion

The new technique to gap-coupled with
parasitic element shows the tunability in frequency and also dual band
operation. Efficiency of an antenna can be used where large bandwidth and
tunable frequency is required.



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*Source: 792123-2008-08-20.xml*