# ESR of motor-run caps?

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#### JoshK

I am trying to model some PSUs in PSUDII and it occurred to me that I am using the default ESR of 2R's for the caps. Does anyone know ball park ranges for ESR of motor run caps?

I have a bunch of different 40uf, 80uf and 100uf in both 370VAC and 500VAC ratings. Any guesses as to what ESR might be?

Greatly appreciated!

#### zigzagflux

Datasheet lists dissipation factor of less than 0.1%.

D.F. = ESR/Xc, where Xc is 1/(2*pi*f*C).

For a 40 uF cap, Xc = 66 ohms at 60Hz or 33 ohms at 120Hz (if used as PS filter).

ESR= D.F. * Xc = 66 milliohms or 33 milliohms at 120Hz.

Thanks!

#### rdf

Another way of looking at it is that the DF of modern polypropylene motor run caps is so low that a typical amp's internal harnessing will swamp ESR.

#### EC8010

zigzagflux said:
Datasheet lists dissipation factor of less than 0.1%.

D.F. = ESR/Xc, where Xc is 1/(2*pi*f*C).

I'm not so sure about that. The implicit assumption is that all the losses come from the ESR. But we know that leakage across the dielectric causes losses...

#### Conrad Hoffman

The formula is correct, and the losses for that one frequency are all lumped together and represented by the single resistor, the ESR. The simple model says nothing about where the losses come from, just what they look like at a single frequency. The nice thing about DF is that it tends to stay more constant over frequency, though it will change somewhat. I find ESR a less useful concept, though it's what one ends up using in a simulation. Also, most people don't include DA in the simple model, much less voltage linearity effects- fortunately small in quality caps, though significant in some ceramics and such.

#### EC8010

Yes, the equation looks like one of those RF (single frequency) equations where the Q of a resonant circuit can be held the same whether a series or parallel resistor is used. But a power supply isn't a single frequency application, hence my doubt as to the validity of the equation.

On a more practical note, PSUD is the exact problem that lead me to make an ESR meter. If I had some motor run capacitors, I'd measure them. They're probably quite low, <0.5 Ohm.

#### JoshK

60hz vs. 120hz? This bring up the question I don't know the answer to. I know the 60hz comes from the line freq of the mains, but what is the 120hz from, or why is the the important freq? Does it have to do with rectification?

#### SY

Yes, a full wave rectifier will output 120Hz (100Hz in Europe). Each half cycle of the AC is rectified, so there are 120 "pulses" each second; think of mirroring the negative-going pulses of each half-cycle to positive.

#### JoshK

ah... almost answered my own question. I guess if I thought it through fully I would have seen that.

Thanks.

#### Conrad Hoffman

But, think about what the new 120 (100) Hz waveform looks like- it's no longer a pure sine wave, though I don't know exactly what an FFT would look like. With very little trouble, you're in a situation where the simple model equation could be in error. Fortunately, the DF of polypropylene caps is so low you can treat it as zero for low frequencies. The only thing better will be polystyrene, Teflon, maybe mica, or air.

#### zigzagflux

My experience with choke input supplies (my preference) is the ripple is very nearly sinusoidal. The higher order harmonics, though undeniably present, do not appreciably add to voltage drop concerns - the percentage is just too low. A perfect sine wave of ripple is a very good and reliable approximation, and produces very accurate results.

Further, though most motor runs are designed specifically for 60 Hz, they also, according to IEEE, have to handle a certain percentage of overvoltage and harmonic content (because harmonics are always present in a power system). So the additional harmonics we create from rectification would be benign to a motor run with respect to its current handling capability. I would also think this to be true even for a cap input supply, as the current magnitudes with tube equipment are so small. The motor run is not your limiting device.

I would also agree, your ESR values in the motor runs are well under an ohm. Once you model it in PSUD, any thing under an ohm will produce little to no difference in output.

#### Conrad Hoffman

It never occured to me that a choke might be used, but that's certainly a point in their favor.

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