Introduction

Modelling stratified media is an important application of the MoM. A stratified medium is one consisting of homogeneous layers of material, each layer having different electromagnetic properties. This includes the general category of printed antennas, of which microstrip is the best known. (Microstrip technology is discussed in more detail in the next chapter.) It also brings with it the problem of dealing with dielectric materials. Central to this is the issue of the Green function for the problem. The MoM relies on an appropriate Green function as the “field propagator.” Due to its perceived complexity, the topic of stratified media is generally regarded as an advanced one, and the coverage tends to be highly theoretical, and frequently impenetrable without lengthy study. One reason for this is that historically, analysis focussed on the problem of a dipole above a dielectric half-space. There are a number of complex issues which this raises, requiring quite sophisticated analytical techniques to understand, in particular for the asymptotic cases where interesting radiation physics can be extracted. However, the analysis of a very important special case, namely the grounded single-layer microstrip line (or patch antenna), can be undertaken without undue complexity, at least for most practical cases where the substrate is relatively thin.

In this chapter, a static analysis of a microstrip transmission line is first undertaken, to demonstrate the basic principles of the spectral domain and the derivation of the Green function. Following this, the dynamic analysis is introduced, and the Sommerfeld potentials derived from first principles. Although the work in this chapter is certainly not original, being based on a synthesis of the literature – in particular [1] – the presentation in the present format does not appear to have been thus undertaken in other works to date.