# Tunnel diode oscillator with series RLC

#### hcc

Joined Jun 24, 2012
1
It is said that negative resistance devices must use a series LC oscillator while a negative conductance device, e.g. a tunnel diode, must use a parallel LC oscillator. However, focusing on negative conductance device, the conductance vs voltage (across the tunnel diode) may be modeled as a (U) parabola as shown in 'g.png'. The minimum is the negative conductance of the device (at optimally biased). With a parallel LC oscillator (and the tunnel diode optimally biased), the oscillation amplitude will increase until the negative conductance decreases (i.e. more positive) and balanced by the positive conductance in the (lossy) oscillator.

Inverting the conductance gives the resistivity and is shown in 'r.png'.

Now, with a series RLC oscillator, where R is smaller than the magnitude of the negative resistance (so oscillation should be able to start) and the tunnel diode is assumed biased (as in the parallel case above), will there be any oscillation with such a series RLC? If there is any response to the RLC at all, what will be observed? (The negative resistance will increase with amplitude if oscillation is possible and the amplitude would diverge.)

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#### mcasale

Joined Jul 18, 2011
210
If I recall way back in my EE classes, I think there are no rules about series/parallel RLC circuits, but I COULD have forgotten it.

My advice is to model your circuit diagram, which you did not post, and then break the feedback loop, and write the system equations (loop gain using complex variables). You will wind up with a REAL part and an IMAGINARY part in the denominator (or determinant). Set each equation to ZERO and that should give you the conditions for oscillation, as well as the frequency.

IMHO mathematics is an under-utilized tool in analog circuit design. It can be fun once you get a reasonable answer, but it can also be a pain in the buttocks when you don't get the right answer.