Ring modulation

In electronics, ring modulation is a signal-processing function, an implementation of frequency mixing, performed by multiplying two signals, where one is typically a sine wave or another simple waveform and the other is the signal to be modulated. 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 function derives its name from the fact that the analog circuit of diodes originally used to implement this technique takes the shape of a 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 modulators frequency mix or heterodyne two waveforms, and 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 outputs, and ideally, not 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 make up. When the oscillators' frequencies are not harmonically related, ring modulation creates inharmonics, often producing bell-like or otherwise metallic sounds. Multiplication in the time domain is the same as convolution in the frequency domain, so the output waveform contains the sum and difference of the input frequencies. Thus, in the basic case where two sine waves of frequencies f1 and f2 (f1 < f2) are multiplied, two new sine waves are created, with one at f1 + f2 and the other at f2 – f1. The two new waves are unlikely to be harmonically related and (in a well designed ring modulator) the original signals are not present. It is this that gives the ring modulator its unique tones. If the same signal is sent to both inputs of a ring modulator, the resultant harmonic spectrum is the original frequency domain doubled (if f1 = f2 = f, then f2 − f1 = 0 and f2 + f1 = 2f). Regarded as multiplication, this operation amounts to squaring. However, some distortion occurs due to the forward voltage drop of the diodes. The carrier, which alternates between positive and negative current, at any given time, makes one pair of diodes conduct, and reverse-biases the other pair. The conducting pair carry the signal from the left transformer secondary to the primary of the transformer at the right. If the left carrier terminal is positive, the top and bottom diodes conduct. If that terminal is negative, then the 'side' diodes conduct, creating a polarity inversion between the transformers. Some modern ring modulators are implemented using digital signal processing techniques by simply multiplying the time domain signals, producing a nearly-perfect signal output. Intermodulation products can be generated by carefully selecting and changing the frequency of the two input waveforms. If the signals are processed digitally, the frequency-domain convolution becomes circular convolution. If the signals are wideband, this will cause aliasing distortion, so it is common to oversample the operation or low-pass filter the signals prior to ring modulation.