Low frequency Pierce oscillator with transistor

Question

I am trying to built an oscillator at low frequeny (32768 Hz). After some research i have chosen to build a pierce oscillator. Here is my schematics : discard

^{simulate this circuit – Schematic created using CircuitLab}

I have tested the amplifier with a function generator producing 32Khz and it worked well, i have observed a gain of approximatively 3.7. The load capacitance of the cristal is about 12.5pF. I am not seeing any oscillation at the collector. Any idea about what could be wrong in my setup ?

Thanks !

Answer 1

The crystal + 2 caps form a PI network:

^{simulate this circuit – Schematic created using CircuitLab}

Lets examine the loop gain and loop phaseshift; here in Signal Chain Explorer, the XTAL model is embedded as Z(feedback) of the Inverting OpAmp stage; crystal inductance is 58.9766 Henry; capacitance series/resonance is 0.8pf; the plate-to-plate capacitance is also 0.8pF; Rloss is 1Kohm.

I reduced the two capacitors of the PI network, here before and after the OpAmp, from 22pF to 4.7pF. I've read the low frequency oscillators need small capacitors, so the energy is not shorted to GND.

Key point is the gain and bandwidth of the OpAmp. With gain of 10dB (3.16x), shown in the far right BODE, the gain is barely above 0dB.

In contrast, examine the 40dB gain, flat to 100KHz, and see a healthy peak (30+dB gain) at the correct frequency.

Does the value of R4 (in the schematic) matter? Lets examine that next.

Answer 2

This is not a Pierce oscillator because there is no feedback. A typical scheme, where R1 is feedback: