ring oscillator 60 degree phase shift?

[exp]

Hi,

A ring oscillator requires 3 inverters. According to Wikipedia, each stage has 120 degree phase shift, making up 360 degrees.

But why 120 degree? If I just plot -1/(1+s^2), the frequency at which 120 degree occur is -6dB. Why this value and not anything else?

Also, one could regarding one inverter as +180 degree, followed by a 1st order RC, which would total in +90 degree. Why is this invalid?

Assuming an ideal inverter with infinite bandwidth (inversion appears in zero time at output), shouldn't 2 inverters (which commonly make up a latch) oscillate? Each inverter would have +180 degree pure shift, making a total of 360 degree.

 

[Audioguru]

You are WRONG. One inverter provides a phase shift of 180 degrees and 3 RC stages provide 60 degrees each. Then the total is 360 degrees.
You can also use any odd number of inverters.

A Budda oscillator has one inverter and four RC stages of 45 degrees each for a total of 360 degrees.

One RC is difficult to make a phase shift of 90 degrees and the frequency is infinite but it is easy to make 45 degrees or 60 degrees at a certain frequency.

Two inverters do not always oscillate because nothing sets the frequency. So they latch instead.

 

[godfreyl]

Two inverters do not always oscillate because nothing sets the frequency.

There's another way of looking at it: The inverters will have a small amount of delay. At any frequency above zero Hz that contributes some additional phase shift, so the phase shift of each inverter is > 180 degrees.

Since zero Hz is the only frequency at which phase shift = exactly 180° per inverter, that's the frequency at which it oscillates. Of course, the zero Hz output is just DC.

 

[exp]

You are WRONG.

With which statement exactly?

One inverter provides a phase shift of 180 degrees and 3 RC stages provide 60 degrees each.

I am not sure if we are talking about the same. What you are describind sounds to me like the phase shift oscillator:

https://commons.wikimedia.org/wiki/File:Phasenschieberoszillator.svg
https://en.wikipedia.org/wiki/Phase-shift_oscillator,

Then the total is 360 degrees.
You can also use any odd number of inverters.


But I can treat a single inverter as a indealized -1/(1+s) system (inverting amplifier + 1st order rolloff). That means the phase shift of one inverter is between 180 and 90 degrees.
If I connect three together, I essentially get (-1/(1+s))^3 as "loop gain":

https://snag.gy/fWIlU.jpg

Again, there is a frequency for which the phase becomes zero and it is where the amplitude is -18dB (which corresponds my -6dB per stage in my original question).
Of course, the transfer function needs a gain of +18dB to fulfill Barkhausens criterion.


But again, why does wikipedia say each inverter has 120 degree phase shift ... and not 176 ... or 141 or 95? The number just sounds "arbitrary" to me.

Thanks

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[...] so the phase shift of each inverter is > 180 degrees.

You mean "< 180 degrees", right?

Because the inversion is +180 degrees, the 1st order system is -X degrees (where X ranges from 0 to 90). So the ideal, 1st order inverter should have 180 degrees at DC and 90 degrees at infinity...

Thanks


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... but I think I got the main point now:

* With an even number of oscillators it would be with an infinite bandwidth because the inverters would not add any phase shift
* Alternatively: With an even number an oscillation would be possible at DC and infinite frequency. E.g. 4 inverters: mod(4*(180-0), 360)=0 at DC or mod(4*(180-90), 360)=0 at infinity
* Only with an odd number, there is a non trivial frequency for which the loop gain has a zero-phase frequency. So the important thing in Wikipedia is merely that there exists a non-trivial frequency where each inverter has 120 degrees shift...

 

[Audioguru]

I guess you are thinking about this useless oscillator:

 

[godfreyl]

But again, why does wikipedia say each inverter has 120 degree phase shift ... and not 176 ... or 141 or 95? The number just sounds "arbitrary" to me.

The phase shift is different at different frequencies, but the circuit will only oscillate at a frequency where the total phase shift is 360°.