The precise theoretical limits of causal Darlington synthesis

Abstract

where Xi is a passive circuit element (a resistor or a capacitor) of the three-terminal RC network, 4 is the phase function of r(&), and 112 is the total number of like elements (resistors or capacitors) of the three-terminal network. The sensitivity of T( jm) to the gain of the amplifier has been utilized here in controlling the gain constant of the all-pass function realized. It is seen from (15b) and (15~) that for the network sensitivities to n and the passive elements xi to be low, the ratio n/K’ must be small. For the all-pass realization, the minimum value of the ratio n/K’ may be seen to be unity for which