Overview

The mathematical relationships of the various parameters involved in guided wave propagation are basic to the construction of the SMITH CHART, or any other chart which portrays these relationships. Accordingly, the applicable transmission line equations are included herein for those who may desire this background information without the necessity of referring to other sources. Also, these relationships serve to provide more exact solutions to specific problems in cases where graphical solutions cannot provide the desired accuracy or when, for example, a computer is available.

In these formulas the sending-end impedance Z _s is the input impedance of a transmission line looking toward the load. Except for its mismatch effect on the transfer of power from generator to line (and/or to load), the value of Z _s is completely independent of the impedance looking toward the generator from this position, and is thus the impedance which would be seen if the line (or other connections to the generator) were cut off at this point. Z _s is thus the impedance at any specified point along the line.

There are an infinite number of input or sending-end impedances along any finite length of transmission line, and the position of the specified sending-end impedance with respect to the receiving-end or load impedance Z _r must be known in order to evaluate it. The receiving-end impedance, like the sending-end impedance, can be referenced to any position along the line provided that it is on the load side of the...