[time-nuts] quartz oscillator injection locking

Attila Kinali attila at kinali.ch
Sat Jul 19 07:23:31 EDT 2014

On Tue, 24 Jun 2014 21:18:20 +0200
Francesco Messineo <francesco.messineo at gmail.com> wrote:

> what would be the best method to try injection locking a butler common
> base crystal oscillator (see figure in
> http://www.eska.dk/oscillator_data.htm for schematic)?
> Any comment about close-in phase noise performance when adding
> injection locking to such oscillators?
> Thanks in advance for any hint.


I cannot give you performance data, but i can point you at some papers
that deal with injection locking.

Probably one of the best known papers is from Robert Adler[1].
It mainly deals with how locking comes to be, what the conditions
for locking are and how to calculate those.

The other big name in injection locking is Kurokawa Kaneyuki.
His first paper [2] deals, as the title suggests, with noise in
coupled oscillators vs noise in single oscillators.
His second paper [3] deals with injection locking itself, similar
to what Adler did, but with a more "modern" terminology, but also
with more math. 
(There are more papers from him on this topic, but i have not had
time to read those)

Chang et al. did a nice work on locking of multiple oscillators in [4]
and how coupling directions affect them.

Razavi did a nice rework of earlier findings on injection locking in [5].
In my opinion, this has one of the easier understandable math in all the
papers i've read on injection locking. Also his liberal use of graphs
simplify the interpretation of the formulas.

Zhang et al. did a quite nice analysis of noise behavoir of coupled
oscillators in [6]. But my main reason for mentioning it here is
the measurements they made, which might give you an indiciation on where
you might end up with your circuit.

If you are more on the simulation side, [7] might give you a point to
start how to model injection locking in spice (though, i must say that
is one paper i stumbled upon and probably not the best in that area).


			Attila Kinali

[1] "A Study of Locking Phenomena in Oscillators", by Robert Adler, 1946
reprinted in Proceedings of IEEE October 1973

[2] "Noise in Synchronized Oscillators", by Kurokawa Kaneyuki, 1968

[3] "Injection Locking in Microwave Solid-State Oscillators", by Kurokawa Kaneyuki, 1973

[4] "Phase Noise in Coupled Oscillators: Theory and Experiment",
by Chang, Cao, Mishra and York, 1997

[5] "A Study of Injection Locking and Pulling in Oscillators", by Behzad Razavi, 2004

[6] "A Theoretical and Experimental Study of the Noise Behavior of
Subharmonically Injection Locked Local Oscillators", by Zhan, Zhou,
and Daryoush, 1992

[7] "Capturing Oscillator Injection Locking via Nonlinear Phase-Domain Macromodels",
by Lai and Roychowdhury, 2004

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