The Generalized Transmission Matrix Stability Criterion
- 1 July 1951
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Transactions of the American Institute of Electrical Engineers
- Vol. 70 (1) , 292-298
- https://doi.org/10.1109/t-aiee.1951.5060404
Abstract
A generalized criterion for stability of a closed tandem connection of double-dinodes is given by the expression A(λ) = a11+a22-|a|-1 = 0 in which the a11 are the appropriate terms of the transmission matrix of the tandem net-work prior to closing the loop. If the λ-roots of A(λ) have positive real parts, the closing the transmission loop; that is, the network is unstable. The generalized criterion is applicable to transmission loops incorporating bilateral amplifiers, and the transmission loop may be opened wherever desired without con-sideration of the impedances to the left and right of the cut. The criterion is not limited to transmission networks employing amplifiers; like-wise, it applies equally well to electro-mechanical networks or servomechanisms.Keywords
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