International Journal of Antennas and Propagation

Volume 2017, Article ID 1691580, 13 pages

https://doi.org/10.1155/2017/1691580

## On the Design of Conical Antennas for Broadband Impedance Matching Performance

Military Institute of Engineering, 22290-270 Rio de Janeiro, RJ, Brazil

Correspondence should be addressed to Maurício Henrique Costa Dias; rb.be.emi@saidchm

Received 29 December 2016; Accepted 7 February 2017; Published 27 February 2017

Academic Editor: Ikmo Park

Copyright © 2017 Francisco Estêvão Simão Pereira and Maurício Henrique Costa Dias. 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

In the scope of broadband radiators, the biconical antenna, or its monopole conical counterpart, is long known to be a proper choice. One common form of such radiator, the spherically capped conical antenna (SCCA), has closed-form solution to its input impedance, from which the broadband performance potential is easily verified. Nonetheless, from the design perspective, apart from a few clues inferred from existing solutions, little is found to accurately guide the choice of the main geometrical parameters of the antenna that will enable it to comply with a set of imposed bandwidth requirements. This paper proposes a simple 10-step sequence to derive conical or biconical antenna design charts. These charts provide straightforward information on the geometrical limits within which the required antenna impedance matching broadband performance is achieved. The method is assessed for the SCCA and the open conical antenna (OCA) using theoretical and simulated estimates of the input impedance. A discussion on the impact of the cap and the feed gap is included.

#### 1. Introduction

Biconical and conical antennas are among the most widely known radiators. They are natural choices for RF communication, broadcasting, or EMI testing, whenever omnidirectional radiation pattern and broadband performance are needed. The basic conical geometry (or biconical in its dipole equivalent) is typically assembled either by a wire grid or by a continuous metal surface [1, 2].

The ideal biconical geometry is actually a frequency-independent antenna, though it is not a feasible one, since it extends to infinity in the axial direction. Its input impedance does not change with frequency. Realistic biconical antennas must be truncated, leading to a broadband rather than frequency-independent response [1, 2].

Truncated versions of the biconical and conical antenna have been addressed as early as the 1940s by Schelkunoff [3], Smith [4] and Papas and King [5, 6], providing analytic approaches to calculate the antenna impedance and field pattern dependence on frequency and on the main geometric parameters (length and flare angle). Those antennas have still drawn attention through the following decades up to the present days. Recent analytical works on the subject may be found, for instance, in [7–9]. Nevertheless, information regarding the design point of view of such antennas, as in [10], for instance, is still scarce in the literature, especially when specific broadband performance criteria must be fulfilled.

A typical question that may arise for the designer of such antenna is how its geometric parameters should be chosen from start. Yet, how can one combine compactness and broadband performance up to the required levels considering such a structure? Though a few clues may be inferred from the mere observation of commercially available antennas, reliable open-source information to accurately aid the antenna engineer in this sense is not easily found.

In the present scope, this work discusses a simple method to derive bandwidth compliance charts for the design of conical and biconical antennas. These design charts set the limits that the main geometric parameters must fall within so that the antenna should be able to comply with a given imposed bandwidth constraint. The method is easily applied to any variant of the conical or biconical antenna, provided that a series of impedance estimates spanning a frequency band large enough and some different flare angle values is obtained. Such estimates may be derived analytically, for instance, when closed-form equations are available, as in the case of the spherically capped conical antenna (SCCA) addressed in [5]. Otherwise, they can be collected by measurements or computed with the aid of antenna analysis tools, such as CST MW Studio, FEKO, HFSS, and NEC implementations. In this work, focus is given to the SCCA and to the open conical antenna (OCA), first analytically for the former, then with data generated by CST MW Studio for both of them. The influence of the cap and the feed gap is also discussed.

Section 2 summarizes the theoretical approach of Papas and King [5] on the SCCA, providing further insight on its bandwidth performance, from the antenna designer perspective. The method to derive design charts for broadband performance is described in the following section, taking as reference the design of an SCCA to be broadband matched to a 50 Ω load. Section 4 applies the proposed method to derive charts for the design of an OCA matched to 50 Ω, using impedance estimates calculated by simulation on CST MW Studio. Both SCCA and OCA bandwidth performances are analyzed, taking into account also the cap and the feed gap impact. Section 5 concludes this paper.

#### 2. SCCA Input Impedance

##### 2.1. Theoretical Model

The reference antenna in the present work is the SCCA fed by a coaxial line depicted in Figure 1. The ground plane is supposed to be ideal, that is, infinitely extended. The cone and the ground plane are also assumed to be perfect electrical conductors (PEC). This conical antenna configuration was assessed by Papas and King in [5] to derive an equation of the input impedance of an antenna of length and flare angle , leading to where is the spherical Hankel function of the second kind, and is the Legendre polynomial of order . The summation in (3) must be over odd integral values. Yet, is defined as the characteristic impedance of the antenna and is the wave number multiplied by the sphere radius or cone side length ( is the free-space wavelength, the frequency, and the speed of light in vacuum).