Derivations of transfer functions from physical insight

K. Hwu, Wen-Zhuang Jiang, Y. Yau
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Abstract

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.
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从物理角度推导传递函数
在电力电子学中,需要补偿器来塑造传递函数的回路增益。整形环路增益传递函数的目的是获得期望的交叉频率、相位裕度和增益裕度。补偿器可由运算放大器(运放)构成。有几个常用的补偿器建立的运放,在这里讨论。采用不同的电阻和电容连接方式,可以得到不同的传递函数。对于补偿器传递函数的求导,传统的方法是使用代数计算。因此,如果补偿器由许多电阻和电容组成,计算过程将变得更加复杂。在这封信中,提出了一种物理洞察方法来推导补偿器的传递函数。采用该方法,补偿器传递函数的求导速度更快。
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