Buck converter controller design

This is the Buck converter with feedback loop.

source: Fundamentals of Power electronics by Erickson and Maksimovic

In this circuit, Vm is set to be 4V. However, in general, in a converter design, how can we determine the value of Vm? Thanks.

• I don't understand those control theory diagrams enough to help, but I did find this free course video that appears to go through the design of the whole control circuit.
– K H
Commented Jan 30, 2021 at 3:04

If you look at this diagram you see that the block you mention models the pulse width modulator (PWM) stage. It is the circuit that converts the dc control voltage coming out from the error amplifier into a switching pattern affected by a duty ratio $$\D\$$. This block is made of a simple comparator fed by a voltage ramp on one input and the setpoint imposed by the error amp on the other side:
It is referred to in the technical literature as a naturally-sampled modulator and its response is flat in magnitude and phase. The magnitude or the insertion loss is simply $$\\frac{1}{V_p}\$$ where $$\V_p\$$ represents the peak voltage of the ramp voltage. Please note that the phase is flat considering a perfect comparator. Should you start to include delays in the loop, then the transfer function of this block becomes $$\\frac{1}{V_p}e^{-st_d}\$$ where $$\t_d\$$ is the comparator response time. For low crossover frequencies (1 to 20 kHz) this effect can be neglected but if you deal with 1-2-MHz converters having crossover frequencies at 100 kHz or above then pure delays like this one must be accounted for.
Edit: I can see in the equivalent schematic excerpted from Erickson and Maksimovic book a front-end divider labeled $$\H(s)\$$ supposedly dividing the monitored voltage. This representation is incorrect if the compensator features a virtual ground, meaning the voltage divider directly biases the inverting pin of the op-amp. In this case, the division ratio indeed plays a role for the dc operating point but the lower-side resistor disappears in ac analysis. If there is no virtual ground as with an OTA, then yes, the division ratio enters the picture. If a virtual ground is present, then there is no division ratio.