How the capacitance of a capacitor is measured?

Many multimeters have the ability to measure capacitance. It is also possible to buy meters which are intended specifically for capacitance. Many of these meters also have the ability to measure other parameters of the capacitor, such as effective series resistance.

With a multimeter. Mine does ohms, volts, amps, farads, Hz, degrees, and hFE. That's why it's a MULTI meter ;-)

There are many ways to determine the capacitance of something (capacitors too).

Handy equations for capacitive reactance, in different forms, can be applied to a given circuit with unknown C, and C calculated based on the response of the circuit. It's possible to use complicated math, but simple factoring skills are all you need for what you want to do.

In one view, capacitance in Farads is a function of parallel plate area A seperated by distance D through which an electric field would permeate (the dielectric - air, mica, plastics, vacuum, cheese slice, etc ) of known dielectric constant K. Included in the equation is a constant, and it's all pretty simple to do. In that case, no voltage, signal, or empirical tests are required, just the physical facts of the capacitor.

If you look at this formula and recognize that, for a given electric field within the capacitor, a force would be required to change seperation distance D. Eventually, one realizes that it is possible to make a motor or generator using capacitive principles only, which is mildly amusing at least.

Well, if you don't have a multimeter, you can rig a Wheatstone bridge and operate it with AC. To an alternating current, a capacitor looks like a resistor, Xc = 1 / (2*pi*F*C).

Alternately, you can set up a very accurate current source and sink (using a number of transistors and a precision resistor), use a pair of comparators to tell when the capacitor's voltage is above or below some limit, and based on these decisions, alternately charge and discharge the capacitor. Since the charge/discharge current is known, the voltage range, and you can measure the time with various sophisticated means, you can refer directly to the capacitor equation I = C * dV/dt and find it to great accuracy.

I mean, as accurate as the capacitor itself is. About the best you get is

1%, with 5% typical for film and +100%/-50% typical for electrolytics.

Tim

-- Deep Fryer: a very philosophical monk. Website:

This points to a useful book on the "coaxial" AC bridges used to measure capacitance in National Standards Laboratories.

Probably an over-kill for your application, but I'd not be parted from my copy.

For most applications Neil Heckt's capacitance meter works very well

I bought mine years ago - on Winfield Hill's recommendation - and it does pretty much everything one needs for looking at regular capacitors and inductors.

The capacitative component of electrolytic electrodes is a much trickier subject, and for them you need an impedance bridge.

Tony Williams recommended the Thurlby-Thandar Instruments TTi LCR400 (Farnell 351-0906) which worked pretty well, until the electrolyte solution corroded the printed circuit board. I would have preferred a second-hand Hewlett-Packard impedance bridge which would have cost about the same from a mate of Winfield Hill's. but my boss preferred to buy something shiny and new, if less flexible.

--
Bill Sloman, Nijmegen
> > >  be worth looking at.... at GBP595-00.

Another limiting factor is leakage current. This depends on dielectric material. Randomly choosing the first spec I see (for a Xicon elcap) I see leakage specified at ".01CV or 3uA, whichever is greater"; I've seen specs that were considerably worse. Using this method, leakage current will appear to make the capacitance smaller than it actually is; the practical effect is that the ramp time measurement Tim mentions needs to be done with currents in the mA range, for electrolytics.

Thanks to all by your answers. I guess that the fastest method to measure the capacitance is with a multimeter equippedd for this purpose.

I will study the other methods for achademical purposes.

** The Capacitor Wizard is an ESR meter - it doe not measure capacitance as such.

It appears to be a simple AC impedance meter, operating at 100khz.

At that frequency, most electro capacitors have AC impedance values lower than the residual resistance of the electrolyte and foil inside them.

So the CW meter finds that residual resistance and displays it as " ESR ".

Useful to determine if the electrolyte has deteriorated or gone from the cap and it need replacing.

........ Phil

This is a good learning question.

Without getting in to deep electronics details

Resistors have resistance R ohms and capacitors and inductors have reactance X ohms. The units are very similar except reactance of a capacitor varies with frequency.

To measure capacitance first measure reactance then compute the capacitance because the frequency and applied voltage ae know.

Voltage across a resistor V= I x R Voltage = V Current = I and R = Resistance

The ideal capacitor V = I x X Reactance at a know frequency

For a capacitor the reactance has the classic formula

X = 1 / (2 x Pi x F x C) reactive ohms Pi = 3.1415 etc and F = frequency Hz C = capacitance in Farads

NOTE clearly here Reactance X is inversely proportional to the frequency and capacitance

As frequency increases X decreases.

HOW TO MEASURE C

-------------------------

Put a known AC Voltage V across a capacitor C and measure the Current I

So compute X = V/ I

Now we know X we can transpose the formula to obtain C - the capacitance

X = V/ I = 1/ (2 x Pi x F x C) all variables are known except for C and and I

==> I/V = 2 x Pi x F x C

==> I

-------------- = C V x 2 x Pi x F

Since V , I and F are know we can compute C

Hence the measured current is proportional to C - the capacitance.

C = S x I

where S is is the scale factor - so you can use a current meter and scale the results to read C - capacitance.

Voltage and Currents should be in RMS values

This is a simplistic idea view of how to measure capacitance.... at the low and high end of typical capacitance values ..... 100uF+ and less than

10nF there are physical properties of a capacitor which make then non-ideal - which lead to incorrect measurements.... watch out for this.

Also the chosen driving Voltage and chosen frequency must also be considered.........

Also 2 - The method of measuring the current current thru the capacitor should be considered.

Just my 2 cents worth.

Regards Joseph Goldburg - Engineer - Australia

Yeah, but they're crap when it comes to smaller capacitances. Best way is to put the cap in parallel (or series) with a precisely known and suitably-chosen reference inductor and measure the resonant frequency of the pair. Then determine the cap value by substitution & transposition into the well-known formula f=1/2pi*sqr(LC)

--

"What is now proved was once only imagin\'d" - William Blake

If you know the expected range of the capacitor then other economical methods can be used.

Eg

Use the capacitor in an oscilator circuit.

EG LC or CR oscilator

The frequency will be in some ways propotional to the capacitance used.

EG for LC Osc

Freq = 1/ (2x Pi x SQUAREROOT(LC))

If L is a know value then Freq varies only with C

Hence F porportional to SQUARE ROOT (C)

All you need is a frequency counter with a Square root calibration curve.

JG