International Journal of Antennas and Propagation

Volume 2016, Article ID 9327167, 7 pages

http://dx.doi.org/10.1155/2016/9327167

## A Circuit-Model-Navigated Design Process and Efficiency Estimation for Short-Circuited Self-Excited EBG Resonator Antenna

The Edward S. Rogers Sr. Department of Electrical & Computer Engineering, 10 King’s College Road, Toronto, ON, Canada M5S 3G4

Received 25 February 2016; Revised 1 May 2016; Accepted 10 May 2016

Academic Editor: Ikmo Park

Copyright © 2016 Mehdi Hosseini. 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

The paper presents a circuit model for the computationally efficient design of a planar Short-Circuited Self-Excited EBG Resonator Antenna (SC SE-EBG-RA). To this purpose, the same circuit model previously presented for the Open-Circuited version of the antenna is modified to be applicable to the SC version. Detailed HFSS modeling and simulation corroborate the accuracy of the model in predicting the antenna resonance. The efficiency of the designed antenna is calculated by a simulated Wheeler Cap Method (WCM) and is compared with the standard efficiency given by the numerical analyzer. The EM modeling is arranged so as to incorporate the effects of the SMA connector, discontinuities, and the WC, emulating a real WC measurement and yielding a high degree of confidence in the results. Overall, a small antenna sized with 93% verified efficiency is achieved, which is also compiled with affordable manufacturing processes.

#### 1. Introduction

Although electrically small antennas (ESAs) have been under study for years [1], it was the recent boom in modern communications systems which truly revealed their importance. On the bright side of this evolution, the gradual shift over to higher frequencies has brought the opportunity of using shorter wavelengths, thus employing physically smaller antennas. However, the insatiable data demand by users continues to put ever-increasing pressure on the design of ESAs. The proliferation of frequency bands and the desire to incorporate as many allocated bands as possible in contemporary design scenarios have also led to the situation. The main challenge in achieving a desirable ESA is the fundamental [1, 2] compromise between bandwidth (BW), gain, and the electrical size of the antenna. When attempting to reduce the electrical size, the typical cost is to have a reduced BW or deteriorated radiation efficiency, or even both, a fact which turns the antenna miniaturization into an art of compromise [3]. One of the main avenues of research, related to ESAs, is to develop computationally efficient analysis methods for the design of such EM structures, which mainly involves developing quasistatic circuit models. Circuit models provide the designer with a set of initial values for time-consuming design optimization processes and, by doing that, streamline the course of achieving the most optimized ESA, even under stringent requirements. Such models can also provide one with a rapid insight into the relationships between performance and structural parameters [4], spurring more innovation and better problem-solving ideas in antenna design. In case the antenna possesses a periodic structure [5–8], first, the unit cell is modeled separately [9, 10], and then the acquired knowledge is fed to the theories such as Bloch [7, 11, 12], to understand the performance of the whole periodic antenna composed of the unit cells.

One of the most recent examples of periodic ESAs, for which a Bloch-based circuit model is proposed, is the so-called Self-Excited EBG Resonator Antenna (SE-EBG-RA) [4, 8, 13, 14]. The SE-EBG-RA was first introduced in [7] as a new type of high-efficiency planar ESA, the principle of operation of which was explained using a Bloch diagram. Most typical EBG antennas are based on an antenna such as dipole [15, 16], patch [17], or other variations [18], placed over a high impedance plane, composed of various kinds of unit cells (e.g., [19]). However, the feature which differentiates the SE-EBG-RA from most of such conventional EBG antennas is its special integrated configuration and radiation mechanism. Few cascaded EBG cells are viewed as a piece of a highly radiating TL, which is directly excited (Self-Excited) by a microstripline (MSL) on one side, while the other side could be open [4, 7], shorted [13], or even terminated [8]. This way, the radiator and the EBG cells form one* unified* radiating structure. Despite such differences in mechanism and structure, the performance of this type of periodic antenna is quite similar to other EBG antennas. Following these efforts, [4] presented a relatively accurate Bloch-based circuit model for rapid analysis and design of SE-EBG-RAs, while the model was* only* applicable when the cells were left open on one side (Open-Circuited), forming an OC SE-EBG-RA. Also, the equations were* only* valid for three unit cells, while not a necessity, as demonstrated later in [13].

To supplement the model in [4], this work presents a new generalized version which is applicable not only to the OC SE-EBG-RA but also to the SC version with any number of cells (Section 2). In Section 3, a sample SC SE-EBG-RA is designed through an efficient design process, navigated by the proposed circuit model. Next, in Section 4, a Wheeler Cap (WC) is modeled along with the designed antenna to numerically estimate the efficiency of the antenna. In-detail numerical modeling and analyses provide two* independent* estimations of . Afterwards, an alternative versification of the EM model is rendered in Section 5, and, then, the paper is concluded by Section 6 in which the effects of extreme truncation of the antenna ground plane on its performance are investigated. All numerical analyses are carried out using the High Frequency Structure Simulator (HFSS).

#### 2. Circuit Model for the SC SE-EBG-RA

The SE-EBG-RA is composed of small periodic metal patches, deployed on a grounded substrate, with tiny gaps in between. The dispersion relation of this periodic structure, considered as a type of periodic TL, is [4]where is the wavenumber [4] of the unloaded MSL (with gaps removed), is ()^{−1/2}, and is the cell size which must be much smaller than free-space wavelength, for validity of (1). and are also found from equations in [4]. The cut-off frequency () of the dispersion diagram is expressed by [4]where is the capacitance caused by coplanar coupling () between the adjacent patches. The parallel plate coupling considered in [4] is neglected in this work as traces are thin. If is much larger than the gap size, as it is in Figure 1(c), can be calculated from (see Figure 1), the equations of which are given in [4]. The resonance frequency () of the -cell OC SE-EBG-RA can be expressed bywhere is and iswhere, for the OC case in [4], . Also, , where is the number of cells. Possibility of using different numbers of cells for SE-EBG-RA was demonstrated in [13]. It was also shown there that the SC version is naturally a quarter-wavelength antenna, as opposed to the OC version which is half-wavelength. Thus, rather than used in [4], we can insert into (1) and find of the SC version in a similar manner. Manipulation of the equations suggests that (1) to (4)* can be reused*, provided that rather than 2 for the OC case. It is noted that, for Figure 1 with 2 cells, . Equations (1) to (4) provide the designer with a new set of relatively accurate closed-form equations which streamline the design process of the 2-cell SC SE-EBG-RA in Figure 1.