Calculating the parasitic inductance of a capacitor

Question

I have looked at this article, but it does not answer my question.

My question is: how would you go about measuring and/or calculating mathematically the self-parasitic inductance of a capacitor if I were to create one myself at home?

The link above just says that to find out what self-inductance value a cap has is to look in the datasheet of the manufacturer, but I will be making one from scratch.

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I have also found this research paper where it talks about exact equations for the inductance of rectangular conductors, which is what a parallel plate cap is composed of.

And I found this equation for a self-inducting plate:

$$L = \frac{0.002}{3a^{2}}\left [3a^{2}l ln\left ( \frac{l+(l^{2}+a^{2})^{1/2})}{a} \right )-(l^{2}+a^{2})^{3/2}+3l^{2}aln\left ( \frac{a+(a^{2}+l^{2})^{1/2})}{l} \right )+l^{3}+a^{3} \right ]$$

Where a is the width of the plate and l is its length. This equation is under the 3rd section called: Self-Inductance Calculations, eq 18.

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Would this equation (and others in the paper) work to finding the parasitic inductance of a homemade cap?

Incidentally: Would the type of material used in between the plates have any effect on the inductance? Like water, air, etc.

Answer 1

The ESL of a cap does not depend on its dielectric but only its electrode arrangement.

If you consider a standard two electrode capacitor, such as virtually all electrolytics and most ceramics, the ESL is given by the loop area that the current has to travel around when passing through the cap. The larger this loop, the larger inductance. The wider the electrode around loop, the lower inductance. Your equation seems to contain the relevant quantities.

The mounting style also matters a lot. THT parts have larger loops usually and thus higher inductance. Bring the terminals closely together and make the cap fit tightly over the PCB for minimum inductance. If you must use leads, then use a twisted pair for minimum loop area.

Here is a nice info graphic that qualitatively shows the impact of the current loop areas and electrode width (e.g. a wider cap with the same loop area will have a lower ESL):

Answer 2

The easiest way to measure the self inductance of a capacitor is to use it to shunt a signal being supplied from some modest impedance signal generator (like 50 or 600 ohms, whatever test gear you have access to).

Vary the signal frequency, and measure the voltage across the capacitor.

• At low frequency, the capacitive reactance is high, and the signal will be large.
• At very high frequency, the capacitor will be very low impedance, and the reactance will be dominated by the parasitic inductance of the capacitor, the signal will again be large.
• At the resonant frequency of the capacitance and the parasitic inductance, they will cancel each other out, and the capacitor will appear to be only its losses, which could be very low impedance, and the measured signal will be at a minimum.

Compute inductance from the resonant frequency and the known capacitance.