Capacitor ESR - UK Vintage Radio Repair and Restoration Discussion Forum

ms660 · 28th Mar 2019, 5:55 pm

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.

G8HQP Dave · 28th Mar 2019, 6:41 pm

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.

ms660 · 29th Mar 2019, 1:52 pm

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.

G8HQP Dave · 29th Mar 2019, 2:24 pm

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.

ms660 · 29th Mar 2019, 2:26 pm

That's the formula I used when I did a comparison.

Lawrence.

28th Mar 2019, 5:55 pm	#1
ms660 Dekatron Join Date: Apr 2011 Location: Cornwall, UK. Posts: 13,454	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
G8HQP Dave Rest in Peace Join Date: Sep 2008 Location: Solihull, West Midlands, UK. Posts: 4,872	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
ms660 Dekatron Join Date: Apr 2011 Location: Cornwall, UK. Posts: 13,454	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
G8HQP Dave Rest in Peace Join Date: Sep 2008 Location: Solihull, West Midlands, UK. Posts: 4,872	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
ms660 Dekatron Join Date: Apr 2011 Location: Cornwall, UK. Posts: 13,454	Re: Capacitor ESR That's the formula I used when I did a comparison. Lawrence.