Isolated buck H bridge control system design

Question

Any references on how to go about modelling an AC/DC mains isolated H bridge buck converter in s or z domain? All the current resources online point to modelling buck converter with a single switch and in non isolated configuration.

The current process that I use for compensator design is that I look out for the frequency region where the LC low filter cutoff happens and at that region, the phase response drops almost to -180 degrees. Then I would design a phase lead lag compensator with some phase being added in the frequency region where the phase response drops to -180 degrees. Then I use the same compensator in the SMPS design without taking into account other components present. Wanted to know how much off I would be if I make this assumption that other components in the converter doesn't add much to phase response?

Answer 1

There are several options to get the control-to-output transfer function you want:

• use an averaged model, a half-or full-bridge converter is a buck-derived topology and can easily be simulated with the PWM switch model in voltage- or current-mode control.
• use a simulator which extracts the ac response from a cycle-by-cycle simulation: Simplis or PSIM do that and their demo version will allow you to simulate this simple structure in open loop.
• use a small-signal model and apply the FACTs.

For a CCM full-bridge operated in voltage mode, the dc gain is that of a forward converter: \$H_0=\frac{NV_{in}}{V_p}\$ with \$N\$ the transformer turns ratio and \$V_p\$ the sawtooth peak voltage. The rest of the transfer function (poles and zero) is similar to that of the buck. You can look at seminars taught at APEC regarding small-signal modeling for both VM and CM.

I have captured a quick sim in Simplis (the demo version, Elements) and if you simulate the below 5-V/10-A circuit:

you get the transient waveforms and the dynamic response of the power stage. You see a gain equal to \$\approx\$23 dB which what the above formula gives (24-V input source with a turns ratio of 0.6). Updating this circuit into a CM mode would not be difficult either.

Answer 2

You can model it in a simulator and, you don't need to model it as a switching converter because a linear model will work. If your switching frequency is (say) 100 kHz you could make an argument that modelling a delay of 10 us is useful to add.

Modelling it as a linear regulator has the main advantage that you can run an AC analysis and produce a bode plot.

May I recommend Micro-cap 11 student edition or if you want to go down to the bargain basement try LTSpice.

In Micro-cap you can model in the s-plane directly using formulae. I'm not sure if it will model in the z-plane because I've never tried but if you do go this route please make an answer to your own question. It will be useful to others I'm sure.