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Low Distortion Audio Oscillator Stabilized Via Trigonometric Identity

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RoGeorge:

--- Quote from: ccktek on October 08, 2019, 04:14:55 pm ---If the sine and cosine outputs of a quadrature sinusoidal oscillator are squared and summed, the result is a D.C. voltage whose amplitude is proportional to the amplitude of the outputs and independent of frequency:

     V2 = A2sin2(ωt) + A2cos2(ωt)      where A is the amplitude of the two outputs;
     V2 = A2(sin2(ωt) + cos2(ωt))
     V = A                                              due to the trig identity sin2(θ) + cos2(θ) = 1.

This voltage in conjunction with a voltage controlled amplifier, FET, or CdS opto-isolator in a servo-system feedback loop can be used to control and stabilize the oscillator’s output amplitude.  In contrast with the control voltage from the more usual rectifier/filter, this voltage is free of ripple and responds nearly instantly to changes in oscillator output level.

--- End quote ---

Brilliant idea, thanks for sharing!   :-+
That constant (and theoretically instant) amplitude detection is priceless, especially at very low frequencies.

Later edit:
Slightly changed the first 2 equations inside the quoted text, by replacing V with V2 and A with A2.

SiliconWizard:
Have you figured how much phase shift (from the ideal pi/2) would make this approach not meet a given amplitude accuracy? (Unless your quadrature oscillator is perfect, there will always be some...)

ccktek:

--- Quote from: dom0 on October 09, 2019, 04:01:05 pm ---I wonder if it may not be simpler and cheaper overall to just use an ADC, micro and digital PGA / multiplying DAC to control the loop gain instead of all the clever analog shenanigans. After all, with precision parts, the control range can be made quite small, and any good audio ADC, which are relatively cheap, would be good enough to serve in this function.

--- End quote ---

Intriguing idea, probably worth trying.  I'd be concerned about digital noise finding its way into the analog shenanigans, as the signal levels there are extremely low.

ccktek:

--- Quote from: SiliconWizard on October 09, 2019, 08:11:49 pm ---Have you figured how much phase shift (from the ideal pi/2) would make this approach not meet a given amplitude accuracy? (Unless your quadrature oscillator is perfect, there will always be some...)

--- End quote ---

No, but this would lead to a useful design criterion, especially if necessary tolerances of the frequency-determining capacitors and potentiometer could be related to phase error.

As Kleinstein points out, matching of capacitors between the integrators is important, but to what degree analytically I don't know.  As mentioned in my original posting I was compulsive about this; I matched as best I could with an LCR meter.

moffy:

--- Quote from: ccktek on October 09, 2019, 03:35:36 pm ---  In retrospect I wish I’d invested in a high quality sound card and FFT software.  Oh, well, working with old technology is still fun, and the equipment was on hand.

--- End quote ---

Even high quality soundcards seem to be limited to about 100db for distortion measurements. You would still need your notch filter, but there is reasonable and free software available for the FFT side. One thing I found out reading some specs is that THD for audio ADC's increases with sampling frequency. 96k gives worse distortion than 48k in general.

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