Elements of Transmission Line Theory

Continuous progress achieved in electronic technologies and telecommunication processes, are opening new opportunities, to apply transmission line theory. In this context, next two examples, based on opposite geometric scales, will serve, as brief overview.

Let’s start with the fast digital circuits where are travelled, short voltage pulses rising and falling in few picoseconds. It is well known, that design of such circuits, involves to take into account the propagation phenomena. Thus, propagation acts like undesirable reflected waves on micro circuit’s tracks connections, so called signal integrity. Although analysis of such phenomena may be efficiently helped by means of simulation codes, sometime, these tools require physical approach, which may be carried out with the transmission line theory, as related in this article.

At another bound of the radiofrequency spectrum, we find the powerline, used as telecommunication waves guide. These systems, better known under the abbreviation PLC (Power Line Communications), are likely to appear on electrical energy cables, standing in buildings and various vehicles (aircraft, railway coach, cars…). As previously evoked for the digital circuits, use of sophisticated predictive tools, to determine the transmission digital channel efficiency, or the PLC ‘s near field radiation, requires, help of the transmission lines theory, as suggested after, but aimed here, to understand the physical approach at more elementary level.

Other extensions in use of the transmission lines theory, deals with electromagnetic compatibility, where various lines are encountered, in many induction or radiation phenomena. But also, in any other field of applied sciences, where the propagation of electric, acoustic, electromagnetic signals is involved, along a single space dimension.

The article subdivided in five chapters, is mainly aimed to provide some rudiments about the transmission lines theory. However, a basic approach doesn’t exclude use of mathematical tools. We shall see in many times, that looking of equations reveals a lot of physical subtilities. Contain of the article will be briefly summarized below, but it should be pointed out that theory supposes, sources of voltages and currents, but also the loads, obey at linear behavior.

Chapter one, devoted to introduce the topic is specially focused on technical vocabulary and how is the transmission lines theory position, in respect of circuit and electromagnetic theories from which it comes.

Chapter two is mainly devoted to build the wave equation and find the solutions presented in terms of simple formulae showing more easily, the way by means the propagation phenomena occur. Furthermore,...