Derivations of transfer functions from physical insight

In power electronics, the compensators are required to shape the loop gain of the transfer function. The purpose of shaping the loop gain transfer function is to obtain a desired crossover frequency, phase margin and gain margin. The compensators can be constructed by the operational amplifier (op amp). There are a few commonly used compensators built up by the op amp, to be discussed herein. By using different connections of the resistors and capacitors, different transfer functions can be obtained. For derivation of the transfer functions of the compensators, the traditional method is to use algebra calculation. Thus, the calculation process will become more complicated if the compensator consists of many resistors and capacitors. In this letter, a physical insight method is proposed to derive the transfer functions of the compensators. With the proposed method, the derivation of the transfer functions of the compensators is faster.