Impact of Spacing and Number of Elements on Array

PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012

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Impact of Spacing and Number of Elements on Array Factor S. F. Maharimi1 , M. F. Abdul Malek2 , M. F. Jamlos1 , S. C. Neoh3 , and M. Jusoh1 1

School of Computer & Communication Engineering, University Malaysia Perlis, Malaysia 2 School of Electrical System Engineering, University Malaysia Perlis, Malaysia 3 School of Microelectronic Engineering, University Malaysia Perlis, Malaysia

Abstract— The impact of spacing and number of elements in terms of gain and half power beam-width (HPBW) are shown in this paper. The antenna’s gain is depending on two parameters which are number of elements and element spacing. These measurements were measured by array factor’s algorithm. The algorithm has been designed to operate with 2, 3, 4 and 10 number of elements at the each specific spacing. The particular spacing are 0.1λ, 0.25λ, 0.5λ and 0.75λ. It is observed that the HPBW and number of side lobes is increased as spacing of elements are increases. And the gain is maintains in the same condition. 1. INTRODUCTION

The capability of an antenna to increase the quality of the performance is depends on their parameters such as number of elements, spacing between elements, phase and amplitude excitation. The main parameters for linear array antenna are the number of elements and spacing elements which must be taken into consideration. Hence, these parameters are used to determine the antenna performance on the gain and HPBW. The array factor is fundamental of the antenna parameters. This paper described the impact of the spacing and the number of elements on gain and HPBW through array factor algorithm for linear array antenna and simulated using MATLAB software as illustrated. 2. ARRAY FACTOR

The array factor depends on the number of elements, the element spacing, amplitude and the phase of the applied signal to each element [1]. The antenna array can aligned either z-axis or x and y-axis. A uniform array is defined by uniformly spaces identical elements of equal magnitude with linearly progressive phase from element to element [2]. The radiation pattern of the array excluding the element pattern is referred to as the array factor. A general form for along the z-axis for linear array is given by [3]. AF = 1 + ej(kd cos θ+δ) + ej2(kd cos θ+δ) + . . . + ej(N −1)(kd cos θ+δ)

(1)

where k = 2π λ , N is the number of elements. The N -elements linear array can be designed to radiate in either broadside array where radiation perpendicular to array orientation the z-axis or end fire array will radiate in the same direction as the array orientation in the y-axis [2]. The array factor of N -elements can be written as [3]: AF (θ) =

XN i=1

e j(n−1)(kd cos θ+δ)

(2)

The term of kd cos θ + δ can be written as ψ, so the array factor becomes AF (θ) =

XN i=1

e j(n−1)ψ

(3)

Refer to (2) the notation of θ is the angle between the array axis and the vector from the origin to the observation point [3]. According to broadside array, the phase shift of δ is equal to zero (δ = 0) such that all element current are in phase. 2.1. Equal and Unequal Spacing N-element Linear Array Antenna

Linear array antenna has two spacing technique elements either equal spacing between elements or unequal spacing elements. The number of elements depends on the designer to put how many in the antenna design. This section described the theory of the N -number elements in equal and unequal spacing in linear array arrangement.

Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 1551 2.1.1. Equal Spacing N-element Linear Array

For equal spacing between elements, the distance for each element to element is equal in lambda. Figure 1 below show the linear array for equal spacing elements. This arrangement is also called uniform linear array [5]. 2.1.2. Unequal Spacing N-element Linear Array

The distances for unequal spacing linear array of an antenna with N -element are nonuniform in z-axis arrangement. Their configuration can be rearranged either in symmetrical or asymmetrical arrangement [5, 6, 8]. Figure 2 illustrates the unequal spacing of d1 till d5 in an arrangement of an antenna in the linear array for 6-elements as an example [5, 6]. Figure 3 illustrates the arrangement of linear array antenna in the symmetrical condition. A symmetrical arrangement could be described that the position of the element number of 1, 2, and 3 in both sides of positive and negative are equal [6–8]. 3. SIMULATION OF N-ELEMENT FOR 0.1λ, 0.25λ, 0.5λ, 0.75λ SPACING ELEMENTS OF LINEAR ARRAY ANTENNA

This section described the simulation method using MATLAB Software where the array factor was used as the algorithms for evaluate the HPBW and gain to achieve better performance in antenna design. The simulation started with 2, 3, 4 and 10 elements in linear array antenna with spacing elements of 0.1λ, 0.25λ, 0.5λ, and 0.75λ as shown in Figures 4, 5, 6 and 7. From the results, the antenna’s gain is measured by array factor algorithm. The gain is rising according to the number of elements. The shape of the graph for the array factor changed when the spacing elements increased. Referring to the result obtained by difference

Figure 1: Linear array antenna for equal spacing.

