# Determining Phase Boost needed to Compensate SMPS

I'm attempting to find the Control-To-Output Bode Plot (open-loop) of a SMPS designed around the TPS54160 so that I can design the type II compensator. The first step in designing a compensator is finding the attenuation and phase boost needed at the crossover frequency (4Khz) using the open-loop gain. Thus, I need the open-loop gain (or the gain of the system without the compensation added). I used the circuit below to find open-loop bode plot, and according to it I need 7.36dB of attenuation at the crossover frequency and some amount of phase boost. I'm not sure about how much phase boost I need (given a phase margin requirement of 60 degrees) because it appears there is 100 degrees of phase margin already since the phase has only shifted 80 degrees at the crossover frequency, since this is a single pole system when open-loop. Perhaps, I'm just confused. Are my model and bode-plot correct? And if so, how do I calculate how much phase boost I need?

In the circuit above G1 is the idealized OTA that the TPS54160 uses for its error amplifier, where R1 and C1 model the bandwidth and DC Open-loop gain of the amplifier. G2 and the output filter form the power stage. I think this model is correct based on the datasheet, which gave relatively simple instructions.

In the bode plot above, I measured V(b) (the output) with an AC source at the input of the power stage. According to this bode plot the phase has shifted 80 degrees at the crossover frequency of 4Khz. The gain is 7.36dB at the desired crossover frequency so it needs to be attenuated.

• Try Nyquist plots. But at least a lead-lag phase shifter is needed. – Tony Stewart EE75 Oct 3 '18 at 1:13
• More important what are your step responses? 10 to 90 and back , 50 to 100% etc and your voltage transient error specs?? there may nonlinear and 3rd effects not in your model that need to be added, step response is the best then Nyquist plots on the real parts. – Tony Stewart EE75 Oct 3 '18 at 2:14
• Your model needs a lot more variables, ESR,ESL more caps , etc etc – Tony Stewart EE75 Oct 3 '18 at 3:26
• Where's your inductance? – Andy aka Oct 3 '18 at 6:58
• Hi Andy, I took the model from the datasheet. In it, it says "The TPS54160A power stage can be approximated to a voltage-controlled current source (duty cycle modulator) supplying current to the output capacitor and load resistor." So no inductor. I'm just trying to understand how to arrive at a number for the amount of phase boost I need. – Alexander Villa Oct 3 '18 at 15:44

Boosting the phase actually means that you will tailor the compensator G so that its argument at the selected crossover frequency $$\f_c\$$ is less than -270°. These -270° are due to the pole at the origin (integrator) and the inverting op-amp which brings an additional 180° phase shift. In the example, the plant H argument at $$\f_c\$$ is -175°. Should you try to close the loop without boost at all with a simple integrator, you would end up with a total shift of -175° -270° = -360°-85°, showing a negative margin.