The low distortion oscillator problem

There have been quite a few postings about 1kHz low distortion sine wave oscillators.
The problem is that if you want a get stable output from a sine wave oscillator you have to add a non-linear element to control the gain around the oscillating circuit.
In the original example - the Hewlett Packard sine wave oscillator which got the company going - the non-linear element was the filament in an incandescent lamp whose resistance increased as it got hotter when the circuit put more current through it. It had enough thermal mass that the resistance didn't change much over a single cycle of the sine wave.
The popular option today is a FET where you can modulate the channel resistance by changing the gate-to-channel voltage. The channel resistance isn't completely independent of the current through the channel - it tends to increase a bit with current, independent of the polarity of the current. There's also some ripple on the control voltage applied to the FET gate.
It can still work very well.
I like precision four quadrant multipliers. You can set one up to add a controlled amplitude copy of the output to vary the gain around the oscillating loop - which is handy at start-up - or subtract it from the output. This means that you can trim the oscillating loop so that the multiplier normally only contributes the minimal correction required to compensate for component drift and temperature excursions.
I've set up an LTSpice simulation which illustrates the point, but it used an AD734 as it's analog multiplier, which was horribly expensive at the time and is $A72.99 now.
In theory you could use good quality DAC to generate the correction waveform. It's going to have more distortion than a good quality analog oscillator, but if you can keep the correction waveform small enough the extra distortion introduced will be less than the distortion coming from the basic oscillator.
If you got fancy, you could use the DAC to generate a distorted waveform which precisely compensated for the distortions introduced by the analog part of the oscillator. You'd have to throw in a precision A/D converter to find out what they were, which would make for a very complicated circuit which would be a pain to set up, and not all that cheap.
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Bill Sloman, Sydney