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### Electrolytic Capacitor Analysis

#### Motivation

It was discovered recently (11.30.10) that one of the electrolytic capacitors in the infamous TB-303 was installed backwards on presumably all production models (http://forums.adafruit.com/viewtopic.php?f=7&t=18322). This prompts the question, what effect does a backwards electrolytic capacitor have? I'm sure we've all had the experience of plugging in an electrolytic capacitor backwards and having it explode on us, so how is it that these 303 capacitors have survived all these years?

This is even more pertinent considering that there are certain situations where you need a very large capacitance, and the capacitor will have to be back-biased for some period of time. It would be good to know the trade-offs being made when using this part in a non-ideal fashion.

#### Experimental Method

All tests were conducted on a single 22uF/16V capacitor, so the results should be taken as a general performance evaluation, with actual values varying with the capacitor you might be using. The test capacitor was connected up to a DC voltage with a 10k resistor to limit the current, and a 100mV AC signal was applied to the capacitor through a 100ohm resistor. The distortion and noise were measured at 100Hz and 1kHz AC signals using a spectrum analyzer. The DC voltage and current were measured with a multimeter. The capacitance was inferred by measuring the RMS voltage across the capacitor, and calculating the RC time constant using the 100ohm resistor.

#### Results

A graph showing the DC bias current versus the DC voltage across the capacitor is linked below:

It can be seen that the current increases exponentially as the DC voltage gets further and further away from its operating points. This is +16V (as expected) for normal operation, and -5V for reversed operation. The capacitor was not taken into heavy conduction to prevent destruction.

Between these two values (-5V to +16V) the capacitor behaved as rated, with the capacitance not showing any variation, and there being no noticeable distortion or noise. Beyond these limits, the capacitance began to vary by a small amount (2%) up until the point where the capacitor began drawing a large amount of current (-10V and +32V). At these points, the capacitors ceased to operate as capacitors, and acted as shorts for all AC signals.

At values approaching the cutoff voltages (-3V to +12V) the low frequency noise increased slightly to -96dB at 100Hz. This level rose as the voltage was increased beyond the limits to -60dB at 100Hz at the point where the capacitor ceased to function. This noise rolled off very quickly, with the level not being noticeable above a few kilohertz.

#### Conclusions

The electrolytic capacitor can be modeled at an ideal capacitor with two back-to-back zener diodes in parallel with it, with each zener representing one of the cutoff voltages. The leakage slowly increases for voltages below these cutoff voltages, and then quickly for levels above the cutoff voltages. The performance is very consistent within these bounds as well, with differences most likely accounted for by heating effects due to the increase in current flow at higher voltages.

So it seems that an electrolytic can be used backwards with negligible change in circuit behaviour, as long as it is within these bounds. These bounds change on both the positive and negative sides with capacitor voltage rating. A 1uF/50V capacitor was tested, and it operated up to -16V in reverse bias, which suggests a linear relationship between forward and reverse breakdown voltages. So if you plan to use a capacitor backwards, give it a quick check first to find out where its reverse breakdown begins. A DC current of 0.1uA is a good threshold to use.