if they are ground referenced inverters an even number of inverters will create a 2 state latch.

if they are differential inverters, you can reverse the polarity of one to get an even number of delay cells to oscillate.

Raj - sure, use a huge cap to bypass one of the inverters

I don't think it can be done. For an oscillator you need something that tends to pull you back down if you are going up. With the proper delay the timing will be such that it reinforces the oscillation.

Hi Raj,


for an even number of stages, when it reaches the latches state, there is no mechanism to bring it out of the latched state. I don't think you can consider this an oscillation at DC...

Aaron

Hi Raj,


what I mean is that once the voltage hits the rail, the loop gain goes to zero. So how can it oscillate? I'm not sure if my explanation is sufficient. Are you looking for a small-signal explanation?


regards,
Aaron

raja.cedt wrote on Jan 30^th, 2012, 1:23am:

I think I need to revise my thinking on my statement. There is a "perfect delay" frequency where the delay would be correct to create an oscillation so there must be another reason why it won't oscillate.

Perhaps the reason it seeks the latched operating point is that all frequencies below this "perfect delay" frequency will have positive feedback with gain more than one. Any noise in that frequency band will reinforce the output so that it hits the rail. On the other hand, any noise above that band would have a gain less than one.

might be over thinking this a bit?

The way I think about this -

cut the ring at a single point so you got an input and output.
tie the input high or low.
steady state look at the output
if the input and output are the same state its not going to oscillate, its going to latch


Now, if you want to apply criteria of sufficient gain,
additive phase per delay cell etc, that's a different game.


A subtle issue - an inverter does not delay the signal by 180 degrees.
It inverts the signal and delays it by some  smaller amount.

That's a little different isn't it?
For a N stage ring oscillator, each stage contributes 360/N degrees of phase.

Hmm..let me give a try..!!

I havent done the home-work to check the same..but here is the explanation in my view.

1. Oscillations here are of large-signal phenomenon.
2. Finite delay between in the loop defines period of oscillations.
3. Lets Consider the debated cases
a. Odd number of inverter chain
b. Even number of inverter chain

Possible states without the knowledge of phase, delay etc. etc.
1. DC
2. AC ( I mean oscillations)

Digging more
DC
Any point between Supply and Ground. No point here for guessing the possibilities are only Supply,GND and VTH ( Threshold of the inverter, assuming all are of same type)

AC
Sustained oscillations , hence the explanation also that total phase is 180 etc.. etc.. but did Barkhausen phase criteria say other-way round

But what is the meaning of 180 phase difference here..!!
Input of an inverter(of the chain) is held for finite/sufficient time to drive its output to opposite polarity, which is guaranteed by X number of inverters in the chain/loop. which means that phase is not 360 but its 180.. Did we miss anything here.?

Key here is its not-a-sustained/controlled sinusoid oscillations, hence 360 is not-valid here. While its ringing, at a given time, complete signal chain is not active ( mean not in rise/fall segment), only few are establishing the ringing.

Cool.. right now lets start with the numbers??

What if only one inverter is in the chain?
Holy cow.. Inverter has gone mad.. there is no way that input(which in this case is output itself) will be constant till the output(which in this case is input also) is driven to opposite polarity.. Hence no oscillations and input/output settles for VTH

What if two inverter is in the chain?
This will be pretty interesting..!!
for analysis of Ring-osc if its assumed that output has zero rise/fall times with finite prop-delay..oh dear.. yes two-stage inverter-chain is going to oscillate.

But catch is in the assumption; output indeed has finite rise/fall times and the delay or phase is equivalent to that of one-stage RC..

If one goes into finer details..it can be seen that inverter is capable of driving its output completely to opposite polarity and its input never starts to drift from stable value.. hence inverter wont able to drive change its state but struck in the same-state.

Simply.. loop doesnt have enough phase difference to sustain it..

The other possible state obviously is VTH..but any noise on this takes to stable state of Supply/GND.

OR
Lets start at VTH and apply BH Crit.. loop phase is 360..but gain is darn high..proper positive feedback circuit. no option but it will saturate.

Three inverters in a chain

Here its always possible that output of inverter is driven to opposite polarity, till then input keeps quite and then starts to change!!
Lets start assuming all nodes are VTH..and noise is induced..What happens..
noise has all frequencies ..only sustainable frequency is at which BH Crit is met. But is it going to sustain??
No because gain is darn high.. but what happens then??

Part of the inverters saturate while others are in the course of transiting to their saturation.. But then all can-not saturate just because input-output of inverter can-not be same and in this case its biiig-inverter with delay..

Hence it will be sustained for ever.. but remember this frequency is different from at which inv chain started to oscillate..

Four inverters in a chain

Putting the same argument as in the previous case.. shouldnt the oscillations sustaining now??
Yes..of-course why not..!!???
But the catch is...
Again Gain of the path is huge..some-body is going to saturate..once saturated even number of inverters can never bring-it out of saturation point..


Hence forth the case for odd-even inverter chain as a ring-oscillator


But oscillations can be sustained with even number of inverter stages with controlled gain.. which are nothing but sinusoidal oscillators and remember here every-stage is in its linear region of operation..!!


Concept of metastability
Take N number of inverter chain and assume delay of 360/N per stage.
Try to get timing plots (assume one input to be step - noise source)

do the same with 360/N+/-delta..

Whether N is odd/even system might stabilize at VTH..( assuming all have the same threshold at VTH)

Repeat the same with one-inverters threshold at VTH+/-delta..

N - odd- oscillates only
N - even -ends up at Supply/GND


Hope i am not too over-board here .. with lot of mistakes..!!!!!

rgds,
ds