# 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

Used to describe the arrangement of timber veneers, such as book-matching, slip-matching and quarter-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 Zl = Rl + jXl or when Rl = ρ and Xl = 0, where Rl is the active part of the impedance and Xl 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 Zs and the load Z, are complex conjugates, that is, when or Rs = ρ = Rl and Xs = – Xl. 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

## matching

[′mach·iŋ]
(computer science)
A computer problem-solving method in which the current situation is represented as a schema to be mapped into the desired situation by putting the two in correspondence.
(electricity)
Connecting two circuits or parts together with a coupling device in such a way that the maximum transfer of energy occurs between the two circuits, and the impedance of either circuit will be terminated in its image.
(mathematics)
A set of edges in a graph, no two of which have a vertex in common. Also known as independent edge set.
The bringing of two or more signals or indications into suitable position or condition preliminary to making a measurement, as on a loran indicator or a sky compass.

## matching

matching, 2
A system of matchboards, or of sheets of wood veneer, arranged to emphasize grain pattern, as in book matching or herringbone matching.
References in periodicals archive ?
We show that if P is in convex position, [n/2] plane matchings can be packed into K(P); this bound is tight.
Theorem 3 For any set P of n points in convex position in the plane, with n even, the maximum number of plane matchings that can be packed into K(P) is [n/2].
Therefore, the number of plane matchings that can be packed into K(P) is at most [n/2].
Now we show how to pack [n/2] plane matchings into K(P).
Theorem 4 For a set P of n [greater than or equal to] 6 points in the regular wheel configuration in the plane with n even, the maximum number of plane matchings that can be packed into K(P) is [n/2] - 1.
Now we show how to pack [n/2] - 1 plane matchings into K(P).
The matchings in M are plane and pairwise edge-disjoint.
Thus, if M denotes any set of plane matchings which can be packed into K(P),we have (note that |X| is odd)
In this section we consider the problem of packing plane matchings for point sets in general position (no three points on a line) in the plane.
Recall that M(P) denotes the maximum number of plane matchings that can be packed into K(P).
4] and Perles (see [29]) showed that by removing any set of at most n/2 - 1 edges from K(P), the resulting graph has a plane perfect matching.
Thus, one may think if the removed edges are disjoint, it may be possible to remove more than n/2 - 1 edges while the resulting graph has a plane perfect matching.

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