Analysis and Design of Gap-Coupled Annular Ring Microstrip Antenna

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.


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.

THEORETICAL CONSIDERATIONS
In the concentric ARMSA, the structure having physical gap is shown in Figure 1(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 twogap-coupled concentric ARMSA radiator can be analyzed by applying the theory of coupled microstrip lines [4,5] and coupled microstrip antenna [6].
The input impedance characteristics of the gap-coupled ARMSA can be analyzed.Figure 1(a) which shows two-gapcoupled annular ring antennas in which inner one is fed at point (x, 0) by a coaxial cable (a 1 < x < b 1 ), where a 1 and b 1 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.

Magnetic wall Inner ring
Outer ring Ground plane capacitances (C f ) 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 C even = C p + C f + C f , where C p = ε r ε 0 (w/h) is the parallel plate capacitance between the strip and ground plane, and C f is the fringing capacitance due to edge conductor [6]: where c = 3×10 8 m/s and Z c are the characteristic impedance of the line and ε eff 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] where The odd mode capacitance is as shown in Figure 2(a) and given by C odd = C p + C f + C gd + C ga , where C gd is the capacitance between two strip lines through dielectric region, and C ga is the capacitance between two strip lines through air.

The gap capacitance
where K(k) and K(k ) are elliptic functions.Reference [5] defined as Since the two strips have the electric flux between the air dielectric region so capacitance (5)

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 of Y 1 , L 1 , C 1 and Y 2 , L 2 , C 2 , where the subscript 1 represents for inner ring and 2 for the outer parasitic ring.The value of Y 1 , L 1 , C 1 can be written as [8] where The values of L 2 , C 2 , and Y 2 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.

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 mode ε e re and odd mode ε 0 re using even and odd mode capacitances [8] as where C a e and C a 0 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, Z in (e), and for odd mode, Z in (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] The return loss can be calculated as

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 the N apertures are [9] where E am and E bm 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.

DESIGN PARAMETERS
The gap-coupled ARMSA is designed with the following specifications as given in Table 1.

DISCUSSION OF RESULTS
Figure 4 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.The return loss of gap-coupled ARMSA is shown in Figures 5(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.
The radiation pattern of the gap-coupled annular ring microstrip antenna in the direction of elevation and azimuth plane is shown in Figures 6(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.

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.

Figure 2 :
Figure 2: (a) Odd mode capacitances of coupled microstrip lines geometry.(b) Even mode capacitances of coupled microstrip lines geometry.

Table 1 :
Designing specification of annular ring microstrip antenna.

Table 2 :
Peak value of input impedance, resonance frequency for upper and lower band for different feed locations.P lower : The peak value of input impedance for lower band.* * P upper : The peak value of input impedance for lower band.# F lower : The resonance frequency for lower band.## F upper : The resonance frequency for upper band. *

Table 3 :
Peak value of input impedance, resonance frequency for upper and lower band for different gap lengths.