Analysis of Non-ideal Amplifiers

In the formula, Ao is the open-loop gain of the amplifier; β is the feedback coefficient. People who have studied feedback system or servo system theory should be familiar with this expression. The closed-loop gain expression of the inverting amplifier shown in the figure is as follows:

In both cases, the feedback factor represents the portion of the output that is fed back to the input and is given by:

Consider 1 + Aoβ, which corresponds to the denominator in the closed-loop gain expression. The open-loop gain of a real op amp is neither infinite nor real (zero phase shift), and the magnitude and phase of Ao are functions of frequency.

To prevent oscillation, the open-loop gain of the amplifier is required to be bandwidth-limited. Below this frequency, the product Aoβ is less than 1, and the phase shift of the amplifier reaches 180°. This can be achieved by turning the gain from the low-frequency end and then continuing to attenuate at 6dB/octave. This stabilization technique is called "frequency correction." It is obvious from the closed-loop gain formula that for links with high closed-loop gain factors, reducing β makes the required frequency correction smaller. In contrast, the voltage follower requires the greatest correction, and an amplifier that can be stable at unity gain is called "unity gain stable."