# Capacitor quick question: (Dissipation factor vs ESR?)

I want a decent small capacitor that is suitable for "high power resonant circuits." On the osciloscope, the waveform looks like 2 well rounded humps, one that is skinny and tall and one shortly following that is shorter but longer, and this is periodic at 30KHz. UPDATE: looking at the waveform closer, it is clearly a damped ringing that is a bit trimmed. The screenshot is uploaded. The maximum measured slew rate was about 25.5MV/S, (which is 25.5V/uS, right?) for a "perfect" 1uF capacitor, that is a peak current of 25.5A! I am unsure of the RMS current due to the non-sinusoidal nature of this waveform. But it must be pretty high as well, explaining why my 3, 1cm diameter 3cm long 0.47uF MMC film capacitors get pretty warm.

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Why do some film capacitor datasheets only give dissipation factor ratings at a few test frequencies (like 10KHz and 100KHz) and others give ESR ratings as well?

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Based on what I googled, I figured out dissipation factor is the ratio of ESR to the capacitive reactance. And since the frequency and capacitance is given it is not hard to calculate the ESR. So then why is this not conveniently already listed on the datasheet? Is it because the dissipation factor is what is directly measured? (like the total measured impedance of the capacitor at a certain test frequency)

## Discussions

2 years ago

ESR varies wildly as a function of frequency, Tan delta expresses things more generally

Answer 2 years ago

Also, I noticed that while the MOSFET is in the ON state, the voltage creeps up approximately linearly to about 10ish volts, but the ON state resistance is 93mOhms, and based on P = V^2/R, that would imply power dissipation peaks of over 1000W!!! That cannot possibly be, my MOSFETs would explode! Wouldn't they?

Answer 2 years ago

Not really. For how long are the levels as you say ? You can only really consider a long term mean - the same argument that says you can't take AC peak value, multiply them together and get a "peak power", it doesn't exist.

Answer 2 years ago

Well, when I get around to it lol I'll measure the inductor current properly. For now though the MOSFET seems perfectly fine and running happy at 25V. However only my biggest capacitors seem to be happy with the circuit, I have melted some smaller ones. I found a datasheet for this capacitor: http://www.mouser.com/ds/2/427/mkt1822-239807.pdf

Which states that the tangent loss angle (same as dissipation factor, right?) is 25*10^-3 at 100KHz, and 15*10^-3 at 10KHz. So I figure that this multiplied to the capacitive reactance should give be the ESR.

25*10^-3 * 1 / (2*Pi*100,000Hz*1*10^-6 F) = 0.039 ohms ESR. :)

15*10^-3 * 1 / (2*Pi*10,000Hz*1*10*-6 F) = 0.2 ohms ESR. :O :( :/

Wait, why is the ESR almost an order of magnitude _HIGHER_ with the _lower frequency!?!?!? That just makes no sense to me! I would expect things like the skin effect to take place within the conductors of the capacitor and hamper performance.

Answer 2 years ago

You're forgetting there is no such thing as a "capacitor" or "inductor", at some limit, which depends on how far you are pushing a part, the single element model breaks down.

You are at the point where the "capacitor" has RESISTANCE. You are also in the presence of dielectric loss and device inductance as well.

Answer 2 years ago

I do understand that much, and that is why some random capacitors get boiling hot within seconds of using in the circuit even though I am not exceeding the voltage rating. I am not anywhere close to the resonant frequency of any of these parts yet, so inductive effects are probably negligible and primarily due to the capacitor package and wiring.

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I have one small unknown 0.47uF capacitor (10mm pin spacing, 17mm long, 15mm tall, 7mm wide) that is a small film, but it stays stone cold! One of these would be perfect, but I cannot find any data for it. It was salvaged from an old TV. This capacitor on mouser seems to have acceptable ratings, but it is obnoxiously huge! http://www.mouser.com/Search/ProductDetail.aspx?R=...

Answer 2 years ago

in the scope screenshot you can see where the ringing abruptly stops and a steady ruse from 0v to 10v across when the MOSFET is on.

Answer 2 years ago

The rise is to be expected, as the current ramps in the inductor, and the IR losses in the device increase.

Answer 2 years ago

So it seems like some random small ( 18*8*15mm) 0.47uF dipped film capacitor salvaged from a TV seems to stay pretty cool, and dissipate even less energy than the large but old MMC capacitors I was using! It seems like all my capacitors that have a good enough working voltage rating (>250Vdc >100WV) stay cool while ones with less than that seem to overheat. Is this what I should look for instead? Is there a correlation between working volts and dissipation factor / ESR?

Answer 2 years ago

yeah, I had the same thought. I calculated the current at the end of that rise to be about 100A! Its 66% more than the absolute maximum current the MOSFET is rated for but still well the peak value.

Answer 2 years ago

Did you ever measure the inductor current, as I suggested ?

Answer 2 years ago

I would expect the ESR to get worse with increasing frequency, but based on my calculations deriving from the dissipation factor, it seemed to be 5 times better at 100KHz instead of 10KHz, how can that be!? I'll redo my calculation to see if I made a mistake.

Answer 2 years ago

Steve pointed out ESR for you !

"ESR varies wildly as a function of frequency,"

Answer 2 years ago

Yeah, I guess he isnt kidding. :/ What surprises me more is that it varies in the wrong direction. A higher frequency operation leads to lower ESR!? I guess it is kinda nice that it is lower at higher frequencies, since the oscillation is at 100KHz, and is what I need.

So then how does it work when I have multiple frequencies (maybe a squareish wave) directly across the capacitor? Lower ESR during the faster rise/falls and higher ESR when it is slower? :/ Capacitors are the most weird and annoying things to fully understand.

Answer 2 years ago

So you think a ceramic capacitor would be a better choice? I have these really small 0.47uF capacitors, just millimeters long and tall, and 4 of those in series/parallel don't even get warm!

Answer 2 years ago

I got some better quantitative data of the voltage present across the capacitor. You can see the damped oscillation that is occurring, at about 75KHz, at a peak of almost 100V. That data was collected with 3 of those 0.47uF capacitors in parallel. What capacitor ESR rating would be safe to use?

2 years ago

The capacitors I have been using and seem to work just fine are these Sprague 0.47uF film cap catalog number 416P-WF2-P47, listed on the 3rd page of this datasheet: (they are rated 200Vdc 0.47uF, 10%)

http://www.33audio.com/enter/data/1972SpragueFilm....

However, there is no data for their ESR, dissipation factor, or anything. It seems these are supposed to be used for audio applications. So I guess my capacitor needs to handle 100WV at 100KHz as a minimum. The sprague capactors are indeed rated for that. The capacitance I used during this measurement was 3 0.47 capacitors, so 1.41uF.