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Message started by raja.cedt on Jan 29^th, 2012, 4:51am

Title: basic doubt regarding oscillator
Post by raja.cedt on Jan 29^th, 2012, 4:51am

hello all,
for example in case of ring oscillator (single ended) always people talk about odd number of inverters, i am expecting it will oscillate with even inverters. here is my explanation.

When we have odd number of inverters, 180 degrees loop phase has to be contributed all inverters and hence the frequency corresponding to the oscillator frequency. So in case of even number also this can be possible becaz all inverters will contribute 360 phase and hence this is the frequency of the oscillator. I have doubt here, even 0 frequency also one solution, so at what frequency oscillator will sustain and why so.

The main intention behind this Question is to learn some basics and i am well ware of ring oscillators and in case of differential delay elements even is posb!!

Thanks,
RAJ.

Title: Re: basic doubt regarding oscillator
Post by loose-electron on Jan 29^th, 2012, 2:02pm

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.

Title: Re: basic doubt regarding oscillator
Post by aaron_do on Jan 29^th, 2012, 4:29pm

Hi,

If I am understanding the question correctly, then I think it is quite interesting. Supposing you have a ring oscillator with an even number of inverters that are AC coupled so that the loop gain at DC is zero, I'm not sure if it would oscillate.

In a cross-coupled oscillator, you do have an even number of inversions, but all possible oscillation frequencies are filtered except for one which is a result of the bandpass function.

Aaron

Title: Re: basic doubt regarding oscillator
Post by RobG on Jan 29^th, 2012, 5:13pm

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.

Title: Re: basic doubt regarding oscillator
Post by raja.cedt on Jan 30^th, 2012, 1:23am

hello guys,
thanks for the reply, ac coupling is interesting but oscillator should have dc operating point, do you think with coupling capacitors it will be posb. But my Question is it can be designed with two operating points, one is at dc and another is at designed frequency, so which operating point oscillator choose.

In general it will be latched at DC, i want the reason.

@robg: i didn't understand this in your previous post...I don't think it can be done

Thanks,
Raj.

Title: Re: basic doubt regarding oscillator
Post by aaron_do on Jan 30^th, 2012, 1:44am

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

Title: Re: basic doubt regarding oscillator
Post by raja.cedt on Jan 30^th, 2012, 2:43am

hello aaron_dc,
yes i know it will be latched at dc. What i mean to ask is out of two operating points why it is selecting DC? (for example take a -ve feedback amplifier and it has one operating point and for +ve feedback there are multiple points).

May be i am wrong i want to understand this clearly

Thanks,
Raj.

Title: Re: basic doubt regarding oscillator
Post by aaron_do on Jan 30^th, 2012, 2:56am

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

Title: Re: basic doubt regarding oscillator
Post by loopantenna on Jan 30^th, 2012, 7:05am

With an even number of single ended inverters there is no oscillating solution. Each inverter introduces a 180 degree phase shift therefore you need an odd number to satisfy the Barkhausen phase criteria to sustain an oscillation . If the first inverter output is high (for example) with an even number of inverters you produce a low signal which fed back to the first one does not produce any change. If you want to look at inverters from the analog point of view they are open loop amplifiers with huge gain therefore in a chain you end up with a large signal which saturates the amplifiers. Hence the only solution for an even chain is the dc.
Does this answer defies your doubts?

Title: Re: basic doubt regarding oscillator
Post by RobG on Jan 30^th, 2012, 8:05am

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.

Title: Re: basic doubt regarding oscillator
Post by raja.cedt on Jan 30^th, 2012, 8:07am

@loopantenna:

Why each inverter contribute 180 deg phase, if so why it is oscillating? The answer is each inverter gives 180+frequency dependent phase, so at some frequency all contribute to 180 and that is the frequency of oscillations. please try to avoid explain like 1 at some point and becomes zero after that inverter and finally it reaches with the inversion (of course during this explanation you are assuming some delay hence phase).

Guys may i didn't explain properly. Let me try it out again.

In case of even inverters, there are multiple solutions.
1. At dc (this is not oscillations only solution it could be oscillation or latching state a.k.a dc)
2. at some frequency each inverter contribute 22.5 deg phase (assume 16 stages), so it can be a solution.
3. At some other frequency each inverter contribute 45 deg, so it can also.
Out of all these solutions, some how it will stay at dc, means that is stable operating point out off listed above.

Thanks,
Raj.

Title: Re: basic doubt regarding oscillator
Post by loose-electron on Jan 30^th, 2012, 9:14am

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.

