Standing Wave Ratio

Prepared by: Prof.Altan M. Ferendeci

The magnitude of the voltage wave along a transmission line can be written as (here z=-d )

Factoring out |V⁺|

Substituting the load reflection coefficient

for the ratio of (V⁺/V^-), and manipulating the resultiing equation, we obtain

Maximum occurs when

here (n) is an integer, and

Minimum occurs when

here (n) is an integer, and

Voltage standing wave ratio (VSWR) is defined as

The length (d) given in Equations 1a and 2a are positive quantities. Therefore, the minus (-) signs in Eq.1a and 2a are to be excluded.
If the integer n is set to zero (n=0 ) in Eq.1a, the distance from the load to the d_max is given by
The distance between the two maxima is l/2. (half a wavelength) and between two minima is also l/2. The distance between a maximum and a minimum is equal to l/4 (quarter wavelength)
If the load is purely real (resistive) and is less than the characteristic impedance Z_c of the line, the voltage minimum occurs at this load location.
If the load is purely real (resistive) and is greater than the characteristic impedance Z_c of the line, the voltage maximum occurs at this load location.

As shown in the figure below and the accompanying Smith chart,

To see an ANIMATION of this Figure click here

The load is located at a distance from the first |V|_max by the length
As we move toward the generator on a constant r_L radius (this also is the corresponding constant VSWR circle), the horizontal axis of the Smith chart is intersected. At this point the impedance is purely real and less than the characteristic impedance. Therefore this is the first location of the voltage minimum.
As we move toward the generator along the constant r_L radius, the real axis of the Smith chart is again intersected. But this time the impedance is again purely real but it is greater than the characteristic impedance of the line. Therefore, this corresponds to the first voltage maximum.
The normalized impedance at the voltage maximum is also equal the VSWR on the line.
As we move toward the generator, these mimima and maxima follow each other every quarter wavelength. As expected, the impedances repeat themselves every half a wavelength.

A short is used as a load and the locations of the voltage minima are recorded and
The short is then replaced by an unknown load and the locations of the new voltage minima are recorded,
From the shift in voltage minimum, the load reflection coeffient is calculated. Once this is known, the Impedance is calculated.

Last Modified: Thu, Apr 9, 1998