I recently came across a rather nice straight-to-the-point application note by RickTek (AN028) on how to calculate approximately the compensation network of a PCM buck regulator.
Link : https://www.richtek.com/~/media/AN%20PDF/AN028_EN.pdf
However I think I need some explanations. At The application note gives an example of design calculations.
At step 4 (page 9), the following equation is given for finding stability margin at crossover frequency 34kHz \$f_c = 34kHz\$ : $$\Phi_{M} = \Phi_{fc} + 180 - 90 + atan(f_c/f_z)\cdot 180/\pi - atan(f_c/f_p) \cdot 180/\pi $$
At step 5, gain is calculated at crossover frequency : $$ G_A = -G_{fc} - 20\cdot log(V_{ref}/V_{out}) + 20\cdot log(ceil(f_c/f_p))-20log(ceil(f_z/f_c)) $$
My questions :
- What are \$\Phi_{fc}\$ and \$G_{fc}\$ expressions? How are they calculated in order to obtain the given values for \$\Phi_M\$ and \$G_A\$? The application note doesn't mention where these expressions come from and how they are computed it seems.
- From where those two equations come from? It's obviously taken from some sort of transfer function, I'm just not sure which?
It would be logical those equations would be derived from the given open loop transfer function \$G_d(s)\$ of a PCM buck converter at \$s = j\omega = j2\pi f_c \$ (i.e. at crossover frequency), but I'm not sure how to pass from onethis expression to the equations mentioned above.