TABLE OF CONTENTS Thus far we have explored the properties of a generic transmission line. We shall now exploit the transmission line as a circuit element, realizing any desired reactance, using it for impedance matching, or as a resonator. The Smith Chart will be introduced as a powerful graphical aid in the design of transmission line circuits. The Smith Chart, a graphical representation of the complex bilinear transform, is also an excellent visualization tool that can give us intuition and insight into transmission line behavior.
The open line is the dual of the shorted line analyzed in the previous section. The open transmission line has infinite VSWR and ? L = 1. At any given point along the transmission line
whereas the current is given by
or
The impedance at any point along the line takes on a simple form
This is a special case of the more general transmission line equation with Z L = ?. Note that the impedance is purely imaginary since an open lossless transmission line cannot dissipate any power. We have learned, though, that the line stores reactive energy in a distributed fashion.
A plot of the input impedance as a function of z is shown in Fig. 9.23a. As evident from the plot of the current and voltage, shown in Fig. 9.23b, the current must be zero at the end of the line due to the open boundary condition, but...
