Measuring absolute capacitance.

[Mr RB]

Perhaps I misunderstood you, but there seems to be a flaw in what you said.

How does constant current negate ESR? The voltage across a cap will be Vc = Integral(i/C, dt) + i.R, where R is the ESR of the cap.
...

MrAl beat me to it. My original point was that the rate of change of the voltage will be based on the current, and not affected by ESR. However my "quickie implementation" of starting from zero volts was flawed as you rightly noticed.

Ok, in the interests of simplicity, why not use a schmidt trigger oscillator of one resistor and one cap. The peak to peak voltage of the cap waveform can be seen on the 'scope, and the resistor can be measured with the multimeter.

Then it can be solved for "true capacitance" based on Vwave, Vdd, and period.

My first pico cap meter was a schmidt trigger inverter I installed in my frequency meter and all I had to do was calibrate the one resistor with a trimpot and click the meter onto "period". It worked like a charm.

 

[MrAl]

Hi again Roff,

That sounds like an interesting method too, a little hard to apply in real life perhaps (like my sine method) but still interesting.
I've also found that the esr has to be pretty high before it starts to affect the reading much, say 50 ohms or something like that, as long as our charge
resistance stays high enough like 2k or above (using a regular method vs a method that eliminates the esr).

The easiest to apply are the standard charge through a resistor and measure the time between two voltage levels, and the constant current method. The constant current method of course will require a programmable current source.

 

[Roff]

I'm a little surprised that I didn't get any comments on post #20, regarding C=I/(dv/dt). Maybe I just have an unhealthy ego.

 

[dougy83]

I'm a little surprised that I didn't get any comments on post #20, regarding C=I/(dv/dt). Maybe I just have an unhealthy ego.

It seemed like a more difficult reverse of the previously discussed usage of a constant current current to charge the cap and measuring the time at 2 points (& therefore slope). C = I/(dv/dt) is used in both cases.

 

[Roff]

It seemed like a more difficult reverse of the previously discussed usage of a constant current current to charge the cap and measuring the time at 2 points (& therefore slope). C = I/(dv/dt) is used in both cases.

Yeah, I guess the only time it really stands out is when C is a function ofvoltage.

 

[Mr RB]

...
That sounds like an interesting method too, a little hard to apply in real life perhaps...
...

Maybe not. If the comparator setpoints are held at specific levels (or actually it just needs a specific voltage hysteresis compared to Vdd) then the cap voltage will rise at one Tc and fall at one Tc, so total period of oscillation will be 2Tc.

So in implementation all it needs is a frequency meter and to know the value of the charge resistor, and solve for Tc = RC;
Tc = 0.5/freq
C = Tc/R

 

[Roff]

Maybe not. If the comparator setpoints are held at specific levels (or actually it just needs a specific voltage hysteresis compared to Vdd) then the cap voltage will rise at one Tc and fall at one Tc, so total period of oscillation will be 2Tc.

So in implementation all it needs is a frequency meter and to know the value of the charge resistor, and solve for Tc = RC;
Tc = 0.5/freq
C = Tc/R

Sounds similar to the circuit I posted in post #8.

 

[MrAl]

I'm a little surprised that I didn't get any comments on post #20, regarding C=I/(dv/dt). Maybe I just have an unhealthy ego.

Hi again Roff,

Actually my post was in reference to that post you are talking about that you posted, but i didnt quote it so MrRB must have thought i was responding to his post. My fault as i should have at least made it clear as to who i was talking to. I edited the post to help make this more clear.
My apologies to MrRB and Roff.

MrRB:
That method does not seem too hard to implement. Did you try a simulation?
We were talking about methods that would eliminate esr though werent we?

 

[Mr RB]

Roff, yes your comparator circuit does the same thing, but it's better as your resistors set the switching thresholds to a known voltage value (provided the CMOS output goes from exactly 0v to 5v).

MrAl, ESR elimination is nice but in the spirit of the OP's question I think he was after a way to quantify a capacitor using simple test equipment and a simple circuit, so once he measures the absolute capacitance value of a test cap he can use it to calibrate a home made capacitance meter? I've been in the same place although I found some 1% caps in a junkbox.

Still it would be nice to have a simple procedure to measure a cap within 1% accuracy using nothing more than a multimeter and a 555 or schmidt inverter or something. The comparator oscillator way is nice but it really requires a frequency meter and known setpoint voltage (or a scope to see the amplitude).

Maybe there is a way using mains AC freq from a transformer (AC volts measured with multimeter) into a cap and resistor? Mains freq won't be a great sine as it is usually deformed flat on peaks but maybe this could get close to a 1% reding of the caps value as at least the mains freq is usually within 0.1% freq accuracy?

