# Digital Multimeters (DMMs) and Precision DC Sources

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## Measure small capacitance in parallel with small resistance.

Hi all,

I'm trying to characterize some opto-couplers which can be modeled as a small capacitance in parallel with a small resistance and I'm hoping to use the 4072 to do this. The opto-couplers' effective capacitance changes with the value of the resistance and this is what I am trying to characterize. I'm modeling this using a 30pf capacitor with a number of different resisitances in the range 50 to 300 ohm in parallel. I have a 4072 but have not been able to make the measurement as yet as the 4072 always reads overrange with this set-up. I have tried putting a 10nf capacitor in parallel with the circuit and can get some sort of measurement when I select the 100nf range but this does not have either the measurement resolution or measurement stability I need for this experiment. Has anyone tried similar measurments with any success? or does anyone have any novel ideas on how this might be achieved?

Thanks,

Nick

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## Re: Measure small capacitance in parallel with small resistance.

Hey Nick,

I'm assuming your measuring the 30 pF cap in the 300 pF range?  Per the Help document, in the 300 pF range, we are expecting an impedance greater than 10 k ohms.

When a cap is placed in parallel with the 30 pF cap, your total impedance will be less than your 50 to 300 ohms in parallel, hence the over-range condition.  Have you tried the 30 pF || 50- 300 ohms in the 10 nF range? Will this give you the stability/accuracy you need?

Also, are you trying to measure just the capacitance?  The 4072 will not be able to measure the parallel resistance in capacitance mode, but you maybe able to take a standard resistance measurement assuming the capacitor part of your DUT is not leaky, or does not change in value with voltage or time.

Let us know what you find.

Thanks!

Brandon G

National Instruments
Precision DC Hardware Engineer
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## Re: Measure small capacitance in parallel with small resistance.

Hi Brandon,

Thanks for your reply. I did initially try to make the measurement in the 300pf range but could not get any measurement as it read overrange. I then tried it in all other ranges but got either the overrange or underrange reading. I guess the resistor is so dominant at the lower ranges giving an overrange reading but then switches to the capacitor being dominant at the higher ranges, but being so small in the range then gives the underrange reading. I did wonder about the table you posted below as I looked at it after failing to get sensible measurements. It quotes a range of capacitances against a range of parallel or serial resistances but I'm guessing that the 10nf range maps more to the 10k impedance and the 100uf range maps to the 10 ohm impedance. If this is true and you map this as a linear relationship (which I'm sure it's not, but anyway) in order to get to a capacitance range that will work with 300 ohms you would be up towards the 100uf range. My problem with this is that I need to measure the capacitor with an accuracy of around +- 1pf. I am just trying to measure the capacitance and the resistance will change in the range 50 - 500 ohm. I have tried this with a network analyzer as well and that has great difficulty making a sensible measurement as well so it was a bit of a punt to try the 4072. If you have any further thoughts I would very much welcome them.

Thanks again,

Nick

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## Re: Measure small capacitance in parallel with small resistance.

Hey Nick,

The resistor will dominant the overall impedance regardless of what range you select.  We use a test frequency of either 1 KHz or 91 Hz for capacitance measurements depending on the range selected.  This results in a minimum cap impedance of 1/(2*pi*1000 *30 p)  = 5.3 M ohm.  Since the resistor impedance is much much smaller than your capacitor impedance, you can approximate your total impedance as your R value ( |Z| = R/sqrt((1+ 2pi*f*c*r)^2)  ~= R @1 KHz ). Your assertion that the impedance level decreases with higher ranges is correct.  Even though we might be in the neighborhood of 50-500 ohms in the 100 uF range, there is still not enough sensitivity to detect a capacitor this small. 500 ohm || 30 pF creates a phase difference of only .00054 degrees @ 1 Khz.

That being said, how high of a frequency did you go up to on your network analyzer?  You should be able to get the cap impedance to drop enough at high enough frequencies.  The corner frequency for a 30 p || 500 ohm will be 1/(2*pi*c*r)  =10.6 MHz.  You should start seeing attenuation at this frequency and then perhaps be able to determine R and C accurately.  Keep in mind however, the lower your resistor goes, the higher in frequency you will have to generate.  This may start to be a limitation depending on your network analyzer.

Let us know if you have any success at higher frequencies.

Thanks!

Brandon G

National Instruments
Precision DC Hardware Engineer
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## Re: Measure small capacitance in parallel with small resistance.

The network analyser should do the job ....

If you stick with the 4072 you can try a bridge measurement @ 300kHz . .. will need more calibration and math ...

At what frequencies are you using the optocouplers ?  If you can't measure the influence at the working frequency , it probably not worth modelling it 😉 and if you can see it, think about using a similar setup to measure it.

Greetings from Germany
Henrik

LV since v3.1

“ground” is a convenient fantasy

'˙˙˙˙uıɐƃɐ lɐıp puɐ °06 ǝuoɥd ɹnoʎ uɹnʇ ǝsɐǝld 'ʎɹɐuıƃɐɯı sı pǝlɐıp ǝʌɐɥ noʎ ɹǝqɯnu ǝɥʇ'

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