High frequency systems have a source of power. A portion of this power is delivered to a load by means of transmission lines as shown in Figure 2
Figure 2: A load and a source connected though a transmission line
Voltage, current and power can be considered to be in the form of wave traveling in both directions along this transmission line. A portion of the waves incident on the load will be reflected. It then becomes incidents on the source, and in turn re-reflected from the source, if , resulting a standing wave on the line.
If this transmission line is uniform in cross section, it can be thought of as having an equivalent series impedance and equivalent shunt admittance per unit length as shown in Figure 3.
Figure 3: Uniform transmission line
A lossless line would simply a series inductance and a shunt capacitor. The
characteristic impedance of the lossless line
At microwave frequencies, most transmission lines have a 50 characteristic impedance. The incident and reflected voltages on a transmission line result in a standing voltage wave on the line. The value of this total voltage at a given point along the length of the transmission line is
and the total current on the line is
Another very useful relationship is the reflection coefficient
which is a measure of the quality of the impedance match between the load and the characteristic impedance of the line. This can be seen more clearly if reflection coefficient is expressed as
To facilitate computations, we can normalize impedances to the characteristic impedance of the transmission line. The normalised load impedance is