Ring modulation multiplies two signals, outputting sum and difference frequencies while suppressing the originals

A ring modulator (also called a four-quadrant multiplier or balanced modulator) directly multiplies two audio signals. For every pair of frequency components it outputs their sum and difference, while suppressing the two original inputs. This follows from the product-to-sum identity sin(A)sin(B) = 0.5(cos(A-B) - cos(A+B)): multiplying sinusoids at C and M yields sidebands at C+M and C-M with the originals absent. For complex inputs, every partial of one signal pairs with every partial of the other, producing dense spectra. Because the outputs are sums and differences rather than harmonics of the inputs, results are generally inharmonic when the inputs are harmonically unrelated: metallic, bell-like, clangorous timbres, and the classic robot/Dalek voice when one input is speech. Ring modulation is a form of amplitude modulation but uses a bipolar modulator that inverts the carrier when the modulator goes negative; ordinary AM differs by keeping the unmodulated carrier (originals) in the output. With a slow sub-20 Hz modulator it becomes tremolo. It differs from a wave folder, a distortion that adds harmonics by folding a waveform on itself.

Examples

A 500 Hz sine ring-modulated by 200 Hz outputs 700 Hz and 300 Hz, with no 500 Hz or 200 Hz present. Two tones at 200 Hz and 30 Hz give 230 Hz and 170 Hz. Detuning one oscillator slightly produces slow beating sidebands; sweeping its pitch morphs the clangorous partials in real time. Voice through a ring mod with a low oscillator gives the classic Dalek robot effect. (Buchla Model 111: originals suppressed by about 55 dB.)

Assessment

Given a ring modulator receiving 500 Hz and 200 Hz, list the output frequencies and explain why the output is absent the originals. Explain why the result usually sounds inharmonic and metallic with detuned oscillators. Distinguish ring modulation from standard amplitude modulation (output spectrum) and from a wave folder.