Ring Modulator Theory

[markphaser]

Ring modulator takes two signals and adds two new notes (one above and one below) based on the sums and differences of the oiginal signals

When there is only one signal (from a guitar) the second signal is generated by an internal oscillator. You can tune the oscillator to any key and the pitch of the new notes changes

ring modulator accepts two inputs and produces the sum and difference frequencies of them.

For example

if two sine waves of 100 and 150 cycles are present at the inputs,
the output will consist of two frequencies 50 cycles (150 minus 100) and 250 cycles (150 plus 100).

A ring modulator has 2 inputs and 1 output. The output mixes 2 signals: the sum and the difference of the 2 input signals. If the input signals are 600Hz and 200Hz sine waves, the output is a mix of a 400Hz sine wave (600Hz - 200Hz) and a 800Hz sine wave (600Hz + 200Hz). With other wave forms you also have harmonic frequencies which makes the output signal much more complex



A ring modulator multiplies two input signals

internal oscillator= the carrier signal

Ring Modulator formulas::

Sum and differences:
f1 = f2
f2 − f1 = 0
f2 + f1 = 2f

distortion occours due to the forward voltage drop of the diodes.

Multiplied:: two sine waves of frequencies

f1 and f2 (f2 > f1) are multiplied, two new sine waves are created, with one at f1 + f2 and the other at f2 − f1.

Multiplied 2 waveforms amplitudes and frequencys

[theundeadelvis]

Wow, I have a lot to learn. That made my head hurt, but I will read and re-read until I somewhat understand it. Thanks Mark!

[markphaser]

 What are sidebands?

What is a carrier frequency?

What does the carrier frequency do?

Does the carrier frequency "mix" or superimposes or FM or AM modulates the other input waveform?

How is a carrier frequency made? what circuit does this?

What does Heterodyne two waveforms mean?

What happens if i "bypass" the ring diodes?

What and where is the Carrier frequency stage/section? which chip takes a waveform input and puts a carrier frequency input?

[markphaser]

Does the carrier frequency "mix" or superimposes or FM or AM modulates the other input waveform?

How does the carrier frequency do this?

[markphaser]

In ring Modulators do they use AM or FM analog Modulators- to combine the carrier and un-modulated signals together?

[petemoore]

What are sidebands?
  >Either of the two bands of frequencies, one just above and one just below a carrier frequency, that result from modulation of a carrier wave.

What is a carrier frequency?
  >A unique frequency used to "carry" data within its boundaries. It is measured in cycles per second, or Hertz.
 
What does the carrier frequency do?
  "carry" data

Does the carrier frequency "mix" or superimposes or FM or AM modulates the other input waveform?
  it "carries" data
How is a carrier frequency made? what circuit does this?
  A ring modulator is a simple device that can be used to create unusual sounds from an instruments output. It effectively takes two signals (each with some frequency), and produces a signal containing the sum and differences of those frequencies. These frequencies will typically be non-harmonic, so the ring modulator can create some very dissonant sounds. For this reason, ring modulation is not a widely used effect. Sound Set 1 is an example of a guitar processed with a ring modulator.
   
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Sound Set 1: A phrase played on guitar, and then the same phrase played through a ring modulator (mixed together with the guitar's output).




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How it Works
Modulation means that we are changing some aspect of a tone, such as it's amplitude, frequency, or phase. In the ring modulator, we are using amplitude modulation (more specifically, suppressed-carrier modulation) which is implemented simply by multiplying two signals. This scheme is illustrated in Figure 1.


Figure 1: A ring modulator multiplies two input signals.



This multiplication results in a new signal that contains frequencies different than those of either of the original signals. More specifically, the multiplication results in an output that contains notes at the sum and difference of the two input signal's frequencies. (For the technical types, these new frequencies are the sidebands - the sums are the upper sideband, and the differences are the lower sideband) This is not a harmonizer - in general, the notes produced by the ring modulator are not related to the inputs by some musical interval or harmonic relationship. Thus, the sound produced is very dissonant and harsh. This sound is often described as being 'gong-like' (bells often contain strong non-harmonic components when ringing). Figure 2 shows a segment of a 400 Hz, a 600 Hz sine wave, and the product of the two. Looking at the multiplied signals, we can see the higher frequency component (at 1000 Hz) added on top of the lower frequency component (at 200 Hz). This 200 Hz component gives the waveform the gentle dip and rise in the figure. Sound Set 2 is an audio example of this case.



