2.1 Introduction
The language of transmission lines was developed in the early days of radio when rf (radio frequency) signals had to be transported from a transmitter to an antenna. The signals were basically a modulated sine wave called a carrier. The problem was to match impedances so that the transported energy reached the antenna and was effectively radiated. In digital electronics, the signals are step functions and the hope is that very little of the energy is radiated. Signals are often transported over and between conducting planes, and this practice was not a prime consideration in early radio.
Transmission line theory uses many terms common to circuit theory. We will be working mainly with step functions and not sine waves. A transmission line can be considered a distributed parameter circuit. Words such as bandwidth and frequency spectrum will apply. We will often use the term impedance but not in a sinusoidal sense.
When a voltage is placed on a transmission line, it is an invitation for nature to use this conductor geometry to move available energy away from the source. At the moment of connection, both voltage and current begin their travel down the line. We will often call this voltage and current flow a signal or a wave.
When a signal (wave) propagates down a transmission line, the source of signal has no way of sensing the length of the line or the type of termination. Energy is sent down the line just as if it was going to be radiated by a terminating antenna. In fact, a wave must reach a discontinuity, reflect and return to the source before the source can react. This type of delayed reaction is not usually considered in linear circuit theory.
The energy that is transported on a transmission line requires the presence of both an electric and a magnetic field. It is correct to consider a transmission line as a distributed inductance and capacitance. A schematic representation that shows lumped parameters would imply that the energy in the line is stored inside these pseudo components. In practice, the field patterns are around the conductors and extend out into space. This is the reason there is some radiation. The lumped parameter model is shown in Figure 2.1 and the field pattern is shown in Figures 2.2(a) and (b). E and H fields exist in all the space around the traces. In regions where the intensity is low, lines may not show.
Figure 2.1 The lumped parameter model of a transmission line. L, inductance per unit length; C, capacitance per unit length.
