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Rarely Asked Questions – Issue 92, April 2013 Multipliers and Modulators
A multiplier has two analog inputs and an output
proportional to the product of the two amplitudes V where K is a constant with the dimension of 1/V. Either signal can be applied to either input and, in theory, the output will not be affected. A modulator (or mixer) also has two inputs, but the signal input is linear, while the carrier input contains a limiting amplifier or is driven with a sufficiently large signal that it limits. In either case the carrier signal becomes a square wave, so its amplitude is relatively unimportant—as long as it is big enough—and its noise or amplitude variation will not appear at the output. The equation becomes V Multipliers are used for analog computation. One example is the calculation of power in a circuit. Signals proportional to the instantaneous voltage and current are applied to a multiplier’s inputs, and its output is proportional to the instantaneous power. Like modulators, multipliers encode the amplitude of the
signal input onto the signal at the carrier input, but unlike modulators,
variations in the carrier signal amplitude also appear at their output.
This variation is unwanted in communications applications where modulators
are used. The simplified V A simple description of a modulator often uses the same equation, but the clipping of the carrier signal to a square wave means that it contains odd harmonics. The simplified equation of a square wave is the odd harmonic Fourier series V(t) = K[cos(ωt) – 1/3cos(3ωt) + 1/5cos(5ωt) – 1/7cos(7ωt) +…] These odd harmonics are also modulated by the carrier, so the modulator output contains the desired fundamental products as well as products of the odd harmonics V(t) = K[cos(ω –1/3{cos(ω +1/5{cos(ω –1/7{cos(ω In many applications, these harmonic products are filtered and ignored, but a correct description of the modulator function must include them. Sometimes they are useful, and sometimes they overlap the fundamental products and cause unexpected results. So before choosing a multiplier, modulator, or mixer,
consider what you want to do, and which one will introduce the least
error. I invite you to comment on Multipliers and Modulators in the Analog Dialogue Community on EngineerZone.
Gilbert, Barrie,
Considering Multipliers (part 1), Brandon, David,
Multichannel DDS Enables Phase-Coherent FSK Modulation,
Bryant, James, Multipliers v Modulators
Have a question involving a perplexing or unusual analog problem? Submit your question to: www.analog.com/askjames
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