Reading very low capacitances with Arduino

Question

I'm trying to measure the capacitance of a very low capacitance sensor (two parallel plates across a block of foam). This is a self-produced force sensor; I'm trying to eventually use some of the work presented here. I'm estimating that the capacitance should be in the neighborhood of 90 pF.

I started with the CapacitanceMeter tutorial from the Arduino web site. I modified it to use micros() instead of millis() and output pF instead of nF. I also swapped in a 10 megohm resistor in place of the 10K ohm one, and updated the code. However, I'm getting readings that swing by over 50 pF.

How can I improve the accuracy of the setup?

Thanks!

Answer 1

You can get an approximate measure of the capacitance with just 2 microcontroller pins, 1 resistor and 1 known capacitor. The circuit looks something like this:

C2 is the unknown capacitance you're trying to measure. C1 is a reference capacitor of known value, and about 50-1000 times the value of C2. R1 isn't too critical, 1k Ohm or so.

The idea is to charge C2 with a known voltage (5 or 3.3 V, whatever V+ is), and then transfer its charge (q = C*V) into C1. Each time we transfer the charge from C2 to C1, C1's voltage increases by a tiny amount proportional to C2. The number of times we have to transfer charge to make C1's voltage exceed some threshold (for us, the logical "1" threshold of pin A) is then inversely proportional to the value of C2.

The trick is to take advantage of the high-impedance state of the microcontroller pins. If we kept the bottom side of C1 grounded while charging C2, then we would also end up fully charging C1. Instead, we let the bottom side of C1 float by configuring pin B as high-impedance. Now, whatever the top side of C1 does, the bottom side does too, always keeping the same voltage across C1.

The measurement algorithm goes like this (in pseudo-C):

// Step 0: discharge C1 to prepare for a new measurement
PIN_A = 0;
PIN_B = 0;
delay(some_time); // long enough to discharge C1

bool under_threshold = true; // has the voltage across C1 exceeded the threshold?
int count = 0;
while (under_threshold)
{
    // Step 1: Charge C2
    PIN_B = Z; // Z means high-impedance
    PIN_A = 1;
    delay(some_time); // long enough to charge C2

    // Step 2: Transfer charge from C2 to C1
    PIN_A = Z;
    PIN_B = 0;
    delay(some_time); // long enough for C2 to discharge into C1

    // Step 3: Check if the threshold is exceeded
    if (PIN_A || (count > COUNT_MAX))
    {
        under_threshold = false;
    }
}
return count;

You can see a demonstration of the circuit at https://www.circuitlab.com/circuit/uq2zs6/cap-sensing/

Answer 2

Small capacitances are best measured using an HF oscillator, and measuring the change in frequency with and without the DUT in the oscillator tank circuit. The capacitance can then be calculated. This could be done automatically on the Arduino, and the result displayed. Here is the schematic for a PCB I designed for the Elsie LC meter which uses that technique.

Using conductive foam and measuring the change in resistance as it is compressed would be easier.

Answer 3

Since you use a capacitive force sensor and you want to know the real time value of the capacitance, you can use a sauty bridge.

^{simulate this circuit – Schematic created using CircuitLab}

With Cx : the capacitance you want to measure. C, R and E are known.

By applying Kirschof's laws, you have :

$$Vm=E.\frac{C-Cx}{2(C+Cx)}$$ By measuring Vm you can have Cx :

$$Cx=C.\frac{E-2Vm}{E+2Vm}$$

The resolution depends on the constants you are using and the quality of the Voltmeter you use.