Standing waves are an important issue when looking at feeders / transmission lines, and the standing wave ratio or more commonly the voltage standing wave ratio, VSWR is as a measurement of the level of standing waves on a feeder.
Standing waves represent power that is no accepted by the load and reflected back along the transmission line or feeder.
Standing wave basics
When looking at systems that include transmission lines it is necessary to understand that sources, transmission lines / feeders and loads all have a characteristic impedance. 50Ω is a very common standard for RF applications although other impedances may occasionally be seen in some systems.
In order to obtain the maximum power transfer from the source to the transmission line, or the transmission line to the load, be it a resistor, an input to another system, or an antenna, the impedance levels must match.
In other words for a 50Ω system the source or signal generator must have a source impedance of 50Ω, the transmission line must be 50Ω and so must the load.
Issues arise when power is transferred into the transmission line or feeder and it travels towards the load. If there is a mismatch, i.e. the load impedance does not match that of the transmission line, then it is not possible for all the power to be transferred.
As power cannot disappear, the power that is not transferred into the load has to go somewhere and there it travels back along the transmission line back towards the source.
When this happens the voltages and currents of the forward and reflected waves in the feeder add or subtract at different points along the feeder according to the phases. In this way standing waves are set up.
The way in which the effect occurs can be demonstrated with a length of rope. If one end is left free and the other is moved up an down the wave motion can be seen to move down along the rope. However if one end is fixed a standing wave motion is set up, and points of minimum and maximum vibration can be seen.
Looking at standing waves from the viewpoint of current and voltage we see that if the load impedance does not match that of the feeder a discontinuity is created. The feeder wants to supply a certain voltage and current ratio (according to its impedance). The load must also obey ohms law and if it has a different impedance it cannot accept the same voltage and current ratio. To take an example a 50Ω feeder with 100 watts entering, it will have a voltage of 70.7 volts and a current of 1.414 amps. A 25Ω load would require a voltage of 50 volts and a current of 2 amps to dissipate the same current. To resolve this discontinuity, power is reflected and standing waves are generated.
When the load resistance is lower than the feeder impedance voltage and current magnitudes are set up. Here the total current at the load point is higher than that of the perfectly matched line, whereas the voltage is less.
The values of current and voltage along the feeder vary along the feeder. For small values of reflected power the waveform is almost sinusoidal, but for larger values it becomes more like a full wave rectified sine wave. This waveform consists of voltage and current from the forward power plus voltage and current from the reflected power.
At a distance a quarter of a wavelength from the load the combined voltages reach a maximum value whilst the current is at a minimum. At a distance half a wavelength from the load the voltage and current are the same as at the load.
A similar situation occurs when the load resistance is greater than the feeder impedance however this time the total voltage at the load is higher than the value of the perfectly matched line. The voltage reaches a minimum at a distance a quarter of a wavelength from the load and the current is at a maximum. However at a distance of a half wavelength from the load the voltage and current are the same as at the load.
Voltage standing wave ratio VSWR
It is often necessary to have a measure of the amount of power which is being reflected.
This is particularly important where transmitters are used because the high current or voltage values may damage the feeder if they reach very high levels, or the transmitter itself may be damaged. The figure normally used for measuring the standing waves is called the standing wave ratio, SWR, and it is a measure of the maximum to minimum values on the line. In most instances the voltage standing wave ratio, VSWR, is used.
The standing wave ratio is a ratio of the maximum to minimum values of standing waves in a feeder.
The reflection coefficient, ρ is defined as the ratio of the reflected current or voltage vector to the forward current or voltage.
It is more common to use the voltage measurement, and therefore the voltage standing wave ratio, VSWR can be expressed as:
From this it can be seen that a perfectly matched line will give a ratio of 1:1 whilst a completely mismatched line gives infinity:1. Although it is perfectly possible to quote VSWR values of less than unity, it is normal convention to express them as ratios greater than one.
Even though the voltage and current vary along the length of the feeder, the amount of power remains the same if losses are ignored. This means that the standing wave ratio remains the same along the whole length of the feeder. Often the forward and reflected power may be measured. From this it is easy to calculate the reflection coefficient as given below:
Pref = reflected power
Pfwd = forward power
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