Analysis of unknown Oscillator Circuit

Hello,

This is my first post on EDAboard so I hope I can explain myself well.

I have been tasked with analyzing a circuit which is used for a capacitive sensor. The circuit is shown on the lower right of the image. The circuit works in such a way that oscillations start once a certain capacitive value on the sensor is reached.

I am working on the lines that this oscillator works on the principle of positive feedback and that AB must be equal to 1 for oscillations to be sustained. Transistor Q1 is configured as a common base amplifier. The output is in phase with the input at the emitter. Positive feedback is fed at the emitter of Q1 through the emitter of Q2 which is configured as an emitter follow. R8 is used to adjust the sensitivity.

However hard I try to calculate the exact point where oscillation start I cannot reach a solution. I was trying to obtain a term for AB using the small signal model of the circuit. I have also simulated in LTSpice (included)

Could anyone provide some insight as to how to proceed? Appreciate any help because I am completely stuck.

If you measure loop gain in small signal analysis, you'll see that the barkausen criterion (complex loop gain = unitity) is met for C = about 2.01 pF. For larger C, loop gain magnitude is > 1 at zero phase. The unusual point is that the loop gain is rising versus frequency (at least in the applied measurement configuration).

In Nyquist diagram, the critical point (1,0 in the present loop gain plot) is clockwise encircled for C > 2.01 pF, means the Nyquist oscillation condition is fulfilled, too.

It should be noticed that the loop gain measurement method depends on an unidirectional signal flow, T1.base is amplifier input and T2.C is amplifier output, which should apply approcimately.

Hi again and sorry. I didn't notice that you have attached the files. I assume the plot file gives information on the traces you were observing. One further question how did you arrive at the capacitance value? Thanks

Yes, the plot file shows how loop gain is calculated in the simulation.

The capacitor limit value of 2.01 pF has been evaluated empirically by a parametric simulation.