Master equation for operational amplifiers: Stability of negative differential converters, crossover frequency and pass-bandwidth

Abstract

The time dependent master equation from the seminal article by Ragazzini, Randall and Russell [J. R. Ragazzini, R. H. Randall and F. A. Russell, "Analysis of Problems in Dynamics by Electronic Circuits", Proc. of the I.R.E. , 35, pp. 444-452, (1947)] is recovered as necessary tool for the analysis of contemporary circuits with operational amplifiers. This equation gives the relation between time dependent the output voltage U0(t) and the difference between the input voltages (U+(t) and U−(t)). The crossover frequency f0 is represented the time constant τ 0 of this equation. The work of the master equation is illustrated by two typical examples: a) the stability criterion of the devices with negative impedance converters, which we consider as a new result b) the frequency dependence of the amplifiers with operational amplifiers given in the technical specifications without citations of time dependent equation. A simple circuit for determination of f0 is suggested and the method is illustrated by determination of crossover frequency for the low-noise and high speed ADA4898 operational amplifier. It is concluded that for an exact calculation of the pass bandwidth of amplifiers with active filters the 70 years old master equation is a useful technique implicitly included in the contemporary software. The frequency dependent formulae for the amplification coefficient of inverting and non-inverting amplifiers are given for the case of non-zero conductivity between the inputs of the operational amplifiers.

The Day of the Inductance. Problem of the 7-th Experimental Physics Olympiad, Skopje, 7 December 2019

“…Introduction: The equaling of the potentials at the input of the operational amplifier is only a low frequency approximation known as golden rule for the operational amplifiers. In the general case we have the relation 13 between the input and output voltages…”