# Isolated buck H bridge control system design

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?

• – Tony Stewart Sunnyskyguy EE75 Feb 15 '18 at 15:24
• It looks like something to do with Inverter stability analysis from abstract. Not sure if it contains useful info for AC/DC converter design. Though I will take a look at it once I am back in school. – renganathan b.s Feb 16 '18 at 9:06

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.

• Great. Thanks. It cleared my doubt. I am planning to control the converter digitally using MCU. Can I replace sawtooth voltage with something else ?. Double poles exists at the LC filter resonant frequency ?. – renganathan b.s Feb 16 '18 at 8:58
• The given example is a voltage-mode (VM) converter. The sawtooth is part of the pulse width modulator or PWM. You can digitally build the PWM pattern or consider a current-mode (CM) converter in which this sawtooth is replaced by an image of the inductive current. In the VM converter, yes, the $LC$ network peaks and compensation needs a type 3 circuit. In CM, the low-frequency response is of 1st order and compensation is simpler (type 2). However, subharmonic poles at $\frac{F_{sw}}{2}$ need to be damped. – Verbal Kint Feb 16 '18 at 13:07

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.

• Thanks I will take a look. Suggestions looks very simple but yet effective assumption for first level design. I haven't tried z plane myself. Will update if I find something. – renganathan b.s Feb 16 '18 at 9:00