[sdiy] 90-degree phase displacement network calculations

Richie Burnett rburnett at richieburnett.co.uk
Sun Jan 24 14:25:30 CET 2021

```Hi David,

I'm not sure what you're intending to use your phase-difference network for.
The application would dictate how accurate the phase conformity needs to be.

If it's for a frequency shifter then the phase error away from the ideal 90
degrees results in imperfect suppression of the unwanted sideband.  So, for
example if you have a signal at 5 kHz and you set the frequency shifter to
shift it up by 1kHz, you should ideally just get a signal at 6kHz.  (I am
calling this the upper sideband.)  However, you will likely also get a
signal at 4kHz too.  (This is the lower sideband.)  Often you can select
which one you want.  i.e. shifting up or down in frequency.  The greater the
phase error the more of the unwanted signal you will get.  Conversely the
better the conformity to 90 degrees difference across the frequency range of
interest, the better the suppression of the unwanted components will be.

-Richie,

-----Original Message-----
From: David G Dixon
Sent: Sunday, January 24, 2021 1:57 AM
To: synth-diy at synth-diy.org
Subject: Re: [sdiy] 90-degree phase displacement network calculations

Hello SDIYers,

I'm just about to commit to a layout for a new frequency shifter, and I have
to decide whether to build a 16-stage PDN or an 18-stage PDN for shifting
frequencies from 0.1 to 10000 Hz.  If I build 16 stages, the maximum phase
error is about 0.5 degrees.  If I build 18 stages, the maximum phase error

My question is this: Does that extra 0.2 degrees have any impact whatsoever
on the performance of the shifter?

Of course, these calculations assume perfect tolerance of all caps and
resistors.  In real life, I will hand-select the caps, but the resistors
will be subject to 1% tolerances, so the actual phase errors could be as
high as about 0.9 degrees for 16 stages, and about 0.7 degrees for 18
stages.

I have formerly built 12-stage PDNs for 15 to 15000 Hz.  The calculated
maximum phase error for those is about 0.2 degrees, but with 1% tolerances
these could be as high as 0.5 or 0.6 degrees.  They have worked perfectly
well.  Hence, I'm tempted to go with the 16-stage version.

Thoughts?  Does anyone have any experience with this particular problem?

Also, one other question: is 0.1 Hz low enough for general phaser duties?
That's one cycle every 10 seconds, and it seems to me that this would be at
or beyond the limit of being able to perceive the phasing effect.  Does
anyone have any thoughts about that?

Cheers,
Dave Dixon

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