Using a simple Arduino to measure capacitor value

As you probably read in this post, capacitance is a measure of the ability to store energy. They are among other things used in rectifiers, as bypass devices and in analog filter circuits.

They are super-important components and critical for making sure applications and other components work.

But how do you measure this super-important “size” (the “capacitance”)

The Time Constant and the Circuit

The time constant is defined as the time it takes for a system to reach a given state from a step input.

In this case we want to find “C” and a circuit with only a capacitor and a resistor (in series) have a known time response.

And that shall we exploit!

So to measure the capacitance of the Capacitor we can just charge it up through a known resistor and measure the time it takes before it reaches ~63,2% of the charging voltage!

The circuit is rather simple:

  • The capacitor under test is connected in series with a known resistor (here: 10 k Ohm).
  • The capacitor circuit is connected to pin 7 on the Arduino.
  • The capacitor was also connected to an analog input on the Arduino to measure the voltage (A0).

The Firmware

The firmware to do this measurement does 3 measurements, averages the result, and prints out the final answer printed on the serial (USB).

The flow is as following:

  1. The Arduino discharges the capacitor circuit by setting pin 7 low. It makes sure the capacitor is empty by reading the voltage over it.
  2. It starts charging the capacitor circuit and starts the timer.
  3. It continues charging until the capacitor until it reaches 3,16 volt (~63,2% of 5 V).
  4. When the circuit reaches 3,16 volt it saves the accumulated time value and goes back to 1 if this is done less than 3 times.
  5. The final answer are an average of all the measurements and the result are printed out on the serial port!
#define NO_MEASSUREMENTS 3

#define analog_pin     A0
#define capacitor_pin  7

#define resistor_value   989000.0F // the value on the resistor in Ohms

unsigned long start_time = 0;
unsigned long accumulated_time = 0;

void setup() {
pinMode(capacitor_pin, OUTPUT);

Serial.begin(115200);
}

void loop() {

accumulated_time = 0;

for(uint8_t i = 0; i < NO_MEASSUREMENTS; i++){

// Make sure the capacitor is dicharged
digitalWrite(capacitor_pin, LOW);
while(analogRead(analog_pin) > 0){}

// set chargePin HIGH and capacitor charging an
digitalWrite(capacitor_pin, HIGH);
start_time = micros();

// 647 is 63.2% of 1023, which corresponds to full-scale voltage
while(analogRead(analog_pin) <= 647){}
accumulated_time += (micros() - start_time);
}

float result_time = ((float) accumulated_time) / NO_MEASSUREMENTS;

float micro_F = ( result_time / resistor_value) * 1000;

Serial.print((long)result_time);
Serial.print(" us before tau / ");

print_float(micro_F, 2);
Serial.println(" uF");
}

// from Peter H. Anderson, Baltimore, MD
void print_float(float f, int num_digits)
{
int pows_of_ten[4] = {1, 10, 100, 1000};
int multiplier, whole, fract, d, n;

multiplier = pows_of_ten[num_digits];

if (f < 0.0){
f = -f;
Serial.print("-");
}

whole = (int) f;
fract = (int) (multiplier * (f - (float)whole));

Serial.print(whole);
Serial.print(",");

// print each digit with no leading zero suppression
for (n=num_digits-1; n>=0; n--){
d = fract / pows_of_ten[n];
Serial.print(d);
fract = fract % pows_of_ten[n];
}
}

This came out from the Serial Monitor:
105404 us before tau / 106,57 uF

(The Capacitor under test was stated 100 uF “big”. This difference can be caused by many different things. Among others:  Inaccurate timing, ADC (un)accuracy, power supply imprecision and of course: Difference between stated and actual capacitance from the manufacturer).

Conclusion

As we saw here: You can measure capacitance using a simple mathematical “bond” that exists between time, resistance and capacitance and a simple and cheap circuit.

But note that this need some “upgrades” (especially on the hardware-side) to become a “high precision” measurement device.

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