# Modelling tunnel diode relaxation oscillator

I have been trying to model this oscillator

I was wondering if we can somehow predict the frequency of the oscillations.For small currents inside a diode from the Shockley diode equation $$ e^{x}-1 = x$$ -> $$I_{D} = \frac{x}{V_{T}}I_{s} \rightarrow \frac{x}{I_{d} } = \frac{V_{T}}{I_{s}}$$ so we can say that for small currents the diode can be replaced with a resistor equal to $$R_{d} = \frac{V_{T}}{I_{s}}$$

Now back to the relaxation oscillator circuit the 2 resistors bias the voltage of the tunnel diode well below $$V_{f}$$ of the tunnel diode so the approximation is valid.But the VI curve of the resistor which replaces the tunnel diode in order to copy the negative differential resistance region must not be a continuous function , it must be discontinuous for voltages from Vp to Vf .

Can we estimate that way the frequency of the relaxation oscillator?

## 1 answer

Unless you know the *exact* formula for the I-V curve, you will never find out anything analytically. Fair warning: very unlikely you will get such formula, since they are strongly non-linear in nature. The analysis of such oscillators is done based on approximations (see the Esaki diode, for example), and it involves a lot of estimations.

But if your *purpose* is a relaxation oscillator then you'll be much better off using some of the already known circuits: reverse BE junction, multivibrator, comparator, etc. All of them rely on a much more analytically-inclined RC time constant, combined with simple thresholds. The tunnel diode has a continuously variable threshold. Plus, they will likely consume much less current.

If you insist in pursuing the tunnel diode analysis then you should know that the way you started is not the way to go. The small signal does not apply here, since the whole behaviour of the oscillator relies on the point on the I-V curve (as depicted on your I-V curve picture) moving all the time. I can't find the right words to describe now, but a picture should be worth a thousand words: take whatever simulator you want, that lets you zoom in and analyze the waveforms.

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