Complete Guide To The Ring Modulation Audio Effect

From radio and telecommunication applications to strange sonic effects, ring modulation is an intriguing and often overlooked audio effect in music and audio production.

In this article, we'll discuss the fascinating effect of ring modulation and how it works to affect audio signals. By the end of this article, you'll have a solid understanding of ring modulation and how to use it in your work, along with a short list of ring modulator examples to consider.

What Is Ring Modulation?

In electronics (and, therefore, audio), ring modulation is a type of amplitude modulation and an implementation of frequency mixing. It effectively creates and outputs sidebands (the sum(s) and difference(s)) of a modulator and carrier signal.

There's a bit to unpack here. Let's break down that first paragraph.

As the name suggests, amplitude modulation is technically any system/process that modulates (alters) the amplitude of one signal by another signal. We'll discuss typical amplitude modulation and how it compares to typical ring modulation later in this article.

Frequency mixing is the electrical process of creating new frequencies at an output from two signals at an input via a “frequency mixer.”

In the most basic sense, which happens to be the case with ring modulation, two signals are “mixed,” and new signals are produced, made up of the sum and difference of the original signal frequencies.

The carrier and modulator signals of a modulation circuit could be any electrical signal. With ring modulators (particularly those concerned with the audio effect), the modulator signal is typically the input/program audio. The carrier is another signal (often a generated sine wave oscillator).

Ring modulators are most often seen as effects units or synthesizer modules.

So then, ring modulation is an effect that takes two signals (a carrier and modulator) and produces sidebands (the sums and differences of the frequencies on the carrier and modulator signals) at the output. Note that the original signals (the carrier and modulator) are not outputted in a ring modulator circuit.

The Ring Modulator Name & Circuit

The term “ring modulation” comes from the analog circuit's basic schematic that produces the effect. This circuit utilizes several diodes in the shape of a ring, as is shown below:

In the following explanation, we'll be referencing the simplified circuit above in which the diodes of the diode ring point in a clockwise fashion.

Note that the diodes in the diode ring can face clockwise or counter-clockwise, depending on the schematic.

The carrier signal (which must be AC) will cause one pair of diodes to conduct electricity and effectively reverse-bias the other pair. Each diode pair is made up of opposite diodes in the ring (in the circuit diagram above, the top and bottom diodes make one pair, and the left and right diodes make the other pair).

Whatever pair is conducting at a given time will carry the audio/modulator signal through the circuit.

Note that ring modulation carrier and modulator signals should be bipolar, meaning their amplitudes pass through moments of positive and negative values.

When the carrier is positive, the top-bottom pair of diodes conduct and pass the modulator signal in its true polarity. The carrier signal's amplitude will affect how much of the modulator signal is passed (similar to amplitude modulation).

When the carrier is negative, the left-right pair of diodes conduct and pass the modulator signal in reverse polarity.

This is because of the polarity inversion between the transformers. The amplitude of the carrier will have an effect on how much of the modulator signal is passed, only in opposite polarity (this is different from amplitude modulation).

This causes the ring modulation circuit to eliminate the modulator signal frequencies from the output and effectively splits the frequencies between the modulator and carrier signals at the output.

Here's a visual representation of ring modulation with a modulator, carrier and output signal labelled:

Note that other ring modulation units may utilize digital signal processing (DSP) or even computer programming to achieve the same effect. Here, the frequencies of the two inputs are detected and used to sum and subtract the two output frequencies mathematically.

Low-pass filters and oversampling are often used in digital ring modulators to avoid aliasing and distortion in the output signal.

Frequency Mixing And The Ring Modulation Effect

Let's now turn our attention to the actual effect that ring modulation has on audio signals. As we touched on in the early paragraphs, the ring modulator is an implementation of frequency mixing.

The modulated product (output) of a ring modulation circuit comprises the sums and differences of all the modulator frequencies and all the carrier frequencies. These “sum and difference” frequencies are called sidebands.

This is also the case with amplitude modulation. The difference is that ring modulation eliminates the original carrier and modulator signals from the output (because the carrier is bipolar and reverses the polarity of the output).

Audio signals are typically rather complex and can be thought of as large collections of different frequencies. Each frequency has a different amplitude and amplitude envelope (side note: that is how additive synthesis works).

The carrier signal of a ring modulator may also have a rather involved harmonic profile with different frequencies.

To explain the frequency mixing effect of ring modulation, let's first consider the situation where both the modulator and carrier signals are sine waves. Sine waves are nice to work with as they only have a single frequency.

