The Transmission Line Theory to Solve Electromagnetic Coupling within Cavities. Part II - Coupling to TEM modes

Let's imagine the emission of a cell phone located in a room lined with metal walls. The frequency of the sinusoidal signal source, close to a few gigahertz, is sufficiently high for the radiation to be assimilated to a large number of plane waves directed simultaneously towards the walls. The waves thus undergo multiple reflections, producing both destructive and constructive interference, reminiscent of the well-known reverberation of acoustic cavities. In this physical context, certain dimensional configurations of the cavity will contribute to the maintenance of synchronous interference, generating resonances that can give rise to large-amplitude standing waves. If we then proceed to calculate the amplitude of the fields, established during the resonances, and in the form of a series composing an algebraic sum of complex variables, convergence proves to be very slow and sometimes marred by numerical instabilities. A more detailed physical analysis shows that the theoretical difficulties are mainly due to the very high reflection coefficient imposed by the high electrical conductivity of the walls.

An alternative to the previous reasoning is to state that the power carried by the electromagnetic waves emitted by the telephone is dissipated in thermal form in the walls. Under this hypothesis, a balance must be established between the active power absorbed and the reactive power contained in the standing waves combining electric and magnetic fields confined in the cavity. This alternative leads to the resolution of an eigenvalue equation leading to stable, large-amplitude fields distributed over an infinitely wide spectrum of resonance frequencies.

In its most fundamental form, electromagnetic cavity theory remains a difficult problem. However, at the cost of duly justified physical hypotheses, the reasoning can be lightened in favor of an analytical formulation borrowed from transmission line theory, which is much simpler to implement.

This is the path that will be followed to build the study of cavities, subdivided into two distinct parts, both in terms of presentation and content.

Part I of this first article will focus on the coupling of HF sources to the TEM mode, while Part II will be extended to the more general problem of coupling to TE (or TM) modes.

The analysis will always give priority to operation at the minimum resonance frequency, also known as the fundamental resonance. Examples of increasing difficulty will validate the orders of magnitude of the various physical variables developed later.

The first part, devoted to coupling to the TEM mode, will comprise two sections enabling the reader to tackle the qualitative aspect of cavities, followed by the...