Error analysis in Miller's theorems

Miller's theorems are important tools to analyze amplifiers with feedback, and also to analyze the oscillation conditions of analog oscillators. The rigorous application of Miller's theorems depends on the previous knowledge of the closed-loop gain which, in turn, allows the calculation of the closed-loop input impedance/admittance. However, this gain is usually not known a priori, and the use of the open-loop gain to estimate the closed-loop gain is frequently found in the literature. This approximation is not always valid. Hence, we present a rigorous analysis of the error associated to this approach.