Standing Waves in Transmission lines 

Standing waves are a key value for any system using transmission lines / feeders where measurements of the Voltage Standing Wave Ratio (VSWR) are important.


VSWR & Transmission Line Theory Tutorial Includes:
What is VSWR?     Reflection Coefficient     VSWR formulas & calculations     How to measure VSWR     How to use a VSWR meter     Simple SWR bridge circuit     What is return loss     VSWR / Return Loss Table    


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.

VSWR definition:

The voltage standing wave ratio, VSWR is defined as the ratio of the maximum to minimum voltage on a loss-less line.

Standing waves represent power that is not accepted by the load and reflected back along the transmission line or feeder.

Although standing waves and voltage standing wave ratio (VSWR) are very important, often the VSWR theory and calculations can mask a view of what is actually happening. Fortunately, it is possible to gain a good view of the topic, without delving too deeply into VSWR theory.

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.

Matched feeder and load are required for maximum power
          transfer
Matched feeder and load are required for maximum power transfer

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.

Power is reflected and sets up standing waves when feeder
          and load impedances do not match
Power is reflected when feeder and load impedances do not match

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.

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.

VSWR voltage and current patterns for small impedance
          mismatch
Voltage and current standing wave patterns for small impedance mismatch with load lower than feeder impedance

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.

VSWR voltage and current patterns for a short circuit
Voltage and current standing wave patterns for short circuit feeder termination

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.

VSWR voltage and current patterns for small impedance
          mismatch with load impedance higher than feeder impedance
Voltage and current standing wave patterns for small impedance mismatch with load higher than the feeder impedance

Then when there is an open circuit placed at the end of the line, the standing wave pattern for the feeder is similar to that of the short circuit, but with the voltage and current patterns reversed.

VSWR voltage and current patterns for a open circuit
Voltage and current standing wave patterns for open circuit feeder termination

Copy from: https://www.electronics-notes.com/articles/antennas-propagation/vswr-return-loss/what-is-vswr.php