# matching

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## matching

(impedance matching) Arranging electrical impedances so that maximum power is transferred from one device to another. This occurs when the input impedance of one device equals the output impedance of the other to which it is connected. See also feeder.## Matching

## Matching

in electrical circuit design, the practice that ensures the transmission of electromagnetic energy and signals with the lowest possible reflection factor, signal loss, and distortion. Matching consists in the proper choice of impedances for the source, transmission line, and load. Line and load are ideally matched when the characteristic impedance of the transmission line p is equal to the impedance of the load *Z*_{l} = R_{l} + *jX*_{l} or when *R*_{l} = ρ and *X*_{l} = 0, where *R*_{l} is the active part of the impedance and *X*_{l} is the reactive part. Under these circumstances, traveling waves characterized by a standing-wave ratio of unity are established in the transmission line.

For lines with negligibly small electrical losses, matching—and, consequently, the maximum effective transfer of energy from the source to the load—is achieved when the impedance of the source *Z*_{s} and the load *Z*, are complex conjugates, that is, when or *R*_{s} = ρ = *R*_{l} and *X*_{s} = – *X*_{l}. In this case, the reactive impedance of the circuit is zero, and the conditions for resonance are satisfied. Such conditions enable electrical systems to operate with better efficiency, for example, with improved use of frequency ranges, better interference rejection, and reduced frequency distortion of radio signals.

Matching is especially important in microwave engineering, where it can be achieved by means of the following: impedance-matching transformers, such as stubs or dielectric sleeves inserted in the transmission line or sections of transmission lines with specially chosen characteristic impedances and lengths; various matching devices that compensate the reactive components of the impedance, such as stubs, phase shifters, and irises, placed in the transmission line; absorbing loads; directional couplers; and various devices for converting from one mode of transmission to another, such as coaxial-waveguide couplers, baluns, and flexible and rotating connections.

The degree of matching can be assessed by measuring the reflection factor and the standing-wave ratio. In practice, matching is considered optimum when the standing-wave ratio in the chosen frequency range does not exceed 1.2 or 1.3 (1.05 for measuring instruments). In some cases, the response of source parameters, such as frequency, power, and noise level, to changes in load, the occurrence of electrical breakdowns in the line, and heating in some sections of the line can serve as indirect indicators of matching.

### REFERENCES

*Fizicheskie osnovy elektrotekhniki*. Edited by K. M. Polivanov. Moscow-Leningrad, 1950.

Valitov, R. A., and V. N. Sretenskii.

*Radiotekhnicheskie izmereniia*. Moscow, 1970.

Lebedev, I. V.

*Tekhnika i pribory SVCh*, 2nd ed., vol. 1. Moscow, 1970.

Gonorovskii, I. S.

*Radiotekhnicheskie tsepi i signaly*, 2nd ed. Moscow, 1971.

V. N. SRETENSKII