Colpitts oscillator from Razavi's book

[Alfie_Guo]

Hi,

I am trying to understand how the Colpitts oscillator works. From Razavi's book, it is indicated that the minimum required gain should satisfy the requirement of gmRp > 4 (Chapter 15.3.3, Eq15.46). Further, there are ideas that the circuit oscillate when the transfer funtion becomes infinity, or when the output resistance has positive real part. I am still a bit confused about the requirement for this circuit to oscillate.

Thank you all for your help.

 

[BradtheRad]

There is more than one Colpitt's oscillator topology. Your schematic A has the inductor in-line with the power supply, thus the power supply needs to be low impedance.

This is not different in principle from the B version. Both circuits have the inductor and capacitors trading energy back-and-forth to create oscillations.

With the transistor version, the aim is to apply a small bit of tank energy to the bias terminal, at the proper moment to build and maintain oscillations.

When M1 turns on, it reduces voltage across itself and across C2, at a frequency which is detected usually automatically based on voltage swings in the LCC loop. This small bit of tank action is often tapped from the node between the capacitors because that is where the right polarity is available at the right moment, to be applied at the bias terminal. Then the LCC loop swings in the other direction. Oscillations continue.

 

[BradtheRad]

Schematic A can work because it operates the transistor in common-base mode. Voltage varies at the emitter leg. This is what changes the base-to-emitter relationship, thus changing current through the transistor.

Voltage applied to the bias pin is constant DC, at just enough amplitude so it turns on the transistor.