How does a Ring Modulator work ?

[Basstyra]

Hello,

I just picked up an original, broken, EHX Frequency Analyzer, I'm fixing it. But anyway...

I'm wondering what exactly does a ring modulator do ?? I mean technically, how does it transform the signal ?

Thanks a lot to anybody who would enlight me !  

[chrishopkins]

It takes 2 signals and then outputs both the sum and the difference of them.

For instance if you had 2 signals that were 440Hz you'd hear the sum (880Hz) and the difference (0 Hz).  I think this is how the Green Ringer achieves an octave up sound.

If you have 2 signals where the frequencies differ you will get some more "interesting" results.

For instance if Signal A is 880Hz and Signal B is 600Hz you would get

Signal A + Signal B = 1480 Hz
Signal A - Signal B = 280 Hz

The result is dissonant and not very musical.  

Most Ring Modulators (especially pedal based ones) utilised an oscillator to effect the input source.

For instance if you talk in a slightly clipped robot way through a Ring Modulator where the oscillator is set to around 20Hz you will get the "Dalek" sound!

[Paul Perry (Frostwave)]

More precisely, it puts out a signal whose value at any point in time is the product of the two input signal values, that is to say, multiplied together.
And it happens, that if you multiply two sine waves together, you get two sine waves produced, which have frequencies equal to the sunm and difference of the input frequencies.

Note that if, at any time, there is no signal going into one ofthe inputs, you get nothing out. Which confuses people, sometimes..

[Mark Hammer]

Just to follow up, the sum/difference products are not harmonically related, which is a big part of what creates the dissonance.

Many people are unfamiliar with how to integrate RM "tuning" into their playing.  Note that the sum/differences can vary in their colour or spread across the fretboard.  If I play a 440hz note, and modulate it at 100hz, the difference is 340hz and the sum if 540hz - not harmonically related.  If I then play a note at 1000hz, the diff is 900hz and the sum 1100hz.  Mathematically these are the same sum and difference but in terms of harmonic relationshiops, they represent a much smaller musical interval.  In general, when using fairly modest modulation frequencies, the sound becomes more "pitched" as you go higher up the fretboard, since the sum/diff tones are much closer (in musical intervals) to the original note.  Conversely, lower notes modulated at the same frequency seem wildly out of tune.

One of the implications of this is that when planning out how the RM is to be used, one needs to figure how pitched you want the effect to sound, and what notes you want it to sound most pitched for.  You then tune the modulation frequency appropriately.

Another thing to consider is that for some notes and modulation freqs, the sum or difference can be inaudible.  If I modulate 1khz with 2khz, their difference is negative 1khz (obviously impossible) and their sum 3khz.  If I modulate a 4khz note with a 10khz signal, the sum may be outside the passband of my speakers, and of course the difference is again impossible.

A third aspect often not thought about is the waveform.  "Traditional" RMs came from the world of pure tones in analog synths.  So, if you modulated a 1khz sinewave with a 200hz sinewave, you got 800hz and 1.2khz, and that's ALL you got.  Modulating a more harmonically complex input waveform from a guitar, with a more harmonically complex waveform (even a pure triangle wave has more "stuff" has a sine wave) produces a rainbow of sums and differences all at the same time.  All that clutter an often render it more noiselike than semi-pitched.  For that reason, rolling off the treble from your input signal can often achieve better, or at least more listenable and less fatiguing, RM tones.

[Basstyra]

I don't understand anything...  :lol:

But don't worry, I'll do, just let me the time to read this more carefully. English isn't my mothertongue, remember...  

Thanks a lot, it seems to be really complete. It should help.  

[Mark Hammer]

I don't understand anything...  :lol:

But don't worry, I'll do, just let me the time to read this more carefully. English isn't my mothertongue, remember...  

Thanks a lot, it seems to be really complete. It should help.  

Je me souviens, mais en même temp, c'est difficile à décrire le fonctionnement d'un ringmodulator en français.

Mais, en tout cas, si je peux simplifier le méssage.....

En utilisant une fréquence plus bas pour faire la modulation, la somme et la différence sont plus proche à la fréquence originale.  Comme la fréquence augment, les deux produits deviens même plus proche, et la note originale devien plus faciement identifiable.  Si on joue une note de 1000hz, en utilisant une fréquence de modulation de 50hz, la somme (1050hz) et la différence (950hz) sont assez proche de l'originale.  Si on joue une note de 300hz, les produits de 250hz et 350hz sont assez loin de l'originale (les intervales sont plus grandes) que ça manque une fréquence identifiable.  La note de 1000hz va sonner plus comme une note, et la note de 300hz va sonner plutot comme le bruit.

