"...other numerically-controlled oscillator sine-wave synthesis and do NOT simply choose sin(phase) for equal phase spacing, I'm very interested."
The Xantrex inverter I mentioned does not use equal spacing of the switching instants, and this leads to interesting behavior of the distortion. I did an analysis of this a while ago, and I think it's still on the computer. Would you like to see it?
By the way, did you see the set of resistors from the E192 series I posted in that other thread that gave -123 dB suppression of the 3rd harmonic?
Yes, this is interesting. It seems to me that to lowest order they are switching transformer windings in and out to shape their output waves, and that this switching has to change timing (and maybe order if not all windings are equivalent) as the load changes. Am I too far off?
Yes, but part of my lack of vocality was that none of the distributors I order from (Mouser and Digikey, mostly) stock E192 values :-).
I did manage to hack together a circuit using a HC595 and the E96 values, driven from a 4046 VCO phase-locked to a GPS-derived frequency standard, to make a sine wave synthesizer with some low-pass filtering. Now I have to make some real-world distortion measurements on it!
Would you tell what aspects of the problem interest you most, or seem most worthy of design effort? Do you want your stepped sine before analog filtering to have a 3rd harmonic 100 dB or more down? Are you after an especially pure sine wave?
I'll post my analysis of the type of stepped sine approximation that the Xantrex inverter uses over in ABSE.
I think you mentioned the desirability of having the 3rd down quite a bit before analog filtering, since if it is already suppressed, then the analog filter doesn't need to have a sharp cutoff, or a notch close to the passband. Another technique to achieve this was used in the Ivie 3rd octave analyzer twenty or more years ago. What they did was to generate two 50% square waves, one at 3 times the frequency of the other; call them Vf and V3f. Recognizing that the fundamental of V3f was at the same frequency as the 3rd harmonic of Vf, they subtracted 1/3 of V3f from Vf, thereby cancelling the 3rd harmonic of Vf. Then they didn't need to worry about the 3rd when designing the analog filter.
I wondered what the waveform would look like if one carried this procedure to higher harmonice, cancelling the 5th, 7th, 11th, (9th is already gone), etc. I'll post some of the waveforms; they look almost fractal-like.
There are 3 transformers; big, medium, and small. The medium xfmr has
1/3 the turns ratio of the big xfmr, and the small has 1/9 the turns ratio of the big xfmr. Their secondaries are in series and the design provides that the steps in the stepped sine wave are proportional to the battery voltage. So, as the inverter is loaded, the battery voltage drops and that plus various IR drops cause the step size to decrease; as the step size decreases, the switching is varied so that more steps are added to keep the output RMS at its nominal value. For any constant load (for a short while the battery voltage will remain nearly constant), the step size is fixed, but the timing of the steps varies in the same manner as the mathematical version I've posted over on ABSE. The number of steps (per quarter cycle) in the actual inverter varies from 6 when lightly loaded, to 13 when heavily loaded.
The current drawn from the battery has a double frequency component that causes some distortion of the waveform, but I don't deal with that in my analysis.
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