# How to Calculate Ripple Current?

How do I calculate the ripple current a capacitor will experience for a given circuit?

For example, let's say I have a smoothing capacitor on the output of a full-wave bridge rectifier (120VAC, 60Hz) which leads into the primary winding of a flyback transformer (peak primary current is 0.775A).

How do I calculate what this capacitor's ripple current rating should be?

• What is RMS current? that depends on your application load not just peak as crest factor varies with design. Mar 24 at 23:27
• I am not sure, how do I calculate the RMS current? Mar 24 at 23:28
• If your Cap current is trapezoidal , I would expect RMS to be closer to 60% of peak rather than 70.7 % for rectified sine. But be sure to derate spec to add margin for longevity at 105'C Mar 24 at 23:43
• @RGBE If you can select a suitable repeating period of time, then you can compute RMS by a special integral equation suited for that calculation. However, you have to know what you are putting into the integral. A full wave bridge and smoothing capacitor isn't sufficient information. And, in any case, the curve includes: (1) a period when the cap is supplying all load current; (2) a period when the power source is supplying both load current and filter capacitor current; and (3) a period when the power source combines with the filter capacitor to supply load current. The curve is non-trivial.
– jonk
Mar 25 at 0:24
• @RGBE Back in the day before computers (1940's) designers used prepared tables for the purpose of selecting a filter capacitor to achieve a desired ripple. (That's assuming that a capacitor type filter approach was chosen.) There was a "first approximation" curve that one could use to start out iterating through the design tables. Or, if you felt you knew more, you could select the right curve to start with. I could share some of these tables with you, if that's all you care about. But if you want to know how to do the detailed calcs for this, it does involve significant analysis to get there.
– jonk
Mar 25 at 3:47

The determination of the bulk capacitor value in a full-wave rectification circuit depends on several parameters:

1. the amount of voltage ripple the downstream load - usually a high-voltage dc-dc converter - can accept in worst-case (minimum input voltage and maximum load). It means that if the ripple brings the valley voltage down to let's say 50 V, then the dc-dc converter must be designed to deliver full power at 50 V with margin. A good starting point for ac-dc converters is to adopt a 30% ripple value meaning that when fed by a 100-V rms input voltage, the rectified voltage will have a valley down to $$\\approx100\sqrt{2}\times0.7=99\;V\$$
2. the hold-up time is also a parameter to be considered: if the input mains loses half a cycle or more, how long can the rectified voltage stay afloat so that the downstream electronics safely signs off in shutdown mode? Usually, this parameter tends to beef up the initial capacitance calculation.
3. the rms current, finally, is the real selection factor for the capacitor type. You may have determined what capacitance is needed to fulfill the voltage ripple needs but, in the end, what matters is how much rms current the capacitor can handle safely to guaranty the longest operating lifetime. There are are tables and derating factors based on the operating temperature that manufacturers provide. Read and understand these numbers carefully as operating temperature is a key parameter for these electrolytic caps. Good quality capacitors from renowned brands are costly but can last very long when adequately selected.

Determining the capacitance value requires a single equation which is given below. It an excerpt from a formula derived in my book on switching converters but you can also find it in a white paper I uploaded on my webpage in 2009. Once you have your capacitance value, I recommend running a quick simulation using either a load resistance or a constant-power source if your downstream load is a dc-dc converter. You can then check your calculation and then update the capacitor value to the normalized value you will finally adopt.

As a final word, stay away from ready-made recipes like "3 µF per watt". In my opinion, it is much better to work the maths behind selecting a component as it teaches where the potential issues could be when writing equations and later when operating the component. I remember that I was taught the O.H. Schade's curves long time ago in university but I never used them and always derived the value I needed. You can also have a look at this article I published some years ago on the subject.

• I used Schade curves meaningful in terms of n * w * RL * C, and very useful for the determination of "peak" & "RMS" current values in capacitor & diode ... I remember also a "rule" such as "using" a 1000 uF for 1 Amp in load (just for verifying). Now, with simulators, it is very easier... :-) Mar 25 at 15:48