Capacitors are weird.
I envisioned several electronic projects that would charge a capacitor during daylight using a solar panel, and then consume that energy to stay awake at night. For some reason, the project prototypes powered down sooner than the capacitor consumption formula predicted.
In modern digital circuits, most capacitors are used to smooth the power supply and reduce circuit noise. When capacitors are used for pulse width modulation or frequency generation they commonly have a variable resistor or crystal to set the timing. When capacitors are used to debounce a switch or hold open a transistor, the exact hold time is often not critical. So, up until now, I didn’t really need to understand capacitor self-discharge.
Unless you need longer-term power storage or unless you are a professional electrical engineer, many of the unusual idiosyncrasies of real-life capacitors won’t affect you. However, you'll definitely want to read this article if you are building a competition solar robot, are using old stock or salvaged capacitors, or if you are attempting to discharge a capacitor for more than a minute.
Surprisingly, much of this article is devoted to the difficulty of measuring discharge without causing the discharge.
To calculate the ideal capacitance that will provide adequate power over a period of time, you need to know the circuit drain, fully-charged voltage, minimum acceptable voltage, and time.
For example, let’s say I want a capacitor to power a red LED (1.9 V) for ten minutes (600 seconds). Assume I have a resistor (350 ohm) that limits the circuit to an average 1 mA current usage when the capacitor is fully charged at 2.5 V until it is drained down to 2.0 V.
capacitance in farads = current draw in amps / ((starting voltage - ending voltage) / time in seconds)
capacitance in farads = 0.001 A / ((2.5 V - 2.0 V) / 600 s)
capacitance in farads = 0.001 A / (0.5 V / 600 s)
capacitance in farads = 0.001 A / 0.00083333333333333 V/s
capacitance in farads = 1.2 F
Wow. A farad is a pretty big capacitor value. Most of us are accustomed to values in the microfarad range (0.000001 F). If you need a value in the farad range, that’s a job for an ultracapacitor.
Depending on the age and quality of the capacitor you choose, the voltage is going to drop below your circuit’s minimum operating voltage much sooner than predicted by that formula. Why?
Like all other electronic components, capacitors are designed to be as small as possible. The trade-off is that the insulating material between layers must be very thin, which is less electrically resistant. The reduced insulation resistance, combined with small imperfections, allows some electrical current to slowly leak through.
Capacitor schematic symbol with resistors to represent leakage between the plates.
The unknown factor in the above formula is how quickly the capacitor will discharge by itself, even if it isn’t connected to a circuit. For the example circuit, we need to include the amount of current leaked by the capacitor, not just the LED, to select a value that will last long enough.
In all of my tests to measure capacitor leakage, the voltage never exceeds the manufacturer’s rating, nor is power applied in reverse of the polarity (+ -) markings. Also, the testing occurs at room temperature.
To begin with, the capacitor is charged to a specific voltage using a desktop power supply or voltage regulator circuit. Then, the capacitor is disconnected from power and the voltage is measured over time.
To avoid an external drain, the capacitor is not installed in a circuit nor a breadboard. The capacitor simply rests on a wooden desk connected to the measuring device via alligator clips.
The most obvious method for measuring voltage is our handy-dandy multimeter. Go ahead and try it for yourself. You'll suspect that every capacitor you own is awful!
Here are the results of measuring a fresh, modern, 1 µF multilayer ceramic capacitor.
Measuring self-discharge of a 1 microfarad capacitor using a multimeter (red line) or a special chip (blue line).
The red line is the drop in voltage (loss of power) when a standalone capacitor is measured with a multimeter. It is almost completely drained in only a minute.
It turns out that the multimeter is causing the drop in voltage. You see, multimeters are designed for flexibility, wide range, low cost, and accuracy, rather than low current consumption. The meter circuitry drains the capacitor.
You can prove this to yourself by first measuring the voltage with a meter connected the whole time. Then, disconnect the meter, recharge the capacitor, wait a couple of minutes, and then connect the meter. Although the voltage will immediately start to drop when the meter is connected, you'll notice that the voltage was a lot higher after a couple of minutes of being left alone then it was when the meter was connected the entire time.
To reduce the effects of the measurement device on the capacitor, you need something with a high-impedance input. The term “high impedance” is saying something has a high resistance, low capacitance, and low inductance. In other words, the input has little effect on the thing it is connected to.
Oscilloscopes generally have high impedance inputs. Another popular choice is to use a CMOS op-amp to buffer the input signal. In my case, I used the Microchip MCP6S22 from my Minifigure Multimeter project. The MCP6S22 has a 1013 or 10,000,000,000,000 Ω input resistance.
Look back at the previous graph and notice the almost flat blue line at the top. That’s the same capacitor measured using the MCP6S22 chip. The comparison between the red and blue lines clearly demonstrates that an off-the-shelf multimeter cannot directly measure the capacitor’s voltage to determine the rate of self-discharge.
Below is another example, with a much larger 220 µF capacitor. In this case, I tested a fresh, modern, aluminum electrolytic capacitor.
Measuring self-discharge of 220 microfarad capacitor.
The curve is similar to the previous graph, but the x-axis is 135 times longer as it is expressed in minutes, not seconds. The larger capacitor contained enough power that the drain of the multimeter had less of an impact, relatively speaking. And yet, the meter drains the capacitor far faster than internal leaks. Therefore, trying to continuously measure self-discharge of even a large-value capacitor with a multimeter will produce inaccurate results.
Theoretically, you could take a quick measurement, disconnect the meter, wait a while, connect again, take another measurement, and so on. It will still introduce some inaccuracy, but may be acceptable if you do not have access to a high-impedance measuring device.
Unfortunately, we are about to find out that even a chip with a 10 trillion ohm input is not enough to accurately measure capacitor leakage.