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

[Ben Bradley]

A "4-quadrant balanced modulator" describes a function, and it can be
done with several different circuits. Perhaps the most ubiquitous
example (that's NOT a ring modulator) is the MC1496 chip.

A "ring modulator" does that too, but the narrow use of the term is
for a specific circuit with four diodes connected in a ring
configuration. A ring modulator isn't "as good" electrically as many
other circuits, because the forward drops of the diodes add distortion
to the output (there's no output until the input signals exceed the
diode forward drop), but like so many faults and imperfections in
sound and music generation/reproduction, people get used to the sound
and end up liking it more than other, "cleaner" circuits.

There are two articles on Wikipedia, both showing the ring modulator circuit:
https://en.wikipedia.org/wiki/Ring_modulation
https://en.wikipedia.org/wiki/Ring_modulator

For multiplication vs. addition, I think of the output as being
multiplication of the two inputs in the voltage domain, and
addition-and-subtraction in the frequency domain.


On Tue, May 16, 2017 at 8:38 PM, David G Dixon <dixon at mail.ubc.ca> wrote:
> I just wanted to say here publicly that I tried to build a Weaver frequency
> shifter from two 4-quadrant balanced modulators, two SV filters, and some
> sinewave oscillators.  All the bits and pieces worked perfectly, and I
> derived, rederived, checked and rechecked all the math and was absolutely
> sure that everything was hooked up correctly.  It didn't work.  I gave up on
> the whole idea.  I don't believe that a musical Weaver frequency shifter can
> be built.
>
> Also, if a "ring modulator" and a "4-quadrant balanced modulator" give
> exactly the same transfer function, then why can't the terminology by used
> interchangeably?
>
>
>> -----Original Message-----
>> From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On
>> Behalf Of Magnus Danielson
>> Sent: Tuesday, May 16, 2017 4:43 PM
>> To: synth-diy at synth-diy.org
>> Cc: magnus at rubidium.se
>> Subject: Re: [sdiy] Ring Mod (was Re: Hadamard Transform Network)
>>
>> 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/
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