Gas station without pumps

2021 September 16

Last to-do note in book done

Filed under: Circuits course — gasstationwithoutpumps @ 10:46
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I’ve finally removed the last to-do note from the text book. This one was an explanation of the threshold voltage for FETs as the transition between the subthreshold conduction, where the on-resistance has exponential behavior with $V_{gs}$ and the on-region, where it is roughly constant.

I don’t like copying graphs from datasheets for the textbook, so I needed to measure the values myself to make a plot. My first attempt, using the PMV20XNE nFETs that we used for the past few years in class, was a failure.  The typical on-resistance is only 23mΩ, which is too small for the crude measuring setups and low currents that I could get with the Analog Discovery 2.  I ended up mainly measuring the resistance of the test setup, with errors larger than the value I was trying to measure, so I couldn’t even subtract off the short-circuit measurement.

I tried again with a low-power nFET (a 2N7000), using a constant load resistor of 150Ω (so the maximum power dissipation in the ¼-W resistor would be $(5V)^2/150\Omega = 167mW$).

I controlled with the gate voltage with waveform generator, and measured both the drain-source voltage and the drain current. I used the oscilloscope tool and averaged both within a sweep and across many sweeps to reduce noise.

Because the Analog Discovery 2 has only 2 measurement channels, I had to manually copy the measurements into a file for gnuplot, as there was no way to record the waveform generator output with the measurements in a single file (well, there might be with the scripting capabilities of Waveforms 3, but I’ve not explored them much).

I noticed some pretty large offsets when measuring small voltages, so I did open-circuit and short-circuit measurements and used them to subtract off offsets (with the understanding that the current for the open circuit would be about 150µA, because of the 1MΩ impedance of the Channel 1 measuring the open-circuit voltage).

The corrections make a big difference at the low end, where on-resistance is comparable to the resistance of the measurement instrument and test currents are tiny. The correction at the high end is smaller, but still noticeable. The transition from the exponential behavior of subthreshold conduction to the on-region is pretty clear. (Click to enlarge)

Now all I have to do for the next release of the book is do the standard final checks (page breaks, spell checks, and URL checks).  This will probably take me another week.