Figure 2: (a) 400 Hz sine wave, (b) 600 Hz sine wave, and (c) the product of the two (a 200 Hz and 1000 Hz sine wave added together). The product is zero when either wave is zero.


   
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Sound Set 2: A pure tone at 400 Hz, followed by a 600 Hz tone (a fifth higher), and then the result of the tones multiplied - a 200 Hz and 1000 Hz tone. (NOTE: You may need to use a pair of headphones to hear the true effect)


Many of the ring modulators you encounter will only have one input for connecting an instrument. The other signal is usually created with some internal oscillator (which is generally considered to be the carrier signal. This signal doesn't appear in the output, hence the name 'suppressed carrier'). In some cases, you may be able to select the frequency of that oscillator, and in others, the frequency may be fixed at some value, or limited to a set of different values. But there's no reason why both signals couldn't be instruments, or why they both couldn't be oscillators for that matter.

Of course, and instrument's sound is usually considered as being a sum of many different sine waves, not a pure tone. And the oscillator used could also generate a complex waveform as well. The number of tones grows quickly as each component produces the sum and difference with all the partials in the other signal, creating a very complex sound.

The ring modulator's output alone may be totally unsuitable depending on one's tastes, but the sound can be smoothed a bit by simply mixing in the original instrument sound. This will give an instrument a strange timbre. Sound Set 3 presents some mixed ring modulator sounds.


   
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Sound Set 3: A simple blues riff dry, and then processed by a ring modulator using a 100 Hz tone (with overtones). This same sound is repeated while mixing in the original instruments input, and then repeated with a 220 Hz oscillator.




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Implementation
Analog
Implementing amplitude modulation in the analog world is not always an easy thing to do. One implementation consists of a ring of four diodes (hence the name 'ring modulator') and a pair of transformers. This is also referred to as a lattice-type modulator, and it can actually be constructed as a passive circuit. Alternatively, a four-quadrant multiplier can be used, which is commonly available as an integrated circuit package.

Digital

Creating a digitally based ring modulator comes down to simply multiplying two numbers each sampling interval which is very easy to accomplish. However, there needs to be some consideration about the signals used as aliasing can create a noisy output. The highest frequency component in the output is the sum of the highest components in each of the signals being used.



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References
Wells, Thomas and Eric S. Vogel. The Technique of Electronic Music, Austin: Sterling Swift Publishing Company, 1974. (ISBN 0028728300)

Dodge, Charles and Thomas A. Jerse. Computer Music: Synthesis, Composition, and Performance. New York: Schirmer Books, 1984. (ISBN 0028646827)

What does Heterodyne two waveforms mean?
  Having alternating currents of two different frequencies that are combined to produce two new frequencies, the sum and difference of the original frequencies, either of which may be used in radio or television receivers by proper tuning or filtering.
  You know what a waveforem is, imagine two of them, now take sum and differences of them and see a whole new frequency emerge

tr.v., -dyned, -dyn·ing, -dynes.
To combine (a radio-frequency wave) with a locally generated wave of different frequency in order to produce a new frequency equal to the sum or difference of the two.


What happens if i "bypass" the ring diodes?
  If they are traveling @ 65mph in a 55 zone, and the difference in speed is 10mph, and a cop sees this happening, you get a ticket, but only if the cop is in the good mood he was in. Waveforms are similar.
  Say you have a row of cops all traveling @ 10MPH, each 60 miles apart. Every 6 hours a cop would pass, if you were watching while sitting still. There is the first frequency for this demonstration 4 'beats' per day {Freq#1}.
  Ok now for the second frequency, we have a Speeder, doing 8 miles an hour, now you have a cop passing by @ the rate of 4 per day, and speeder dudes [1mile apart like the cops]...you see them pass at a rate of 3 per day{Freq #2}. Things just got much more complex.
  Now instead of a steady pulse, you have 'equational' pulses, which follow a more complex pattern than either independant frequency has.
  If you start counting cops, speeders, and the rate at which a speeder passes the cops...you have a third frequency, independant and completely unique when compared to frequency #1 or #2.
  Plus, as an added benefit, you can count an 'artifact' rate like when a speeder is adjacent to you And a cop while being passed.
   

