Measuring Capacitor ESR
Recently, while selecting components for a power supply, I came across the following statement in the datasheet for the voltage regulator... "The output capacitor must have an ESR of less than 3 ohms."
When I looked up the retailers who supplied the capacitors in my parts bin I found that none of them listed the ESR for the capacitors that they sold. So, somehow, I needed to measure this value.
After some research I came up with the simple approach described below. It relies on some good test equipment and, while you may not want to repeat the test, the results should be informative.
Equivalent Series Resistance (ESR) is the internal resistance that appears in series with the device's capacitance. No capacitor is perfect and the ESR comes from the resistance of the leads, the aluminium foil and the electrolyte. It is often an important parameter in power supply design where the ESR of an output capacitor can affect the stability of the regulator (ie, causing it to oscillate or over react to transients in the load).
You can buy ESR meters but I just wanted to know if any of the capacitors in my parts bin had an ESR of less than 3 ohms. So, how to test them?
The method that I used is quite simple and is shown in the diagram below.
I used a function generator to generate narrow pulses (1µS wide) with a slow repetition rate (1KHz). This drove a voltage divider with the test capacitor in the bottom leg and 100Ω in the top leg. Because of the narrow pulse, the capacitor did not have enough time to build up a charge, so the voltage across it represented the voltage drop caused by its ESR.
With the voltage of each pulse set at 10V this arrangement meant that the height of the pulse (in mV) across the test capacitor divided by 100 was equivalent to the capacitor’s ESR in ohms. For example, a pulse height of 80mV represented an ESR of 0.8Ω.
This is illustrated on the right. The vertical sensitivity of the oscilloscope was 10mV per division and the height of the pulse was about 30mV. This means that the capacitor’s ESR was approximately 0.3Ω (the capacitor under test was a 330µF 50VW aluminium electrolytic).
This method will work for values of ESR from 0.1Ω to greater than 10Ω. Alas, it is not very accurate - but then the ESR of a capacitor is not a precise value anyway and I was only looking for an approximation.
The main problem with this technique is that it is not very effective with capacitors below 10µF. With these small values the charge on the capacitor will rapidly rise making it difficult to estimate the height of the pulse before the effect of charging takes over – although, with some guesswork it can be still used for values down to 1 µF.
This is illustrated in the screenshot on the left. The capacitor on test was a 2.2µF 63VW electrolytic and it is possible to estimate that the start of the pulse is about 130mV (vertical scale is 50mV/division). This gives an ESR of 1.3Ω.
When you are using this technique it is important to minimise the resistance of the connections to the capacitor under test as any contact resistance will be added to the measured ESR..
The following table lists the results for a representative collection of aluminium electrolytic capacitors in my parts collection. The manufacturers were Elete and Lelon and they were bought from Futurlec and Jaycar (in Australia). They represent the typical components that a hobbyist would have access to.
I also tested two standard through hole Tantalum capacitors, one 10µF 16V and the other 47µF 16V. Both measured the same with an ESR of 0.4Ω.
All the capacitors had an ESR of 2 ohms or less and most of the values that you would use in a power supply (22µF and up) had an ESR of less than 1 ohm. As a rule of thumb, higher valued capacitors with higher working voltages had a lower ESR, although there were some exceptions so this cannot be guaranteed.
Keep in mind that the ESR for standard electrolytic capacitors increases with lower temperatures. For example, it will typically increase by 20 to 30 times when the temperature drops from 25°C to -40°C.