 

[Roff]

Still it would be nice to have a simple procedure to measure a cap within 1% accuracy using nothing more than a multimeter and a 555 or schmidt inverter or something. The comparator oscillator way is nice but it really requires a frequency meter and known setpoint voltage (or a scope to see the amplitude).

You don't need to measure any voltages if you use precision resistors.

 

[MrAl]

Roff, yes your comparator circuit does the same thing, but it's better as your resistors set the switching thresholds to a known voltage value (provided the CMOS output goes from exactly 0v to 5v).

MrAl, ESR elimination is nice but in the spirit of the OP's question I think he was after a way to quantify a capacitor using simple test equipment and a simple circuit, so once he measures the absolute capacitance value of a test cap he can use it to calibrate a home made capacitance meter? I've been in the same place although I found some 1% caps in a junkbox.

Still it would be nice to have a simple procedure to measure a cap within 1% accuracy using nothing more than a multimeter and a 555 or schmidt inverter or something. The comparator oscillator way is nice but it really requires a frequency meter and known setpoint voltage (or a scope to see the amplitude).

Maybe there is a way using mains AC freq from a transformer (AC volts measured with multimeter) into a cap and resistor? Mains freq won't be a great sine as it is usually deformed flat on peaks but maybe this could get close to a 1% reding of the caps value as at least the mains freq is usually within 0.1% freq accuracy?

Hi again MrRB,

Many cheaper meters these days do measure frequency, but probably not as accurately as you wanted.

You can use the mains frequency for some value caps, but some are going to be too small for this i think. I have however used a frequency generator (sine wave output) in the past to measure capacitance and inductance, but i wasnt looking for 1 percent accuracy. It's quite simple really, just use a resistor that gives some reasonable value of voltage across the cap and do the math

Also of some interest is that the series resistance required to get 1/2 of the sine voltage across the cap is equal to:
R=sqrt(3)/(2*pi*f*C)
for what it is worth.

I also updated the sine method that eliminates the esr that i posted previously, but unfortunately that method requires some very precise measurements to get decent accuracy out of it.

 

[Mr RB]

...
Also of some interest is that the series resistance required to get 1/2 of the sine voltage across the cap is equal to:
R=sqrt(3)/(2*pi*f*C)
for what it is worth.
...

I did some cap "absolute" testing tonight with my 1kHz sine generator. A cap and a variable resistor in series, the resistor adjusted so AC volts are the same on both components so R = Xc.

C was determined by solving for capacitive reactance at 1000 Hz using;

C(uF) = 1000000 / (6283.18 * R)

It worked pretty well, no problem getting the C value to better than 1% accuracy.

 

[Roff]

I did some cap "absolute" testing tonight with my 1kHz sine generator. A cap and a variable resistor in series, the resistor adjusted so AC volts are the same on both components so R = Xc.

C was determined by solving for capacitive reactance at 1000 Hz using;

C(uF) = 1000000 / (6283.18 * R)

It worked pretty well, no problem getting the C value to better than 1% accuracy.

What values of C did you test? I would think your AC voltmeter input capacitance would be at least tens of picofarads. Of course, that goes in parallel with the R when you measure it also, so it tends to be self-compensating.

 

[Mr RB]

Hi Roff, I used two matching Fluke meters permanently connected to the cap and resistor. Swapping the meters had no effect, they were factory matched to the last digit <1mV AC (apparently). From memory I think their input impedance is in the megohms which would have little effect on the 400mV measured.

I did 3 caps; 0.22uF, 0.056uF and 0.001uF. Xc was 721 ohms, 3002 ohms and 163.2kohms (where I thought it best to call it a night). I'll put the photos and stats up on my "precision sine generator build" page soon as the write up is alomost done. I was hoping MrAl could provide the THD spec on the 3 stage filter first (grin).

 

[MrAl]

I did some cap "absolute" testing tonight with my 1kHz sine generator. A cap and a variable resistor in series, the resistor adjusted so AC volts are the same on both components so R = Xc.

C was determined by solving for capacitive reactance at 1000 Hz using;

C(uF) = 1000000 / (6283.18 * R)

It worked pretty well, no problem getting the C value to better than 1% accuracy.

Hi again MrRB,

I was getting this formula mixed up with another one...Let me correct this...

By that formula i was just showing a method that might be interesting because when we measure the cap voltage we measure a voltage that is exactly half of the supply voltage. Solving for C we get a nice neat formula:
C=sqrt(3)/(w*R)
where
w=2*pi*Freq

If you want to measure both voltages to be the same, then of course we would use instead:
C=1/(w*R)

which is handy if you want to measure both voltages to be the same.

There are other interesting ways to do this too.


I did the harmonic distortion calcs and posted in the other thread.
Next i'll look at the effect of meter capacitance as Roff suggested and see how much it affects the readings.

Having two meters exactly the same would have the exact same capacitance, which would be nice if they read exact as you said.


