# How to calculate capacitor value to reduce PWM load ripple?

I have a simple MOSFET PWM circuit switching a 12v/8A load at a rate of 500Hz. This is being powered by a 120w switch mode power supply.

The power supply is buzzing loudly and generally unhappy with this arrangement. From my reading it appears that I need to smooth the load ripple created by the PWM circuit, by strapping a low ESR capacitor across the +/- input to the PWM circuit.

Is this correct, and if so, how do I calculate the correct value for the capacitor given the load characteristics?

Edit: PWM and PSU are commercial off the shelf units - I can't modify them. I'm after a relatively simple ad-hoc solution to go between the two units.

• A schematic and perhaps a picture would help a lot here. There are a lot of factors involved that those would provide. You'll definitely need to give us more about the load. Such things have many characteristics other than their DC current draw that affect these choices. In particular, maximum ripple current is likely to be a key factor here influencing capacitor choice more than just getting the capacitance ($\mu F$s) right. – scanny Aug 23 '16 at 0:51
• Thanks for the reply. The power supply is a COTS 'black box' figuratively and literally - I don't have a schematic. The PWM circuit is also COTS, however I can see that it is very simply a mosfet in between the load v- and supply v-, v+ is common. No other components in the path, probably a terrible design. The load is a high wattage LED strip. I cannot redesign the circuits, I was after a 'rule of thumb' solution that I can try between the PSU and PWM. Maybe asking too much given what I have to work with though? – Satellite Aug 23 '16 at 1:13
• Wouldn't it be easier to increase the driver signal on PWM frequency from 500 Hz to 50kHz and put a 10A choke in-between with a reverse clamp diode, unless the 500Hz is COTS too. Then a 100x smaller cap is needed. – Sunnyskyguy EE75 Aug 23 '16 at 2:38

Without knowing much about the power supply how your power source was designed, just assume the worst case. Which is that it doesn't have significant output capacitance to absorb the ripple. Then calculate how much capacitance you need to achieve a certain amount of voltage ripple. Any capacitance your power source has will just make that estimate more conservative.

The voltage ripple on a capacitor is calculate as.. dv = I * dt / C

dv = the peak to peak voltage ripple in Volts. I = the current which is being switched in Amps. dt = the time that the capacitor is supplying current in seconds. C = the capacitor value in Farads.

In your case of a 500Hz signal, at 8A, we have dt = 1ms, and I = 8A. Lets say we want the voltage ripple (dv) to be less than 0.1V then...

C = I * dt/dv = 8A * 1ms / 0.1V = 80mF

Some power supplies become unstable when large capacitances are added to their output. Therefore you may want to add a small value resistor or inductor between your supply output and the capacitor. Something on the order of 0.1 ohms, 10W is about right.

• I was about to post something like that. I'd used 200mV as my ripple figure and came up with 40mF. So we were thinking alike. Upped you. I also had broken it up into two capacitors with an R between them for the reason you mention. And I'd used 0.1 ohms for that, as well. – jonk Aug 23 '16 at 1:43

You probably need multiple capacitors and probably some inductors as well.

I've found it easiest to calculate this as a low pass filter. You can treat the PWM circuit as a signal source, and you want to design a filter that passes DC, but blocks the noise from reaching the power supply.

So step 1 is to measure the noise -- oscilloscope with AC coupling on the supply side of the PWM circuit -- and then design an LC filter that suppresses this signal. The inductors need to be strong enough to carry the full current (plus some headroom for the inrush), and the capacitors need an appropriate voltage rating as well.

Keep in mind that the capacitors are not ideal, so they have parasitic inductance, which turns your lowpass into a bandpass, essentially, so you have to combine multiple filters for different frequency ranges, placing the filters with higher cutoffs nearer to the load (which is essentially why you place smaller bypass capacitors nearer to the IC).

• Unfortunately I don't have access to an OSC right now. As per my reply above, the PWM and PSU are commercial off the shelf. I was hoping for a rule-of-thumb solution that I can stick between them to smooth the ripple. This is a one-off solution, not something I'm doing in volume. Do you have any ideas for solving this with limited resources? – Satellite Aug 23 '16 at 1:18