[sdiy] Phasing circuit

[Theo]

Yep, used these for audio.
A common audio application is feedback reduction for PA systems.

Below are some numbers and formulas for phaseshifter circuit normalized on
1Hz.
The good news is ultra easy mathematics :)
Bad news you need the tables and I am not in the mood to copy the complete
tables.
So here are only the numbers for full audio bandwidth applications.
Source for these numbers is a Dutch language book about filters by H.
Baggen.
BTW the book is badly written, not recommended as a text book, but the
tables are useful)

The implementation of the circuit is a little bit different, but the
function is the same:
Take two parallel allpass networks and make their outputs 90 degrees out of
phase relative to each other.
Lets call these the N and the P network.
Every section is a opamp buffered allpass circuit.
Please see the attempted ASCII schematic below.

           +----R---+
           |        |
   +---R---+--|\    |
   |          | \   |
---+          |  >--+---
   |          | /
   +---C---+--|/
           |
           R1
           |
          GND

The number of sections needed depends on the phase error and band with.
A 6th order filter uses 6 sections, 3 for the N and 3 for the P network.
The next numbers are for use with the full audio bandwidth.

Normalized on 1Hz, fh/fl=1150:

6th order: Error is 7 degrees.
xN = 272,6 | 12,73 | 0,754
xP = 52,37 | 3,101 |  0,1451

8th order: Error is 2 degrees
xN = 375,6 | 30,75 | 3,699 | 0,4361
xP = 90,58 | 10,67 | 12,84 | 0,1049

10th order: Error is 0,7 degrees
xN = 476,8 | 52,37 | 9,60 | 1,764 | 0,3072
xP = 128,6 | 22,39 | 4,112 | 0,754 | 0,0829

First you need to know the highest and lowest frequency of your band.
Assume fl = 20 hz  and  fh = 22000 hz then fh/fl = 1100 therefore the
numbers of the table above apply.
Next calculate the central frequency of your band:
fc=sqr(fl*fh)
In this case: fc=sqr(20*22000) = 663 hz

Now first select a value for R and C for the sections of the ASCII
schematic.
For example R=10k and C between 1n and 22n
Now calculate for each section the value of R1:
R1= 1/(fc*xN*C) for the N network and
R1 = 1(fc*xP*C) for the P network.
Done :)

HTH
Theo


----- Original Message -----
From: Magnus Danielson <cfmd at swipnet.se>
To: <patchell at silcom.com>
Cc: <synth-diy at dropmix.xs4all.nl>
Sent: Friday, April 25, 2003 2:46 AM
Subject: Re: [sdiy] Phasing circuit


> From: patchell <patchell at silcom.com>
> Subject: Re: [sdiy] Phasing circuit
> Date: Thu, 24 Apr 2003 15:36:02 -0700
>
> >     Now you are asking a really hard question...well, not too hard...of
the
> > 11 notebooks that have EN in them, fortunately, I have only skimmed
through
> > 3 of them....so hold on, while I look through the most probable
> > notebook....
> >
> > Found it...that didn't take too long...did it?
>
> No, just a single line... and this machine can scroll fairly quick over
it, so
> no worries!
>
> >     EN #83 page 15 shows a circuit using two six stage phase shifters to
> > give the 90 degree shift.
> >
> >     They also show the pole locations for the stages:
> >
> >     Side A:
> >         5.41Hz
> >         41.1Hz
> >     167Hz
> >     671Hz
> >     2694Hz
> >     11977Hz
> >
> >     Side B:
> >     18.8Hz
> >     83.5Hz
> >     355Hz
> >     1344Hz
> >     5472Hz
> >     41552Hz
> >
> >     Hopefully I didn't get any typos in there.
>
> Does it explain in any way how those numbers where calculated or
generated?
> Is there any references to other articles?
>
> (actually, when I asked about references I really meant, what does that EN
> reference, but I agree knowing which EN is also good)
>
> >     The article for the frequency shifter starts on page 5 of EN #83
> > pretty cool article.
>
> Me and EN#83 is dislocated in space and/or time.
>
> Beam me up Jim! ;O)
>
> Cheers,
> Magnus
>