Plant Transfer Functions of All the Topologies

Let us discuss the three major topologies separately here. Note that we are assuming voltage mode control and continuous conduction mode. Further, the ESR zero is also not included here (introduced later). 

The transfer function of the plant is also called the control-to-output transfer function  

The control-to-output transfer function is a product of the transfer functions of the PWM, the switch and the LC filter (since these are cascaded stages). Alternatively, the control-to-output transfer function is a product of the transfer functions of the PWM stage and the transfer function of the power stage . 

The question really is — what happens to the output when we perturb the duty cycle slightly (keeping the input to the converter, Vin, constant) Here are the steps for a buck  

And this is the required transfer function of the intermediate duty-cycle-to-output stage  

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