Standing wave ratio

The standing wave ratio (SWV) and also known as ripple ( English standing wave ratio , SWR) is an expression in the field of communications engineering and high frequency technology for the correspondence of the line wave resistance with the impedance of a load connected to this line. If the line impedance deviates from the impedance of the load, a transmitted wave is reflected at the transition point and a reflected wave is formed. The superposition of the two waves, the forward wave ( V ) and the returning wave ( R ), forms a so-called standing wave along the line and the ratio of the forward and backward waves on almost lossless lines describes the standing wave ratio.

In this context, a line can be implemented in different physical ways. For example, it can be an electrical line such as a coaxial cable or ribbon cable , or a waveguide or another suitable waveguide . The wave size on an electrical line is usually the electrical voltage ; in the English-language specialist literature, the standing wave ratio is therefore also synonymous with English voltage standing wave ratio , VSWR . However, depending on the reference, any other physical wave quantity, such as the electric current in the line or the electric field strength in a waveguide, can also be understood in this sense.

Without reflection, when the line terminates with its line impedance, the standing wave ratio is 1. The entire power fed in by the wave is transmitted to the termination of the line. This case is also known as power adjustment. If the line is short-circuited or open, the incoming wave is completely reflected, and the standing wave ratio is then infinite. No power is transmitted, but the wave is completely reflected.

Superposition (red) of a wave advancing to the right (blue) and a wave reflected to the left (green). Part of the forward wave is transmitted to the right (blue). The SWR is 4.

Historical

Experimental set-up from 1888 developed by the physicist Ernst Lecher to measure wavelengths and frequencies.

Shortly after the detection of electromagnetic waves by Heinrich Hertz discovered Ernst Lecher that the voltage between the two longer, parallel wires by a Hertzian oscillator are fed, is not the same everywhere. This test arrangement became known as the so-called Lecher line . If the power is high enough, Geissler tubes can be approached at periodic intervals of λ / 2 to measure maximum voltage differences U _max . The voltage is zero exactly in the middle, which is why you can short-circuit both lines there without any problems.

The wavelength of the original measurements should have been 1 m and corresponds to today's VHF range ; In the following years it was proven that the laws discovered apply unchanged to all other wavelength ranges. With this arrangement it was later discovered that this “mid-voltage” is no longer zero, but rather assumes a minimum value U _min if the end of the line is loaded with an ohmic resistance. By choosing a certain value of this load resistance it can even be achieved that U _max  =  U _min . This value of the resistance is called the line impedance and in this case there is no reflection.

General

Different standing waves (SWR = 4, 2, 9). The envelope represents the measurable voltage curve along the line

If the standing wave ratio is greater than 1, the stationary wave causes a standing wave to occur on the line that is assumed to be approximately lossless, and fixed maximum and minimum values ​​of the wave size are formed in the line depending on the wavelength along the line Reference of the electrical voltage. The maxima are repeated with half the wavelength, as are the minima as shown graphically on the enveloping curve shape for three standing wave ratios with SWR = 4, 2, 9 in the adjacent figure. It can be seen that the closer the SWR is to 1, the smaller the difference between the maximum and minimum amplitudes of the wave size.

From this follows the definition of the standing wave ratio as the relation between the maximum voltage value and the minimum voltage value along the line: ${\displaystyle {\text{SWR}}}$

${\displaystyle {\text{SWR}}={\frac {U_{\text{max}}}{U_{\text{min}}}}={\frac {|U_{\text{V}}|+|U_{\text{R}}|}{|U_{\text{V}}|-|U_{\text{R}}|}}}$

${\displaystyle U_{\text{max}}}$Designates the maximum electrical voltage that can be measured at a certain point on the line, the minimum electrical voltage at a distance of a quarter of a wavelength . The two expressions and are equivalent for the forward and reverse voltage wave. It can be seen that the value of the point stress maxima with a standing wave ratio of ∞ is twice the amount compared to the adjusted case with a standing wave ratio of 1. With a standing wave ratio of 1, the voltage along the line has the same absolute value everywhere. ${\displaystyle U_{\text{min}}}$ ${\displaystyle U_{\text{V}}}$ ${\displaystyle U_{\text{R}}}$

