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The expression of the standing wave ratio SWR is:
We consider , the guided wavelength on a transmission line.
It is assumed that the load impedance is different from the characteristic impedance of the line. This results in voltage antinodes (maximum amplitude) and nodes (minimum amplitude). The distance between two successive voltage antinode and node isWe consider a transmission line of length and a characteristic impedance connected to a generator delivering a sinusoidal voltage and to a load of impedance .
The reflection coefficient at is defined by:
In the case of a lossless line, the characteristic impedance of the line is:
We consider a transmission line with the propagation constant
A wave propagates along the increasing x axis. The expression of the wave in the time domain is:
The sinusoidal wave propagates on a transmission line with a propagation constant denoted with et real numbers. In this expression, the parameter corresponds to:
The sinusoidal wave propagates on the transmission line with a propagation constant denoted with et real numbers. in this expression corresponds to:
The signal transmission to the load is perfect when the VSWR (Voltage Standing Wave Ratio) is:
We consider a transmission line with the associated primary constants and . The expression of the propagation constant is:
Laplace's laws apply to: