## Capacitance meter (Part 1)

Part 1234

Identifiying a capacitor is no big deal as long as the labelling is readable: Depending upon the package type, we will use some conversion formula, like: However, identiying a surface mount capacitor may be tricky! In this case a capitance meter is necessary. There are some available on the market, but why buy one when we have an Arduino in hands?

Will it be the ultimate capacitance meter? Probably not! There are many DIY microprocessor controlled capacitance meters available on the net. Most are combinations of capacitance and inductance meters, based on the principle of resonating LC tanks. Some of them include more or less sophisticated auto calibration sections which make these tools easy to use and pretty reliable.

Once again (or say, “as usual”!), the proposed meter differs slighlty from the common, mainly because it does not require a calibration, as long as measurements are performed with precision resistors at a reasonnably stable room temperature. The other advantage is that the meter is totally imune versus Arduino power supply because of the analysis of the discharge instead of the charge of the capacitor. This capacitance meter shall include a self ranging feature in order to have an extended range of operation from 1pf to 1000µF. But the main difference versus most capacitance meters lies in the calculation process!

Let’s go back to some fundamentals.
In an RC circuit, the value of τ (tau) (expressed in seconds) is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e. τ = R × C

OK, fine, but what shall we do with this?

The time constant is the time required to charge the capacitor to ≈ 63% of its full charge. In the same way, it is the time required to discharge the capcaitor to ≈ 37% of its initial voltage. These values are derived from the mathematical constant e, specifically (1 − e^− 1) and (e^− 1) respectively.

Ah, that’s better. Most designers stopped their reading at this point and mananged to design charging devices associated with analog to digital converters and timers in order to capture the start event and the time at which the charge is about 63% of the feeding voltage. So far so good, but my first intuition is that this type of design might by prone to noise related errors. The second intuition is to prefer the discharge cycle because it is imune toany power supply disturbancies.

An in deep approach of the discharging equation:
V = E (1 – e^-t/RC)

With:
• V et E in volts
• t in seconds
• R in ohms

shows that the tangent to the transient curve crosses the time axis at τ !

And here is a real life example taken for the discharge cycle of a 300 pF capacitor through a 10 MOhms resistor. The theoritical time constant would be T = R.C = 3.0 10E-3, while the calculated value is 2.8 10E-3. Hum, looks good! How to get there? The acquisition, calculation will decompose in the following steps

• Charging the capacitor to its max (or almost max value), say 4.5 V
• Start measuring the capacitor voltage in scan mode
• Stop measuring the capacitor voltage
• Compute the equation of the transient curve
• Compute the equation of the tangent to the origin of the transient curve
• Compute the abscissa of the section point common to the time axis and to the tangent to the origin of the transient curve

And now that we have our time constant and knowing the value of the resistor, we can deduce the capacitance!

You may say that this is a lot of maths before getting to the result! True, but here, your are lucky, because the simplification of the equations makes the calculation almost easy

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