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Coulomb meter

Introduction: what is a Coulomb
A Coulomb (C) is the unit of electric charge.
When a body is electrically neutral (not charged), the number of protons is equal to the number of electrons in it.
When there are more protons then electrons, there is a positive charge.
When there are more electrons then protons, there is a negative charge.
One Coulomb is approximately equal to the charge of 6.24x10^18 protons, or -6.24x10^18 electrons.
One Coulomb is the amount of electric charge transported in one second by a steady current of one ampere.

Examples of charge
We can create a charge for instance by rubbing a PVC rod with wool.
The rod becomes negatively charged, and the wool positively.
The charge made in this way, is maybe some nano-Coulomb (nC) per square cm.

Another example of charge, is a charged capacitor.
The positive pole of the capacitor has an excess of protons, while the negative pole has an equal excess of electrons.
The charge (in Coulomb) stored in a capacitor is equal to the voltage across the capacitor (in Volt) multiplied by the capacitance (in Farad).

How to measure charge.
One property of charge is , that charges of opposite sign will attract each other.
A charged body likes to attract an equal amount of the opposite charge.
We can use this property for making a Coulomb meter. In this picture, we see:
A negative charged insulated rod (A) from which we will determine the charge.
A metal plate (B) connected to the Coulomb meter and located near the charged rod .
The Coulomb meter consists of a capacitor (C) with a voltmeter across it.
The bottom lead of the capacitor is connected to ground

When the rod A is brought near plate B, the negative charged rod A will attract an equal positive charge to plate B.
The charge going to plate B, is coming from the upper capacitor plate, leaving this negatively charged.
This will then attract an equal positive charge from ground to the lower capacitor plate.
Capacitor C is now charged, and the voltmeter can measure a voltage across it, proportional to the measured charge.

The measurement works the best (most accurate) when the rod (A) is very close to the plate (B).
They may even touch each other, this makes no difference for the measurement.
On the spots they touch, the opposite charges will cancel out each other, leaving both rod A and plate B discharged.
But capacitor C stays charged.

In this set-up, only the charge of the rod facing plate B (at short distance) is measured.
The rest of the rod at some distance of plate B may also be charged, but this has little influence on the measurement.
This is because the attraction between charges reduces with the square of the distance between them.

The circuit diagram of the Coulomb meter Connector CN1 is the input connector of the Coulomb meter.
Connector CN2 must be connected to ground.
Capacitor C1 converts the charge, to a voltage.
Because C1 is 100 nF, every volt across C1 corresponds to a charge of 100 nC.
C1 must have low leaking current, and must be rated for at least 100 Volt.
Component A1 is a gas discharge tube, it protects the input for voltages higher then 90 Volt.

Op-amp IC1 is a buffer amplifier with gain of +1.
The most important properties for this amplifier are.
- Very high input impedance, in this case about 1000 GΩ
- Very low input current, in this case about 3 pA.
Both properties are important to prevent the Coulomb meter output to drift away from it's measured value

With potentiometer R4 one can adjust the amplifier output voltage to exactly 0 Volt (with input shorted to ground).
This removes the input offset voltage of the op-amp, in my case I could adjust the output voltage between -13 mV and + 7 mV with R4.

Resistor R1 limits the op-amp input current to a safe value of below 1 mA, in case the voltage across C1 reaches 90 Volt.
Resistor R5 was recommended in the datasheet of op-amp CA3140E  in case the input voltage could be higher then the supply voltage.

The circuit is powered by rechargeable batteries, the positive supply voltage is + 4.8 Volt.
The negative supply voltage is -2.4 Volt.
With this configuration, the output can reach plus and minus 2 Volt, which I wanted to drive a digital voltmeter.
The total supply voltage is not higher then necessary, to keep the amplifier input current as low as possible.

Led D1, is the on-indicator and also indicates the status of the batteries.
As long as D1 shines brightly, the batteries are o.k..
The total current consumption of the circuit is about 5 mA. A look inside the Coulomb meter.
As you might see, the opamp is laying upside down.
It is mounted to the copper PCB board with some heatsink compound between.
This is done to keep the op-amp as cool as possible, and through this the op-amp input current as low as possible. The red connector at the top is the input (CN1).
The black one at the right is the ground connector (CN2).
The 2 connectors at the bottom are the voltmeter outputs.
The potentiometer is for removing the offset voltage. The probe for measuring the charge of a surface, it can be connected onto the input connector of the Coulomb meter.
The probe has a aluminium plate with an area of 10 cm² Before starting a measurement, the Coulomb meter must be discharged, by shortly connect the ground connection to the input connection.
The voltmeter must now read 0.000 Volts.
Eventually adjust the potentiometer if there is some offset voltage. The Coulomb meter in action.
A charged Plexiglas plate is held just above the probe.
Every volt on the voltmeter corresponds to 100 nC (nano-coulomb) of charge.
So in this case we measure a charge of -4.1 nC.
Because the probe has an area of 10 cm², the charge of the Plexiglas is -0.41 nC per cm².
When the charged surface is not touching the probe, the meter will return to zero, after the charged surface is moved away from the probe. When the charged surface has touched the probe, the charge can transfer from the surface to the probe.
Now the charge is stored in the coulomb meter, and will stay there when the (now discharged) surface is moved away from the probe.

Extending the measuring range For measuring larger quantities of charge, the measuring range of the Coulomb meter can simply be extended.
Just connect an extra capacitance between input an the ground connector.
In this picture, I have added a 10 μF capacitor.
The measuring range is now 10.1 μC per Volt.
If you want exactly 10 μC / V you might use 3 capacitors of 3.3 μF in parallel, or select a 10 μF capacitor with -1% tolerance.

Voltage drift
Once the Coulomb meter is charged, the output voltage should stay constant, as long as you don't add new charge.
But in practice, there will be some leaking current, which will slowly discharge capacitor C1.
This causes the output voltage to drift away slowly from the measured voltage.
Another cause of voltage drift is the input current of IC1, which slowly charges capacitor C1, this can especially be seen when the output voltage is about 0 Volt. This picture shows the voltage drift of my Coulomb meter.
The output voltage drift (in mV) is shown as function of time.
The red line is when the Coulomb meter is charged to -1.5 Volt.
The yellow line is when the Coulomb meter is charged to +1.5 Volt.
The blue line is for a discharged coulomb meter (0 Volt).

For measurements over a long period, the voltage drift can influence the measurement results.
But for fast measurements, the effect of voltage drift can be neglected.

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