Standing wave ratio

Impedance mismatches result in standing waves along the transmission line, and SWR is defined as the ratio of the partial standing wave's amplitude at an antinode (maximum) to the amplitude at a node (minimum) along the line.

In practice most transmission lines used in these applications are coaxial cables with an impedance of either 50 or 75 ohms, so most SWR meters correspond to one of these.

By measuring the magnitude of the impedance mismatch at the transmitter output it reveals problems due to either the antenna or the transmission line.

This especially applies to transmission lines connecting radio transmitters and receivers with their antennas, as well as similar uses of RF cables such as cable television connections to TV receivers and distribution amplifiers.

The easiest way of achieving this, and the way that minimizes losses along the transmission line, is for the imaginary part of the complex impedance of both the source and load to be zero, that is, pure resistances, equal to the characteristic impedance of the transmission line.

The source then sees a different impedance than it expects which can lead to lesser (or in some cases, more) power being supplied by it, the result being very sensitive to the electrical length of the transmission line.

For instance, if there is a perfect match between the load impedance Zload and the source impedance Zsource = Z*load, that perfect match will remain if the source and load are connected through a transmission line with an electrical length of one half wavelength (or a multiple of one half wavelengths) using a transmission line of any characteristic impedance Z0.

This condition (Zload = Z0) also means that the load seen by the source is independent of the transmission line's electrical length.

So in practice, a good SWR (near 1:1) implies a transmitter's output seeing the exact impedance it expects for optimum and safe operation.

At some points along the line the forward and reflected waves interfere constructively, exactly in phase, with the resulting amplitude

Note that the phase of Vf and Vr vary along the transmission line in opposite directions to each other.

Since the power of the forward and reflected waves are proportional to the square of the voltage components due to each wave, SWR can be expressed in terms of forward and reflected power: By sampling the complex voltage and current at the point of insertion, an SWR meter is able to compute the effective forward and reflected voltages on the transmission line for the characteristic impedance for which the SWR meter has been designed.

In the special case of a load RL, which is purely resistive but unequal to the characteristic impedance of the transmission line Z0, the SWR is given simply by their ratio: with the ratio or its reciprocal is chosen to obtain a value greater than unity.

According to the superposition principle the net voltage present at any point x on the transmission line is equal to the sum of the voltages due to the forward and reflected waves: Since we are interested in the variations of the magnitude of Vnet along the line (as a function of x), we shall solve instead for the squared magnitude of that quantity, which simplifies the mathematics.

To obtain the squared magnitude we multiply the above quantity by its complex conjugate: Depending on the phase of the third term, the maximum and minimum values of Vnet (the square root of the quantity in the equations) are

Depending on the location of the load and phase of reflection, there might be a peak in the magnitude of Vnet at x = 1.3 m .

The most common case for measuring and examining SWR is when installing and tuning transmitting antennas.

The impedance of a particular antenna design can vary due to a number of factors that cannot always be clearly identified.

For a frequency of 3.5 MHz, with that antenna fed through 75 meters of RG-8A coax, the loss due to standing waves would be 2.2 dB.

[5](pp19.4–19.6) Thus, a better match of the antenna to the feed line, that is, a lower SWR, becomes increasingly important with increasing frequency, even if the transmitter is able to accommodate the impedance seen (or an antenna tuner is used between the transmitter and feed line).

Analog TV can experience "ghosts" from delayed signals bouncing back and forth on a long line.

FM stereo can also be affected and digital signals can experience delayed pulses leading to bit errors.

[8] The common type of SWR / power meter used in amateur operation may contain a dual directional coupler.

Other types use a single coupler which can be rotated 180 degrees to sample power flowing in either direction.

Unidirectional couplers of this type are available for many frequency ranges and power levels and with appropriate coupling values for the analog meter used.

The forward and reflected power measured by directional couplers can be used to calculate SWR.

Bridge circuits can be used to directly measure the real and imaginary parts of a load impedance and to use those values to derive SWR.

[9] Stand alone antenna analyzers use various measuring methods and can display SWR and other parameters plotted against frequency.

Thus the terms PSWR and Power Standing Wave Ratio are deprecated and should be considered only from a legacy measurement perspective.

In microwave electrosurgery an antenna that is placed directly into tissue may not always have an optimal match with the feedline resulting in an SWR.