The use of transmission lines has increased considerably since the author began his lectures on them at the University of Kent at Canterbury in October 1968. Now the mighty internet involves huge lengths of optical fibres, estimated at over 750 million miles, and similar lengths of copper cables. The ubiquitous mobile phones and personal computers contain circuits using microstrip, coplanar waveguide and stripline. However, despite all these widespread modern applications of transmission lines, the basic principles have remained the same. So much so, that the many classic textbooks on this subject have been essential reading for nearly a hundred years. It is not the purpose of this book to repeat the content of these standard works but to present the material in a form which students may find more digestible. Also this is an age where mathematical calculations are relatively simple to perform on modern personal computers and so there is less need for much of the advanced mathematics of earlier years. The aim of this book is to introduce the reader to a wide range of transmission line topics using a straightforward mathematical treatment which is linked to a large number of graphs illustrating the text. Although the professional worker in this field would use a computer program to solve most transmission line problems, the value of this book is that it provides exact solutions to many simple problems which can be used to verify the more sophisticated computer solutions. The treatment of the material will also encourage ‘back-of-envelope’ calculations which may save hours of computer usage. The author is aware of the hundreds of books published on every aspect of transmission lines and the myriads of scientific publications which appear in an ever increasing number of journals. To help the reader get started on exploring any topic in greater depth, this book contains comments on many of these specialist books at the end of each chapter. Following this will be the reader's daunting task to search through the scientific literature for even more information. It is the author's hope that this book will establish some of the basic principles of this extensive subject which make the use of some of these scientific papers more profitable.

In the preceding five chapters the topic of attenuation has been largely omitted. One reason for this was to simplify the text as the ‘loss-less’ or ‘loss-free’ theory is much easier than that for ‘lossy’ lines. Another reason is that attenuation in many transmission lines is not the major characteristic, particularly for short lengths of line. This means that the discussions in the previous five chapters are sufficient if the losses are small. However, no account of transmission lines would be complete without a discussion of the main causes and effects of attenuation. The chapter will begin with a return to the equivalent circuit method as this enables the two main mechanisms for attenuation to be introduced in a straightforward manner. After that, the concepts will be extended to those transmission lines that require electromagnetic waves for their solutions. Finally, some other aspects of attenuation will be discussed, including dispersion and pulse distortion.

Attenuation in two conductor transmission lines

At the beginning of Chapter 1, an equivalent circuit for a short length of loss-less transmission line was shown in Figure 1.1. In order to introduce the two main sources of attenuation, this diagram now needs amending. Firstly, any conductors will have some electrical resistance (curiously even for superconducting wires at microwave frequencies there will be some resistance, if there are still some unpaired electrons!) and this resistance can be represented as a series distributed resistance, R, which will have the units of Ωm−1. The other source of attenuation is the loss that occurs due to a dielectric having a small conductance. This can be represented by a parallel distributed conductance G with units of Sm−1. The effect of both of these resistive elements is to remove energy from the wave in proportion to the square of its amplitude. Not surprisingly, this results in an exponential decay of a sine wave.

This chapter will complete the discussion about photons on transmission lines. In the first three chapters, the equivalent circuit technique was used to develop many aspects of transmission lines. This involved a one dimensional analysis which has stood the test of time and still produces a useful, although incomplete, picture. However, in the second section, the analysis using electromagnetic waves was given, revealing the three dimensional nature of transmission lines. This showed features that the first section was not able to do; in particular, the velocity and the characteristic impedance of the waves as well as the propagation of higher order modes and the causes of attenuation. The electromagnetic wave approach is outstanding in its accurate prediction of the complex nature of transmission lines. In Chapter 7, a third method was considered using only plane waves travelling at the velocity of light. It was assumed that these plane waves were made up of linearly polarised photons. In this chapter, some more aspects of photons will be considered to see what other properties of transmission lines can be revealed. The use of photons is sufficiently new to be less well established and accepted as the other two approaches to transmission lines used so far. One problem lies in the separation between classical and quantum electrodynamics. The classical theory can be used quite satisfactorily for large numbers of photons. However, if individual photons are being considered, only the quantum theory will describe the phenomena adequately. The full treatment of photons using quantum mechanics is beyond the scope of this book but, where appropriate, the results of such a treatment will be quoted. The other problem lies in the somewhat conflicting theories that currently exist. This chapter should therefore be read with some caution as the picture presented may well change in the near future. Fortunately, the contents of the first seven chapters are sufficiently uncontroversial to not need changing within the lifetime of this book.