Help understanding Smoothing Capacitor Ripple Current

[RhythMick]

I've been away from designing and building for a while mostly due to family illnesses and recent bereavements. Now dipping my toe back into the water.

I've been refamiliarising myself with selection of smoothing caps based on the transformer secondary RMS, required voltage, load current. I think I'm good with all of that.

Say we have a transformer with a Vsec of 12v into a bridge rectifier with a smoothing cap, with the output going to a voltage regulator driving a load of 1A. 50Hz supply. 12vRMS will give a peak voltage of 15.6V at the cap (12 x SQRT(2) less 2 diode drops). With a load of 1A a 5600uF smoothing cap will result in a ripple voltage around 1.8V so the minimum output voltage will be 13.8V. No problems understanding all that, with the help of a spreadsheet to crunch the numbers.

I would choose a cap with a rating of 25V as no load voltage will get close to 16V. I want to check the ripple current rating required on the cap. At the minimum point of the charging cycle the voltage on the cap will be 13.8V. Vin rises to 15.6V, sinusoidally not instantaneously but for worst case lets assume a square wave ie instantaneous rise. The cap sees a differential voltage of 1.8V across it's terminals. If the ESR of a cap is (say) 14milliohms this is in series with the secondary transformer winding resistance (0.3783R) for a total of 0.3923R. I'm ignoring primary resistance for now.

1.8V / 0.3923R gives current inflow of 4.6amps.

Do I need to select a capacitor with a ripple current rating in excess of this ? The "square wave" worst case assumption above is obviously wrong and makes this ripple current calculation far higher than it needs to be but I'm not sure how to calculate it using the sinusoidal rise.

Or am I overcomplicating it all as usual and should just use the load current ?

[Nick]

The primary effect ripple current has on a cap is internal heating. Because of that, you need to consider the RMS equivalent value, not the peak which you are trying to extract in your example. So the actual RMS value will be a combination of the peak value and the duration over the cycle that the cap is charging. So even if you model using rectangular pulses, you need to add the "mark space ratio" as well. Of course the duration and the peak will be related.

Of just work out a worst case and feel happy that you have added a big safely factor.

[Morgan Jones]

PSUD2 has a column for RMS measurements, so it can determine capacitor ripple current for you. It tends to over-estimate slightly because it doesn't know about transformer saturation limiting ripple current to a practical 4-6 times load current and often assumes 7 times. But that will give you a safety margin. Capacitor ripple current ratings are in RMS (even though they rarely say so).