Analog Design   

Kevin Aylward B.Sc. 

Phase Noise

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These tutorials are designed to explain phase noise in a way that best allows for design of real low phase noise oscillator systems. There is much confusion in phase noise. For example, a key issue in phase noise analysis of oscillators is, what causes up-conversion of low frequency 1/f noise to noise around the carrier?  


To correctly understand phase noise, an understanding of where understanding went wrong is surely useful. Repeating past mistakes is not usually a good strategy.

A relatively well known noise analysis approach was introduced by Hajimiri-Lee “A General theory Of Phase Noise In Oscillators” based on a Linear Time Variant (LTV) model.  However, various aspects of this approach has been definitively shown to be seriously in error, e.g. by A. Demir - “On the Validity of Orthogonally Decomposed Perturbations in Phase Noise Analysis”. Several authors also acknowledge this, however, there appears to be some level of politically correctness that prevents them making clear statements as the worth of that approach. For example:

The actual abstract of the HL paper emphasis and states:

“…In particular, it explains the details of how 1/f noise in a device up-converts into close-in-phase noise and identifies methods to suppress this up-conversion…”

However, Hegazi, Real, Abidi – “The Designers Guide To High Purity Oscillators” book state:

“…[HL] does not formally address flicker noise at all. The treatment of flicker noise in the original paper is performed without clear analysis or conclusive answers…”

The problem with all this politeness is that it does not really hit the nail on the head. The HL paper, gives an erroneous understanding to the cause of up-converted 1/f noise, and erroneous methods with which to design low up-converted phase noise oscillators. These erroneous ideas then, unfortunately, persist into the minds of real analog ic designers. The method is still taught at universities, despite its mathematically basis being internally inconsistent.

A summary may be said to be:

"The Hajimiri-Lee method can be shown to be valid for spherical chickens in a vacuum."  

"روش لي ال تي وي حاجي ميري، ميتواند بيانگر معتبر بودن جوجه كروي در خلا' باشد "


Basic Phase Noise Tutorial                     General phase noise overview

Basic Phase Noise In Oscillators            General phase noise in oscillators overview  

Invalidity of The LTV Model                  Proof that the Linear Time Variance theory is, essentially, useless for analyzing real circuits.

Invalidity Of Orthogonal Perturbation     Demonstration that phase disturbance persists in real circuits when an impulse is instigated at the peak of the voltage waveform 

Flicker Noise Nullification                      Demonstration of true, complete nullification of 1/f flicker noise down to 1Hz offset from a 500 MHz oscillator.

Design Ideas

Lower 1/f Phase Noise Differential Oscillator


Lee-Hajimiri-PN.pdf - A General Theory Of Phase Noise In Oscillators

A-Demir.pdf - On the Validity of Orthogonally Decomposed Perturbations in Phase Noise Analysis

© Kevin Aylward 2013

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Website last modified 30th August 2013