In electronics, ring modulation is a signal processing function, an implementation of frequency mixing, in which two signals are combined to yield an output signal. One signal, called the carrier, is typically a sine wave or another simple waveform; the other signal is typically more complicated and is called the input or the modulator signal. A ring modulator is an electronic device for ring modulation. A ring modulator may be used in music synthesizers and as an effects unit.
The name derives from the fact that the analog circuit of diodes originally used to implement this technique takes the shape of a ring: a diode ring. The circuit is similar to a bridge rectifier, except that instead of the diodes facing left or right, they face clockwise or counterclockwise.
Ring modulation is quite similar to amplitude modulation, with the difference that in the latter the modulator is shifted to be positive before being multiplied with the carrier, while in the former the unshifted modulator is multiplied with the carrier. This has the effect that ring modulation of two sine waves having frequencies of 1,500 Hz and 400 Hz will produce as output signal the sum of a sine wave with frequency 1,900 Hz and one with frequency 1,100 Hz. These two output frequencies are known as sidebands. If one of the input signals has significant overtones (which is the case for square waves), the output will sound quite different, since each harmonic will generate its own pair of sidebands that won't be harmonically-related.
Operation
Denoting the carrier signal by , the modulator signal by and the output signal by (where denotes time), ring modulation is described by the formula
If and are sine waves with frequencies and , respectively, then will be the sum of two (phase-shifted) sine waves, one of frequency and the other of frequency . This is a consequence of the trigonometric identity
Alternatively, one can use the fact that multiplication in the time domain is the same as convolution in the frequency domain.
Ring modulators thus output the sum and difference of the frequencies present in each waveform. This process of ring modulation produces a signal rich in partials. As well, neither the carrier nor the incoming signal are prominent in the output, and ideally, not present at all.
Two oscillators, whose frequencies were harmonically related and ring modulated against each other, produce sounds that still adhere to the harmonic partials of the notes but contain a very different spectral makeup. When the oscillators' frequencies are not harmonically related, ring modulation creates inharmonics, often producing bell-like or otherwise metallic sounds.
If the carrier signal is a square wave of frequency , whose Fourier expansion contains the fundamental and a series of reducing-amplitude odd harmonics:
and the carrier frequency is at least twice the maximum frequency of the modulating signal , then the resulting output is a series of duplicates of at increasing regions of the frequency spectrum. For example, let represent a sine wave at 100 Hz, and the carrier be an ideal square wave at 300 Hz. The output will then include sine waves at 100±300 Hz, 100±900 Hz, 100±1500 Hz, 100±2100 Hz, etc., at decreasing amplitudes according to the Fourier expansion of the carrier square wave. If the carrier frequency is less than twice the upper frequency of the signal then the resulting output signal contains spectral components from both the signal and the carrier that combine in the time domain.
Because the output contains neither the individual modulator or carrier components, the ring modulator is said to be a double-balanced mixer, where both input signals are suppressed (not present in the output)—the output is composed entirely of the sum of the products of the frequency components of the two inputs.
History
The ring modulator was invented by Frank A. Cowan in 1934 and patented in 1935 as an improvement on the invention of Clyde R. Keith at Bell Labs. The original application was in the field of analog telephony for frequency-division multiplexing for carrying multiple voice signals over telephone cables. It has since been applied to a wider range of uses, such as voice inversion, radio transceivers, and electronic music.
While the original Cowan patent describes a circuit with a ring of four diodes, later implementations used FETs as the switching elements.