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Capacitance Meter and RC Time Constants

Overview: A resistor will charge a capacitor in TC seconds, where

• TC = R * C

• TC = time constant in seconds
• R = resistance in ohms
• C = capacitance in farads (1 microfarad [ufd] = .0000001 farad = 10^-6 farads )

The voltage at 1 Time Constant equals 63.2% of the charging voltage.

Example: 1 megohm * 1 microfarad = 1 second
Example: 10k ohms * 100 microfarad = 1 second

Experimental Setup

This sketch works because the Arduino pins can be in one of two states, which are electrically very different.

• Input State (set with pinMode(pin, INPUT);)
  • High Impedance (resistance) - Makes very little demand on the circuit that it is sampling
  • Good for reading sensors but not lighting LED's

• Output State (set with pinMode(pin, OUTPUT);)
  • Low Impedance - Can provide 40 mA source (positive voltage), or sink (negative voltage)
  • Good for lighting LED's, driving other circuits - useless for reading sensors.

Additionally the pins can be HIGH (+5 volts), to charge the capacitor; or LOW (ground) to discharge the capacitor

Alogrithm for capacitance meter sketch

• Set discharge pin to INPUT (so it can't discharge the capacitor)
• Record the start time with millis()
• Set charge pin HIGH
• Check the voltage repeatedly in a loop until it gets to 63.2% of total voltage.
• After the cap is charged, subtract the current time from the start time to find out how long the capacitor took to charge.
• Divide the Time in seconds by the charging Resistance in ohms to find the Capacitance.
• Discharge the capacitor. To do this:
  • Set the charge pin to Input
  • Set the discharge pin to OUTPUT and make it LOW
• Read the voltage to make sure the capacitor is fully discharged
• Loop and do it again

Arduino Sketch

/*  RCTiming_capacitance_meter
 *   Paul Badger 2008
 *  Demonstrates use of RC time constants to measure the value of a capacitor 
 *
 * Theory   A capcitor will charge, through a resistor, in one time constant, defined as T seconds where
 *    TC = R * C
 * 
 *    TC = time constant period in seconds
 *    R = resistance in ohms
 *    C = capacitance in farads (1 microfarad (ufd) = .0000001 farad = 10^-6 farads ) 
 *
 *    The capacitor's voltage at one time constant is defined as 63.2% of the charging voltage.
 *
 *  Hardware setup:
 *  Test Capacitor between common point and ground (positive side of an electrolytic capacitor  to common)
 *  Test Resistor between chargePin and common point
 *  220 ohm resistor between dischargePin and common point
 *  Wire between common point and analogPin (A/D input)
 */

#define analogPin      0          // analog pin for measuring capacitor voltage
#define chargePin      13         // pin to charge the capacitor - connected to one end of the charging resistor
#define dischargePin   11         // pin to discharge the capacitor
#define resistorValue  10000.0F   // change this to whatever resistor value you are using
                                  // F formatter tells compliler it's a floating point value

unsigned long startTime;
unsigned long elapsedTime;
float microFarads;                // floating point variable to preserve precision, make calculations
float nanoFarads;

void setup(){
  pinMode(chargePin, OUTPUT);     // set chargePin to output
  digitalWrite(chargePin, LOW);  

  Serial.begin(9600);             // initialize serial transmission for debugging
}

void loop(){
  digitalWrite(chargePin, HIGH);  // set chargePin HIGH and capacitor charging
  startTime = millis();

  while(analogRead(analogPin) < 648){       // 647 is 63.2% of 1023, which corresponds to full-scale voltage 
  }

  elapsedTime= millis() - startTime;
 // convert milliseconds to seconds ( 10^-3 ) and Farads to microFarads ( 10^6 ),  net 10^3 (1000)  
  microFarads = ((float)elapsedTime / resistorValue) * 1000;   
  Serial.print(elapsedTime);       // print the value to serial port
  Serial.print(" mS    ");         // print units and carriage return


  if (microFarads > 1){
    Serial.print((long)microFarads);       // print the value to serial port
    Serial.println(" microFarads");         // print units and carriage return
  }
  else
  {
    // if value is smaller than one microFarad, convert to nanoFarads (10^-9 Farad). 
    // This is  a workaround because Serial.print will not print floats

    nanoFarads = microFarads * 1000.0;      // multiply by 1000 to convert to nanoFarads (10^-9 Farads)
    Serial.print((long)nanoFarads);         // print the value to serial port
    Serial.println(" nanoFarads");          // print units and carriage return
  }

  /* dicharge the capacitor  */
  digitalWrite(chargePin, LOW);             // set charge pin to  LOW 
  pinMode(dischargePin, OUTPUT);            // set discharge pin to output 
  digitalWrite(dischargePin, LOW);          // set discharge pin LOW 
  while(analogRead(analogPin) > 0){         // wait until capacitor is completely discharged
  }

  pinMode(dischargePin, INPUT);            // set discharge pin back to input
} 

Further things to try

• Measure capacitors in parallel and in series, check to see if your observations agree with electronic theory
• Average together a group of readings for more accuracy
• Fight with "Serial.print" to print out decimal point and fraction (see Stopwatch sketch)
• Swap out several charging resistors on different pins to make an "auto-ranging" capacitance meter
  • Substitute in larger resistors if the charging time is too short, smaller resistors if the charging time is too long.