Editing Waveguide (section)

=== Impedance matching ===
In [[circuit theory]], the [[Electrical impedance|impedance]] is a generalization of [[Electrical resistance and conductance|electrical resistance]] in the case of [[alternating current]], and is measured in [[ohm]]s (<math>\Omega</math>).{{sfn|Balanis|1989}}  A waveguide in circuit theory is described by a [[transmission line]] having a length and [[characteristic impedance]].{{sfn|Marcuvitz|1951}}{{rp|2–3,6–12}}{{sfn|Beranek|Mellow|2012|loc=[https://www.sciencedirect.com/topics/physics-and-astronomy/acoustic-impedance#:~:text=The%20characteristic%20impedance%20is%20the,medium%20(%CF%810c) Characteristic Impedance]}}{{rp|14}}{{sfn|Khare|Nema|2012}} In other words, the impedance indicates the ratio of voltage to current of the circuit component (in this case a waveguide) during propagation of the wave. This description of the waveguide was originally intended for alternating current, but is also suitable for electromagnetic and sound waves, once the wave and material properties (such as [[pressure]], [[density]], [[dielectric constant]]) are properly converted into electrical terms ([[Electric current|current]] and impedance for example).{{sfn|Beranek|Mellow|2012|loc=[https://www.sciencedirect.com/topics/physics-and-astronomy/acoustic-impedance#:~:text=is%20defined Pressure and density effects]}}{{rp|14}}

[[Impedance matching]] is important when components of an electric circuit are connected (waveguide to antenna for example): The impedance ratio determines how much of the wave is transmitted forward and how much is reflected. In connecting a waveguide to an antenna a complete transmission is usually required, so an effort is made to match their impedances.{{sfn|Khare|Nema|2012}}

The [[reflection coefficient]] can be calculated using: <math>\Gamma=\frac{Z_2-Z_1}{Z_2+Z_1}</math>, where <math>\Gamma</math> (Gamma) is the reflection coefficient (0 denotes full transmission, 1 full reflection, and 0.5 is a reflection of half the incoming voltage),  <math>Z_1</math> and <math>Z_2</math> are the impedance of the first component (from  which the wave enters) and the second component, respectively.{{sfn|Zhang|Krooswyk|Ou|2015|loc=[https://www.sciencedirect.com/topics/computer-science/reflection-coefficient#:~:text=fundamentals Reflection coefficient]}}

An impedance mismatch creates a reflected wave, which added to the incoming waves creates a standing wave. An impedance mismatch can be also quantified with the [[standing wave ratio]] (SWR or VSWR for voltage), which is connected to the impedance ratio and reflection coefficient by: <math>\mathrm{VSWR}=\frac{|V|_{\rm max}}{|V|_{\rm min}}=\frac{1+|\Gamma|}{1-|\Gamma|}</math>, where <math>\left|V\right|_{\rm min/max}</math> are the minimum and maximum values of the voltage [[absolute value]], and the VSWR is the voltage standing wave ratio, which value of 1 denotes full transmission, without reflection  and thus no standing wave, while very large values mean high reflection and standing wave pattern.{{sfn|Khare|Nema|2012}}