What is the standing wave ratio (SWR)?

In rf electronics, we often characterize a component or antenna by its standing wave ratio (SWR). What is the definition of this parameter and how does it affect a circuit?

The motivation for this question is that while answering another question, it would have been useful to be able to refer to a definition of SWR within the site in order to explain how the SWR is measured.

Any transmission line has a characteristic impedance, usually denoted Z0. If a transmission line is terminated with impedances that match Z0, a signal launched at one end will be completely absorbed at the other end, and no energy will be reflected back to the source. The voltage and/or current measured at any point along the line will be the same as any other point.

However, if a termination impedance is not matched to the transmission line, energy will be reflected back into the line, and this "reverse" signal will interfere with (add to or subtract from) the "forward" signal.

If the signal is a fixed-frequency sinewave, this interference will produce "standing waves" on the transmission line. This means that the measured voltage or measured current in the line will vary periodically with the distance from the impedance discontinuity. If the termination impedance is greater than Z0, there will be a voltage maximum at that point; if it is less, there will be a current maximum there.

The definition of "standing wave ratio" (SWR) is the ratio between the maximum voltage (or current) found at any point along the line to the minimum value found at any other point along the line. Sometimes the term VSWR is used to explicitly denote the voltage ratio. The value of this ratio is directly related to the ratio of Z0 to the termination impedance ZT. Specifically,

SWR = ZT/Z0, if ZT > Z0

SWR = Z0/ZT, if ZT < Z0

When a component or antenna is characterized with an SWR measurement, this is always specified with respect to a particular nominal transmission line impedance (usually 50Ω or 75Ω, depending on the intended application). This is just another way of stating how close the impedance of the device is to the nominal value.

• Isn't SWR always a real number? Can't Z_T / Z_0 be a complex number? Commented Dec 29, 2012 at 15:25
• Z_0 is real, but I suppose Z_T could be complex. What we're really interested in here is the magnitude of Z_T at the measurement frequency. The definition of SWR is not dependent on phase relationships. Commented Dec 29, 2012 at 15:38
• Z_0 does not have to be real any more then a load does, but we generally ignore how lossy our transmission line is. I feel like we are missing a magnitude being taken though. Commented Jan 1, 2013 at 1:34
• @Kortuk: If the line is that lossy, then SWR will not be constant along its length, and we're really starting to depart from the realm in which a simple measurement like SWR is at all useful. Commented Jan 1, 2013 at 2:19
• that statement is more for fun, but all lines are a little lossy, the important thing is magnitude, I think your equations should be taking it. Commented Jan 1, 2013 at 2:39

As Dave Tweed showed in his answer, standing wave ratio (SWR) is a way to characterize the quality of a load in an rf system. That is, it characterizes how closely a loading component matches the characteristic impedance of the system.

SWR can be specified in terms of the voltage or current signals on the transmission line, although most often we use the voltage, and then specifically refer to the VSWR.

The SWR gives similar information to the load impedance ZL or the reflection coefficient $\Gamma$ (also known as the s-parameter S11). However the SWR does not fully specify those parameters because while the load impedance and reflection coefficient are complex numbers, the SWR is a real number. The SWR value can be completely determined by the magnitude of the reflection coefficient (the phase of $\Gamma$ doesn't affect the SWR).

VSWR was used historically because it can be measured using by a simple manual method. An air-dielectric coaxial transmission line is used, with a slot in the outer conductor allowing a probe to be inserted to contact the center conductor. The probe is moved along the line to find the points of maximum and minimum signal amplitude, which of course immediately gives the VSWR. This technique is not used for coaxial lines today due to the availability of automated network analyzers, but it is still used in waveguide systems with a probe setup like this:

VSWR is often used to characterize rf components when we want to specify how well-matched they are as loads on a transmission line, without reference to whether they produce negative or positive reflections.

VSWR is also often used to characterize antennas, because its only needed to know the magnitude of the reflection to determine the fraction of the source power radiated from the antenna.