Theoretical investigation on the effect of individual stage-gain selection on the 3-dB bandwidth of three-op-amp difference amplifiers

The differential gain of a three-op-amp difference amplifier is determined by the product of the gain values of its two stages. Usually, the total desired differential gain is assigned to the first stage while the gain of the second stage is set to unity in order to achieve higher common mode rejection ratio (CMRR) values. On the other hand, the effect of this choice on the frequency response of the amplifier is not fully understood. For this purpose, this paper presents a theoretical study on the influence of gain choice for the first and second stages of the amplifier on its 3-dB bandwidth. To achieve this, the closed-loop transfer function of the amplifier is derived while considering the effect of the finite open-loop gain and bandwidth of the op-amps used to implement this type of amplifier. The equations presented here demonstrate that the 3-dB bandwidth is increased considerably when the gain of the first stage is reduced and that of the second stage is raised while keeping the value of the total differential gain constant. Although this happens at the expense of CMRR, designers of this type of amplifier should consider the tradeoff between the two.