# [sdiy] frequency shifter

David G Dixon dixon at mail.ubc.ca
Wed Mar 11 08:28:18 CET 2020

```I built a frequency shifter following the Bode plan.  This is frequency
shifting by manifesting certain trigonometric product-to-sum formulae using
electronic circuits:

sin u sin v = 0.5 [cos(u - v) - cos (u + v)]

cos u cos v = 0.5 [cos(u - v) + cos (u + v)]

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):

cos (u - v)

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.

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:

cos (u + v)

With both the down- and up-shifted signals, you can get a stereo effect.

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).

The circuit works great and sounds super freaky.  I'm going to be building
another one for one of our members here shortly.

_____

From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On Behalf Of
ColinMuirDorward
Sent: Tuesday, March 10, 2020 7:01 PM
To: *SYNTH DIY
Subject: [sdiy] frequency shifter

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?).

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.

Is the APF method used by anyone? What are its limitations, and what is it
even doing?

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.

Cheers,

Colin

--

https://www.instagram.com/colinmuirdorward/

- <https://www.instagram.com/colinmuirdorward/>

https://www.instagram.com/ssdp_synthesis/

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://synth-diy.org/pipermail/synth-diy/attachments/20200311/99bc63f8/attachment.htm>
```