So then, let’s say the modulator sine wave has a frequency (f_m) of 1,500 Hz and the carrier sine wave has a frequency (f_c) of 700 Hz.

The ring modulator's output would have two new frequencies: the sum and difference (sidebands) of the two input signals. They would be:

• f₁ = f_m + f_c = 1,500 + 700 = 2,200 Hz
• f₂ = f_m + f_c = 1,500 – 700 = 800 Hz

As another example, let’s consider a modulator sine wave that has a frequency (f_m) of 1,000 Hz and a carrier sine wave that has a frequency (f_c) of 500 Hz. The resulting output sidebands would be:

• 1,000 Hz – 500 Hz = 500 Hz
• 1,000 Hz + 500 Hz = 1,500 Hz

Perhaps we have a situation where f_m and f_c are equal. Let's say 1 kHz (1,000 Hz). In this case, we'd only have one sideband:

• 1 kHz – 1 kHz = 0 Hz (no signal)
• 1 kHz + 1 kHz = 2 kHz

It's critical to note that the bandwidth of human hearing is only from 20 Hz to 20,000 Hz, so frequencies beyond these limits cannot be heard and are, therefore, often omitted from audio signals to free up headroom in the signal.

Let's consider a sine wave carrier signal of 1 kHz and a typical audio signal made up of various frequencies, harmonics and even noise.

For every frequency represented in the audio signal, the ring modulation will output two sidebands at ± 1 kHz (some sideband frequencies may be outside the 20 Hz – 20 kHz range and may be filtered out of the ultimate output signal).

The relative amplitude of each pair of sidebands to every other sideband will largely be defined by the relative amplitude of each modulator frequency to every other frequency in the modulator.

Therefore, low-level noise will be under-represented in the output, while the fundamental frequencies and important harmonics will be well-represented in the output.

Things can get rather complex rather quickly when a signal other than a sine wave is used as the carrier (or modulator).

Many ring modulators will have built-in oscillators that feed the carrier input. Some ring modulators offer different waveforms in their oscillator section.

Basic waveforms and their harmonic profiles include:

Sine Waves

Sine waves have a single fundamental frequency.

Triangle Waves

Triangle waves have a fundamental frequency with infinite odd-order harmonics of decreasing amplitude, defined by the following equation:

A_n = \frac{A}{n^2}

Square Waves

Square waves have a fundamental frequency with infinite odd-order harmonics of decreasing amplitude, defined by the following equation: (A_n = A • 2/πn)

A_n = \frac{A}{n}

Sawtooth Waves

Sawtooth waves have a fundamental frequency with infinite odd and even-order harmonics of decreasing amplitude, defined by the following equation: (A_n = A • 1/n²)

A_n = \frac{A}{n}

So if we have a typical audio signal as the modulator signal and anything other than a sine wave as the carrier signal, we can see that the sideband profile would become rather complex. Each harmonic in the carrier signal would produce two sidebands with each frequency of the modulator.

Not only is this complex in terms of math, but it may be too complex to sound good. For that reason, many ring modulators (and especially those used in effects units) utilize a sine wave as the carrier signal.

That being said, when ring mods are used in audio synthesis and are dealing with basic waveforms in the modulator/input, some slightly more controllable sounds can be produced by using square, triangle and sawtooth waves as the carrier.

Of course, I'll reiterate that any signal can be used as the modulator or carrier. I'm simply stating what is typical to help deepen our understanding of ring modulation.

Ring Modulation Parameters

Ring modulation, like any audio effect/process, is not static. There are several alterable parameters worth mentioning and understanding when it comes to adjusting the performance of a ring modulator.

Ring modulators will often have many (if not all) of the following controls:

• Carrier Selection
• Oscillator Waveform
• Carrier Frequency
• High/Low (Speed)
• Filter
• Mix
• LFO Section

Carrier Selection

Oftentimes the ring modulator will have simple inputs for the modulator and carrier signals. However, many ring modulators are designed with an oscillator that will produce the carrier signal within the effect unit itself.

If the ring modulator offers both a carrier signal (control voltage) input and an internal oscillator, there will be some way of selecting between the two.

Perhaps the oscillator is engaged by default, and the carrier input (sometimes referred to as the sidechain) is only activated when a plug is inserted into the jack.

Conversely, there may be a switch that the user must toggle to alter between the input/sidechain and oscillator carrier signals.

Oscillator Waveform

If the carrier signal of the ring modulator is indeed an oscillator, there may very well be an option to alter the carrier signal's waveform.