Figure 2: Linear array for unequal spacing in asymmetric array arrangement.

Figure 3: Linear array for unequal spacing symmetrical array arrangement.

Figure 4: Array factor for 0.1λ spacing elements.

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PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012

Figure 5: Array factor for 0.25λ spacing elements.

Figure 6: Array factor for 0.5λ spacing elements.

Figure 7: Array factor for 0.75λ spacing elements.

number elements, although the gain become increasing according to the number element but their gain was maintains when the spacing element is increasing towards to the lambda. Whole gain for these different spacing elements is not changed but their HPBW reduce when the spacing element is increase. The each element’s gain is not change though the spacing element has increase. Comparing all the result in Figures 4, 5, 6 and 7, the number of ripples or side lobes strictly increased when the spacing elements increased. The width of the main lobe decreased when the number of elements and spacing elements were increased. From the results observation, the increasing number of elements and spacing elements have affected on their radiation pattern.

Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 1553 Table 1: HPBW and gain for N = 2, 3, 4, and 10 at 0.1λ, 0.25λ, 0.5λ and 0.75λ spacing elements. Element 2 3 4 10

HPBW 90.83◦ 87.39◦ 85.44◦ 53.37◦

0.1λ Gain (dB) 2 5 9 19

HPBW 89.8◦ 70◦ 62◦ 23.62◦

0.25λ Gain (dB) 2 5 9 19

HPBW 83.77◦ 42◦ 29.76◦ 10.29◦

0.5 λ Gain (dB) 2 5 9 19

0.75 λ HPBW Gain (dB) 52.57◦ 2 ◦ 27.64 5 19.63◦ 9 ◦ 6.8 19

4. CONCLUSIONS

As a conclusion from the results obtained, HPBW was increasing according to the number and spacing elements and when the gain was increasing according to the number elements. The result achieved a good performance in the antenna design at the highest gain of 19 dB at spacing element is equal to 0.1λ. Furthermore, increasing the spacing elements in the gain is unsuitable for application seeking to improve system performance when degradation is mainly caused by interference or jamming. ACKNOWLEDGMENT

The authors would like to thank everyone for their helps and support especially to Embedded Computing team members and University Malaysia Perlis. Special thanks to the Ministry of Higher Education in Malaysia for their financial support. REFERENCES

1. The Basics of Antenna Arrays notes, 2010, Available: http://www.orbanmicrowave.com. 2. Antenna Arrays notes, 2009, Available: http://www.ece.msstate.edu/˜donohoe/ece4990notes 6.pdf 3. Zooghby, A. E., Smart Antenna Engineering, Artech House, Inc., U.S., 2005. 4. Gross, F., Smart Antenna for Wireless Communication with Matlab, The McGraw-Hill Companies Inc., U.S., 2005. 5. Jin, N. and Y. Rahmat-Samii, “Advances in particle swarm optimization for antenna design: Real-number, binary number, single-objective and multiobjective implementations,” IEEE Transaction on Antenna Propagation, Vol. 53, 556–567, Mar. 2007. 6. Tan, M. N. Md, S. K. A. Rahim, M. T. Ali, and T. A. Rahman, “Smart antenna; weight calculation and side lobe reduction by unequal spacing technique,” IEEE International FR and Microwave Conference Proceedings, 441–445, Kuala Lumpur, Malaysia, Dec. 2008, 7. Tan, M. N. Md, T. A. Rahman, S. K. A. Rahim, M. T. Ali, and M. F. Jamlos, “Elements reduction using unequel spacing technique for linear array antenna,” PIERS Conference Proceedings, 568–572, Xi’an, China, Mar. 2010, . 8. Balanis, C. A., Antenna Theory, Canada, A John Wiley & Sons, Inc., U.S, 2005.