Ring modulation

Denoting the carrier signal by c(t), the modulator signal by x(t) and the output signal by y(t) (where t denotes time), ring modulation approximates multiplication: :y(t)=x(t) \; c(t). Mini-Circuits SBL-1 with four Schottky diodes. LO level +7 dBm (1.41 Vp-p) and RF 1–500 MHz (ADE-1: 0.5–500 MHz) File:Ring modulation two forms Diode-clipping or 'chopper' RM.svg|thumb|upright=1.1|An example of ring modulation on a sine wave of frequency f and a square wave of frequency 12f, resulting in a complex sound using analog FM known as diode-clipping or chopper RM, producing a variation in amplitude of the square wave-like frequency on 12f 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. == Circuit description ==

The ring modulator includes an input stage, a ring of four diodes excited by a carrier signal, and an output stage. The input and output stages typically include transformers with center-taps towards the diode ring. While the diode ring has some similarities to a bridge rectifier the diodes in a ring modulator all point in the same clockwise or counterclockwise direction. 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 carries 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, but create a polarity inversion between the transformers. This action is much like that of a DPDT (double pole, double throw) switch wired for reversing connections. A particular elegance of the ring modulator is that it is bidirectional: the signal flow can be reversed, allowing the same circuit with the same carrier to be used either as a modulator or demodulator, for example, in low-cost radio transceivers. ==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. == Limitations ==

Any DC component of the carrier degrades the suppression of the carrier, and thus in radio applications the carrier is typically transformer- or capacitor-coupled; in low frequency (e.g., audio) applications, the carrier may or may not be desired in the output. Imperfections in the diodes and transformers introduce artifacts of the two input signals. In practical ring modulators, this leakage can be reduced by introducing opposing imbalances (e.g., variable resistors or capacitors). == Applications ==

Radio communications Ring modulation has been extensively used in radio receivers, for example, to demodulate an FM stereo signal, and to heterodyne microwave signals in mobile telephone and wireless networking systems. In this case, the circuit is sometimes called a ring demodulator, one of many possible chopper circuits.) also calls for it. Indeed, several entire compositions by Stockhausen are based around it, such as Mixtur (1964), one of the first compositions for orchestra and live electronics; Mikrophonie II (1965), where the sounds of choral voices are modulated with a Hammond organ; Mantra (1970), Analogue telephone systems An early application of the ring modulator was for combining multiple analog telephone voice channels into a single wideband signal to be carried on a single cable using frequency-division multiplexing. A ring modulator in combination with carrier wave and filter was used to assign channels to different frequencies. Early attempts at securing analog telephone channels used ring modulators to modify the spectrum of the audio speech signals. One application is spectral inversion, typically of speech; a carrier frequency is chosen to be above the highest speech frequencies (which are low-pass filtered at, say, 3 kHz, for a carrier of perhaps 3.3 kHz), and the sum frequencies from the modulator are removed by more low-pass filtering. The remaining difference frequencies have an inverted spectrum: high frequencies become low, and vice versa. == See also ==