What and where is the Carrier frequency stage/section? which chip takes a waveform input and puts a carrier frequency input?
  dunno..I'd sure like to take a look at one though. You have a schematic?

[markphaser]

What are sidebands?
  >Either of the two bands of frequencies, one just above and one just below a carrier frequency, that result from modulation of a carrier wave.


So are sidebands from the carrier frequency or the non-modulation frequency?

where is the sidebands at?

Are sidebands modulating the carrier frequency?


What does the carrier frequency do?
  "carry" data

Does the carrier frequency "mix" or superimposes or FM or AM modulates the other input waveform?
  it "carries" data


What kind of "Data" does the ring modulator carrier frequency?

Whats a suppressed-carrier modulation?

How can the ring modulator multiply frequency when its f1-f2 and f1+f2 thats not multipling thats adding and subtracting

[DiyFreaque]

The ring modulator does not multiply frequency, it multiplies amplitude.  It's a four quadrant multiplier to be more exact.

Examples for a 'Perfect' ring modulator:

When the modulator is 0V and the carrier is 3V, 0*3 = 0.  Output = 0V

When the modulator is 3V and the carrier is 0V,
3*0 = 0V.  Output = 0V

When the modulator is 2V and the carrier is 3 V, 3X2 = 6. Output = 6V

When the modulator is -2V and the carrier is 3V, 3X(-2) = -6V.  Output = -6V

When the modulator is 2V and the carrier is -3V, (-3)X2 = -6.  Output = -6V

When the modulator is -2V and the carrier is -3V, (-3)X(-2) = 6.  Output = 6V

When you have two audio frequencies mutliplied together in four quadrants, it produces the upper and lower sidebands.  In a perfect ring modulator, you will not see the modulator frequency or the carrier frequency - the output is the four quadrant multiplication of the amplitude of the two frequencies.

In real life, analog ring modulators are not so perfect - there will always be a bit of minute bleed-through of the modulator and carrier.  The output will almost always be scaled by some fixed value as well.  For example, if your modulator is 2V and your carrier is 3V, you don't very well want a 6V output, do you?

To understand the theory behind this, you need to start reading up on RF modulation techniques - there is a lot more info there than in this application.  It's called SSB modulation/demodulation, though sometimes we in the biz just call it 'FM' (F**kin Magic) 

Cheers,
Scott

[DiyFreaque]

Hey, MP, we just hit 300!  Took me a bit longer......

[Mark Hammer]

"Sidebands" is simply the name for the sum and difference frequencies produced.  Because they are higher and lower than the original note, they are "off to the side".

If I am keeping my terms straight, the carrier is the signal being modulated, and the modulator is the signal doing the modulating.  So, if I modulate a 440hz carrier with a 100hz modulator, the sideband products will be 440hz minus 100hz (340hz), and 440hz plus 100hz (540hz), and NOT 100-440 (negative 340hz ) and 100+440.

Please note that all of the math you always see for ring modulators is based on *pure* tones.  That is a pure sine carrier, being modulated by a pure sine modulator.  In reality, and especially in the world of guitars, the signal being modulated is miles away from being a "pure" tone, and the modulator is often not very pure either.  The result of this is that, even when you pick one note, many different frequencies are being modulated by many other different frequencies, all at the same time.  Fortunately, the fundamental in the carrier and modulator are the strongest parts of each, so you can still hear identifiable pitches in there.  But you should remember that the ring modulation you get from synthesizer oscillators is not the same thing as what you get from string instruments.

[markphaser]

Thanks alot DiyFreaque and Mark Hammer for the information

A ring modulator usings a AM modulator chip

How do i control the "Depth of modulation" is there a trim pot for the AM modulator chip?

Why is ring modulators only AM modulations? why not FM modulation?

What causes the "Bleed through" of the un-modulated signal and the carrier frequency?

How do u get more "Bleed through" and how do u get Less "bleed through?

[Mark Hammer]

Thanks alot DiyFreaque and Mark Hammer for the information

A ring modulator usings a AM modulator chip
How do i control the "Depth of modulation" is there a trim pot for the AM modulator chip?

The modulator is just another signal.  You can stick a volume control in front of it.  It will depend on HOW you are doing the modulation, though.  I can't get into specifics because there are different ways.


