Injection Locked Frequency Divider

[mawyatt]

Here's some references for review so we won't dive into much detail on the Peltz Oscillator used.

https://www.eevblog.com/forum/projects/simple-sinusoidal-oscillators

https://www.eevblog.com/forum/projects/injection-locked-peltz-oscillator-with-bode-analysis

This delves into the fascinating world of non-linear circuit behavior, specifically the Injection Locking phenomenon.

The Peltz oscillator was configured with a pair of 2N3904 transistors, 1K emitter resistor, 10uH Inductor and ~2.5nF achieved with 2.2nF & paralleled capacitor. The bias supply was "tweaked" to ~2 V to bring the oscillator frequency close to the desired 1MHz.

Note the DSO and AWG don't agree frequency-wise as if the AWG is set to 1MHz the DSO reads 1.000011MHz.

Injection sine-wave signal was by way of a series 10K R and 10nF Cap to the oscillator 2N3904 common emitters, and the signal derived from a 50 ohm AWG.

Here's the results showing division from 2 thru 10 (see counter results), also note the division by 20 in PNG #11, and by 30 PNG #12!! These plots were obtained by triggering the DSO on the Oscillator Output (CH1 Yellow) and CH2 is the Input AWG Signal.

Edit: Added PNG # 13 which shows an "Unlocked" condition, this was created by changing the AWG frequency by 500Hz @ 5MHz, thus outside the Injection Locking range.

It's interesting to "see" the effects of locking and the phase relationship between the Oscillator and Injection signals, and one can study these effects and begin to understand the "preferred" Injection behavior of even order harmonics.

BTW long ago we've used Injection Locking Dividers with ECL/CML Resonate Frequency Dividers up to ~100GHz

Anyway, hope some folks find this interesting, and it's quite easy to assemble on the protoboard as shown

Best, 

[mawyatt]

Here we show the unlocked (PNG2) and locked (PNG3) spectral behavior of Frequency Divider @ 1/3X {Added 1/10X (PNG1), 1/4X (PNG4) and 1/5X (PNG5)}. Note the dramatically improved Phase Noise when locked, especially the even order divisions. Even divisions produce better PN results and wider lock range due to the complex behavior of the non-linear effects within the oscillator mechanics and best left to serious researchers to investigate (read deep dive into non-linear oscillator locking dynamics).



Best,

[mawyatt]

To show the Locked and Unlock close in Phase Noise effects better we've narrowed the Bandwidth to +-200Hz around 1MHz, and RBW to 1Hz. The plots were created with no averaging to reveal the effects. In all cases injection signal is sine-wave from an AWG.

PNG2a is without Injection Locking, PNG5a is Injection Locked @ 1/5X and PNG10a is @ 1/10X. Note how the 10X (even order) has better close in PN than 5X (odd order) which shows the more subtle effects of the Injection Locking behavior.

Best

[tggzzz]

Even divisions produce better PN results and wider lock range due to the complex behavior of the non-linear effects within the oscillator mechanics and best left to serious researchers to investigate (read deep dive into non-linear oscillator locking dynamics).

Too true.

But then even the dynamics of a simple PLL becoming locked isn't simple!

[mawyatt]

Even divisions produce better PN results and wider lock range due to the complex behavior of the non-linear effects within the oscillator mechanics and best left to serious researchers to investigate (read deep dive into non-linear oscillator locking dynamics).

Too true.

But then even the dynamics of a simple PLL becoming locked isn't simple!

Sure, PLLs can be quite complex when one dives into their detailed behavior. Recall from way back my favorite text on PLLs was Floyd Gardners Phaselock Techniques, vaguely remember the fascinating PLL loop used for the Voyager he developed to allow Viterbi's digital comms to work!!

We did some early work with PLLs and developed an interesting "Enhanced Phase Detector" (see patent 4904958) which really worked well and developed some SOTA tracking receivers around this, but that's another subject if anyone is interested.

Best,

[RoGeorge]

I might have a dead-simple explanation for the different phase noise when locking at odd vs. even multiples of the free running frequency, by thinking about the locking phenomena in terms of the energy exchanged between the two oscillators, rather than looking at the voltage waveforms.

According to my theory, the lock "preference" in regards to odd/even multiples should not be affected by the non-linearity of the circuits.  With or without non-linearities, the preference should still be there.  However, you mention non-linearity as playing an important role, a role that might not be obvious without careful investigation, which makes me think I might be wrong trying to justify the locking preference in terms of energy.

Even divisions produce better PN results and wider lock range due to the complex behavior of the non-linear effects within the oscillator mechanics and best left to serious researchers to investigate (read deep dive into non-linear oscillator locking dynamics).

Was that remark mostly about the locking range, or about the phase noise at even vs odd multiples?


Anyway, the injection locking experiment looks so tempting to try right away. 
Maybe not right now (being in the middle of something else), added to the wish list.

The weather is very hot here, and running the instruments for hours will make the room even hotter.  I wonder if the experiment can be run in audio, with a big enough coil to make a 1kHz LC, then using the soundcard as AWG+DSO+SA. ("WaveForms", the software made by Digilent for their Analog Discovery, can also use the soundcard as a lab instrument , with or without an Analog Discovery board).

[mawyatt]

The Injection Locking characteristics are very complex indeed, probably best to study various references, here's a few for starters.

Adler's original paper from 1946 that begins the journey.

https://ieeexplore.ieee.org/document/1697085

Hajimiri @ Cal Tech in 2 papers

https://chic.caltech.edu/wp-content/uploads/2019/07/08753733.pdf

https://chic.caltech.edu/wp-content/uploads/2019/07/BHongGenTheor-II_JSSC2019_Postprint.pdf

Razavi @ UCLA

http://www.seas.ucla.edu/brweb/papers/Journals/RSep04.pdf

Lee @ Stanford

http://smirc.stanford.edu/papers/JSSC99JUN-hamid.pdf

Beware this is a deep dive and the above references are for starters, be sure to check out the various references within these papers.

The device that's being locked must have some inherent non-linearity, otherwise locking can not occur. All electronic oscillators have some form of non-linearity to limit the waveform excursions which infers a cycle by cycle "gain" of identically unity at steady state (Barkhausen Criterion). If the gain is slightly greater than unity the waveform will grow, thus not steady state, if the gain is less than unity the waveform will decrease and not steady state. Obviously all electronic oscillators must posses a gain greater than unity to start up and as the waveform grows some form of "limiting" occurs which forces the gain back to unity under steady state conditions.

You should be able to experiment at any frequency, we chose ~1MHz as convenient for use with our SA. Over 2 decades ago we were working at ~100GHz with these techniques, and they also work at lower frequencies like here:

https://www.eevblog.com/forum/projects/injection-locked-peltz-oscillator-with-bode-analysis/msg4424434/#msg4424434


Best,

[mawyatt]

Here using the DSO XY Plot function shows the Sub-Harmonic or Frequency Division Injection Locking better than the usual DSO display in our 1st post.

Shown are XY plots where you can see the division ratio by the number of vertical peaks on horizontal axis.

PNG 25 is 1X, 26 2X, 27 4X, 28 6X, 29 8X, 30 10X and PNG31 20X.

Best,