Precision-matched capacitor pairs are commercially available items, but only in a limited range of values, working voltage, and dielectrics.
Plus, sometimes an extra critical application with extra tight tolerances (or an extra tight budget) can dictate a little (or a lot) DIY. For example, see “Inherently DC accurate 16-bit PWM TBH DAC” (Reference 1)
Figure 1’s matchmaker circuit can help make the otherwise odious chore of searching through a batch of parts for accurately matching pairs quicker and a bit less taxing. Best of all, it does precision matchmaking (potentially to the ppm level) with no need for pricey precision reference components.
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| Figure 1. | Flip-flop U2b generates complementary excitation of the A and B capacitors under test. |
Here’s how it works.
Complementary (equal but opposite) excitation of the A and B capacitors under test implies that if CA = CB, then the charges passed will exactly cancel out, yielding a null at OUTPUT. If they differ, however, then an integrated output signal of 50 mV per % of mismatch will result if C3, C5, C4, and CAB (capacitors randomly selected from the trial batch) are equal in value, e.g., 0.68 µF. This signal is synchronously rectified by U1b, then integrated and buffered by the U1c and A1 feedback loop.
If CA > CB, the “A > B” output polarity will be positive relative to “B > A”. The reverse is also true: If CB > CA, the “A > B” output polarity will be negative relative to “B > A”.
Resolution of the match measurement will depend on the voltage resolution of the digital voltmeter (DVM). If that’s 1 mV, then matching to ±1/50th of 1%, or ±0.02%, will be possible. If it’s 100 µV (typical of a standard 3¾ digit multimeter with a 300 mV scale), then matching to ±0.002%, i.e., ±20 ppm, is doable. And so on…
Measurement gain is inversely proportional to C4. So, if you need more resolution, simply decrease C4 to gain gain.
Note that the U1aU2a clock’s frequency precision and stability is somewhat dubious (even if we’re charitable). Happily, the accuracy of the ultimate CA/CB match doesn’t depend on a stable clock. Neither does match accuracy depend on the output impedances of U2b’s complementary outputs, not even on their symmetry!
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| Figure 2. | The U1aU2a multivibrator waveforms; the green waveform is the R3R4 junction, and the red waveform is U2 pin 6. The frequency is 0.1 mHz/C3. |
Both insensitivities derive from the fact that it’s the transferred charge that forms the basis of matchmaking precision, and therefore neither current nor voltage matters very much.
However, due to the temperature sensitivity of some dielectrics, it’s probably a good idea to handle tested devices with thermally insulating gloves. This will save time and frustration waiting for them to equilibrate, not to mention possible outright erroneous results. Those are also known to cause frustration!
Reference
- Woodward, Stephen. "Inherently DC accurate 16-bit PWM TBH DAC."