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Components and Circuits For discussions about component types, alternatives and availability, circuit configurations and modifications etc. Discussions here should be of a general nature and not about specific sets. |
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28th Mar 2019, 5:55 pm | #1 |
Dekatron
Join Date: Apr 2011
Location: Cornwall, UK.
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Capacitor ESR
I've just come across a formula for converting the leakage resistance of a capacitor to an equivalent series resistance, it's shown below:
Rs = Xc squared/Rsh….where Rs = the equivalent series resistance, Xc = the capacitive reactance and Rsh = the shunt resistance. Is that accurate or just an approximation? Lawrence. |
28th Mar 2019, 6:41 pm | #2 |
Rest in Peace
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Location: Solihull, West Midlands, UK.
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Re: Capacitor ESR
It is an approximation, although in some cases it can be quite a good approximation. However, you need to remember that it only applies at one frequency. Both leakage and ESR can be frequency dependent but in different ways as they arise from different causes.
What the formula does is convert (approximately) from the parallel to series form for an impedance. If you had a perfect capacitor in series with a resistor then the formula used in reverse would allow you to calculate an equivalent parallel resistance, but this resistance would tell you nothing at all about the DC leakage (which would be zero for a perfect capacitor). So use with caution. |
29th Mar 2019, 1:52 pm | #3 |
Dekatron
Join Date: Apr 2011
Location: Cornwall, UK.
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Re: Capacitor ESR
Here's where I came across the formula under discussion (page 3):
https://www.americanradiohistory.com...ox-1935-03.pdf Here can found other editions of the Aerovox Research Worker: https://www.americanradiohistory.com...Researcher.htm Lawrence. |
29th Mar 2019, 2:24 pm | #4 |
Rest in Peace
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Re: Capacitor ESR
The accurate formula is
Rs = Rsh Xc^2 / (Rsh^2 + Xc^2) If Rsh >> Xc then the second term in the denominator can be ignored so we get Rs = Rsh Xc^2 / Rsh^2 = Xc^2 / Rsh They introduced that formula in the article in order to show that capacitor leakage (for a non-faulty component) can be ignored for all except DC purposes. It is not a valid way of calculating ESR from DC leakage. |
29th Mar 2019, 2:26 pm | #5 |
Dekatron
Join Date: Apr 2011
Location: Cornwall, UK.
Posts: 13,454
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Re: Capacitor ESR
That's the formula I used when I did a comparison.
Lawrence. |