A method for obtaining the transfer function of inverting and non-inverting op-amp circuits based on classical feedback theory

Abstract

This paper presents an alternate approach for deriving the transfer function (gain, bandwidth) for both inverting and non-inverting Op-amp circuits. The approach uses classical feedback theory, in which the Op-amp circuit is represented in terms of its corresponding closed-loop, (feedback) block diagram. The characteristics of the Op-amp (open-loop), together with the equivalent transfer function of the accompanying circuit components, are incorporated into the classical, general feedback block diagram. The equivalent transfer functions (pre-filter and feedback) are obtained by means of superposition. Then, all the blocks are reduced into a single transfer function by means of the simplification formula: P(s)G(s)/(1+G(s)H(s)). The resulting transfer function shows the gain for each configuration (-R F/R A for the inverting Op-amp and 1+R F/R A for the non-inverting configuration) and bandwidth. It also shows that the Gain*Bandwidth product is constant for the non-inverting configuration, but not so for the inverting configuration. This approach is straightforward and insightful, specially for those students who have previously been exposed to feedback theory and who have backgrounds in fields other than electronics.