Estimation of the Substrate Size with Minimum Mutual Coupling of a Linear Microstrip Patch Antenna Array Positioned Along the H-Plane

Abstract

Mutual coupling between antenna elements of a linear microstrip patch antenna array positioned along the H-plane including the effect of edge reflections is investigated. Simple formulas are presented for the estimation of the grounded dielectric substrate size with minimum mutual coupling. The substrate sizes calculated by these formulas are in good agreement with those obtained by the full-wave simulation and experimental measurement. The substrate size with minimum mutual coupling is a function of the effective dielectric constant for surface waves and the distance between the antenna centers. The substrate size with minimum mutual coupling decreases as the effective dielectric constant for surface waves on a finite grounded dielectric substrate increases.

1. Introduction

Microstrip patch antennas have become one of the most popular antennas because they have many advantages such as low-profile, light weight, low fabrication cost, and easy integration with monolithic microwave integrated circuits (MMICs) [1]. While microstrip patch antennas fabricated on high-permittivity substrates are compact and easily integrated with MMICs, they can excite large surface waves. Surface waves could increase the mutual coupling between antenna elements in phased array antennas, which degrades the performance of phased array antennas such as a decrease in the scan range and an increase in the sidelobe levels [2].

Various methods have been developed to suppress mutual coupling effects, such as electromagnetic band-gap (EBG) structures [3-6], defected grounded structures (DGSs) [7], inductive loaded microstrip patch antennas [8], a U-shaped microstrip line section inserted between antenna elements [9], and a pattern etched onto the ground plane between antenna elements [10]. However, the effect of edge reflections on the mutual coupling was not considered in those studies.

In a practical microstrip patch antenna array fabricated on a finite grounded dielectric substrate, the effect of edge reflections on the mutual coupling between the antenna elements in antenna arrays must be considered. Recently, the effect of edge reflections on the mutual coupling of a linear microstrip patch antenna array positioned along the E-plane was investigated [11].

In this paper, simple formulas are presented for the estimation of the grounded dielectric substrate size with minimum mutual coupling of a linear microstrip patch antenna array positioned along the H-plane. To validate these formulas, mutual coupling of a two-element linear microstrip patch antenna array positioned along the H-plane was investigated through an experiment and a simulation using HFSS. In Section II, simple formulas obtained by using geometrical optics are presented to estimate the substrate size with minimum mutual coupling. In Section III, both the numerical and experimental results are presented for antenna arrays with various distances between the antenna centers fabricated on various high-permittivity substrates. Finally, Section IV concludes this paper.

 

2. Simple Formulas for the Estimation of the Substrate Size with Minimum Mutual Coupling

Fig. 1 shows the schematic diagram of a two-element linear microstrip patch antenna array positioned along the H-plane and a conceptual representation using geometrical optics for the estimation of the substrate size with minimum mutual coupling between two antennas. The quantity d represents the distance between the antenna centers. The distances between the antenna center and the substrate edges on the E-plane and H-plane are represented by the quantities dE and dH, respectively. A coaxial probe feeding method is used to excite the microstrip patch antennas. The probe-fed point xf is offset from the center of a rectangular patch (L×W ) in the x-axis.

Fig. 1.A schematic diagram of a two-element linear microstrip patch antenna array positioned along the H-plane.

Since surface waves mainly propagate along the E-plane direction [12], the effect of the reflected surface waves from the substrate edges on the H-plane on the mutual coupling between the antenna elements positioned along the H-plane can be very small compared to that of the reflected surface waves from the substrate edges on the E-plane. Thus, the mutual coupling between the antenna elements positioned along the H-plane can be determined by the following three types of surface waves: ① one that is directly propagated between two patch antennas; ② one that is caused by the reflection from the substrate edges on the E-plane; and ③ one that is caused by the reflection from the corner of the substrate.

The geometrical optics shown in Fig. 1 was used to derive the simple formulas for the grounded dielectric substrate size with minimum mutual coupling of a linear microstrip patch antenna array positioned along the H-plane. In this paper, the quantities dE and dH that have minimum mutual coupling are represented by the quantities dE,min and dH,min, respectively.

The quantity dE,min is dE at which the phase difference of π between the direct surface wave ① and the reflected surface wave from the substrate edges on the E-plane ② occurs. The simple formula for dE,min can be expressed as

where denotes the guided wavelength of surface waves on a grounded dielectric substrate. The effective dielectric constant for surface waves on a grounded dielectric substrate, εsw, is given by (βsw / k0)2, where βsw is the propagation constant of the TM0 surfacewave mode and k0 is the free-space wave number. The effective dielectric constant for surface waves on a grounded dielectric substrate increases as the dielectric constant and thickness of a dielectric substrate increase [13].

The quantity dH,min is dH at which the one round-trip phase delay of 3π for the reflected surface wave from the corner of the substrate ③ occurs because the quantity dE is usually longer than λg /4 in practical antenna arrays. The simple formula for dH,min can be expressed as

 

3. Numerical and Experimental Validations

Since mutual coupling becomes very significant when the substrate is relatively thick and has a high permittivity, a 3.18-mm-thick Taconic CER-10 substrate (εr = 10.8) and a 3.18-mm-thick RF60A substrate (εr = 6.75) were selected for this study. Microstrip patch antennas with a resonant frequency fr of 5 GHz were positioned along the H-plane with the distances between the antenna centers of 0.5 λ0 and 0.7 λ0, respectively, where λ0 denotes the free space wavelength. Table 1 shows the dimensions and parameters of the patch antennas printed on a CER-10 substrate and a RF60A substrate.

