Phase Shifter - John Dunn, Consultant, Ambertec, P.E., P.C.

The following is a general plan for producing two sinusoidal signals whose relative phase can be adjusted arbitrarily between zero and 180°.

Starting with two equal amplitude sinusoids in quadrature with each other, sitting 90° out of phase, we assign one of them to be a "cosine wave" and the other one to be a "sine wave" from which we can produce two new sinusoids whose phase angle can be arbitrarily adjusted as desired.

 

 

We let the cosine wave attenuation be K1 and let the phase shift angle between the two outputs be Theta. We find the K1 coefficient as follows: K1 = 1 / sqrt ( 1 + Tan² (Theta/2) ).

Then the sine wave attenuation will be K2 = sqrt ( 1 - K1² ). This keeps the amplitudes of the phase shifted outputs of constant amplitude.

 

Comments

[George Storm]

Use analogue multipliers (e.g. Gilbert cells) instead of the attenuators and you have a standard all-phase I-Q modulator...

[Jeff Furman]

I've used tunable all pass filters for variable phase shift in the audio range. Half lattice rc networks are often used. An application:
http://www.ocs.net/~jfurman/selectoject/selectoject1.txt
http://www.ocs.net/~jfurman/selectoject/selectoject.JPG

[John Dunn]

Indeed, Jeff.

There was an article once in Electroic Design written by Fredrick Shirley with whom I had once worked at Sanders Associates in Nashua, NH. Fred used cascaded all-pass filters to make a quadrature phase generator for the audio spectrum. Although I remember the article, somehow I lost my copy of it and never got around to searcing that journal's archives to find it.