Limiting values of impedances and transfer functions

IN DESIGNING electrical circuits it is often important to know the bounds of the magnitude and phase of impedance networks. For example, it is necessary to know impedance variations when designing devices to drive these networks. The effect of variations on gain and phase of transfer functions is particularly important in closed loop servo systems for stability considerations. A method is suggested which will determine precisely the effect of component tolerances and frequency variations on the magnitude and phase of transfer functions. Conversely, allowable tolerances can be set on these quantities.