Equivalent to this, the SWR can also be expressed in terms of the power transported by the forward ( ) or backward ( ) waves as: ${\displaystyle P_{\text{V}}}$ ${\displaystyle P_{\text{R}}}$

${\displaystyle {\text{SWR}}={\frac {{\sqrt {P_{\text{V}}}}+{\sqrt {P_{\text{R}}}}}{{\sqrt {P_{\text{V}}}}-{\sqrt {P_{\text{R}}}}}}}$

The relationship with the reflection factor , which corresponds to the scattering parameter , is given as: ${\displaystyle \Gamma }$ ${\displaystyle s_{11}}$

${\displaystyle {\text{SWR}}={\frac {1+|\Gamma |}{1-|\Gamma |}}={\frac {1+|s_{11}|}{1-|s_{11}|}}}$

and

${\displaystyle |\Gamma |={{\text{SWR}}-1 \over {\text{SWR}}+1}}$.

The reciprocal of the standing wave ratio is called the adjustment factor: ${\displaystyle m}$

${\displaystyle m={\frac {1}{\text{SWR}}}={\frac {1-|\Gamma |}{1+|\Gamma |}}}$

The adaptation factor, the name is derived from antenna technology , is 1 if the antenna feed line is perfectly matched to the antennas. The adjustment factor is 0 when the supply line is open or short-circuited.

The return loss is an expression for the attenuation between the forward and the reflected backward traveling wave and is usually expressed as a logarithmic relation in dB as: ${\displaystyle a}$

${\displaystyle a_{\text{dB}}=20\cdot \log \left({\frac {1}{|\Gamma |}}\right)=20\cdot \log \left({\frac {{\text{SWR}}+1}{{\text{SWR}}-1}}\right)}$

Measurements

→ Main article : Standing wave measuring device

Standing wave measuring device when displaying an SWR just above 1

The standing wave ratio can be measured with a standing wave measuring device. A common use of the standing wave measurement is the energiser a transmitting antenna and the matching of the transmit feed line to the impedance of the antenna. The standing wave ratio can have the following values:

• SWR equals 1: In this ideal case, there is no reflection, there is power adjustment. The antenna impedance is exactly the same as the line impedance.
• SWR just above 1: Practically achievable in many cases and is available, for example, after a comparison. The alignment of an antenna feed line to the antenna is carried out in larger transmitter systems in a separate transmitter building . Voltages and currents differ only slightly at different points on the antenna feed line.
• SWR well above 1: A bad SWR means that the line impedance differs significantly from the value of the antenna's impedance. Only a small part of the power fed in by the transmitter output stage is radiated via the antenna, the majority of the power is reflected and, without protective measures, can lead to thermal destruction of the transmitter system. Voltages and currents differ greatly at different points on the line.
• SWR equal to ∞. If the line end is open or short-circuited and the antenna is missing, the power is completely reflected. No service can be transferred. For operation without a transmission antenna, for example in the context of experiments, the transmission feed line is therefore terminated with a substitute load .

literature

• Otto Zinke , Heinrich Brunswig: High Frequency Technology 1: High Frequency Filters, Lines, Antennas . 6th edition. Springer, 1999, ISBN 978-3-540-66405-5 .
• Alois Krischke, Karl Rothammel: Rothhammels Antennenbuch . 13th edition. DARC Verlag, Berlin, ISBN 978-3-88692-065-5 , Chapter 5.8: Processes on lines.

Web links

• Construction of an SWR meter

Individual evidence

1. ^ Sophocles J. Orfanidis: Electromagnetic Waves and Antennas . Ed .: ECE Department, Rutgers University. 2016, Chapter 11.12: Standing Wave Ratio ( Online ).
2. ↑ Video of a voltage scan