Is there a way to take this buck diagram and reduce it to an AC transfer function?

Question

I am semi-dangerous with switchers but I've never really delved into the innards of them so I'd like to ask about this TPS23750 diagram. I would like to develop a model of this feedback loop of a buck converter. I would like to do this so I can look at the loop dynamics and compensate the loop appropriately in spice or on paper.

Source: https://www.ti.com/lit/ds/symlink/tps23750.pdf page 20

How can I take this diagram and create an AC model of it? What would the equations be for the transfer function?

This is how far I've got, one of the problems is I don't know what to put in for translator, because there is an error amp and I assume I could model the transistor as voltage dependent current source. One of the problems I have is I don't know what the gain would be or if I could pull it from the datasheet.

Source: Modified from above

It would be nice if someone could check the graphical model and see if that's a sufficient, I'm also a little unclear if the front end is right.

Also, once you get the AC model, you can simulate it in spice: https://www.analog.com/en/analog-dialogue/articles/step-by-step-process-to-calculate-a-dc-to-dc-compensation-network.html

Answer 1

The configuration of this floating buck converter is not very common and a quick tweak of my buck operated in current mode gives the operating point quickly:

The differential sensing amplifier is modeled with unity gain and its frequency response is considered flat. I believe the TI data-sheet would have mentioned its ac response if it had to be factored in. They simply underline the op-amp output which is divided by 5 before driving the peak current setpoint. The power stage is then compensated for an optimistic 10-kHz crossover frequency and the phase margin approaches 60°. Pushing crossover like this implies a good op-amp featuring a large GBW otherwise the type 2 response might be distorted in magnitude and phase boost:

With this graph on hand, confirming the stable situation, we can now run a load-step exercise and see how the response looks like:

The components values of the compensator are automated by the macro and this new PoE buck will be included in my list of ready-made templates so that you can download and run it if you wish. It runs with the free demo.

Answer 2

Gain seems to be 1, or close to it.

Pin descriptions:

• SENP: Voltage-level translator's positive reference voltage (sense positive) used in conjunction with SEN. Tie to the regulated voltage positive rail when the translator is used, and VDD otherwise.
• SEN: Voltage-level translator's sense input and enable; connect to RTN to disable. SEN is regulated to 1.5V below SENP by the control loop when the translator is used. Typically used in a low-side switch buck converter.

(My emphasis)

A slightly different spec is given in the table (1.492V) implying a slight gain error, but not enough to matter.

Possibly it is implemented as a fully differential amplifier, using resistor values large enough to meet the claimed input bias. Or it could be a more specialized circuit, like a calibrated current source and mirror. SENP current is higher of the two; perhaps it varies with sensed voltage, which would suggest it is the common/supply node of such a circuit.

The NPN transistor in the diagram seems erroneous. Perhaps the intent was not so much to say that there's a diode drop, but that the output is one-way; a diode would've been better visual indication. There isn't much trust one can place in TI's block diagrams these days, unfortunately.

There doesn't seem to be any way to infer the transfer function (frequency response) of this element. We can at least assume it will be faster than typically required voltage feedback, or some kHz.

If you need more information, open a thread on TI E2E™ design support forums. If you get a satisfactory answer, you're welcome to add it here.