kT is indeed relevant for a physical implementation. - Mike 

Mike B. Feher, EOZ Inc.
89 Arnold Blvd.
Howell, NJ, 07731
732-886-5960 office
908-902-3831 cell

-----Original Message-----
From: time-nuts [mailto:[email protected]] On Behalf Of Richard (Rick) 
Karlquist
Sent: Thursday, August 11, 2016 1:40 PM
To: Discussion of precise time and frequency measurement; [email protected]; 
[email protected]
Cc: [email protected]
Subject: Re: [time-nuts] State of the art of crystal oscillator measurements



On 8/11/2016 5:01 AM, Mike Feher wrote:

> This may be a naive question, but, how can you achieve results that 
> are so close to, and sometimes at further out are below kT? Thanks & 
> 73 - Mike

> Mike B. Feher, EOZ Inc.
>

kT per see is not the relevant parameter.  It is the ratio between kT and 
signal level that determines the limit on phase noise.  Also, when you extract 
an oscillator signal through the resonator, then at offsets from the carrier, 
the resonator filters out noise and the output noise can be way below kT.  
Ulrich first published on this in 1977.  Earliest reference I know of.
I actually remember reading it in 1977.

The old HP608 signal generator routinely produced far out phase noise floor 
well below kT.  AFAIK, for this particular spec, it better than any other 
signal generator ever built.  What's the secret?  It has a tracking 
POST-selector filter that follows the oscillator when you turn the mechanical 
tuning knob.  There is a little tracking adjustment knob to peak it.  Not 
really magic.

Rick
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