# Gas station without pumps

## 2015 July 5

### Measuring voltmeter input impedance

Filed under: Circuits course — gasstationwithoutpumps @ 21:30
Tags: , , ,

In Voltmeter impedance, I talked about measuring the input impedances of the bench AC voltmeters by using a pair of voltmeters.  Today I worked out a way to measure the impedance of my cheap RadioShack pocket voltmeter using just the voltmeter itself, my new FG085 function generator, and a 3.3MΩ resistor.  The idea is simple: at a number of different frequencies, measure the voltage of the function generator with the voltmeter, then put a 3.3MΩ resistor in series with the function generator and measure the voltages at the same frequencies.  This technique doesn’t even require a breadboard—just clip leads.

The idea is that the voltmeter and the 3.3MΩ resistor forms a voltage divider, and what we are measuring is the output of the divider. Because the impedance of the voltmeter is always high enough that it provides a negligible load for the 50Ω-output of the function generator, we can safely estimate that the input to the voltage divider is the voltage we measured without the resistor.  So we can use  $\frac{V_{out}}{V_{in}} = \left| \frac{Z}{Z+R} \right|$ to estimate $|Z| = R \frac{g}{1-g}$, where $g= \frac{V_{out}}{V_{in}}$. We can then fit the magnitude of the impedance to a model of a resistor and capacitor in parallel.

The estimate of 10.87MΩ in parallel with 18.54pF seems quite plausible. The fitting had to be stopped at 10kHz, as beyond that frequency the R||C model no longer fits.

I’m not surprised that the fitting had to be stopped at 10kHz, as the plot I did in FG085 function generator output impedance showed the voltmeter having a 2nd-order low-pass filter with a cutoff frequency around 9.3kHz. Although the low frequency at which the measurements start failing is annoying, the >10MΩ and <20pF input impedance are actually quite good.

I would have measured my Fluke 8060A multimeter, but it seems to have died—I might try opening the case and doing the troubleshooting suggested in the manual, but I suspect that replacement parts are needed, which may be difficult to obtain.

I tried measuring the DT-830B \$5 voltmeter I have, but it is rather difficult, as it does not have a low-voltage range for AC—its lowest voltage range is 200V, with a precision of 0.1V (though who knows how bad the accuracy is).  I ended up using a 180kΩ (measured at 178.6kΩ) series resistor, in order to still have a measurable voltage over a reasonable frequency range.

The DT-830B cheap multimeter has a relatively low input impedance (under 0.5MΩ). I had to stop the plot at 100kHz, not only because the voltmeter was on its lowest reading (0.1V), but because the function generator is not very sinusoidal above 100kHz.

The very flat line up to 1kHz for the DT-830B may be a bit misleading—all the measurements were the same because of the limited resolution of the multimeter.  Changing the least significant digit by one count would make a huge difference in the estimated impedance.

This is a simple enough lab that I think I’ll add it to the book—I don’t know whether I’ll add it to the class, because we’re already running short on lab time.