Arbitrary phase calculation (was: Ensemble Circuit Configuration Questions)

[Steven Cook]

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.

> 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?

Thanks,

Steven Cook.