[sdiy] Ring Mod (was Re: Hadamard Transform Network)

[Magnus Danielson]

Hi,

The frequency shifting is just a Single Side Band (SSB) modulator.

One version of frequency shifter popular in synthesizer world uses two 
all-pass filters to create outputs with near 90 degrees phase-angle, 
i.e. I and Q output.

Once in a lab far far away, another approach was tried, in which a 
poly-phase filter was created, which had interaction between the 0, 90, 
180 and 270 degree angles rather than being independent filters. Such 
filter had been used within radio-context.

Another approach to create SSB, which is known in ham radio context, is 
to do normal AM, and then let a sharp filter, i.e. a crystal filter, to 
remove one side-band and carrier. For use in a audio frequency shifter 
context, you would mix up with one frequency, remove the lower 
side-band, and then mixdown with another frequency. The frequency 
difference between the frequencies would introduce the frequency shift.
The same frequency source could be used and then could the second 
frequency be generated by mixing the up-shift frequency with a shift 
oscillator frequency. Due handling of mirror frequencies needs to be 
done. This is what we do with two radios on regular basis as one is not 
in tune to another.

As for ring-mods, those refers to the ring-modulators that is also 
called double-balanced mixers. Those by itself is not necessarily square 
wave mixing, that is only one of many operational modes. It is also not 
what I think about for sounding best. I want sine as one signal for 
purest ring-mod sound.

Cheers,
Magnus

On 05/16/2017 08:38 PM, Mattias Rickardsson wrote:
> It seems like everyone suddenly trigged on this trig' question.
> Trig-OhNo!-metry.
>
> Apropos the sum & difference frequencies:
> Frequency shifting can be done with two ringmods (that are fed with sine
> & cosine, and adding clever all-pass filtering to phase shift them into
> cancellation of unwanted parts), but this involves quite an advanced
> setup. Are there any other useful but simpler tricks you could do with
> combinations of ringmods?
>
> /mr
>
>
> Den 16 maj 2017 6:56 em skrev <mskala at ansuz.sooke.bc.ca
> <mailto:mskala at ansuz.sooke.bc.ca>>:
>
>     On Tue, 16 May 2017, Tim Ressel wrote:
>     > But you bring up an interesting point: 4QMs multiply, but they
>     produce x+y,
>     > x-y tones. Anyone got the math on that?
>
>     It's a basic trig identity:
>
>     (cos a)(cos b) = 1/2 [ cos (a+b) + cos (a-b) ]
>
>     If a and b are two different multiples of t (time), then cos a and cos b
>     are two sine waves of different frequencies, and then you end up
>     with the
>     sum and difference frequencies.
>
>     One could prove this identity with the power series expansion for
>     cos, if
>     necessary.
>
>     --
>     Matthew Skala
>     mskala at ansuz.sooke.bc.ca <mailto:mskala at ansuz.sooke.bc.ca>
>            People before principles.
>     http://ansuz.sooke.bc.ca/
>     _______________________________________________
>     Synth-diy mailing list
>     Synth-diy at synth-diy.org <mailto:Synth-diy at synth-diy.org>
>     http://synth-diy.org/mailman/listinfo/synth-diy
>     <http://synth-diy.org/mailman/listinfo/synth-diy>
>
>
>
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at synth-diy.org
> http://synth-diy.org/mailman/listinfo/synth-diy
>