Later:
Using one meter to measure both voltages causes the meter capacitance to cancel out completely, at least theoretically anyway. Using two meters with the same exact capacitance would do the same. This works because the parallel capacitance only appears in the denominator of the equations for both voltage across the resistor and voltage across the capacitor, and when solving for C both denominators cancel so we are left with only C, w, and R. In other words, with some meter capacitance the formula comes out to be the same as with no capacitance, as long as both measurements are made with the same capacitance and high resistive part of the impedance of the meter.
Added:
It appears that even the meter resistance cancels out, so a meter that didnt have super high impedance would work too.
I had proved this theoretically, but then decided to double check using a simulation. It's easy to simulate really, just use two resistors and two capacitors and measure the lower voltage in one plot and the upper difference voltage in another plot but plot them on the same scale. With two equal resistors and two equal capacitors (to simulate both ways of measuring) simply add another resistor in parallel to a small capacitor across the lower cap in one section and another set across the upper resistor in the other section, then plot the two voltages again to show that the two voltages are equal no matter what the extra resistance and capacitance is made equal to.
The shame of it is that the two voltages although the same are out of phase with each other so it would take a little more complexity to work it into a zeroing type bridge where we would just use the meter to adjust to a perfect zero, which theoretically could get pretty darn accurate.

 

[Mr RB]

Thanks for the clarification Mr Al. I later checked those "absolutely" measured caps agains some other cap meters and the smallest cap 1000pF measured somewhere around 100pF (about 10% low) low using the sine method.

I'm not sure if this was because it's Xc was so high (163k) or because it's capacitance was so low and affected by the meter capacitance in parallel. Maybe it was some combination, including the ohmmeter's ability to read a high resistance.

I did not expect that reading to be great, however the 0.22uF and 0.056uF cap readings held up pretty well.

Interesting suggestions for techniques with one meter! I started trying to use one meter but quickly changed to using a pair of matched meters, for the reason that it was extremely painful trying to make micro adjustments on the trimpot and then move the meter probes and see the results. Using two meters was very quick and easy as I could trim the trimpot and see both AC millivolt readings simultaneously. Then an occasional meter swap showed both meters were well matched.

 

[MrAl]

Hi MrRB,

Oh yeah, switching back and forth can be a pain, but how about a SPDT switch perhaps? Might not bother the readings too much.

 

[Mr RB]

That could work. I was mainly after a couple of "absolute tested" caps as this thread inspired me to test some caps and compare them against my cap meters.

 

[MrAl]

Hi MrRB,

Oh right. Just to note, the big electrolytics are interesting to test too. I did mine with a scope and square wave generator. I was mainly after the ESR though which can be seen by noting the amount the voltage jumps up suddenly. I think i got the capacitance from the slope at some point on the wave.
These tests came about after my computer would shut down by itself for no apparent reason. I pulled the power supply and tested some of the electros and found that almost all of the ones used for filtering the main supply voltages had very high ESR and also the capacitance had decreased by 10 times or more. With a normal 5 to 10 ohm test the power supply would turn on, but as soon as the 12v line was loaded it would shut off. After replacing all the caps it worked really nice again. Had a tiny problem getting the slightly larger caps in there, but there was just enough room.
Most of the caps had leaked and so i figured it was built with those Chinese fake caps that were going around a while back.

 

[The Electrician]

Whilst I could order some relatively expensive 1% (even seen some 0.3% silver mica's) before I do so, as a little 'test' I was thinking about a very accurate way to measure absolute capacitance... one that doesn't require a precision capacitor in the first place

When people who are in the metrology business, such as at the National Institute of Standards and Technology (NIST; formerly the National Bureau of Standards) here in the U.S. refer to "absolute" electrical standards they mean a component whose value can be determined from, typically, its mechanical dimensions. For capacitors they will construct a device whose capacitance can be determined by a theoretically exact formula involving only its dimensions.

Making something like that would require a machine shop, but an "absolute" inductance can be made by a layperson fairly easily. A single layer solenoid can be made to fairly accurate dimensions and there is a formula for the inductance that is capable of parts per million accuracy.

I've made one (see the attached image) by procuring a piece of 1 inch plastic water pipe and measuring its diameter with a micrometer at several places along its length to make sure it's truly round and of constant diameter. Then measure some suitable magnet wire with a micrometer, and account for the thickness of the insulation. Wind a single layer with the turns tightly against each other. Count the turns and knowing the various dimensions you can calculate the inductance.

The inductor in the image was measured with a .02% accurate LCR meter and its inductance agreed with the calculated value to within .2%

Having such an accurately known inductor, one can resonate it with a stable (silver mica, perhaps) capacitor and thereby determine the capacitance.

Since frequency measurements are easily made to several digits nowadays, it is a good thing if you can cause a frequency to be the thing you measure to determine a component's value.