Electronics > Projects, Designs, and Technical Stuff
Power supply topology - will it work? (Control theory, stability)
T3sl4co1l:
Note that ringing is a symptom of control loop stability, phase margin and all that.
The total (peak) magnitude of over/undershoot is determined by the capacitor, at the very least.
Simply, the control cannot respond instantly, so until it does, the output has the relationship:
I = C * dV/dt
For a delay of, say, 1us, and a specified stability of 1% or better (i.e., +/-1V transient out of a 100V supply), and say 100mA load step, the capacitor must be V = I * dt / dV = (0.1A) * (1us) / (1V) = 0.1uF. Or more for longer time scales, or tighter regulation, and so on.
For the ESR to matter, it has to have a comparable voltage drop, i.e., on the order of (1V) / (0.1A) = 10 ohms.
There can exist no such arbitrary rule as "1 to 10 ohms ESR". A very low current, very high voltage regulator will see even 100 ohms as a short circuit. Whereas a very low voltage, high current regulator will need as many milliohms to have acceptable output impedance. Only the time constant ESR * C matters, and it will be proportional to the loop time constant.
This way, you can figure out the ballpark C and ESR that is desirable for any power supply.
Tim
T3sl4co1l:
Note that the overshoot is excessive in the above simulation, because the op-amp has to slew a huge voltage range (from cutoff to normal operating voltage), and is limited by its own speed, and the compensation network across it (where the capacitor is dominant -- note that the resistors are both 10k, so an input step into that amplifier will only make an equal amplitude output step, with slew rate limiting added, and rising slowly over time as the capacitor charges).
If a quiescent load is introduced (say, changing the ISTEP from 0 to 42mA, to 10 to 52mA), then it will behave much nicer.
It will behave nicer still, in the current range where the 22 ohm source resistor is dominant (i.e., gm > 1/(22 ohm)). This is where the MOSFET becomes a nearly linear transconductance amplifier (voltage in, current out). In this region, the control loop response no longer varies with average current level.
Tim
Yansi:
Thank you for responses guys!
I have made another set of step measurements. This time at 40V output (I had to lower the output, otherwise the mosfet would get some hot soup!) as my set of resistors for high voltage loads is not variable enough. When stepping from 27mA to 51mA, the responses are much nicer. With the 10uF added load, the ringing is quite damped now. Without the 10uF load, the step from 27 to 51mA yields only about 1.2V overshoot and undershoot. With the 10uF cap connected, both under half a volt. I should also test with larger capacitive load like 100+ uF, but am afraid the mosfet might get killed, as no current limiting is being implemented now. (But sure will be soon)
Please note the 10uF cap should be external load to this PSU, the internal cap should be only the 1uF foil plus the 1ohm ESR. By the way, isn't this similar function to the "zobel network" used in many audio amps (to present a load at higher freq)?
Yes, the LM324 is slow. But was the first opamp in reach with "input commonmode include gnd" and also being a quad OPAmp. The other two will be later used one for current limiting and one for pre-regulator control. (a stepdown converter will be used - prototype is mostly finished and seems working and happy).
TLC272 you say? I have a feeling I should have few TS274 opamps somewhere. Should be even faster and the quad I need. But let me tell ya, I made a mistake soldering the 324 directly to the veroboard. Doh! Thanks for the tip, I'll try to find them.
The 22ohm current shunt has been chosen due to two things: I wanted larger sense voltage, so that the opamp's offset voltage will have less influence on stability. 22ohms will result about 3V at 150mA. (however the target is 300mA using two IPW90R1K0C3 in parallel - but that might be in a future). The second reason I have chosen higher source resistance was me thinking I will linearize the mosfet output characteristic - but I might be wrong ??
I will try to desolder the 324 and put there a TS274 socket and TS274 in it and try again.
T3sl4co1l: Interesting to know, I had thought there would be a more complicated relationship. Will try to take that into account. What would you suggest to be the spec for a decent amateur built 400V 300mA general purpose PSU?
Yansi:
TS274 has been successfully found and socketed on board. It works. Without touching the compensation networks, the overshoot/undershoot are slightly better, say by a tenth of a volt. (1V instead of 1,1V). It also seems there might be less damping when the 10uF load is used.
After having modified the compensation according to your latest sim, the results are way better. 480mV no cap, 280mV with 10uF load. :-+
Jay_Diddy_B:
Hi,
I am not a big fan of this topology from a control theory point of view.
You start with a pole in the error amplifier, this is because there is a capacitor in the feedback loop to ensure that there is no d.c. error.
The power stage is a transconductance stage with a load capacitor. This is another pole.
So we have a double at the origin (or low frequencies) The combined double pole has 180 degrees of phase shift.
The power stage pole moves with the addition of output capacitance as we have seen.
To stabilize the loop I added a pole zero pair in the divider get phase advance at the frequency were the gain = 0dB. I also added a zero, by placing a resistor in the feedback path of the error amplifier to remove the error amplifier pole.
There are other contribution to consider.
The zero formed by the ESR in the output capacitor is included, in the model, to show its effect. With the values shown it is too high frequency to be useful, it is higher frequency than the loop bandwidth.
With the values that I have chosen there is little benefit to using faster op-amps. The gain of the op-amp sections is determined by the passive components around the op-amps, as it should be in a good design.
Regards,
Jay_Diddy_B
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