International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 351439, 8 pages

http://dx.doi.org/10.1155/2015/351439

## Beam Tilt-Angle Estimation for Monopole End-Fire Array Mounted on a Finite Ground Plane

School of Information and Electronics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, China

Received 2 October 2014; Revised 2 December 2014; Accepted 15 December 2014

Academic Editor: Ana Alejos

Copyright © 2015 Jia Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A modified method for the beam tilt-angle estimation of monopole end-fire array mounted on finite ground plane is proposed. In the simplified model, the monopole array and ground plane are approximated to two line sources of transverse and longitudinal electric current, respectively. It is deduced that the beam tilt angle is a function about the length of ground plane in front of array , the length of monopole array , and the phase constant . After verifying the optimizing principle of monopole end-fire array, a 10-element monopole Yagi-Uda antenna satisfying Hansen-Woodyard condition is designed and measured for the analysis. By comparison and analysis, the value of is demonstrated to be the key point of the proposed method. And a slow wave monopole array is proved to be able to achieve a low beam tilt angle from end-fire with only a short-length ground plane.

#### 1. Introduction

End-fire antennas are useful in all applications that require low profile, for example, in airborne and vehicular environments. After decades of research and developing, the performance of end-fire antennas has been greatly advanced in several fields, like broadband, gain enhancement, and pattern reconfiguration [1–4]. However, those end-fire antennas mounted in or on a finite ground plane suffer from a serious problem: the main beam is tilted at some angle from the horizontal plane by diffraction effects from conductive ground, which prevents a true end-fire condition.

By image theory, the conclusion can be easily obtained that the beam tilt angle will disappear when ground plane extends to infinite. Meanwhile, as a majority of radiation power distributes in the positive half-space, the value of the beam tilt angle mainly depends on the effective ground plane length in front of end-fire antenna. This phenomenon was first described by Elliott in 1954 [5].

Based on Huygens’ principle, a simplified method for determining the effect of finite ground plane was demonstrated by Walter in his book, by which the aperture of antenna and the ground plane were simplified to a uniform line source of magnetic current and electric current, respectively. As a result, the beam tilt was proved to be a function of both (given antenna length) and (effective ground plane length). For small values of beam tilt (), this function reduced to where is in degrees [6].

Nevertheless, this method with high accuracy is not suitable for the monopole end-fire array vertical to the ground plane. That is not only because of the model abstracted from the flush-mounted end-fire antenna which is a kind of aperture antenna parallel to the ground, but also due to no consideration about the influence from phase constant’s varying. Thus in the former research, the beam tilt-angle analysis of this kind of monopole end-fire array could only be obtained by whole model simulation using simulation software, far-field measurement, or numerical calculation method [7], with high cost, long time, and various operations.

A beam tilt-angle estimation method, which is modified for the monopole end-fire array mentioned above, is proposed in this paper. Firstly, a simplified source model is applied to this kind of antenna. The key point of this model simplification is evaluating the phase constant of the surface wave along monopole end-fire array. Secondly, monopole Yagi-Uda antenna is introduced to validate the validity and accuracy of this method. The estimated tilt angles present a good agreement with CST simulation results. Furthermore, comparison between the proposed method in this paper and Walter’s method shows an advantage of monopole end-fire antenna with slow wave characteristic. This advantage, that a low tilt angle can be achieved with a short ground length, is demonstrated by the experimental results of the 10-element monopole Yagi-Uda antenna.

#### 2. Simplified Model for Monopole End-Fire Array and Ground Plane

Figure 1 shows the configuration of an -monopole end-fire array mounted on a ground plane with certain size (). Assume it is working at the frequency point , with a wavelength , and is the corresponding angular frequency. Consulting the original method in [6], the simplified model should be composed of two parts: one line source approximated from the monopole array current distribution and another one approximated from the current on the ground plane. Note that only far-field patterns in -plane are taken into account for the beam tilt-angle problem, as the main lobe direction is always in this plane when the ground is symmetric about the -axis.