Why is ring modulators only AM modulations? why not FM modulation?
Sometimes they ARE.  If you use an LFO with a very fast speed to modulate a chorus or flanger, you are not modulating the AMPLITUDE of the carrier.  Instead, by changing the time delay up and down very quickly, you are actually modulating the frequency.  This does not sound *exactly* like an AM-based ring modulator, but it comes very close.

What causes the "Bleed through" of the un-modulated signal and the carrier frequency?
How do u get more "Bleed through" and how do u get Less "bleed through?
That will depend on how you are doing the ring modulation in the first place.  Different technologies will require a different solution.

[markphaser]

Thanks Mark Hammer

Does a Flanger or chorus have carrier frequencys? what is the carrier frequency in a flanger or chorus?

What different ways is there to do modulation? with a modulator? what other ways?

Ring modulations modes
                        1.) X^2   frequency squared to the 2nd
                        2.) X^3   frequency squared to the 3rd
                        3.) X2     frequency multipled by 2
                        4.) X3     frequency mutlipled by 3

How do i get these different ring modulation modes please?

How can i convert a Ring modulator into a octave up pedal or vise visa how can i take a octave pedal and convert it to a ring modulator?
what stages need to be added or left out please?

[DiyFreaque]

It's a special subset of an AM modulator actually - AM is a two quadrant multiplication function.  A modulated AM signal contains the carrier as well as the sideband products of modulation.  If you amplitude modulate a 1 MHz carrier with a 1 kHz tone, the sidebands will appear 1 kHz above and below the carrier.  When using a spectrum analyzer, the ratio of carrier amplitude to sideband amplitude can be used to calculate the percent of modulation.  This does not apply to SSB transmissions, because the carrier is absent.  In the case of the SSB receiver, the carrier signal is generated internally and mixed with the received SSB signal.  Any difference in this reintroduced carrier frequency and the original carrier frequency can translate into voice demodulation sounding more like Donald Duck on a helium binge than an actual human voice.  It would also make a helluva guitar effect (and actually has more or less - it's called frequency shifting).

I worked with a guy about fifteen years ago who confided in me that he had perfected a method for transmitting 'sideband-less' AM, though he wouldn't tell me how he did ("That's MY secret", he would reply).  It was going to revolutionize the telecommunications industry.

I couldn't convince him that sideband-less AM had been around for at least a hundred years (they call it an un-modulated carrier).

But, I digress.

RM can be accomplished a number of different ways - using a double balanced mixer, an OTA, a specialized IC (MC1496, AD633, etc.) or some other method (I'm sure there are others). 

Without getting into the Whole World of AM, normally with a ring modulator (at least with semiconductor based devices) you trim each input (modulator and carrier) for a 0V offset by injecting a signal with the opposite input grounded.  You null the amount of signal present at the output to as close to 0V as you can get.

Depth of modulation can determined by how much modulator signal you inject.

Why not FM?  Because you're talking about ring modulators.  RM is an apple, FM is an orange.


Specifically for IC based devices:

Bleedthrough can be caused by the signal inputs being unbalanced by a DC offset.  Remember that the voltages of both inputs are multiplied.  If your perfect ring modulator has exactly 0V at the modulator input and 5V at the carrier input, the output will be 0V.

Say your ring modulator is not so perfect, instead of 0V, your modulator has a .1V offset in it for whatever reason.  The output in this case would be .5V, when you wanted 0V.

You can purposefully unbalance a ring modulator by mixing DC with an input.  You can also just allow a variable mix of the input signal with the output, too. 

I've never built a passive ring modulator.

Genuine octave-up would require a perfect sine wave, though I suppose it would be interesting guitar-wise.  Input a 500 Hz tone into both inputs.  What's the sum?  What's the difference?  Bingo.  It won't be perfect, far from it, wayyyy to many harmonics, but still, give it a try, what can it hurt?  After all, the fundamentals will still add, too, along with all the other content.......

Flangers, etc - that's just a whole different kettle of fish. 

Cheers,
Scott

[Mark Hammer]

Thanks Mark Hammer

Does a Flanger or chorus have carrier frequencys? what is the carrier frequency in a flanger or chorus?
There is no real carrier or modulator in a chorus or flanger.  Rather, if the LFO goes very fast (more than 20hz),  you start to notice different things that you wouldn't notice at slower LFO speeds. 

