[time-nuts] injection locking crystal oscillator

Sat Mar 2 05:37:32 UTC 2019

In the June 1946 issue of "Proceedings of the I.R.E.", Robert Adler published "A Study of Locking Phenomena in Oscillators*. I believe this is the first full study of injection locking. This paper was so important that it was republished in the October 1973 issue of "Proceedings of the IEEE". This paper give the required condition (under a small signal approximation) for injection synchronization as:

(Einj/E)  >  (2 Q) | delta w / w |     (equation 13b)

I can't accurately reproduce this equation in plaintext, but it states that the ratio of the injected voltage to natural oscillator voltage must be greater than twice the product of the circuit Q and the absolute value of the fractional frequency error between the injection frequency and natural oscillator frequency. From this equation it would appear that for a large Q (such as 100,000) the lock range of the injection frequency would be much less than  +/- 5 ppm, since the injection voltage would normally be much less than the natural oscillator voltage. For lower Q circuits a larger lock range would be available as long as the injection voltage wasn't too weak.

Access to the Adler paper from either of the publication dates requires IEEE membership or related credentials, but the principles laid out there are extended in the freely available papers below:

** "A Study of Injection Locking and Pulling in Oscillators" (Behzad Razavi in IEEE Journal of Solid-State Circuits, September 2004) :
http://www.seas.ucla.edu/brweb/papers/Journals/RSep04.pdf

This paper derives in a different manner "Adler's equation" [ equation (28) in the paper ], which describes the behavior of LC oscillators under injection. This should also be applicable to crystal (and other resonator) oscillators.

Section III (Injection Pulling) C (Quasi-lock) describes the behavior when the injection frequency is outside the lock range.

Section IV (Requisite Oscillator Nonlinearity) shows that nonlinear behavior in the oscillator is necessary for injection locking to work.

Section V (Phase Noise) describes the reduction of the phase noise of an oscillator by a low-noise injection source.

Section VI describes the effect of injection pulling on a PLL.

** "Gen-Adler: The Generalized Adler’s Equation for Injection Locking Analysis in Oscillators" (Bhansali and Roychowdhury in IEEE 2009 Asia and South Pacific Design Automation Conference):
http://potol.eecs.berkeley.edu/~jr/research/PDFs/2009-01-ASPDAC-Bhansali-Roychowdhury-GenAdler.pdf

The second paper listed above uses "Perturbation Projection Vector (PPV)" analysis, which I don't understand. The authors derive a Generalized Adler's equation which is valid for any type of oscillator. Ring oscillators are discussed, and oscillator waveforms are shown when the injection has a sine, square wave, or exponential waveform.

I post this in case anyone wants to use an analytical approach to investigating injection locking. 

--
Bill Byrom N5BB

On Fri, Mar 1, 2019, at 9:00 AM, Neil wrote:
> I have five systems using injection locking. There are a few issues to 
> watch.  If you inject at too high a level, any noise on the reference 
> will appear in the oscillator output.  I use a 56 ohm resistor to 
> terminate the reference signal coax input, then a 100pF cap and a series 
> resistor connected to on leg of the crystal.  The resistor value needs 
> to be selected so I can get a solid pull-in and lock over an 
> acceptably-wide range.  In most cases, I am multiplying the crystal osc 
> up to 3.3, 5.6 or 10.2 GHz and using a PLL chip driven from an Rb as the 
> reference to generate 0dBm at the correct locking frequency around 117 
> MHz for example.
> 
> If the crystal free-runs close to the lock frequency, say within 200ppb, 
> the series resistor can be 5k or so, and there is almost no effect on 
> close-in noise, and no sign of spurs.  If I have to pull the crystal 
> more than about +-500ppb, the resistor needs to be a few hundred ohms, 
> and the synth noise sidebands start to be seen in the osc output.  With 
> a 70 ohm series resistor, the noise of the osc is only about 10dB down 
> on the noise of the synth, but the lock-in range is around +-1200 ppb, 
> slightly more on the LF side.
> 
> When the osc drifts too far away from the reference, or the level is too 
> low, you get a spread of frequencies out of the oscillator as it tries 
> to pull into lock, but doesn't make it.  As the lock level rises, it 
> pulls closer in, but still with a spread of frequencies until it finally 
> jumps into lock.  There is considerable hysteresis, so check thoroughly 
> that it will pull in under all likely conditions of voltage and temperature.
> 
> Remember that the coax lead is going to have a major influence on the 
> oscillator, so keep it short and watch for mechanical vibration or 
> ringing or temperature variation effects on the cable.  Make certain the 
> connectors are torqued well.  If there is a trimmer on the osc, remember 
> to tune it to the correct frequency with the cable and distribution amp 
> connected, but not delivering a signal, as it will probably be pulled a 
> little by the cable capacitance and any reflections from the far end.  
> Keep that series resistor high to reduce those effects.  Also, make sure 
> the resistor and cap are solidly fixed so you don't get microphony 
> effects. A little hot-melt glue seems to work well to keep the 
> components from moving and causing wobbles during the 
> tap-it-with-a-screwdriver stability tests.
> 
> The modified Butler overtone circuit from a G4DDK Anglian 144MHz 
> transverter running at 116MHz seems to give the best locking range 
> versus noise performance.  The single-transistor circuit used in the 
> Kuhne G2 transverters is much tougher to drive. I managed to get a solid 
> lock with a 47k series resistor on the Anglian.
> 
> There is a rule of thumb saying that if you inject into the side of the 
> crystal furthest from the output of the oscillator, the crystal acts as 
> a bandpass filter and makes it cleaner.  Not sure I'd subscribe to that, 
> it depends on your oscillator circuit.
> 
> If your GPSDO is clean and quiet, and you aren't multiplying it up by a 
> large factor, then just pick a series resistor that allows you to lock 
> over the desired range with a 6dB attenuator between the GPSDO and the 
> locking input, and then ditch the attenuator and you'll have plenty of 
> headroom.
> 
> Good luck
> 
> Neil
> 
> On 28/02/2019 23:43, Thomas S. Knutsen wrote:
> > Hello.
> >
> > I have a device that consists of a PLL, that has as its reference a
> > 10MHz crystal.
> > What I would like to do, is to inject this with 10MHz from a GPSDO,
> > when that is available, and to use the internal crystal when that is
> > not available.
> >
> > Would it be feasible to just connect it to one leg of the crystal
> > oscillator with a small capacitor, and with that get injection
> > locking?
> > The crystal oscillator is on chip, there is a couple capacitors that
> > allow for frequecy adjustments, other than that, I know nothing about
> > what is on the chip. The PLL is SP5769.
> >
> > Br.
> >
> > Thomas
> >
> 
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