Switching Frequency Effect on Loop Gain

[csolis_GT]

Does any one know what is the effect of the switching frequency on the loop gain of a DC-DC switching converter? I know it should add phase lag in the loop gain but I am looking to find an analysis. Any pointers or references will be highly appreciated.

 

[mtwieg]

The primary constraint is that state space averaging will only give accurate predictions of small signal gain at frequencies below half the switching frequency.

If the converter is operating in CCM, then varying the switching frequency should not affect gain, so long as the above condition is met. If the converter is operating in DCM, then changing the switching frequency will also change duty cycle and therefore gain must be recalculated using the new duty cycle.

This is assuming you define gain according to state space averaging analysis.

 

[csolis_GT]

Thanks for the reply.

I am trying to design a fast DC-DC converter and like you mentioned, when you consider an analysis of the average small-signal quantities, it is accurate until half the switching frequency. However, in my case the crossover frequency is near/past half the switching frequency and I want to explore how the switching frequency will come into play in the loop gain.

 

[mtwieg]

Thanks for the reply.

I am trying to design a fast DC-DC converter and like you mentioned, when you consider an analysis of the average small-signal quantities, it is accurate until half the switching frequency. However, in my case the crossover frequency is near/past half the switching frequency and I want to explore how the switching frequency will come into play in the loop gain.

Well then you have to explain what your mathematical definition of "gain" is if it's not based on SSA. Above half the switching frequency, control signals are mixed by the PWM stage and the image frequency components will appear within the loop bandwidth. You basically can't treat the system in a linear fashion, and terms like gain, phase, and crossover frequency lose their meanings.

What sort of switching frequency are you dealing with? Is it a current or voltage mode converter?

 

[csolis_GT]

The switching frequency is 1 MHz. It is a current-mode converter. I know it is unpractical for the moment, but I am assuming that the current loop has an infinite bandwidth or at least much higher than the voltage loop so that it does not introduces any pole or phase lag in the voltage loop. I am trying to analyze how much I can push the crossover frequency in the voltage loop, I am getting to the point in which since the cross over is approaching half the switching frequency, there is an additional phase lag that appears on the phase lag by using transients simulations.

What do you refer to gain based on SSA? For me, SSA is just one approach to evaluate low frequency gain and parameters of the loop. My definition of gain is simple vout/vin at the frequency that it is being evaluated, small amplitudes for small signal, and transient analysis since I am simulating using the injected voltage method.

 

[mtwieg]

The switching frequency is 1 MHz. It is a current-mode converter. I know it is unpractical for the moment, but I am assuming that the current loop has an infinite bandwidth or at least much higher than the voltage loop so that it does not introduces any pole or phase lag in the voltage loop.

At very high frequency you can't simply characterize the converter with terms like bandwidth, that's the fundamental problem. You are trying to characterize a nonlinear, time varying system with language that only applies to LTI systems. So your results are always going to be incoherent.

What do you refer to gain based on SSA? For me, SSA is just one approach to evaluate low frequency gain and parameters of the loop. My definition of gain is simple vout/vin at the frequency that it is being evaluated

At high frequencies, a pure AC perturbation will not produce a periodic response with the same frequency. That's why you can't characterize the system with a simple "gain."

 

[csolis_GT]

I agree with your statements when you are, in this case, at high frequencies near 500kHz to the 1MHz switching frequency. However, I have two comments:

1) The system is nonlinear and time varying at all frequencies, low and high, SSA is just a way to approximate the system as an LTI at low frequencies up to 500kHz. I do agree that near & beyond that, the non-linearity gets more complicated yielding other signals due to mixing.

2) The additional phase lag I am seeing, it is noticeable (> 10 deg) from frequencies near 100kHz where it is still 10 time smaller than fsw. That is why I think there should be some room to improve phase prediction at least in the frequency range between 100 kHz to 500 kHz.

 

[mtwieg]

2) The additional phase lag I am seeing, it is noticeable (> 10 deg) from frequencies near 100kHz where it is still 10 time smaller than fsw. That is why I think there should be some room to improve phase prediction at least in the frequency range between 100 kHz to 500 kHz.

Then something is likely wrong with the way your simulation is set up, or with how you are deriving complex gain from the transient waveforms. Can you post an example of the transient model?

 

[FvM]

Without an exact system description, you can't derive the continuous time equivalent transfer function you are looking for. It's particularly the pwm modulator characteristic (e.g. natural versus regular sampling) that produces different phase responses.