# Ring oscillator phase noise

1. ## Ring oscillator Q factor

Let's take an N stage ring oscillator.

If the Q factor is defined as,

Q=2pi * maximum energy stored/ energy dissipated per cycle

since the max energy stored in the cap is CV2/2 and energy lost in the resistors as heat every cycle is CV2, I get Q < pi ~ 3.14. But I read that ring oscillators have Q ~ pi/2 as N-> ∞.
What's wrong here? (is it something to do with the harmonics?) Does it depend on number of stages in the ring, as I don't see an obvious dependence on 'N' since for each cycle, all inverters store and dissipate the amount described before.

•

2. ## Re: Ring oscillator phase noise

Ring oscillators are not really resonant, I wonder whether
you are just setting yourself a task with no useful result.
They certainly are not small-signal resonant once you get
to a significant number of stages - at some point the
signals become bang-bang, square, and there is nothing
linear going on except momentarily as stages cross the
inverter's linear region one after the other.

Ask yourself what use any calculated Q number would
have.

If you want to get at phase noise, you should look to
stage edge-rates and supply / ground rejection (slim
to none), the edge rate slope transforms voltage noise to
"time noise" (jitter, phase noise depending on how you
care to express it) during the linear intervals of the
stage's cycle.

I wouldn't expect (but could be wrong) a Q:PN relation
based on a small signal linear type tank oscillator to
hold much relevance to a RO's behaviors. Transistor
noise is going to be dwarfed by all of the thrashing.

--[[ ]]--