Belevitch's theorem

The theorem of Belevitch (English Belevitch 's theorem ) is a by Vitold Belevitch named and used in the electrical circuit theory theorem to determine whether a given S- matrix of a two-port network is basically lossless and rationally realized.

Lossless means in this context that the two-port network can be realized inside only by ideal capacitors and coils without lossy ohmic resistors. Rational means that only rational functions are used to describe the S- matrix. Implicit is set so that the two-port devices only focused occur ( discrete components ) in the form of capacitors and coils.

General

The given S- matrix of a two-port network of degree is in the form:

With the complex frequency, the steady Zuständ reduces to, with the angular frequency. The degree is in existence, the number of contained in the two-port network concentrated capacitors and coils on.

The theorem of Belevitch now states that such, lossless two-port network and rational if and only exists when the S- matrix can be represented in the following form:

With the following conditions:

For everyone.