Transmission matrix stability criterion

Abstract

AMONG THE methods for predetermining the stability of networks—that is, whether or not self-sustained oscillations may exist—the Barkhausen and Nyquist criteria often are applied to those configurations employing electron-tube amplifiers for which a principal closed transmission loop may be delineated. In these networks the concept of “retroaction” or feedback is useful, since this provides a mental picture of a signal progressing unidirectionally through the electron tube, the feedback network, back to the tube input, and so on. It also leads to a simple scheme for computing the ratio (often denoted by μβ) of output to input voltage for the open transmission loop, upon which the stability of the network apparently rests. However, these criteria are limited to unilaterally transmitting networks, and the determination of μβ must be made, in effect, with the transmission loop cut at zero admittance grid-cathode terminals of an electron tube.