The options are often limited (typically between a sine wave and a square wave) if the unit offers something other than a sine wave at all.

That being said, in theory, the oscillator can produce any waveform as the carrier signal. Remember that the more complex the modulator and carrier signals are, the more complex (and arguably less musical) the ring modulator's output will be.

The Way Huge Ringworm offers a whopping 5 different modes with 3 different carrier waveforms, an envelope and random.

Carrier Frequency

Some ring modulators that offer an internal carrier signal oscillator will allow users to change the waveform. All of them will allow you to control the frequency of the oscillator.

This parameter will sweep the carrier signal waveform's fundamental frequency and thus alter the sidebands produced via the ring modulator's modulation signal.

A carrier signal's frequency range is typically in the audible range of frequencies when we're dealing with ring modulators. More specifically, to produce audible sidebands, the carrier oscillator frequency range is generally between about 20 Hz to 4,000 Hz (rather than all the way to the upper audible limit of 20,000 Hz).

These controls are often labelled simply as “frequency” and can have coarse and/or fine adjustments.

The Electro-Harmonix Ring Thing offers both coarse and fine-tuning of its carrier frequency.

High/Low (Speed)

In an upcoming section of this article, we'll discuss the differences between ring modulation and tremolo. For now, know that some ring modulators can offer both effects in a single unit by dropping the carrier signal oscillator into the low-frequency oscillator (LFO) range of frequencies (below 20 Hz).

If the ring modulator offers such a control (typically labelled as high/low or ring modulation/tremolo), then the aforementioned carrier frequency parameter will apply to the LFO frequency of the carrier.

Rather than producing audible sidebands, the LFO carrier will cause noticeable variations in the amplitude of the output signal. This is an effect known as tremolo, which we'll discuss in greater detail shortly.

The Fairfield Circuitry Randy’s Revenge allows us to toggle between ring modulation carrier frequencies (HI) and tremolo LFO frequencies (LO). The frequency control (FREQ) applies to both.

Filter

If the modulator and/or carrier signal of a ring modulator has overly complex harmonic profiles, the resulting sidebands can be rather chaotic. The high-end of the resulting output, then, can get quite harsh and even unusable.

Some ring modulators will offer a low-pass filter option to filter out/remove the high-end if it happens to become overly harsh.

Other ring modulators may offer other filters, including a high-pass filter to help remove low-end rumble from the output. However, the low-pass filter is typically the most common (if the ring modulator has a filter at all).

Mix

By the nature of the ring modulator circuit design, neither the modulator nor the carrier signal is passed through to the output. It is only the resulting sidebands that are outputted from a ring modulator.

Of course, this design can be bypassed by allowing the dry inputs (modulator and carrier signal) to pass through directly to the output. Many ring modulators will offer an output mixer that can effectively mix the carrier signal, modulator signal, and sidebands before the effect unit's final output.

LFO Section

To increase the complexity (and the functionality) of ring modulator designs, some manufacturers include an additional LFO section (complete with its own frequency, waveform and amplitude parameters) that will, typically, modulate the frequency of the carrier signal oscillator.

When engaging these LFO sections, interesting results will occur as the pitch of some sidebands is modulated upward while others are modulated downward (and vice versa).

The Moog Moogerfooger MF-102 (now discontinued) has an entire section dedicated to its LFO.

Ring Modulation Vs. Amplitude Modulation

Let's compare ring modulation (RM) to amplitude modulation (AM) in this section.

Amplitude modulation is generally associated with radio transmissions for broadcasting and two-way radio communication applications.

When used in wireless communication, amplitude modulation typically uses the audio signal as the modulator and some radio frequency wave as the carrier.

The tremolo effect is technically an effect that modulates an audio signal's amplitude with a low-frequency oscillator. This effect causes audible variations in the signal's amplitude.

However, as mentioned, the term “amplitude modulation” typically refers to communications applications. The AM radio bandwidth range is roughly about 550 to 1720 kHz.

Ring modulation, as an audio effect, will generally use audio signals to modulate other audio signals.

That all being said, these two types of signal modulation can be achieved using any carrier and any modulator signal (though results may vary)!

Ring modulation and amplitude modulation are similar but not exactly the same.

One of the key differences in the effects of ring and amplitude modulation is in the output. AM will effectively keep the original modulator signal frequencies in the output signal while RM removes the original signal frequencies and only outputs the sidebands of the carrier and modulator.

