Parametric Oscillator Experiment

The final section in my previous article about Parametric Mixers got me thinking about doing some work on parametric RF devices, so today I dug out a selection of inductors and varactors and went to work experimenting with them.

It was surprisingly easy to get a degenerate parametric oscillator to work. I simply put a pair of varactors across a tank and fed a pump signal into their cathodes through a capacitor. When the pump signal was large enough and at near twice the frequency of the tank an oscillation was easily produced.

Description of the Circuit
Description of the Circuit
(2.081 Mbytes)
Tuning the Pump across Resonance
Tuning the Pump across Resonance
(4.934 Mbytes)
Test Parametric Oscillator Circuit

Varactors are moderately expensive and somewhat rare devices, so I tried swapping them out for red LEDs. Some previous unpublished experiments suggested they work pretty well as varactors. The oscillator still worked fine using the LEDs, but needed DC biasing to keep them well reverse biased. I also found that putting the LEDs in "backwards" so they would conduct a small bias current worked even better, producing a much larger output for the same pump amplitude. In this configuration, the LEDs glowed dimly, with their brightness proportionate to the symmetry of the waveform seen on the CRO. This is an interesting side effect, but not all that useful, although it does give you some idea what is going on without looking at the waveform as you vary the pump from DC up to twice the tank resonance.

Using a pair of red LEDs as Varactors
Using a pair of red LEDs as Varactors
(3.998 Mbytes)

At half the tank resonance, there is a relatively efficient frequency doubling effect. There is a weak tripling effect at one third the resonant frequency too. This is parametric multiplication, or second and third harmonic generation. At the tank resonant frequency there is normal (but slightly distorted) resonance. At twice the tank frequency there is degenerate parametric oscillation.

Rectifier diodes were tried next, they worked quite well too. I used 1N4007s, and could get the circuit working with a pair, or just one of them. The DC reverse bias was not as critical with the rectifiers.

Using 1N4007 as Varactors
Using 1N4007 as Varactors
(3.190 Mbytes)


Great, so I've made a frequency halver, what use is that? The same result can be achieved with a digital divider, but this is completely passive, and sufficiently efficient to be useful. It is smaller and simpler than a digital divider, which still needs a resonator/filter to clean up the output.

If the pump amplitude is reduced to just below the threshold for oscillation, significant gain is experienced. This is one, slightly odd, way of making a regenerative receiver.

I couldn't experiment with this particular application very much with the configuration I was using, however in principle it appeared to work, I could amplify an AM signal from another generator before the onset of oscillation. Beating seemed to be a problem, but the "BK Precision" generator I was used for the pump is not a true RF source and was causing me a lot of grief. It is quite badly FMed and in general is a terrible instrument for this kind of work, but my RF generator had insufficient amplitude to pump the circuit and its vernier is cactus making tuning it precisely difficult.

More experiments with parametric amplification are indicated, especially non-degenerate configurations, which might make an interesting IF system; a converter with gain with very few parts and quite low noise.

Self Tuning Effect and Metamaterials

Using the real varactors (MVAM109s) I noticed a curious effect, I could reduce the amplitude of the pump waveform and the oscillation would initially drop in amplitude, then recover in a second or two. If I dropped it slowly enough, I could go far below the normal threshold of oscillation with the pump amplitude before the oscillation collapsed. If I dropped the pump amplitude quickly and caused an oscillation collapse the oscillation would recover in a few seconds. I assumed this was being caused by a DC bias building up on the varactors and the slow recovery was due to leakage. I state this on the video, and at that point thought I had ruled it out, however it turns out that this was in fact what was happening. The non-linearity of the system was causing a DC bias to be developed on the varactors and I had misplaced the biasing resistor into an unconnected part of the prototype board, basically leaving their cathodes floating.

Self-Tuning Effect
Self-Tuning Effect
(7.990 Mbytes)

It turns out what I was seeing is a form of self-tuning. Where the DC bias tends towards the point that maximises the signal across the tank. This has some interesting applications. After some thought I believe (but can't seem to prove) that this could be used to make broadband self-tuning left-handed metamaterial! In principle this could make it possible to build phase conjugate mirrors at RF. Not only phase conjugation is possible, but tunable material with gain, perfect lenses and mirrors which amplify the signal wave a controllable amount.

The idea of regenerative lenses and phase-conjugating reflectors seems a little exotic, but I could see applications in radar and electronic warfare. In particular; perfect cloaking material which exhibits massive return loss over wide bandwidths and arrangements that could perfectly copy signal energy around a shrouded "inner space" preventing shadowing as well as reflection.

The main problem I see with this would be the pump energy leakage, which could be trivially detected if you knew about it. However, it might be possible to arrange perfect reflection of the pump at the border of the material while still allowing other radiation through in both directions. Alternatively it might be possible to pump the system with a vastly different frequency, like light or mechanically, or even just supply DC power to every node in the material and design it to use that as a degenerate energy supply. Un-pumped passive systems could achieve pretty good, but not perfect cloaking, their losses would be visible no matter now perfectly isotropic they were, but if you add gain in the medium it would be possible to tune it to have essentially perfect properties, limited only by the granularity of the implementation.

Building such complex metamaterial is likely beyond current technology, even at the fairly macroscopic sizes required for RF frequencies. It would also be bulky, but that might not be a problem for some applications.

It is already possible to synthesize a phase conjugated beam at RF with a relatively simple assembly of oscillators, mixers and amplifiers. Several such phase conjugation nodes can be combined to make an array that retrodirects a beam of RF energy back to a source. This has been investigated commercially for cellular systems that steer a signal back to each mobile unit. The phase isn't perfectly conjugated in practice, and is modulated to carry the intelligence. With large arrays of interconnected nodes significant gain is achievable. The system is essentially an automatic electronic beam-former that requires no computational effort to track the mobile nodes.

For communication, such systems are excellent, but for radar cloaking (anti-phase equi-power conjugation, aka "active absorption") they are limited by the physical granularity of their construction (and bandwidth). By implementing the same thing in a broadband isotropic metamaterial with gain, much more perfect "absorption" cloaking would be possible, and perhaps the "ray bending" discussed above. Pumped non-linear resonators sound like one way to implement such a metamaterial with gain.



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Test Parametric Oscillator Circuit Source application/postscript 11.276 kbytes