Waveguide - A Sketch of The Theoretical Analysis - Impedance Matching

Impedance Matching

In circuit theory, the impedance is a generalization of electrical resistivity in the case of alternating current, and is measured in ohms . A waveguide in circuit theory is described by a transmission line having a length and self impedance. In other words the impedance is the resistance of the circuit component (in this case a waveguide) to the 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 (current and impedance for example).

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 that their impedances are matched.

The reflection coefficient can be calculated using:, where is the reflection coefficient (0 denotes full transmission, 1 full reflection, and 0.5 is a reflection of half the incoming voltage), and are the impedance of the first component (from which the wave enters) and the second component, respectively.

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:, where 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.

Read more about this topic:  Waveguide, A Sketch of The Theoretical Analysis

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