Compact Antennas for Wireless Communications and Terminals: Theory and Design

Chapter 2Transmission Line Model ¹

 

 

 

2.1. Introduction

The transmission line model is derived from the assimilation of a rectangular antenna with a section of very wide microstrip line. Owing to the fact that this line has a finite length and is open at both its extremities, a standing wave will be established as resonant in character if the line length L is roughly equal to half the guided wavelength λ_g.

We assume for this purpose that the transition formed by each of the open extremities is a source of radiation. When the two sources radiate at the same time, as is the case when L ≈ λ_g/2, then this section of line can form an efficient antenna.

First, we will establish the equivalent circuit of the rectangular antenna, based on the transmission line model. Having declared the constituent elements of this circuit, we will then specify the value of the input impedance of the antenna as a function of the position of the feeding point.

2.2. Equivalent circuit

2.2.1. Effective permittivity

The open nature of the microstrip lines leads to a partial wave propagation in air and not solely in the substrate. As the propagation medium is not homogeneous, we cannot settle for ε_r to describe the medium and so we introduce effective permittivity ε_eff given by [BAL 89]:

[2.1]

We observe that ε_eff becomes closer to ε_r when the substrate thickness h is low and the line width W is significant, ...