Table 1.Dimensions and parameters of the microstrip patch antennas printed on a CER-10 substrate and a RF60A substrate

Fig. 2(a) shows the simulated mutual coupling values between the two patch antennas printed on a 3.18-mmthick CER-10 substrate and a 3.18-mm-thick RF60A substrate, respectively, for the quantity d of 0.5 λ0 and 0.7 λ0 versus the quantity dE ranging from 0.3 λ0 to 1.0 λ0, with a step size of 0.05 λ0. In the vicinity of dE,min, simulations were performed in detail with a step size of 0.01 λ0 . The quantity dH was fixed at 0.5 λ0 in all the cases considered.

Fig. 2.Simulated mutual coupling between the two patch antennas printed on a 3.18-mm-thick CER-10 substrate and a 3.18-mm-thick RF60A substrate, respectively, for the quantity d of 0.5 λ0 and 0.7 λ0 versus (a) the quantity dE and (b) the quantity dH.

Fig. 2(b) shows the simulated mutual coupling values versus the quantity dH ranging from 0.3 λ0 to 1.0 λ0 , with a step size of 0.05 λ0 . In the vicinity of dH,min , simulations were performed in detail with a step size of 0.01 λ0 . For each case in Fig. 2(b), the quantity dE was fixed at 0.5 λ0 . In Fig. 2, the variation in the mutual coupling increases with the substrate permittivity due to the increase of surface wave power. Furthermore, as the distance between the antenna centers increases, the variations in the mutual coupling versus dE and dH increase for the same substrate permittivity.

From Fig. 2, we can see that the quantities dE,min and dH,min decrease as the substrate permittivity increases. This phenomenon can be explained as follows. As the substrate permittivity increases, the guided wavelength of the surface wave, λg , decreases because εsw increases. Thus, the quantities dE,min and dH,min decrease as the substrate permittivity increases, as shown in formulas (1) and (2). It is also seen that the quantity dE,min decreases as the distance between the antenna centers decreases, as shown in formula (1). The variation of the quantity dH,min with the decrease of the quantity d is small compared to that of dE,min because there is no dependence of d, as shown in formula (2).

Figs. 3(a) and (b) shows the experimental results on the mutual coupling between the two patch antennas, the simulation results of which are shown in Fig. 2(a) and (b), respectively. The experiment results agree well with the simulation results. In Fig. 3(a), the variations in the mutual coupling versus dE for d =0.5 λ0 and 0.7 λ0 are about 12.1 dB (5.8 dB) and 24.3 dB (11.2 dB), respectively, for the CER-10 substrate (the RF60A substrate). In Fig. 3(b), the variations in the mutual coupling versus dH for d = 0.5 λ0 and 0.7 λ0 are about 6.8 dB (4.0 dB) and 21.2 dB (10.0 dB), respectively, for the CER-10 substrate (the RF60A substrate).

Fig. 3.Measured mutual coupling between the two patch antennas printed on a CER-10 substrate and a RF60A substrate, respectively, for the quantity d of 0.5 λ0 and 0.7 λ0 versus (a) the quantity dE and (b) the quantity dH.

As the substrate permittivity increases, the variations in the mutual coupling versus dE and dH increase for the same distance between the antenna centers. Furthermore, as the distance between the antenna centers increases, the variations in the mutual coupling versus dE and dH increase for the same substrate permittivity.

The results of the simulation and experiment are summarized and compared with the results of formulas (1) and (2) in Table 2. The results calculated by using the simple formulas are in good agreement with the simulation and experimental results. It can be seen that the quantities dE,min and dH,min decrease as the substrate permittivity increases. It is also seen that the quantity dE,min decreases as the distance between the antenna centers decreases. The variation of the quantity dH,min with the decrease of the quantity d is small compared to that of dE,min.

Table 2.Comparison of the values of dE,min and dH,min obtained by the simple formulas, simulation, and experiment, for two different pairs of patch antennas printed on a 3.18-mm-thick CER-10 substrate and a 3.18-mm-thick RF60A substrate.

 

4. Conclusion

The mutual coupling between antenna elements of a linear microstrip patch antenna array positioned along the H-plane is investigated. Simple formulas obtained by using geometrical optics are presented to estimate the grounded dielectric substrate size with minimum mutual coupling. The substrate size with minimum mutual coupling is easily calculated by using the simple formulas. The substrate sizes calculated by using the simple formulas are in good agreement with the results obtained by the full wave simulation and experimental measurement.

The substrate size with minimum mutual coupling is mainly determined by the effective dielectric constant for surface waves on a grounded dielectric substrate. Since the effective dielectric constant for surface waves increases as the dielectric constant and thickness of a dielectric substrate increase, the substrate size with minimum mutual coupling decreases as the dielectric constant and thickness of a dielectric substrate increase. When the substrate is a Taconic CER-10 with a thickness of 3.2 mm and a dielectric constant of 10.8, significant 12.1 dB and 24.3 dB mutual coupling reductions are achieved by adjusting the substrate size for the distances between the antenna centers of 0.5 λ0 and 0.7 λ0, respectively.