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Why do ring oscillators have poor Quality factor? (Read 1098 times)
Venky_analog
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Why do ring oscillators have poor Quality factor?
Nov 14th, 2015, 2:49pm
 
I am trying to reason out why ring oscillators have lower quality factors than LC oscillators, but I am not able to find an explanation for this. Your answer would be of great help to me. Thanks in advance.

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Re: Why do ring oscillators have poor Quality factor?
Reply #1 - Nov 16th, 2015, 2:45am
 
Hello---
Please derive an expression for open loop Quality factor for an N-stage ring oscillator, when number of stages (N) tends to infinity, Quality factor equals to Pi/2, means around 1.5. where as in case of LC vco if you are close to the resonance frequency you will always get much higher than this(above 10, if you are below 10Ghz and around 5 in the 20-30ghz carrier frequency range and assume you are not limited by varactor Quality factor). Intuitively in case of LC tank inductor energy will be transferred into capacitor energy almost, rest of the energy from supply where as in case of ring oscillator, every node will be discharges in every cycle and energy being pulled from supply to charge it again, hence more power loss so less Q.

Hope this helps----

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Raj.
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Re: Why do ring oscillators have poor Quality factor?
Reply #2 - Dec 8th, 2015, 11:04pm
 
google:

ali hajimiri ring oscillator Q

should be useful

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subtr
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Re: Why do ring oscillators have poor Quality factor?
Reply #3 - Jan 9th, 2017, 10:25am
 
I'll give an answer which is not really a mathematical proof. But this is some kind of rough intuition. There is something called Van der Pol Oscillator. It's not a real oscillator, but it's a model of oscillator. It's a differential equation which models both relaxation as well as sinusoidal oscillators. The equation has a parameter mu :

https://en.wikipedia.org/wiki/Van_der_Pol_oscillator

You can look at the first equation in the wikipedia link. It looks like a complicated equation. Solving it requires non linear dynamics, phase plane etc. But let's linearize it at some point and see. The equation is non linear because there is a dependence for the first order term with amplitude. A linear system would not have it. By assuming amplitude is small, we will find that poles lie in the RHS and when amplitude goes high above 1, the poles will go to LHS making it damp. Thus the poles move between RHS and LHS every cycle in a crude sense.

If this movement is large, then it's almost a relaxation oscillator. The value of mu thus at zero makes the movement very small, but at higher values makes it jump like a ball in the tennis court. Now what has this to do with the Q?

1. Q is in a sense how good the pole sits on the jw axis.

2.Secondly Q in a non linear fashion is : How much say does the amplitude have in deciding the oscillator frequency. Clearly if mu is non zero, frequency depends on amplitude which is the non linearity.

If amplitude decides the frequency you probably can make it oscillate at a different frequency by forcing it. You can call it a sloppy oscillator which agrees to oscillate at a forced frequency. This concept is called injection locking. This sloppy oscillator is more prone to phase noise because amplitude has say on its dynamics. If the value of mu was less, external forcing becomes less powerful in injecting signal. A linear oscillator cannot be injection locked.

Now ring oscillator is a relaxation oscillator and has a very bad linearity. In LCVCO, the frequency is decided clearly by the LC which are linear components. The current in the LC is still a square wave. But the LC does a good job of filtering the harmonics and selecting the fundamental. The cross coupled pair(XCP) is just providing a -gm to compensate for the resistance in the LC. These are my intuitions. I'm not sure if you would find these in any materials. I have not validated this, but after a lot of thinking this is what I felt it really could be.
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« Last Edit: Jan 10th, 2017, 1:14am by subtr »  

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Subtr
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