Unlike AM, the RM carrier signals will have negative amplitudes in their waveform periods/cycles. This switching of carrier signal polarity will similarly affect the polarity of the output signal.

AM carriers have a positive bias/offset and maintain a positive amplitude throughout their waveforms. Since the carrier signal is always positive, it will not cause any polarity switches in the output signal.

To visualize this, I've included an illustration.

Below, we can see ring modulation on the left and amplitude modulation on the right. Each has a sine wave modulator signal with frequency X (top) and a carrier frequency with frequency 8X (middle). Notice the 0 amplitude line of the carrier signals:

So both RM and AM have bipolar modulator signals (signals with positive and negative amplitude values). However, the RM carrier is bipolar, while the AM carrier is unipolar.

The resulting outputs show that RM effectively removes the original frequencies from the output. The AM output shows both original signals clearly.

Ring Modulation Vs. Voltage-Controlled Amplifiers

Ring modulators (RMs) and voltage-controlled amplifiers (VCAs) are both commonplace in audio, especially in synthesizer technologies. Let's consider the differences between the two to develop our understanding of ring modulation further.

As the name suggests, a voltage-controlled amplifier is an electronic amplifier that varies its gain based on a control voltage (CV). VCAs are used to control the output amplitude of an input signal with this control voltage. They effectively allow one signal to pass (at varying amplitude levels) when another signal is present.

VCA control voltages are often either envelopes or LFOs.

If the control voltage/modulator is at its maximum, then the entire carrier signal amplitude is passed through. If either the CV or the input signal is at 0 volts, there will be no output.

If the CV is positive and the carrier is negative, the output will be negative. However, (and this is the important part) if the CV is negative (below 0 volts), then no carrier signal will pass through to the output.

To help visualize, I've included the following illustration of a VCA signal flow graph:

If we were to compare the two, we could draw parallels between the control voltage of the VCA and the carrier signal of the RM and between the audio input or the VCA and the modulation signal of the RM.

To push the comparison further, let's consider a similar illustration of a ring modulator signal flow graph:

Like the VCA, the ring modulator’s carrier signal “allows” the modulator to pass at various amplitudes. However, when the carrier drops to a negative voltage/amplitude, it still passes the modulator.

VCAs are called 2-quadrant multipliers because they handle both positive and negative voltages/amplitudes in the audio/carrier input, but only positive voltages/amplitudes on the modulation input. This results in no output when the modulator runs at and below 0 volts.

On the other hand, ring modulators are referred to as 4-quadrant multipliers or “balanced modulators” since they can output negative and positive voltages/amplitudes in both the carrier and modulator input signals.

As mentioned in the section comparing RM to amplitude modulation, the ring modulator output phase is inverted (relative to the modulator/input) when the carrier is negative. This is not the case with VCAs and in amplitude modulation.

To illustrate the differences further, I've included a side-by-side representation of a VCA and ring modulator.

The VCA has a sine wave CV with frequency X, and the ring modulator has a sine wave carrier signal with frequency X (top). The VCA's audio input and the ring mod's modulator signal both have frequency 8X (middle). The difference in output signals (at the bottom) are shown:

As another example, we have a VCA to the left and a ring modulator to the right. This time there is a sine wave CV/carrier with frequency x (top) and a square wave audio/modulator with a frequency 8x (middle). The output signals (at the bottom) are shown:

Ring Modulation Vs. Tremolo

As mentioned previously, the tremolo effect is technically an amplitude modulation effect that modulates a signal's audible amplitude via an LFO (or other slow-changing control voltage).

So then, the difference in operation is practically the same as the difference between RM and AM. Notably that RM only outputs sidebands while tremolo would output the “carrier” and “modulator” (LFO/CV and input signal).

The only main difference, in terms of the audio effect, has been mentioned as well. Ring modulation audio effects require two audio-frequency signals to interacts with one another. On the other hand, tremolo requires an audio input and a relatively slow controlling signal to produce an audible variation in the output amplitude.

Because the effects are so similar in design, many ring modulators will offer tremolo functionality in addition to RM.

Ring Modulator Examples

Before we wrap things up, it’s always a great idea to consider some examples. Let’s look at 5 different ring modulators to help solidify our understanding of this strange modulation effect.

In this section, we’ll discuss:

• 500 series ring modulator: Meris Ottobit
• Ring modulation effect pedal: Fairfield Circuitry Randy’s Revenge
• Ring modulation Eurorack module: Random*Source Ring
• Ring modulation plugin: KiloHearts Ring Mod Snapin

Meris Ottobit

The Meris Ottobit is primarily a bit crusher but has ring modulation capabilities built-in. Meris is known for producing powerful two-(or more)-for one effects unit.

