# Low frequency Pierce oscillator with transistor

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 !

• Your diagram appears wrong. Hopefully this is not the same as your circuit. | The xtal is short circuited by a wire. Presumably the LH end of xtal should connect to Q1 collector. | R1 = 3.2 Ohm - should that be 3.2 k Ohm??? | Gain is approx R1 / (R2 + 26/Ic_ma) . For R1 = 3K2 gain is ~~~ 7. | Vb~= 1.7V. So Ie ~= (1.7-0.6)/470 ~= 2 mA. VR1 = VR2 x R1/R2 = 1.1 x 3k2/470r = 7.5V. Vce ~+ 12-1.1-7.5 = 3.4V so transistor is not hard on (which is good) – Russell McMahon Apr 13 '17 at 15:17
• Oh yes my bad, that the first i use the schematics editor, the LH of the xtal is connected to the collector. Yes R1 is 3.2K. Thanks a lot @Russel : I have carrefully designed the amplifier part (that the first timefor me ^^) – Nicolas Apr 13 '17 at 15:28

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. • Nice! Can you send me your simulation? Question : are they the bode diagrams for the closed loop ? What is the parameter whose value is changing for the three first left diagrams ? – Nicolas Apr 14 '17 at 9:31
• @ Nicolas The changing param is the UnityGain Bandwidth of the opamp. Leftmost sim has 40dB gain, with rolloff at 1KHz (for a 32KHz oscillagtor). Left-1 sim has 40dB gain, rolloff at 10KHz (for a 32KHz oscillator). Left-2 sim (which shows the snappy phase changes, desirable for accurate oscillation) has 40dB gain, rolloff at 100KHz. – analogsystemsrf Jul 3 '18 at 3:26

This is not a Pierce oscillator because there is no feedback. A typical scheme, where R1 is feedback: • The wire from lh end of crystal on his diagram should go to collector. The cct is then similar to yours. His R1 is vastly too low - which may be a typo. – Russell McMahon Apr 13 '17 at 15:19
• How do i choose the value of R1 of the above diagram ? 1MOhm ? – Nicolas Apr 13 '17 at 15:28
• R1 and C1 provide a phase delay of 65 °(link) to the feedback signal. – AltAir Apr 13 '17 at 15:47
• Another example link. With a value of components. – AltAir Apr 13 '17 at 16:00
• @RussellMcMahon Actually, OPs R4 was too low (though he fixed that in edit), his R1 is still entirely nonexistant (straight trace from XTAL to collector, no resistor) – Robherc KV5ROB Apr 13 '17 at 16:33