[SOLVED] Question regarding phase shift and oscillation criteria in VCOs

[FvM]

The answer had been given in post #14. -60 degree additional "RC" phaseshift per stage.

3*(-180 - 60) = -720

 

[amsdesign]

The answer had been given in post #14. -60 degree additional "RC" phaseshift per stage.

Yeah that's the part I don't get. Why does an RC stage produce only 60 phase shift?

 

[FvM]

I fear, we took too much circuit theory basics for granted. Please look at the transfer function of a first order low-pass, particularly the phase:



Copied from: https://www.tedpavlic.com/teaching/osu/ece209/lab3_opamp_FO/lab3_opamp_FO_phase_shift.pdf

You'll notice that a phaseshift of -60 degree is achieved for ωRC = √3

 

[LvW]

Yeah that's the part I don't get. Why does an RC stage produce only 60 phase shift?

Of course, an RC stage CAN produve phase shifts between 0 and -90 deg - however, in the case under consideration there is only one phase shift of each stage (-60deg) which can fulfill the oscillation criterion!
And if the circuit can oscillate at this single frequency - it does oscillate!

 

[amsdesign]

I fear, we took too much circuit theory basics for granted. Please look at the transfer function of a first order low-pass, particularly the phase:

View attachment 121965

Copied from: https://www.tedpavlic.com/teaching/osu/ece209/lab3_opamp_FO/lab3_opamp_FO_phase_shift.pdf

You'll notice that a phaseshift of -60 degree is achieved for ωRC = √3

I know that, but that wasn't my question.

Consider a phase shift oscillator. It has one inverter and 3 capacitors.The transistor provides the negative feed (180 phase shift) so the remaining 180 is split across 3 other externally added RC stages. So each RC is designed to produce a phase shift of 60 degrees.


Now for a ring oscillator, the capacitors are just the Cgs of the next stage and can't be configured. So the three inverters provide 3*180=360+180 which is as good as 180, so where is the remaining 180 being produced? Since there are no externally caps how is that additional 180 phase shift added to the circuit?

 

[FvM]

Post #20:

The caps are inside the transistors but they still cause a phase shift.

Post #25:

Since there are no externally caps how is that additional 180 phase shift added to the circuit?

I give up. Consider to read a text book thorougly.

 

[amsdesign]

Post #20:

Post #25:


I give up. Consider to read a text book thorougly.

Lol those two statements of mine are not contradictory. You have 3 caps as part of the transistor which are fixed, so does it mean R is varied to get the 60 degree phase shift for each RC stage?

 

[FvM]

Of course there's no difference between the working of "designed" external capacitors and internal transistor capacitances. They cause poles in the transfer characteristic and at a specific, well calculatable frequency a phase shift of -60 degree. So the phase part of the oscillation condition can be fulfilled. If the loop gain magnitude at this frequency is > 1, oscillations can start.

B.T.W. in a phase shift oscillator, neither R nor C are primarly varied. They have specific values setting the oscillation frequency. You may vary it, but you don't need to.

 

[amsdesign]

Of course there's no difference between the working of "designed" external capacitors and internal transistor capacitances. They cause poles in the transfer characteristic and at a specific, well calculatable frequency a phase shift of -60 degree. So the phase part of the oscillation condition can be fulfilled. If the loop gain magnitude at this frequency is > 1, oscillations can start.

B.T.W. in a phase shift oscillator, neither R nor C are primarly varied. They have specific values setting the oscillation frequency. You may vary it, but you don't need to.

Phew! Thank you. I will close this thread now :-D

 

[amsdesign]

Is each stage in a 3 inverter Ring Oscillator contributing a 60 or 120 phase shift?

Consider this equivalent of a 3 stage ring oscillator.

Each stage is contributing a total of 270 degrees : a 180 from the -gm and phase shift by each pole.

Hence for oscillation to occur each stage contributes 120 degrees. Is this assumption correct?

To achieve oscillation, the ring must provide a phase shift of 2pi and have unity voltage gain at the oscillation frequency. Each delay stage must
provide a phase shift of pi=N, where N is the number of delay stages. The remaining phase shift is provided by a dc inversion

But if I look at the text, it says each stage is contributing to 60 and the DC inversion contributes to the additional 180. What exactly is the DC inversion here? Isn't it the -gm of the first stage after the feedback?

 

[FvM]

Each stage is contributing a total of 270 degrees : a 180 from the -gm and phase shift by each pole.

No. A total of 180 + 60 = 240 degree at the oscillation frequency. A pole has 90 degree phase shift only at infinite frequency.

Total ring phase shift 3 x 240 = 720 degree.