Reciprocity Relations in Active 3-Terminal Elements

A vacuum-tube or a transistor, operating linearly under small-signal conditions, may be represented as a resistive (i.e., non-reactive) 3-terminal network element. Such an element may be considered as composed of a tri-angle of resistors and a 3-terminal gyrator. If the element is active, at least one of the resistors is negative. The activity or passivity of the element is shown to be dependent on the three resistors, while the reciprocity relation is obeyed or violated according to whether the gyrator is absent or present, respectively. It is also shown that an active 3-terminal element cannot obey reciprocity and remain stable, so that the gyrator has a stabilizing effect. Some general relations are derived concerning three-terminal active elements. These relations apply to any active element that is described by a 3-terminal resistive network, without regard to the physical principles underlying its operation.