Standing Wave Ratio - Relationship To The Reflection Coefficient

Relationship To The Reflection Coefficient

The voltage component of a standing wave in a uniform transmission line consists of the forward wave (with amplitude ) superimposed on the reflected wave (with amplitude ).

Reflections occur as a result of discontinuities, such as an imperfection in an otherwise uniform transmission line, or when a transmission line is terminated with other than its characteristic impedance. The reflection coefficient is defined thus:

is a complex number that describes both the magnitude and the phase shift of the reflection. The simplest cases, when the imaginary part of is zero, are:

• : maximum negative reflection, when the line is short-circuited,
• : no reflection, when the line is perfectly matched,
• : maximum positive reflection, when the line is open-circuited.

For the calculation of VSWR, only the magnitude of, denoted by ρ, is of interest. Therefore, we define

.

At some points along the line the two waves interfere constructively, and the resulting amplitude is the sum of their amplitudes:

At other points, the waves interfere destructively, and the resulting amplitude is the difference between their amplitudes:

The voltage standing wave ratio is then equal to:

As ρ, the magnitude of, always falls in the range, the VSWR is always ≥ +1.

The SWR can also be defined as the ratio of the maximum amplitude of the electric field strength to its minimum amplitude, .