The simple capacitor equivalent circuit taught in school

Inductors are more like a resistor in series with an ideal inductor, resistors can be inductors as well, and well, capacitors aren’t just simply a capacitance in a package. Little with electronics is as plain and simple in reality as basic theory would have you believe. [Tahmid Mahbub] was measuring an electrolytic capacitor with an LCR and noticed it measuring 19 uF despite the device being rated at 470 uF. This was because such parts are usually specified at low frequencies, and at a mere 100 kHz, it was measuring *way* out of the specification they were expecting. [Tahmid] goes into a fair bit of detail regarding how to model the equivalent circuit of a typical electrolytic capacitor and how to determine with a bit more accuracy what to expect.

An aluminium electrolytic capacitor is more like this

The basic equivalent circuit for a capacitor has a series resistance and inductance, which covers the connecting leads and any internal tabs on the plates. A large-valued parallel resistor models the leakage through the dielectric in series with the ideal capacitance, which is responsible for the capacitor’s self-discharge property. However, this model is still too simple for some use cases. A more interesting model, shown to the left, comprises a ladder of distributed capacitances and associated resistances that result in a progressively longer time-constant component as you move from C1 to C5. This resembles more closely the linear structure of the capacitor, with its rolled-up construction. This model is hard to use in any practical sense due to the need to determine values for the components from a physical part. Still, it is useful to understand why such capacitors perform far worse than you would expect from just a simple equivalent model that looks at the connecting leads and little else.

To get real answers with a practical application, if key data are not published, it is necessary to characterise your parts, which is exactly what [Tahmid] did next. Using the excellent Digilent Analog discovery tool, a measurement setup was constructed to determine the reactance versus frequency characteristic and make an estimate for the paralleled capacitance and inductance components. Straight off the screen, the reactance can dip sharply at around 40 kHz, corresponding to the self-resonance frequency. This is the frequency you need to steer well clear of if you want to get anywhere close to the specified capacitance in your application. Since [Tahmid] was designing a switched-mode buck converter, which operated around 80-200 kHz, using this part in the input circuit would be bad news – the desired 23 mVpp voltage ripple would be more like 463 mVpp, and that’s just not going to work great. Time to gently place the electrolytic parts back in the parts bin to await a different application.

The not-so-humble capacitor is a much more complicated part than it looks at first glance. Entire books have been written about them, but for a quick history tour, check this out first. Want to *make* your own electrolytics? No Problem. What about when they go bad?

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