Dissipation in Electrolytic capacitor with multiple ripple current frequencies in it

When doing a Boundary conduction mode PFC stage, ive always gone on the thermal test of the electrolytic capacitor at the BCM PFC output as being king.

However, the current ripple in the PFC’s output capacitor has components at the switching frequency (say 70kHz). …but also has a significant component at the twice line frequency (100Hz), due to the PFC operation.
Since electrolytic capacitors have a much higher ESR at 100Hz than 70khz, is it really very pertinent to actually do a FFT on the capacitor ripple current so that the power dissipation of this 100Hz component with the (increased) ESR can be found?

(When measuring the capacitor ripple current RMS on the scope over a 10ms period, it obviously just spits out an IRMS measurement, and doesn’t tell you what is the IRMS of the actual 100Hz component.)

Most oscilloscopes do FFT, but the approach sounds like overengineering. 100 Hz Irms component can be easily calculated from bus voltage and PFC power based on the known sinusoidal input current and respective 100 Hz power ripple. It doesn't depend on the pwm mode.

Thanks, if the current was based on smooth half-sines (obviously with zero dc component in the capacitor in steady state), then i could understand that one should consider the 100hz esr value for the IRMS^2.ESR calculation.
However, the current ripple is going into the capacitor in the form of 70khz pulses......so even though the amplitude of these pulses is changing at the 100Hz frequency, surely the internal chemistry of the capacitor isnt "really going to see" this 100hz component, and therefore, we should consider only the 70khz ESR value.?

treez said:

we should consider only the 70khz ESR value.?

Click to expand...

Correct; let us say that a square pulse is made up of so and so number of sine waves of such amplitudes.

The sine waves form the basis set; the effect of individual sine waves can similarly be added to get the effect of the same square wave pulse.

The superposition principle holds as long as the effects are linear. I am not so sure about the present case but we can always assume linearity as an approximation.

You can certainly add the effects of the 100Hz sine wave ripple (modulation) and the 70kHz square waves independently and separately, at least as an approximation.

I suggest a different approach. 100 Hz fundamental can be easily calculated, there's an additional 70 kHz component depending on the pwm scheme. In case of boundary conduction, the rms value can also easily calculated. Both components have to be considered for capacitor rating.

I understand that when there is a low frequency envelope which modulates the high frequency waveform that flows in an electrolytic capacitor then the increased ESR must be considered for the low frequency component. (because as you know, electrolytic capacitor ESR is always higher for the lower frequencies)
….However, is this really true?....for example, consider a 100khz Flyback power supply running constantly for 2000 days. Now consider that for one day it is run at full load, then for the next day it is suddenly switched to run at half load, then suddenly back to full load….etc etc , continuously. So what we have is a modulating envelope in the electrolytic capacitor ripple current that has a period of 1 day. Now, from our theory concerning that ESR is greater for lower frequencies…would we have to consider the increased ESR for the 1 day period component?
I suspect that we would not……however, the 1 day period component is definitely there.
So I suspect that low frequency modulating envelopes of high frequency capacitor ripple current do not actually have to be taken into account in the assessment of the actual ESR. Do you agree?

The only real reason we need to be interested in ripple current is that it creates a temperature rise. I would just be monitoring surface temperature of the electrolytic, that will take everything into account.

Thanks, yes we will do that.
The thing is, we have a repetitive capacitor charge discharge circuit to build. We can either charge the ‘lytic cap with a constant 70khz output of a flyback……..or the same again but with a 100Hz envelope on the 70khz ripple (since there wouldn’t be a primary side ‘lytic in that case, -[its an offline flyback]).
We want to do it the coolest running way for the cap.
So we wish to know how much the 100hz component is going to have an effect.

We can build it both ways and do the temperature comparison but that will take longer. If we can calculate it first that will help

Since electrolytic capacitors have a much higher ESR at 100Hz than 70khz, is it really very pertinent to actually do a FFT on the capacitor ripple current so that the power dissipation of this 100Hz component with the (increased) ESR can be found?

Click to expand...

The ESR of a electrolytic capacitor at 100Hz is the same as it is at 70khz. The ESR does not start to drop until the frequency is above 150Khz. I have measured many different capacitors to empirically determine this

The ESR is quite complex, its a mixture of real resistance and skin effect.
For energy storage requirements at 70 Khz, the required capacitance usually produces a self resonant frequency much lower than 70 Khz.

We can either charge the ‘lytic cap with a constant 70khz output of a flyback……..or the same again but with a 100Hz envelope on the 70khz ripple

Click to expand...

If the average DC is the same in both cases, the 70 kHz ripple can't be "the same", the 70 kHz RMS is of course larger in the 100 Hz modulated case.

At first I thought you were talking about high frequency ripple whose amplitude is modulated at a slower rate (i.e. sin(ax)*sin(bx)). If you do the analysis this scenario actually has zero frequency content at the slower rate.

But now I assume you're talking about the normal 100hz ripple that results from a nearly constant load drawing from the PFC caps which are charged periodically at a rate of 50hz*2. This is real ripple and can't be removed from the analysis. On the other hand ripple current depends on frequency and 50hz ripple is orders of magnitude less than your switching frequency. It seems unlikely it's going to be a major factor.

asdf44 said:

... about high frequency ripple whose amplitude is modulated at a slower rate (i.e. sin(ax)*sin(bx)). If you do the analysis this scenario actually has zero frequency content at the slower rate...

Click to expand...

If it is a ripple, I understand that it is riding on a DC with a small amplitude. I mean DC+(small percentage of DC)*sin(100*t).

Because the ripple current is proportional to the ripple voltage, the power lost is small (I^2)*R loss

On the other hand, the 70 kHz is really not a ripple because it is not riding on a DC. If it is the output after the filtering, then we can call this a ripple because it will be mostly DC with 70 kHz ripple.

I also think that ESR will be higher at 100 Hz compared to 70 kHz but the proportions are not large (perhaps within a factor of 2). I plead my ignorance.

Why the two effects (losses) cannot be added, even if it is an approximation?

70 KHz ripple:

DC=alpha; ripple=beta (percent of DC); some people specify ripple in absolute volts.

voltage=alpha+alpha*beta*0.01*sin(100*t);

100 Hz ripple; gamma (percent of DC);

voltage=alpha+alpha*beta*gamma*0.001*sin(100*t)*sin(70000*t);

using sin(a)*sin(b)=-0.5*(cos(70100*t)-cos(69900*t))

I guess 100 Hz frequency is not going to have much effect.

yes, you need to calculate the real effective 100Hz rms current, mult by the 100Hz esr, same for 70kHz, same for 140kHz, 210kHz...