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<p>I wanted to just give a thumbs up to the Quadnet software Dave
suggested for phase-shift networks.<br>
It took a few moments searching online to find - quite old &
windows only, but useful! <br>
<a class="moz-txt-link-freetext" href="http://tonnesoftware.com/quad.html">http://tonnesoftware.com/quad.html</a><br>
<br>
One minor wondering - on other phase shift stages I've seen the
resistor in series and cap to ground - QuadNet has it the other
way around - am I right to presume it doesn't make a difference
which way around?<br>
(yes, I should try it - and/or - do some maths..!)</p>
<p>Tom<br>
</p>
<div class="moz-cite-prefix">On 11/03/2020 07:28, David G Dixon
wrote:<br>
</div>
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<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">I built a frequency
shifter following the
Bode plan. This is frequency shifting by manifesting
certain
trigonometric product-to-sum formulae using electronic
circuits:<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:10.0pt;font-family:Arial;color:navy"
lang="PT-BR">sin u sin v = 0.5 [cos(u –
v) – cos (u + v)]<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:10.0pt;font-family:Arial;color:navy"
lang="PT-BR"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:10.0pt;font-family:Arial;color:navy"
lang="PT-BR">cos u cos v = 0.5 [cos(u –
v) + cos (u + v)]<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:10.0pt;font-family:Arial;color:navy"
lang="PT-BR"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">So, if you have two
signals with their
90-degree quadrature signals (say, u is the audio you want
to shift and v is
the on-board quadrature oscillator), then if you multiply
the signals together
(using a four-quadrant multiplier) and also multiply their
quadrature signals
together (using a second four-quadrant multiplier) then
you can sum the
multiplier outputs together, and you will get the
following (by adding the two
equations together):<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">cos (u – v)<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">This represents the
audio signal u which
has been frequency-shifted downward by the frequency of
the oscillator signal
v. Of course, the audio signal probably has many
frequencies u occurring
simultaneously, and they will all be shifted down by v.
That’s what
makes frequency shifting sound so alien and weird.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">By being clever with
the summations of the
multiplier output signals (based on a little bit of
algebra), you can also recover
the up-shifted audio:<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">cos (u + v) <o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">With both the down-
and up-shifted signals,
you can get a stereo effect.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">The entire circuit
consists of a 90-degree
phase displacement network to generate the cosine of the
incoming audio (I designed
mine with 12 stages from 15 Hz to 15 kHz using a little
thing I found on the
internet called QuadNet), a quadrature oscillator to
generate both sine and
cosine waves at frequency v (mine is TZFM and consists of
two Rubicon cores
with sine shapers, with one syncing the other in such a
way that the two are
always 90 degrees out of phase), two four-quadrant
multipliers (I built a dual
unit from a single 2164 chip – two linearized VCAs), and a
couple of
output amplifier stages for doing the summing. The key to
success is to
AC couple the signals into the multipliers to eliminate DC
offsets in the
incoming signal, which is the single largest source of
error in the circuit.
If that is done properly, the multipliers require no
trimming (if accurate
summing resistors are chosen).<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy">The circuit works
great and sounds
super freaky. I’m going to be building another one for
one of our
members here shortly.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial" color="navy"><span
style="font-size:
10.0pt;font-family:Arial;color:navy"><o:p> </o:p></span></font></p>
<div>
<div class="MsoNormal" style="text-align:center"
align="center"><font size="3" face="Times New Roman"><span
style="font-size:12.0pt">
<hr tabindex="-1" width="100%" size="2" align="center">
</span></font></div>
<p class="MsoNormal"><b><font size="2" face="Tahoma"><span
style="font-size:10.0pt;
font-family:Tahoma;font-weight:bold">From:</span></font></b><font
size="2" face="Tahoma"><span
style="font-size:10.0pt;font-family:Tahoma"> Synth-diy
[<a class="moz-txt-link-freetext" href="mailto:synth-diy-bounces@synth-diy.org">mailto:synth-diy-bounces@synth-diy.org</a>] <b><span
style="font-weight:bold">On
Behalf Of </span></b>ColinMuirDorward<br>
<b><span style="font-weight:bold">Sent:</span></b>
Tuesday, March 10, 2020 7:01
PM<br>
<b><span style="font-weight:bold">To:</span></b> *SYNTH
DIY<br>
<b><span style="font-weight:bold">Subject:</span></b>
[sdiy] frequency shifter</span></font><o:p></o:p></p>
</div>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span
style="font-size:
12.0pt"><o:p> </o:p></span></font></p>
<div>
<div>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span
style="font-size:
12.0pt">Hi, I got a little lost trying to understand
what a frequency shifter is.
I mean the pre-digital method used by Moog (I think?).<o:p></o:p></span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span
style="font-size:
12.0pt">I recently built a 4pole APF, and was really
impressed with some of the
pitching effects I could achieve with it. I'm guessing
this is an entirely
different method than the frequency shifters like Moog
and JH have done.<o:p></o:p></span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span
style="font-size:
12.0pt">Is the APF method used by anyone? What are its
limitations, and what is
it even doing? <o:p></o:p></span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span
style="font-size:
12.0pt">Well, I guess I'm just looking for some
conversation on the topic of
analog frequency/pitch shifting methods. If anyone has
any thoughts/experience
they'd like to share.<o:p></o:p></span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span
style="font-size:
12.0pt">Cheers,<o:p></o:p></span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span
style="font-size:
12.0pt">Colin<o:p></o:p></span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span
style="font-size:
12.0pt"><br>
-- <o:p></o:p></span></font></p>
<div data-smartmail="gmail_signature">
<div>
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<div>
<div>
<div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:
12.0pt"><a
href="https://www.instagram.com/colinmuirdorward/"
target="_blank" moz-do-not-send="true">https://www.instagram.com/colinmuirdorward/</a><o:p></o:p></span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:
12.0pt"><a
href="https://www.instagram.com/colinmuirdorward/"
target="_blank" moz-do-not-send="true">-<br>
</a><o:p></o:p></span></font></p>
</div>
<div>
<p class="MsoNormal"><font size="3"
face="Times New Roman"><span
style="font-size:
12.0pt"><a
href="https://www.instagram.com/ssdp_synthesis/"
target="_blank" moz-do-not-send="true">https://www.instagram.com/ssdp_synthesis/</a><o:p></o:p></span></font></p>
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