176	G. A. Sarkar and S. K. Parui

triangular shape DRA element with H-plane beam shaping except [13], where E- plane beam shaping and H-plane beam shaping have been studied. Since then, as far as the authors knowledge, no one has investigated on two-element antenna arrays for E- plane beam shaping. In this paper, we have investigated a two-element antenna array on hemispherical shape geometry. Each HDRA antenna elements are excited using microstrip line and a 3 dB power divider is used for equal power distributions. The antenna structure is designed and simulated using Ansoft High-Frequency Structure Simulator based on the FEM method.

2 Antenna Array Design

2.1 Resonant Frequency

A HDRA can support TE and TM mode. For TE mode, Er and EØ vanish at θ 90°, whereas for TM mode Er and EØ vanish at θ 0°. For a hemispherical cavity, the resonant frequency of lowest order TE111 mode can be calculating using [18] and is represented as

f	r	4.775 × 107Re(kR)			(1)
		√		R
			r

2.2 Study of Coupling

Study of mutual coupling is very essential before designing an antenna array as it has a great impact on resonance frequency, impedance bandwidth, and radiation patterns. Owing to coupling effects, the resonant frequency can be shifted from its desired value, also radiation patterns may be degraded. If the distance between the antenna array element increases isolation increased, results in more directive radiation with increased sidelobe levels and vice versa. Here coupling is studied for a separation gap between two elements of λ0/2 (λ0 free space wavelength). The simulated coupling and reflection coefficient is depicted in Fig. 1.

2.3 Antenna Array Geometry

The authors’ have investigated on single-element HDRA fed by microstrip line in [10] and avoided the discussions here. Instead, they have used the same single antenna element for designing a two element E-plane HDRA array and depicted in Fig. 2. The array is designed on Arlon AD270 (dielectric constant 2.7 and loss tangent 0.0023)

Microstrip Line Fed Two Element E-Plane HDRA Antenna Array

177

Fig. 1 Simulated S11 and

S21

substrate of area L × W mm2. The radiating element is made of Eccostock HiK materials. It has dielectric constant 20 and loss tangent 0.002. The design dimensions of the array are given in Table 1.

Fig. 2 Schematic diagram of DRA array

	Table 1 Design parameters	Parameters	La	L1	L2	L3	L4
	of array
		Value (mm)	89	5.935	7.77	8.68	18.055
		Parameters	L5	Wa	W1	W2	W3
		Value (mm)	5.7	48	2.13	1.2	2.13

178	G. A. Sarkar and S. K. Parui

2.4 Study of Coupling

The simulated reflection coefficient is presented in Fig. 3. From the figure, it has been observed that S11 minima occurred at 6.4 GHz. At S11 minima, the array offers 10 dB impedance bandwidth of 6.25% covering the frequency range of 6.2–6.6 GHz. The antenna array radiates in broadside direction as array elements are excited with fundamental mode TE111. The electrical field distributions of fundamental modes are shown in Fig. 4. In Fig. 5a, b, simulated normalized radiation patterns are depicted for E-plane and H-plane, respectively. 3 dB beamwidth for E-plane and H-plane has been found as 50° and 78°, respectively. Peak gain in broadside direction has been observed as 9.3 dBi. A comparative study is carried out in a tabular format and is given in Table 2. From the table, it is clear that our proposed designed have comparable performance with others but DRA element consumes the smallest volume among all.

Fig. 3 Simulated S11 of the proposed array

Fig. 4 Electric fields distributions for fundamental

TE111

Microstrip Line Fed Two Element E-Plane HDRA Antenna Array

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Fig. 5 Simulated normalized radiation patterns a for E-plane and b for H-plane