If faut se sounvenir aussi que l'idéée des RM venait de l'époque dont on utilisait les fréquences "pures", comme des ondes sinusoidales.  Les signales des guitares sont beaucoup plus complexes et moins stables que les signales "pures" d'un oscillateur.  Le tonneur plus musicale vien quand les signales sont plus simples et plus stables.

Ça aide?

[Basstyra]

LOL !!
Un peu.

But don't worry, really, I'll just take some time someday to fully understand all this, with the effect at hand.  :wink:

[cd]

This should be useful:

http://harmony-central.com/Effects/Articles/Ring_Modulation/

[Transmogrifox]

Generally, a ring modulator is a multiplier.

Input 1 = guitar
Input 2 = carrier frequency (sythesized by an oscillator in the pedal itself)

Output = (Input 1) x (Input 2)

Mark Hammer did an excellent job of explaining the implications of this.
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Mark:  You made mention of the "negative frequency" phenomena.  If, for instance you modulate a 1 kHz frequency with a 3 kHz frequency, you get a 4kHz and "negative" 2 kHz.  

That "negative" 2 kHz is not inaudible.  This effect is called "folding".  You will hear a 2 kHz tone.  This is how a Theremin starts at a low frequency and increases in pitch as you get closer to the antenna.   You start with two frequencies tuned together, and as you move close to the antenna, the oscillator frequency gets lower, so the "negative frequency" product goes more negative.  It is in effect "folded" over 0 Hz, so you hear a pitch that is moving more positive....So all it is is that the difference is getting larger.

Here's another, more intuitive way to think of it:  What if you modulate a 3 kHz signal with a 1 kHz signal?  It's blatantly obvious that the sum an difference terms are 4 and 2 kHz.  By the commutative property of multiplication, this is equivalent to the first example.  This goes for the Theremin example, too.

[Mark Hammer]

Mark Hammer did an excellent job of explaining the implications of this.

In which language!?! :lol:

Seriously, I was previously unaware of the "folding" notion, so thanks for expanding my knowledge.  I suppose if one thinks about the multiplication of frequencies, it makes sense mathematically to consider the multiplication as being transitive (i.e., F1*F2 = F2*F1).  Being a humble tinkerer, I never took trig and only a smidgen of calculus (enough to pass the stats course), so the mathematical aspects of the concept never really found an entry point into my thinking.  Just goes to show you how much I missed out on.

Keep your math up, kids!

[Transmogrifox]

En francais! (of course)
Actually, I only recognized a few words--the english one looked great to me, so if you repeated about the same in the Quebecois, the you're all good.

I'm glad you found some of that useful.

You may have missed some interesting details by missing trig and calculus, but you also missed hours of banging your head on the wall, pulling your hair and asking, "Why isn't it resolving into a nice little expression like the professor had in class???!".  Then you realize after a few hours that you missed a "-" sign 2 pages back. :lol:

[Basstyra]

Ok, so there is in this pedal (EHX Frequency Analyzer) only a gain, a frequency synthesis, a multiplier, and a switchable filter.

So the multiplier has to be a simple Gilbert cell, anyone can confirm ? If yes, considering that a Gilbert cell works fine with a fast and a slow signal, could comeone tell me what signal is the fast one, and what signal is the slow one ?

I didn't really studied the Gilbert cell, but I know it. It works also to have the same signal multiplied by itself, so I think the slow and fast are a little... not so very important, but anyway...

[krellmusician]

With regards to the "negative frequency" phenomenon, the same trigonometric identities that lead from the product of two sinusoids to two sinusoids with the sum and difference frequencies also tell us that the sine of a negative frequency is the same as the negative of the sine at that frequency.

Put more succinctly, it's 180 degrees out of phase, or inverted.

Paul Camann

[Basstyra]

Hm...

If some are confused by trigonometric stuff such as -sin(x)=sin(-x) which means a phase rotation of Pi (or 180 degrees, it's the same), I would highly recommand some work on it. It's the basis of what a signal is all about.

I never heard of "negative" frequency as you speak there... For me is so natural that a sin function (or a periodic function, which is the same, with Fourier) don't have negative frequency, the "-" only refers to the phase.

Anyway, thanks everybosy, I begin to have a better look to this stuff.