ring modulation

, showing ring of diodes 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. The ring modulator takes its name from the original implementation in which the analog circuit of diodes takes the shape of a ring: a diode ring. The circuit is similar to a bridge rectifier, except that all four diodes are polarized in the same direction. Ring modulation is 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 signal is multiplied with the carrier. This has the effect that ring modulation of two sine waves having frequencies of 1,500 and 400 Hz produces an output signal that is 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 sounds quite different, since each harmonic generates its own pair of sidebands that is not harmonically related.

, showing ring of diodes 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. The ring modulator takes its name from the original implementation in which the analog circuit of diodes takes the shape of a ring: a diode ring. The circuit is similar to a bridge rectifier, except that all four diodes are polarized in the same direction. Ring modulation is 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 signal is multiplied with the carrier. This has the effect that ring modulation of two sine waves having frequencies of 1,500 and 400 Hz produces an output signal that is 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 sounds quite different, since each harmonic generates its own pair of sidebands that is not harmonically related. y(t)=x(t) \; c(t). Mini-Circuits SBL-1 with four Schottky diodes. LO level +7 dBm (1.41 V p-p ) and RF 1–500 MHz (ADE-1: 0.5–500 MHz) If c(t) and x(t) are sine waves with frequencies f_c and f_x , respectively, then y(t) is the sum of two (phase-shifted) sine waves, one of frequency f_c+f_x and the other of frequency f_c-f_x . This is a consequence of the trigonometric identity: \sin(u) \, \sin(v)=\frac{1}{2}\left(\cos(u-v)-\cos(u+v)\right). 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. Neither the carrier nor the incoming signal is 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 f_c , whose Fourier expansion contains the fundamental and a series of reducing-amplitude odd harmonics: c(t) = \sin f_ct + \frac 1 3 \sin 3f_ct + \frac 1 5 \sin 5f_ct + \frac 1 7 \sin 7f_ct + \ldots and the carrier frequency f_c is at least twice the maximum frequency of the modulating signal x(t) , then the resulting output is a series of duplicates of x(t) at increasing regions of the frequency spectrum. For example, let x(t) represent a sine wave at 100 Hz, and the carrier c(t) be an ideal square wave at 300 Hz. The output then includes 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. ==Integrated circuit methods of ring modulation== 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 causes aliasing distortion, so it is common to oversample the operation or low-pass filter the signals prior to ring modulation. The SID chip found in the Commodore 64 allows for triangle waves to be ring modulated. Oscillator 1 gets modulated by oscillator 3's frequency, oscillator 2 by oscillator 1's frequency, and oscillator 3 by oscillator 2's frequency. Ring modulation is disabled unless the carrier oscillator is set to produce a triangle wave, but the modulating oscillator can be set to generate any of its available waveforms. However, no matter which waveform the modulating oscillator is using, the ring modulation always has the effect of modulating a triangle wave with a square wave. On an ARP Odyssey synthesizer (and a few others from that era as well) the ring modulator is an XOR function (formed from four NAND gates) fed from the square wave outputs of the two oscillators. For the limited case of square or pulse wave signals, this is identical to true ring modulation. Analog multiplier ICs (such as those made by Analog Devices) would work as ring modulators, of course, with regard to such matters as their operating limits and scale factors. Use of multiplier ICs means that the modulation products are largely confined to the sum and difference frequencies of inputs (unless the circuit is overdriven), rather than the much more complicated products of the rectifier circuit. ==References== ==External links==

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