In addition to all the bit crushing control, which is for another article, the 500 Series Ottobit offers control over the carrier oscillator's frequency and waveform.

Pitch tracking can effectively match the ring modulator carrier frequency to the input signal's pitch for a more musical/harmonically sound style of ring modulation.

Fairfield Circuitry Randy’s Revenge

The Fairfield Circuitry Randy’s Revenge is a simple yet powerful all-analog ring modulator in guitar pedal format.

Randy’s Revenge has 4 knobs, 2 toggle switches and a bypass footswitch. These controls the following:

• Volume knob: adjusts the volume of the output signal.
• Mix knob: adjusts the mix of the modulated and input signals.
• LPF knob: sets the cutoff frequency of the second-order low-pass filter.
• Freq knob: adjusts the frequency of the carrier signal.
• Sq|Si toggle switch: toggles between a square wave and sine wave carrier signal.
• Hi|Lo toggle switch: toggles between two different ranges for the carrier signal frequency. Hi (18 Hz – 2.4 kHz) gets us a ring modulation sound while Lo (0.5 Hz – 45 Hz) gets us a more tremolo-like effect.

The pedal also featured a programmable control voltage jack. This 1/4-inch TRS jack acts as a 2-channel port to control parts of the circuit.

There are 6 microswitches in this pedal that can be set up in different combinations to personalize the CV jack in different ways. The TRS connection has the first 3 switches on the tip, the last 3 switches on the ring, and the sleeve as ground. The microswitches and their associated controls are as follows:

1. CVO: oscillator frequency (connected to tip).
2. CVF: filter frequency (connected to tip).
3. OSC: oscillator output (connected to tip).
4. CVO: oscillator frequency (connected to ring).
5. CVF: filter frequency (connected to ring).
6. REF: reference voltage (connected to ring).

With different microswitch combinations, we could have an external expression pedal control the internal oscillator, filter or both.

Random*Source Ring

The Random*Source Ring is an improved version of the Serge Ring Modulator R9.

The Random*Source Ring features an input jack for the modulator and an input jack for the carrier signal, along with two output jacks. The signal (modulator) and carrier levels can be adjusted via the Signal and Carrier knobs, respectively.

Pushing the carrier level past half will being to wave-shape the carrier signal. This distortion adds harmonics to the carrier and, therefore, additional sidebands to the ring-modulated output.

This unit offers continuous manual control over a wide spectrum of modulation. The control goes from zero modulation (only the input signal is outputted) to amplitude modulation on its way to full-out ring modulation.

The CV input allows a control voltage to control the carrier signal's amplitude for additional versatility in the simple yet powerful ring modulation module.

KiloHearts Ring Mod Snapin

The KiloHearts Ring Mod Snapin is a relatively simple plugin that offers an excellent range of ring modulation capabilities.

In the case of the KiloHearts Ring Mod, the input signal is technically the carrier. The modulator, then, can be either an internal sine/noise generator or a secondary input.

This plugin has the following controls:

• Bias knob: controls the amount of positive bias to add to the secondary input.
• Rectify knob: controls the amount of positive or negative rectification to apply to the secondary input.
• Frequency knob: adjusts the internal oscillator's base frequency or filter cutoff for the internal noise generator.
• Spread knob: shifts the internal generator's frequency slightly for left and right channels to achieve a stereo effect.
• Modulator: selects the secondary input.
• Mix knob: controls the dry/wet mix of this effect.

Related Questions

What is the chorus effect in audio? Chorus is an effect that thickens and/or widens a sound by producing copies of a signal (the original signal and each of its copies have their own “voice”) and modulating the pitch of each additional voice slightly. Each voice interacts with the other voices to produce slight modulation and an overall larger-than-life sound.

What is the difference between chorus and flanger? Chorus and flanger are based on the same basic design: a modulated delay circuit that causes phase modulation in the mixed output signal. The chorus effect sounds like multiple voices with slight detuning, while the flanger effect sounds like a sweeping comb filter. The major differences in design are:

• Flangers typically only use two voices (wet and dry). Chorus may have multiple wet voices (though a 2-voice effect is also common).
• Flangers have shorter delay times (below 10 ms) while choruses have longer delay times (above 10 ms). There is crossover between these values.
• Flangers utilize a feedback loop in the delay circuit while choruses do not.