What different ways is there to do modulation? with a modulator? what other ways?
"Modulation" just mean "change".  If an effect changes in some way, and you can make those changes fast enough, you will start to hear other things.  So, if you could move your foot up and down 30 times a second on your wah-wah, you would hear something that sounded like a ring modulator.  The same is true of a phaser, and many other effects.  Ring modulation is kind of like "reverse tofu": you make tofu taset like anything, but in this case you can make almost anything sound like a ring modulator...if you do it fast enough. 

Ring modulations modes
                        1.) X^2   frequency squared to the 2nd
                        2.) X^3   frequency squared to the 3rd
                        3.) X2     frequency multipled by 2
                        4.) X3     frequency mutlipled by 3
How do i get these different ring modulation modes please?
I don't know anything about these things.  Can't help you.

How can i convert a Ring modulator into a octave up pedal or vise visa how can i take a octave pedal and convert it to a ring modulator?
what stages need to be added or left out please?
Whenever you modulate a carrier with another frequency, you will get the sum and difference of the two frequencies.  So, logically, if you modulate a carrier with itself, you will get the carrier frequency PLUS itself, and the carrier MINUS itself.  Carrier plus self is an octave up and carrier minus itself is silence.

[markphaser]

Thanks alot mark hammer and DiyFreaque

What a block diagram for a ring modulator?

Input#1>>>un-modulated waveform>>> Modulators input pin#1>>>Combined>>>modulation signal>>>diode ring section>>output
Input#2>>> the carrier frequency>>>> Mdoulators input pin#2>>>


Where do u find some "analog modulator chips" for guitar ring modulators?
What do most ring modulators use which chip numbers please?

Does the Modulators do the sum and difference? the modulator chip does the f1-f2 and f1+F2? inside the chip?

[zachary vex]

for video demonstrations of the newest Z.Vex Effects sequenced ring modulator, the RingTone, visit this page:

http://www.zvex.com/ringtonevids.html

they are large (24M each) and they require full download before play (right-click and download or, on mac, control-click and select download.)

[markphaser]

Bleedthrough can be caused by the signal inputs being unbalanced by a DC offset.

So Bleedthrough parameter trim would put DC offset on the Modulators chip input pins?

Bleedthrough means to make the Modulators chip "unbalanced"?


"Depth of modulation" can determined by how much modulator signal you inject.

So how can i have a trim pot to adjust the "Depth of modulation" from 0-100% percent please?

Does the Modulator chip adjust or trim the "depth of modulation from 0-100% percent is it FIX or variable?

[markphaser]

how do i make the modulator chip "unbalanced"?

What is unbalanced? The top part and the bottom part?

Yes how do u make the sidebands "unbalanced" the upper and lower parts?

Or the modulator chip is self how to make it unbalanced?

[DiyFreaque]

Bleedthrough can be caused by the signal inputs being unbalanced by a DC offset.

So Bleedthrough parameter trim would put DC offset on the Modulators chip input pins?

Yes.

Bleedthrough means to make the Modulators chip "unbalanced"?

Yes, in a manner of speaking.

"Depth of modulation" can determined by how much modulator signal you inject.

Yes, as far as 'depth of modulation' really applies in a ring modulator.

So how can i have a trim pot to adjust the "Depth of modulation" from 0-100% percent please?

Pot on the input wired as a voltage divider.  By '%' you're applying AM terms to this, which don't really apply in the same sense.

Does the Modulator chip adjust or trim the "depth of modulation from 0-100% percent is it FIX or variable?

The chip doesn't adjust or trim anything.  It just processes the signals.

how do i make the modulator chip "unbalanced"?

See above.

What is unbalanced? The top part and the bottom part?

What you call bleedthrough.  There is no important top part or bottom part in any sense of what's going on, or rather what I think you're getting at.

Yes how do u make the sidebands "unbalanced" the upper and lower parts?

I believe you are asking whether you can just put out the upper SB or lower SB?  If that's the case, you want a frequency shifter.  Understand the RM first.

Or the modulator chip is self how to make it unbalanced?

Just use the methods already mentioned.  Unbalanced only means that the inputs aren't balanced anymore and will come through whether the opposite signal is there or not.  It has nothing to do with sidebands, upper or lower or anything else that fancy.  Build a ring modulator and go from there. 

Cheerio,
Scott