## How a multimeter measures capacitance

13.03.2020 10:57

I've recently bought a Keysight U1241C multimeter. One of the features it has is a capacitance measurement. Since this is my first multimeter that can do that I was curious what method it uses. I was also wondering what voltage is applied to the capacitor under test and whether the probe polarity matters (for example, when measuring electrolytic capacitors).

The Figure 2-16 in the User's Guide seems to imply that polarity is important. The red probe (V terminal) is marked as positive and the black probe (COM terminal) is marked as negative: Image by Keysight Technologies

The description of the measurement method is limited to this note and doesn't say what voltages or frequencies are involved, but does give a rough idea of what is going on: Image by Keysight Technologies

Connecting an oscilloscope to a capacitor while it is being measured by the multimeter reveals a triangle waveform. I made the following screenshot with a 47 μF electrolytic capacitor connected to the multimeter set to the 100 μF range. The oscilloscope was set to DC coupling, so the DC level is correctly shown as 0 V at the center of the screen: Since current into a capacitor is proportional to the time derivative of the voltage, a triangle-shaped voltage means that there is a constant current flowing alternatively in and out of the capacitor. Connecting different capacitors revealed that the current and the amplitude of the voltage stay constant for each measurement range, while the period of the signal changes. So the multimeter applies a known current source I to the probes and measures time t it takes for the voltage to rise (or fall) for a present difference Upk-pk. From the measured rise (or fall) time it then calculates capacitance:

C = \frac{I\cdot t}{U_{pk-pk}}

These are the approximate current and voltages used by the multimeter for each range:

Range [μF] I [μA] Upk-pk [mV]
1 1.5 800
10 15 800
100 150 800
1000 340 200
10000 340 200

Note that 1000 μF and 10000 μF ranges seem identical in this respect. I'm guessing the only change is how the time is measured internally. Perhaps a different clock is used for the counter.

If a high range is selected while a small capacitor is connected, the voltage on the capacitor can reach much higher amplitudes. The highest I saw was about 2 V peak-to-peak when I had a 4.7 nF capacitor connected while the instrument was set to 100 μF range. In conclusion, the polarity of the probes isn't important. The applied signal to the capacitor is symmetrical and the capacitor will be alternatively polarized in the positive and negative direction regardless of how it is connected to the multimeter. The voltages do seem low enough that they probably don't damage polarized electrolytic capacitors.

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