The no-gain property for networks containing three-terminal elements

Necessary and sufficient conditions are presented such that a three-terminal element is a "no-gain element," that is, such that any connected network containing that element, positive resistors, and independent sources, possesses the familiar no-voltage-gain and no-current-gain properties. The implications of the results are discussed, when applied to networks containing various three-terminal semiconductor devices such as bipolar transistors, field-effect transistors, and siliconcontrolled rectifiers. In particular, it is shown how one can establish that such elements are no-gain elements. Furthermore, it is shown that three-terminal elements are not no-gain elements as a consequence of their passivity, but rather, that the converse is in fact true. Finally, the nogain property is used to extend significantly an earlier result wherein the existence of solutions to the dc equations of certain classes of transistor circuits is proved.