Arbitrary phase calculation (was: Ensemble Circuit Configuration Questions)

[mbartkow at ET.PUT.Poznan.PL]

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

> Hi,
> 
> mbartkow at ET.PUT.Poznan.PL wrote:
> 
> > My idea is to build a normal quadrature pair LFO which outputs two sine waves
> > shifted by 90 degrees. Now it is very easy to obtain an arbitrarily shifted
> > sine by mixing these two in appropriate proportions.
> 
> Do you (or anyone else) have any idea how the proportions are calculated? 

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.

> An
> LFO capable of outputting multiphase sines would seem to be an interesting module.

Yes, indeed. Very useful for various modulation configurations.

regards,

MB


--

Maciej Bartkowiak, PhD
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