The Perfect Gain Control

Perfect gain control is achieved when variation of an adjustable immittance affects only the magnitude of a specific network function. The adjustable immittances considered are those which can range between an open and short circuit, and for which the network function has finite values at these extreme points. It is shown that an adjustable element of this type behaves as a perfect gain control if 1) its immittance is proportional to the Th6venin immittance seen from its terminals looking into the network, and 2) the network function with the adjustable element open is proportional, but not equal, to the network function with the adjustable element short-circuited. For instance, a resistance can only act as a perfect gain control if the Thévenin immittance is resistive, and the ratio of the value of the network function when the variable resistance is zero to its value when the variable resistance is open is a real constant other than unity.