Arbitrary phase calculation (was: Ensemble Circuit Configuration Questions)

[mbartkow at ET.PUT.Poznan.PL]

Steven Cook <steve at babcom.u-net.com> wrote:

> > This is very easy even without complex algebra. One of the most popular
> > trigonometric equations does the trick: sin(x+y)=sin(x)*cos(y)+cos(x)*sin(y).
> > Take the two outputs of a quadrature oscilator, sin(t) and cos(t) and mix
> > with the proportions cos(phi) and sin(phi), respectively. Here, phi is the
> > desired phase shift. In analogue domain it requires two nonlinear shaping
> > circuits (or at least one) to obtain these scaling terms.
> 
> Presumably, such nonlinear shaping circuits would only be required for
> *moving* phase angles? I was thinking that it would be possible to simply use
> a pair of resistors for each phase output, together with appropriate amplitude
> adjustment - would this work?

Yes, of course nonlinear dependence is only required for changing (esp. modulating)
the phase shift. For constant phase difference a simple summing cicruit with precal-
culated coefficient resistors is sufficient.


Martin Czech <martin.czech at intermetall.de> wrote:

> Before starting a lot of complicated circuitry, one should consider
> that a sync feature is a usefull thing for lfos.
[...]
> The easiest way seems to be the multiwaves idea for sawtooth (I have
> forgotten the original title). It is just combining pwm with a saw wave
> (same frequency, pwm average is null) and gives multiple saw waves with
> the same frequency , but arbitrary phase. Perhaps this scheme could be
> changed to work with triangle waves, I don't know yet, if not, well use
> a saw->tri converter.

Indeed, this is a neat solution. Note however, that here nonlinear shaping
is needed anyway to obtain the sinusoidal LFO output. And speaking about sin-
usoidal modulation, I personally would prefer using smooth "true" sine waves 
(like those obtained from Wien bridge or quadrature oscillator) for pha-
ser/chorus delay modulation. In fact, I don't like piecewise-linear approxima-
tion of the sine in this very application. Why ? As the perceived detuning 
effect is proportional to the first derivative of the BBD delay, using piece-
wise-linear sine approximation results in unpleasant piecewise-constant 
detuning with almost abrupt steps between consecutive segments.

regards,

MB


--

Maciej Bartkowiak, PhD
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