# Gas station without pumps

## 2013 January 7

### Negative resistance oscillator

Filed under: Circuits course — gasstationwithoutpumps @ 06:50
Tags: , , , , ,

In More mess in the FET modeling lab, I reported observing an S-type negative resistance in the nFET that I had not expected:

Negative resistance 12mA and 50mA. (click to enlarge)

I decided to see if the negative resistance was really there and usable by making a negative resistance oscillator. The usual such oscillator for a negative resistance is a loop containing an inductor, a capacitor, and the negative resistance. Because I wanted an audio frequency oscillator, I needed a fairly large inductor (the angular frequency is $\omega=\frac{1}{\sqrt{LC}}$). However, I am also constrained by the resistance of the inductor, since the sum of the resistance around the loop has to remain negative. Estimating the negative resistance by fitting a straight-line to the appropriate part of the V-vs-I curve gave me a negative resistance of –2.145Ω. So the inductor needs a DC resistance under 2Ω.

Inductors are not something I have many of, but I looked through my parts drawers for any I might have gotten years ago in surplus grab-bag of parts. I found some tiny transformers with unknown specifications, so I tried measuring one to see if it had a high enough inductance with a low enough resistance. Transformers seemed more promising to me than simple coils of wire, because they are likely to have a ferrite core to increase the inductance without increasing the resistance, and the secondary coil gives another possibility for resonance.

I measured the DC resistance of the transformer and found that the tapped coil has a resistance of about 106Ω and the untapped coil about 0.1Ω (but my meter is not too good at resistances less than 1Ω). I then tried measuring the inductance using the same techniques I used for characterizing loudspeakers and electrodes (see Better measurement of conductivity of saline solution or Characterizing tactile transducer again), making a number of measurements of RMS voltage across the device and across a series resistor at different frequencies, then fitting a model.  Since I was looking mainly for the inductance in a simple R+L series model, I mainly looked at higher frequencies.  For the tapped coil, I got R=107.2Ω, L = 0.0226H, and for the untapped coil I got  R<0.1Ω and  L=6.76µH (I hadn’t gone to low enough frequencies to estimate R well, and I didn’t really care, since it was much less than 2Ω).

I tried the tapped coil first, but as expected from the resistance, could not get an oscillation.  I then tried the untapped coil with an electrolytic capacitor, and still couldn’t get an oscillation.  Finally, I tried the untapped coil with a 4.7µF ceramic capacitor and got an oscillation around 29.9kHz with a bias current around 21mA.  The waveform was not pretty:

Waveform of the negative resistance oscillator with no load on the secondary of the transformer. Bias is about 21mA. Note, the oscilloscope is connected across the secondary coil of the transformer, which appears to have around 3300 times as many turns as the primary, making the voltage larger and easier to observe with the BitScope USB oscilloscope.

I tried cleaning up the waveform by adding a capacitor across the secondary coil of the transformer. Too large a capacitance killed the oscillation and too small a capacitance did little to clean up the signal. I got the best results with a 680pF capacitor:

Waveform with a 680pF capacitor loading the secondary coil of the transformer.

Here then is the final circuit:

Negative resistance oscillator using the unexpected S-type negative resistance of the NTD5867 nFET. Biasing the diode-connected nFET around 21mA produced oscillations.

This is not a particularly practical circuit, as 21mA is a lot of current to get rather feeble, noisy oscillations, but it does show that the negative resistance I observed is a real phenomenon, and not an artifact of sloppy measuring on my part (as I had first feared). I wonder whether the negative resistance when switching from subthreshold to above-threshold conduction is a common property of diode-connected power FETs (or of FETs in general), or whether it is something specific to this part. I’ve never heard of it before, but I only used FETs in nMOS and cMOS digital VLSI design, where simple models sufficed—no one bothered to teach me anything about how FETs behave in this region.

For those interested in the spectra of the oscillations, I took screen grabs of Bitscope’s spectrum analysis. Unfortunately, the cursor obscures the fundamental peak—there doesn’t seem to be any way to see the peak and display the frequency at the same time. (I also hate the black-background display, which is only there because scopes have “always” had dark backgrounds—they are no longer a necessary evil, just an evil.)

Spectrum without a capacitor on the secondary coil of the transformer.

Spectrum with 680pF on secondary coil of transformer.