The Generalized Transmission Matrix Stability Criterion

A generalized criterion for stability of a closed tandem connection of double-dinodes is given by the expression A(¿) = 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 ¿-roots of A(¿) 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.