Analysis and Design of Gap-Coupled Annular Ring Microstrip Antenna

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.

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 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 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)

(b)

Figure 1 

(a) Concentric annular ring microstrip antenna. (b) Parallel gap-coupled microstrip lines.

The input impedance characteristics of the gap-coupled ARMSA can be analyzed. Figure 1(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 width 𝑊₁=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 (C_p) and two fringing 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_𝑟𝜀₀(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]: 𝐶_𝑓=12√𝜀_eff𝑐𝑍_𝑐−𝐶_𝑝,(1) where 𝑐=3×10⁸ 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] 𝐶^𝑓=𝐶_𝑓1+𝐴ℎ𝑠tanh1ℎ0𝑠⁻¹𝜀𝜀^𝑟_eff^1/2,(2) where 𝐴=exp(−0.1exp(2.33−2.53𝑤/ℎ)).

(a)

(b)

Figure 2 

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

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 𝐶_ga=12𝐾(𝑘^)𝜀⁰𝐾𝑘,(3) where 𝐾(𝑘) and 𝐾(𝑘^) are elliptic functions. Reference [5] defined as 𝑘=𝑠/ℎ(𝑠/ℎ)+2(𝑤/ℎ),𝑘^𝐾𝑘_=√1−𝑘²,𝐾𝑘=⎧⎪⎪⎨⎪⎪⎩1𝜋ln21+√𝑘^1−√𝑘^𝜋,0≤𝑘≤0.5,ln21+√𝑘/1−√𝑘,0≤𝑘≤1.(4) Since the two strips have the electric flux between the air dielectric region so capacitance 𝐶_gd=𝜀⁰𝜀_𝑟𝜋lncotℎ4𝜋ℎ𝑠+0.65𝐶^𝑓(0𝑠./0ℎ2)√𝜀_𝑟+1−1𝜀^2𝑟.(5)

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 of Y₁, 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] 𝐿₁=𝜇ℎ𝜋𝑘²¹𝑛,𝑚𝐽^𝑛𝑘¹𝑐𝑌^𝑛𝑘¹𝑎_𝑒−𝑌^𝑛𝑘¹𝑐𝐽^𝑛𝑘¹𝑎_𝑒²,(6) where 𝑛1,𝑚=2𝑘²¹𝑘²¹𝑏²¹−1𝐽_𝑛𝑘¹𝑏_1𝑒𝑌^𝑛𝑘¹𝑎_1𝑒−𝑌^𝑛𝑘¹𝑏_1𝑒𝐽^𝑛𝑘¹𝑎_1𝑒²−4𝜋²𝑘²¹𝑎_1𝑒𝑘²¹𝐶𝑎^21𝑒−1₁,=𝜇𝜀⁰𝜀_𝑟𝐿₁𝑘²¹𝑌₁,=𝜋ℎ𝐸𝐸^𝑎_𝑏²𝑔(𝑎,𝑎)+𝐸^𝑏𝐸_𝑐²𝑔(𝑏,𝑏)−2𝐸^𝑎𝐸_𝑏𝐸^2𝑐𝑦(𝑎,𝑏).(7) 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)

(b)

Figure 3 

(a) Modified equivalent circuit of gap-coupled ARMSA for odd mode. (b) Modified equivalent circuit of gap-coupled ARMSA for even mode.

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 mode 𝜀^𝑒_re and odd mode 𝜀⁰_re using even and odd mode capacitances [8] as 𝜀^𝑒_re=𝐶^𝑒𝐶^𝑎𝑒,𝜀⁰_re=𝐶⁰𝐶^𝑎0,(8) where 𝐶^𝑎𝑒 and 𝐶^𝑎0 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] 𝑍_in=𝑍_in(𝑒)+𝑍_in(0).

The return loss can be calculated as 𝑅=20log||Γ||.(9)

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 the N apertures are [9] 𝐸_am where 𝐸_bm and 𝑚=1 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 → and 2 in the above equations.

3. Design Parameters

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

Table 1 

Designing specification of annular ring microstripantenna.

4. 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.

Table 2 

Peak value of input impedance, resonance frequency for upper and lower band for different feed locations.

Table 3 

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

Figure 4 

Variation of input impedance with frequency for different gap length at C  =  3.001 cm.

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.

(a)

(b)

Figure 5 

(a) Variation of return loss with frequency for different feed location at S  =  0.095 cm. (b) Variation of return loss with frequency for different feed location at S  =  0.11 cm.

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.

(a)

(b)

Figure 6 

(a) Variation of radiation pattern 𝐸𝜙 with angle for S  =  0.095 cm. (b) Variation of radiation pattern with angle for S  =  0.095 cm.

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.