[sdiy] XOR as 'digital' ring modulator

[cheater cheater]

Hi Magnus,
thanks for your explanations. They were really helpful.

On 11/11/2010, Magnus Danielson <magnus at rubidium.dyndns.org> wrote:
> On 11/10/2010 11:24 PM, cheater cheater wrote:
>> Magnus,
>> I'm afraid I didn't understand what you said there. Could you elaborate
>> please?
>
> A ring-modulator... the double-balanced diode ring, which is used for
> modulation and demodulation, a radio device... approximates a 4-quadrant
> multiplication. It does not have "a selectable gain of + or - 1".

Oh yes, that's definitely understood.

However, the "xor ring modulator", if realized with ternary logic
circuits, is just like a normal ring modulator put through a sgn(x)
function. The sgn(x) function has some very interesting properties.
It's on the one hand very much like a hard clipper. 0V goes to 0V,
anything above goes to say +5V, anything below goes to, for example,
-5V. So you can see it as a signal similar to one you could derive by
shaping a real ring modulator. One other important thing here is that
it keeps the zero crossings and therefore periods of at least some
fundamental most of the time, a property which makes our ears
associate the sound with a real ring modulator.

> The original ring-modulator isn't particular "linear", it has quite a
> bit of distortion in fact. It is also quite bulky for audio use due to
> the transformers. The Gilbert cell is another approach to achieve the
> same, using transistors rather than diodes. Linearisation is also attempted.
>
> As for 4-quadrant multiplication is means multiplication covering the 4
> quadrants (of a circle) i.e. having both polarities on both input
> signals, but it assumes continuous scale to the respective inputs.
>
> So, when I talk about ring-mod, I mean that... 4-quadrant multiplication.

Oh yes, ok. Fully agreed that's the right definition. The xor circuit
is only a derivation off the real ring mod. That is, you could take a
normal ring mod, and just have a comparator-based shaper (hard
clipper) after it, and have the same or nearly the same output. So,
this circuit is fun, but maybe not something original ring modulators
could do already.

> Similar effects may be achieved using for instance switch-able gain, but
> it isn't a ring-mod, a ring-mod doesn't do that unless you use a
> balanced digital signal as input, but then you can't cover all the
> aspects of a ring-mod which a triangle and sine would cover for instance.

Not sure what you mean here?

Cheers,
D.


> This is why I disagree with Tim.
>
> Cheers,
> Magnus
>
>> Thanks
>> D.
>>
>> On 10/11/2010, Magnus Danielson<magnus at rubidium.dyndns.org>  wrote:
>>> On 11/10/2010 09:27 PM, Tim Ressel wrote:
>>>> As a hopefully interesting side note, there are 2 ways to obtain the
>>>> "ring
>>>> modulator" function. The popular one for the synth crowd is a  linear
>>>> multiplier
>>>> like the AD633. The other way is by polarity reversal.  This is how true
>>>> "ring
>>>> modulators" work: the carrier signal goes  through an amplifier that has
>>>> a
>>>> selectable gain of + or - 1.  The  modulation signal's sign determines
>>>> the
>>>> gain
>>>> polarity: when the mod  signal is positive the gain is +1, when
>>>> negative,
>>>> -1.
>>>>
>>>>
>>>> This is of course not nearly as clean as the linear multiplier, but hey,
>>>> clean
>>>> is over-rated.
>>>>
>>>>
>>>> The XOR ring mod works as a true ring mod, as an XOR gate is a
>>>> digitally-controlled inverter.
>>>>
>>>> We return you now to your regularly scheduled programming.
>>>
>>> No. The true ring mod does not have gain which shift between +1 and -1.
>>> It has a gain shifting between those two extremes. A true ring mod
>>> actually always have losses.
>>>
>>> Modern ring-mod equivalents such as Gilbert cells can also be made to do
>>> 4-quadrature multiplications like the old double-balanced diode rings.
>>>
>>> Cheers,
>>> Magnus
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>
>