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

Let’s imagine a cell phone located in a room covered with metal walls, and transmitting radiofrequencies waves in the gigahertz range. Under such conditions, radiation within the room, is similar that the combination of many plane waves impacting the conductive walls. The waves reflected on the walls are submitted to interferences phenomena, which lead to increase or decrease dramatically the resulting field amplitude inside the room. Thus, such interferences remind the well-known reverberation as established in acoustic cavities. At peculiar frequencies the standing wave within the room may reach a resonance. This occurs when the phase angles of the reflected waves are a multiple of 2π, thus the resulting wave rises at very high amplitude. Now, if we compute field’s amplitude at resonance, in summing the reflected waves to form a series expansion, this converges slowly, and sometimes with inaccurate fashion. A more deeply analysis shows that the uncertainties are mainly due to reflection coefficient of high conductive walls which behave like a perfect mirror.

Another approach to determine the field amplitude within the room, would be to consider that radiated power from the cell phone is converted into thermal losses in the conductive walls. Thus, a steady state must be achieved between the thermal power and electromagnetic power of the standing waves established in the room. Such physical approach is related in waves equation, whose solutions expressed in terms of eigenvalues, leads to infinite range of resonances frequencies and fields of high amplitude. Even in the scope of waves equation, solving the electromagnetic cavities remains a difficult task, which may be lightened in applied the transmission lines theory. However, this supposes use of approximations as fully justified later. Afterward, computation of the field amplitudes as found at resonances frequencies, will be solved with analytical way alone.

This theoretical approach will be followed to present the article under two separated parts, both in terms of topics and forms. Part I will be focus on the coupling of RF sources to the TEM mode, while Part II will be extended to the TE (or TM) modes.

Analysis of the coupling phenomena will be especially concerned by the lower frequency leading to resonance, so called “fundamental resonance”. Furthermore, lot of examples will be considered, to take into account various order magnitude attached to the physical data, but also to gradually increase the theoretical hardness.

Part I devoted to the TEM mode will be organized following two chapters. Chapter one will consist to introduce the EM coupling with the cavities related to most problems of electromagnetic compatibility (EMC) in aircraft industry. Then, this...