Title: Re: basic doubt regarding oscillator
Post by raja.cedt on Jan 30^th, 2012, 10:34am

hello looselectron,
What do you mean by an inverter does not delay the signal by 180 degrees. It inverts the signal and delays it by some smaller amount.
.

Inverting the signal means 180 deg phase only, in fact if it is not giving the 180 deg phase then how could it be satisfies Barkerson criterion.

Thanks,
Raj.

Title: Re: basic doubt regarding oscillator
Post by despap on Jan 30^th, 2012, 10:48am

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 :P

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.. :P

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?? :P
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

Title: Re: basic doubt regarding oscillator
Post by raja.cedt on Jan 30^th, 2012, 11:20am

hello,
seems you spend lot of time to post this, good. could you please explain he following bit clear.
output has zero rise/fall times with finite prop-delay..oh dear.. yes two-stage inverter-chain is going to oscillate

Finally what do you say about even inverters, will it oscillate or not.

Thanks,
raj.

Title: Re: basic doubt regarding oscillator
Post by loose-electron on Jan 30^th, 2012, 12:49pm

raja.cedt wrote on Jan 30^th, 2012, 10:34am:

Nope.

if I have 5 inverters in a ring, each one
provides 1/5 of the delay around the ring, correct?

360 degrees in additive phase around the ring correct?

Inverting the signal and phase delay are two different things
and a lot of literature does not draw the distinction.

Title: Re: basic doubt regarding oscillator
Post by loose-electron on Jan 30^th, 2012, 12:53pm

despap wrote on Jan 30^th, 2012, 10:48am:

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

A single inverter with its output connected
to its input, in a CMOS technology, is the equivalent
of a diode connected PMOS in series with a diode
connected NMOS connected between power and ground.

Go look at the schematic, at the transistor level.

Title: Re: basic doubt regarding oscillator
Post by despap on Jan 30^th, 2012, 6:08pm

@loose..
Who said its not.. Whats bothering?
When PMOS and NMOS diodes are connected between Supply/GND.. Voltage of drain of either is nothing but the Threshold of the inverter.(VTH)

Title: Re: basic doubt regarding oscillator
Post by despap on Jan 30^th, 2012, 6:11pm

@Raj..

No.. even no of inverters in a ring never oscillate.

Please spend time to understand why/how ring oscillators oscillate.. its a large-signal phenomenon. BH is not valid once the signal here reaches rail-to-rail.

Thanks!!

Title: Re: basic doubt regarding oscillator
Post by despap on Jan 30^th, 2012, 7:05pm

Previoulsy posted by loose-electron

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

is the precise explanation ..why even no.of inverter loop cant oscillate.

Title: Re: basic doubt regarding oscillator
Post by Lex on Jan 31^st, 2012, 1:04am

I like the thought experiment, raj.

I doubt that oscillation (with long term stability) is possible with even order. BH does apply in case you are exactly in the metastable point, but the reaction to a step response will always be latching.

There is one thing I would like to share though: suppose you have a large chain of inverters. If you create a pulse somewhere in the chain, that is just long enough to flip the inverter, then you will see that your pulse will live on for some periods.

I wonder if you would have a chain (of even inverters) that is very long, would the oscillation last very long (or maybe indefinitely) if you kickstart it properly?

I simulated it in some generic 018 technology, where from 1 pulse, several pulse could be made. Here's the schematic + simulation results. For the non believers, try it yourself =)

http://imageshack.us/photo/my-images/580/forumrt.png/ (for the large picture)

Title: Re: basic doubt regarding oscillator
Post by raja.cedt on Jan 31^st, 2012, 1:42am

hello despap,
please understand that no oscillator oscillate with out satisfying BH criterion, and while starting every oscillator is small signal and due to non-linearity finally it will go steady state and this is large signal. Please correct me if any thing wrong. This statement even no of inverters in a ring never oscillate worng. check the following pap.
http://www.imec.be/esscirc/essderc-esscirc-2003/papers/all/311.pdf

However they have taken extra care such that it wont latch at DC.

Title: Re: basic doubt regarding oscillator
Post by raja.cedt on Jan 31^st, 2012, 2:01am

hello lex,
seems you understood problem clearly. What you are saying is apply pulse at some node for the duration more than one stage delay and it would run along the chain for some time. did i understand correctly? Infact if we can provide the same delay as odd number of inverters oscillations should sustain..what do you say?

@despap: man i don't why you always say 1 come's to this inverter and it becomes zero and it go's to another point so on, but why you are not considering phase or delay? is there any special reason?

Thanks,
raj.

Title: Re: basic doubt regarding oscillator
Post by despap on Jan 31^st, 2012, 3:47am

@Raj
First lets get some-things clarified here..!!

