VSWR, DEFINITION, DERIVATION and MEASUREMENT

VSWR, or voltage standing wave ratio, is a measure of how well the components of the RF network are matched in impedance. When the impedances are improperly matched, you lose signal power, which results in weak transmissions, poor reception or both.
Maximum power transfer between two system components occurs when their respective impedances are matched. If the impedances are not identical, some RF power will be reflected back, resulting in a reduction in the amount of power delivered to the load. These reflections cause voltage standing waves.
VSWR is defined as the ratio of the maximum voltage to the minimum voltage in the standing wave. The larger the impedance mismatch, the larger the amplitude of the standing wave.
A perfect impedance match would cause no voltage standing wave, so the ratio of the maximum voltage to the minimum would be 1 (1:1).
Most RF systems have a characteristic impedance of 50Ω. All of the devices in the transmitter and receiver sections are designed to have input and output impedances of 50Ω. This includes the coaxial cables that are used to interconnect the devices. These devices include multiplexers, bandpass filters, duplexers, low-noise amplifiers, combiners, power amplifiers etc.
Although the concept of VSWR is easy to comprehend, it is extremely difficult to measure directly. For that reason, you need to measure other parameters, such as return loss and then from that calculate the magnitude of the reflection coefficient, ρ (lower case Greek letter Rho) which can then be used to calculate VSWR.
Return loss is the difference in power (expressed in dB) between the incident power and the power reflected back by the load due to a mismatch. It can be measured directly in dB with a Spectrum Analyzer or Network Analyzer along with a few key components. It is expressed as:
Return loss (RL) = -10log(Preflected /Pincident )
A perfect match would result in no reflected power (as it is all delivered to the load), so the return loss would be infinite. Conversely, an open circuit would reflect back all power, so the return loss would be zero. When dealing with return loss, the higher the value, the better the impedance match.
Once the Return Loss is known, the next step is calculate ρ :
By definition, ρ = √(Preflected /Pincident )
But since RL = -10log(Preflected /Pincident ) we can manipulate this expression to get ρ as a function of RL.
-RL/10 = log(Preflected /Pincident )
Then raise both sides to the power of 10:
10-RL/10 = 10(log(Preflected /Pincident )) = (Preflected /Pincident )
Thus we get:
(Preflected /Pincident ) = 10-RL/10
Now we take the square root of each side:
√(Preflected /Pincident ) = √10-RL/10 = 10-RL/20
Thus ρ = 10-RL/20
VSWR can then be calculated using the following formula:
VSWR = (1+ ρ )/(1- ρ )
The Return Loss can be measured in several different ways using a directional coupler along with some level measuring device such as a common Spectrum Analyzer/tracking generator, power meter or Network Analyzer. The directional coupler is first set up with a short or open circuit which reflects all of the power, so that Preflected /Pincident. Substituting the load in question for the short circuit allows the actual reflected power to be measured. The difference, in dB, between the power reflected with a short and the power reflected by the load at any given frequency becomes the RL for that frequency. Next, ρ can be calculated and then VSWR can be calculated
You also can use a time domain reflectometer to measure the reflection coefficient and apply that value to calculate VSWR.
Keep in mind that the reflection coefficient, Γ (upper case Greek letter Gamma), and the magnitude of the reflection coefficient, ρ (lower case Greek letter Rho) are related but not the same.
ρ = | Γ |
Γ is a complex number with real and imaginary components. Γ is a function of the complex impedance of the load and the characteristic impedance of the transmission line. It is given by Γ = (Z1-Z0)/(Z1+Z0) where Z1 is the complex impedance of the load and Z0 is the characteristic impedance of the transmission line. Z1 is not easily measured directly.
The reflection coefficient is a voltage ratio and must be squared to be used for power calculations. It is sometimes easier to think of reflected power in terms of reflection coefficient than in return loss. Reflected power is equal to the incident power multiplied by the reflection coefficient squared.