How to find ESR of cap?

No, didn't you guys even look at a graph or anything? Here's one -

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Here's another -

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and another -

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and another -

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(from AP Instruments - Products **broken link removed** **broken link removed** and **broken link removed** respectively)



Now I know what you're thinking - "Gee Duff, there's a problem at radio frequencies with high impedance" - right? Trying to pass FCC and your .1µF ceramic decoupling cap is letting all kinds of noise through? That's resonance, and it's a different issue.

This is an ancient discussion but amazingly easy to find when Googling the topic.

Consider the formula presented by Rubicon (capacitor manufacturer):

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Specifically:

tan Delta = 2*π*f*C*R

Where R = ESR

Now consider this Nichicon datasheet:

https://www.mouser.jp/datasheet/2/293/e-upx-876312.pdf

We want to know ESR, which in and of itself is not so easy because we must decide "at which frequency." But the Nichicon datasheet tells us its value of tan is when using 120Hz, so we use 120Hz!

Let's say we want the 16V rated capacitor, which according to that Nichicon datasheet yields:

tan Delta = 0.16

Now let's say we want to know the ESR for the 220uF capacitor, at 16V:

tan Delta = 0.16 = 2*π*f*C*R

Solving for R(ESR) we have:

R = 0.16 / (2*π*f*C)

And plugging in our values we get:

R(ESR) = 0.16 / (2*3.14159265*120*220E-6) = 965mΩ (about 1 ohm)

But of course, this is not too useful since a lot of ESR ratings we see that are not on a graph (a datasheet graph would be ideal) are usually at a frequency of 10k or 100k. Even so, this would appear to be the correct way to calculate ESR when a datasheet only gives tan .

Nigel Goodwin said:

As far as I know ESR at low frequencies would be lower than at 100KHz, certainly it's never mentioned or considered a problem at low frequencies.

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Data from:Type 380LQ 85 °C Compact, High Capacitance, Snap-In Aluminum Capacitors
This data sheet show ESR at 120hz and 20khz + Ripple Current at 120 and 20k.

Note in Ron Simpson's chart that a 220uF cap measured at 120Hz has an ESR of 900mOhms. You'll note in my previous post that the calculated value for the Nichicon 220uF cap at 16V came to 965mOhms, roughly the same and will vary by manufacturer. So the calculations presented in my previous post are sound. But it's best if you can find datasheets that show not just a couple ESR values at fixed frequencies, but show the actual graph covering most frequencies. That gives the clearest picture of all. But when nothing but TAN Delta is given, you have to calculate.

ESR is one problem. I often have problems with "ripple current". It is not good to have hot capacitors. ESR and ripple current and power lost in the cap are all related.

Yes, of course. There are many benefits to choosing a capacitor that has a high ripple current rating.

But when considering ESR, especially in cases where you are swapping out capacitors in older hardware, it is sometimes the case that you don't want an ESR too low. Some designs actually have problems when the ESR is too low. That happens quite often when an old electrolytic is swapped out for a modern ceramic which may have an ESR of 5mOhms. So choosing organic polymer aluminum electrolytic capacitors to get a low ESR may not be in the capacitor buyer's best interest. Some circuit analysis would need to be done to determine how low the ESR can be or if a limit even applies.

a "quick and dirty" method of measuring the ESR of caps is to use an audio function generator with a known output impedance (usually 50 ohms). set the output to a particular voltage that simplifies the math (such as 5V p-p) at 50khz, 100khz or 200khz (you want Xc to be very low, less than an ohm) and connect an oscope. then connect the cap, and measure the voltage. the resulting voltage is proportional to the ESR, and the rig can be treated as a voltage divider with a high side resistance of 50 ohms.

ronsimpson said:

ESR is one problem. I often have problems with "ripple current". It is not good to have hot capacitors. ESR and ripple current and power lost in the cap are all related.

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ESR and the capacitor heating up eventually becomes a failure mode for the capacitor. the ESR causes internal heating of the cap, which dries out some of the electrolyte, which increases the ESR, which increases the temperature, and so on.... until the cap dries out completely. as the ESR increases, the process accelerates, eventually to the point where the cap bursts.

unclejed613 said:

a "quick and dirty" method of measuring the ESR of caps....

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As demonstrated in this video:

I used the technique myself just a few days ago and diagnosed some "iffy" capacitors in my 40 year old Tuner/Amplifier.

JimB

How to “measure ESR“ is very useful information; however, the original starter of this thread mentioned that he is seeking information on how to determine the ESR of a capacitor before purchase when using data sheets that do not post the ESR numbers or graphs. In those cases we unfortunately have to do the math based on the given value of Tan Delta.

JimB said:

As demonstrated in this video:

I used the technique myself just a few days ago and diagnosed some "iffy" capacitors in my 40 year old Tuner/Amplifier.

JimB

Click to expand...

I used the same procedure to eliminate the problematic ones in my junk box.