What is the kind of gain of the inverter you are talking about.. is it controlled?
And what are the kind of oscillators - sinusoidal or square wave.?

In both case BH is required to start oscillations but later-on its different based on gain in the loop.

normal inverter chain - even number - doesnt oscillate.

For a ring-ocsillator(normal CMOS inverter)
its required to get a phase difference of 180 in the loop for square-wave oscillations. which in digital perspective 0 giving 1 and vice-versa.

whether its odd/even .. both start to ring at the frequency at which BH is met.
since the gain here(i am not talking about any-other case) is more than one and large.. as the signal propagates through .. it gets saturated.
but still to maintain/sustain oscillatons.. is it ok to have 360 loop-phase?

Once that point is reached.. what do you represent as delay and relate it to BH.?

Bottom line: for ring oscillators DC 0/1 at should produce 1/0 after traversing through the loop.

Title: Re: basic doubt regarding oscillator
Post by despap on Jan 31^st, 2012, 4:02am

@Raj
In the link you provided.
Please take a closer look and there are controlled loops with three-inverters.

Quadrature delay is obtained by controlling the oscillations with three-inverter loop chain.

Correct me if i am worng.

Title: Re: basic doubt regarding oscillator
Post by despap on Jan 31^st, 2012, 4:05am

Cut the loop and this is still valid.

for ring oscillators DC 0/1 at should produce 1/0 after traversing through the loop.

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

Title: Re: basic doubt regarding oscillator
Post by raja.cedt on Jan 31^st, 2012, 4:17am

hello despap,
thanks for your help, may be i have to read a lot about this.

Thanks,
raj.

Title: Re: basic doubt regarding oscillator
Post by despap on Jan 31^st, 2012, 4:22am

@Raj
Please keep posting if you understand more on this..
I might be blatantly wrong in my concepts. :(

Let me also get cleared on your thoughts/reasons. :-?

Thanks a ton..

Title: Re: basic doubt regarding oscillator
Post by RobG on Jan 31^st, 2012, 7:16am

Raj - I did some digging. Referring to here: http://www.ti.com/sc/docs/apps/msp/journal/aug2000/aug_07.pdf

Quote:

The oscillator gain must equal one (Ab = 1Ð–180°) at the
oscillation frequency. The circuit becomes stable when the
gain exceeds one and oscillations cease. When the gain
exceeds one with a phase shift of –180°, the active device
non-linearity reduces the gain to one. The non-linearity
happens when the amplifier swings close to either power
rail because cutoff or saturation reduces the active device
(transistor) gain.

Now I believe that with an ring oscillator the circuit will start to oscillate where the phase is 180 degrees if the gain is more than one. However, as the amplitude of the signal grows the feedback will become MORE NEGATIVE (i.e. phase will decrease). Think about it: if the output is at one rail the feedback will cause it to move away from the rail so the feedback must be negative when the signal is large.

On the other hand, think about a signal whose frequency is at the 180 degree point of an even-numbers ring of inverters. The output will tend to grow, but the phase will become MORE POSITIVE feedback as the signal becomes larger. Thus the signal will keep increasing until it hits the rail. Again, think about the case where the output is at the rail; the feedback is positive at that point.

So positive feedback is needed for an oscillator, but the feedback must become less positive as the signal gets larger. This is not true with an even-numbered inverter chain. In fact, the feedback becomes more positive as the signal gets larger so it will grow without bounds.

That's my story at the moment anyway, :)
rg

Title: Re: basic doubt regarding oscillator
Post by loose-electron on Jan 31^st, 2012, 12:21pm

Don't overthink it too much folks. When in doubt, go build it, plug it in and see what happens.

On this:

Lex wrote on Jan 31^st, 2012, 1:04am:

There is one thing I would like to share though: suppose you have a large chain of inverters. If you create a pulse somewhere in the chain, that is just long enough to flip the inverter, then you will see that your pulse will live on for some periods.

I wonder if you would have a chain (of even inverters) that is very long, would the oscillation last very long (or maybe indefinitely) if you kickstart it properly?

What you are describing here is something that has been dealt with in the area of ring oscillators in PLL's when used in a high radiation environment, and receive an ion hit.

One inverter in the ring flips over and sends a pulse propagating around the ring.

I am very familiar with this, having dealt with it for a satellite PLL IC I did a while back.

What happens?

Well, two different things.

In a simulation, the pulse can propagate forever around the loop if you model a fairly ideal system.

In the real world, the pulse has some randomness in propagation and delay and it will eventually die out.

You can even introduce that slow die out of the pulse into simulation if you start introducing some noise and variance in the propagation delays into the system.

Which if you think about it, when you power up a ring oscillator some random glitches like that exist as part of the power up process.