Op-amp compensation (advanced)

Question

I would be very happy if anyone can help me understand the compensation made by TI in UCC28950 Phase Shifted Full Bridge Converter Datasheet.

I am providing the the related pages as follow:

• 1'st picture is the schematic of the converter in which anyone can see the opamp compensation components at the upper left corner
• 2'nd picture is the beginning of the calculation of transfer function.
• 3'rd picture is the calculation of the compensation components
• 4'th picture is the Gain- Phase Plot

My questions are as follows :

1. How do we produce Gco(f) expression in 2'nd picture? It seems very hard.

2. What is double pole frequency? What is it related to? Why it is the half of switching frequency in 2'nd picture?

3. fc is called crossing the voltage loop in 3'rd picture. Is this the frequency that we cross the 0 dB?

4. Why does the fc equal to fpp/10? How do we decide that?

5. Lastly, I completely didn't understand the rest of calculations for R5, R4, C2 and C1 because they involved the Gco(f) and fc in 3'rd picture. This is the first time I see this type calculation. How should I go with Gco(f) and fc?

1'st picture
Source: TI-UCC28950 Green Phase-Shifted Full-Bridge Controller With Synchronous Rectification- https://www.ti.com/lit/ds/symlink/ucc28950.pdf?ts=1699857647561&ref_url=https%253A%252F%252Fwww.google.com%252F

2'nd picture
Source: TI-UCC28950 Green Phase-Shifted Full-Bridge Controller With Synchronous Rectification- https://www.ti.com/lit/ds/symlink/ucc28950.pdf?ts=1699857647561&ref_url=https%253A%252F%252Fwww.google.com%252F

3'rd picture
Source: TI-UCC28950 Green Phase-Shifted Full-Bridge Controller With Synchronous Rectification- https://www.ti.com/lit/ds/symlink/ucc28950.pdf?ts=1699857647561&ref_url=https%253A%252F%252Fwww.google.com%252F

4'th picture
Source: TI-UCC28950 Green Phase-Shifted Full-Bridge Controller With Synchronous Rectification- https://www.ti.com/lit/ds/symlink/ucc28950.pdf?ts=1699857647561&ref_url=https%253A%252F%252Fwww.google.com%252F

Answer 1

The first thing you need for the compensation strategy of this phase-shifted full bridge (PSFB) is the control-to-output transfer function (TF). You can obtain it either by analytical analysis and derive a Laplace-domain expression - see the model I built in 2009 here - or you can use a piece-wise linear simulator like SIMPLIS and obtain the ac response straight from the switching circuit.

If you download the free ready-made templates from my webpage, you will see one of the PSFB examples:

This circuit runs on the free demo version and it delivers the ac response in a few seconds:

Once you have the TF of this buck-derived topology, you can determine the components values of the type 2 compensator based on an op-amp. Some of my compensators templates automate the compensation process and it is easy to use:

The macro is based on the k factor method which works well for a type 2 compensator. The principle is to select a crossover frequency from the control-to-output transfer function, extract the magnitude and phase at that frequency and calculate the compensator values with the macro or manually to crossover with a good phase margin.

I have actually updated the templates with a PSFB featuring an op-amp and it is shown below. It runs on the demo version which is good:

I have selected a 1-kHz crossover and the macro automates the compensation at the considered operating point. Of course other load/input voltage combinations must be explored and the simulation template is well suited for this exercise:

Good luck with this design!