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Colpitts oscillator - role of feedback resistor
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aneevuser:
In the following video:



Mr Offset Voltage discusses a Colpitts oscillator. There is a feedback resistor R1. At about 24:00 (https://youtu.be/3c5u_HRp8m8?t=1456), he briefly mentions this resistor having some kind of transconductance effect.

To my mind, "transconductance" would involve some kind of I->V or V->I transformation, but I don't see how that applies here. AFAICS, R1 merely forms a potential divider with the tank circuit.

I am not sure what he is getting at here - can anyone explain?
Audioguru:
The total positive feedback causes the oscillation. Transconductance has nothing to do with it.
Wimberleytech:

--- Quote from: Audioguru on February 02, 2019, 06:46:25 pm ---The total positive feedback causes the oscillation. Transconductance has nothing to do with it.

--- End quote ---

Total positive feedback indeed is required for sure.

If the amplifier were an ideal opamp, it would have zero output resistance.  With a zero output resistance, C1 is meaningless.  To get a total loop phase shift of 0 degrees, you will need to get 180° to add to the 180° of the inverting amplifier.  But, since the inverting opamp circuit has actual input resistance less than infinity, you cannot get the 180° you need.  By adding the extra feedback resistor, you can introduce an additional phase shift via R and C1.  That is enough to scooch you to 180°.

Let me know if you think I am Barkhausen up the wrong tree!  :-DD
David Hess:
Transconductance is voltage in and current out which is the case for transistors and tubes.  But operational amplifiers do not have transconductance and are voltage output devices making them unsuitable to directly drive the tank circuit.  If he had used an operational transconductance amplifier without Rf, then the output resistor R1 would not be necessary and instead of adjusting the voltage gain of the operational amplifier with feedback resistor Rf, the transconductance of the operational transconductance amplifier would have been adjusted with a separate input.

Incidentally, current to voltage is transimpedance.  Transconductance is measured in mhos (reciprocal ohms) and transimpedance is measured in ohms (reciprocal mhos).
aneevuser:

--- Quote from: David Hess on February 03, 2019, 04:50:58 am ---Transconductance is voltage in and current out which is the case for transistors and tubes.  But operational amplifiers do not have transconductance and are voltage output devices making them unsuitable to directly drive the tank circuit.  If he had used an operational transconductance amplifier without Rf, then the output resistor R1 would not be necessary and instead of adjusting the voltage gain of the operational amplifier with feedback resistor Rf, the transconductance of the operational transconductance amplifier would have been adjusted with a separate input.
--- End quote ---

At the moment, I'm unconvinced that we need to consider transconductance at all.

I've been pondering the Colpitt's circuit in the video, and it seems to me that all we have is:

a) an inverting voltage amplifier with gain set by RF and RI in the usual way
b) a phase shift network formed by R1/C1 and L1/C2, with R1 variable

The phase shift network is tweaked to give 180 degrees shift via R1, and it is this inverted voltage that the op amp sees, and amplifies.

Also, although the phase shift network does have a resonant frequency, this doesn't necessarily align with the frequency for 180 degree shift (AFAICS), so the fact that we have a tank circuit sitting there is somewhat secondary.

All IMHO, of course, but I see no need to analyse this circuit via anything other than the voltages at the moment.

I'll try and analyse the phase shift network more theoretically when I get a bit of time, to see if I can justify my remarks above.


--- Quote ---Incidentally, current to voltage is transimpedance.  Transconductance is measured in mhos (reciprocal ohms) and transimpedance is measured in ohms (reciprocal mhos).

--- End quote ---
Useful distinction - I'll note that for future reference.
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