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Editors' NotesVolume 38, Number 1, 2004

MULTIPLIERS
Some 33 years ago, we noted the introduction of the AD530—the world’s first complete analog multiplier-on-a-chip—with a rambling historical discourse appropriately dubbed, “Multiplier Memories and Meanderings.” Eighteen years later, with many successful generations of multipliers—and a growing family of other translinear devices—in our portfolio, you could have read a column entitled, “Multiplier Meanderings—Revisited,” as we feted the arrival of the 500-MHz AD834. Now—and for no overriding reason, other than an implied promise buried in the last issue—we continue to meander and furnish the newer generation of readers with thoughts about multipliers—and related devices—originating farther up the stream of time, as well as  to jog the memories of readers whose ripening with time may have paralleled our own.

An analog multiplier is in a special category of nonlinear electronic devices, since it can represent either an externally applied linearly adjustable (modulating) influence or a means of introducing a parabolic (i.e., 2nd-degree) function for analog computation—and can be connected in a feedback loop to perform division.

Although our earliest and ongoing primacy is in analog multiplier design, we should note that, as the world’s “house of multipliers” Analog Devices is no stranger to IC electronic multipliers of digital- and hybrid (“mixed-signal” in today’s lingo) provenance. One of our first DSP products was a fast digital multiplier in CMOS (1983) ; and our very first 10-bit CMOS D/A converter, the AD7520 (1974), was a multiplying DAC.

In the vacuum-tube years, well before silicon and the Gilbert approach, the design of analog multipliers with adequate linearity and bandwidth posed daunting challenges. Servos were accurate, but too slow for repetitive computation (and they had mechanical parts that could wear out). Linear modulator circuits were available, but the gain and biasing required to operate at the standard voltage levels and polarities needed for computing made them impractical for general-purpose applications. The elegant “quarter-square”* relationship for a while seemed to offer the method of choice, since it offered a direct, symmetrical, mathematical solution—if one could only provide two accurately matched, stable squaring circuits and could accompany them with instantly responding accurate sums, differences, and coefficients at zero drift! This concept, elegant as it was, merely lacked accuracy in practice. As you may surmise, analog multipliers of that era were large and clumsy, hot, expensive, imprecise, and usually of undependable fidelity.

The hottest applications of ICs that involve multiplication (and its logarithmic cousins) are currently in RF, where one finds modulators, demodulators, log amps, mixers, power detectors, rms-to-dc converters, AGC, AFC, VGA, gain- and phase measurement. The strictures of our budget permit little discussion, in this cramped space, of the concepts and applications of multiplication and translinear circuits. The wisest use of the remaining space may be to provide you with pointers to some of the material we’ve published in these pages that you can find either on-line in our Archives[1], elsewhere in a search of the www.analog.com web site, or in your library:

“Accurate gain/phase measurement at radio frequencies up to 2.5 GHz,” by John Cowles and Barrie Gilbert. Analog Dialogue 35 (2001), pp. 5-8. Archives: find it in Volume 35, 2001.

 “Accurate, low-cost, easy-to-use multiplier,” by Barrie Gilbert. Analog Dialogue 11-1 (1977). Archives: Find it in (PDF) The Best of Analog Dialogue, 1967-1991.

“Complete monolithic multifunction chip,” by Lew Counts, Charles Kitcin, and Steve Sherman. Analog Dialogue 19-1 (1985). Archives: Find it in (PDF) The Best of Analog Dialogue, 1967-1991.

 “Monolithic IC rms-to-dc converter,” by Lew Counts, Barrie Gilbert, and Dave Kress. Analog Dialogue 11-2 (1977) Archives: Find it in (PDF) ) The Best of Analog Dialogue, 1967-1991.

“Nonlinear circuits handbook,” edited by D. H. Sheingold. Norwood, MA: Analog Devices, Inc., 1976 (out of print).

 “Now–True rms-to-dc measurements, from low frequencies to 2.5 GHz.” Analog Dialogue 34 (2000), p. 45. Archives: find it in Volume 34, 2000.

 “X-Amp™, a new 45-dB, 500-MHz variable-gain amplifier (VGA) simplifies adaptive receiver designs,” by Eric J. Newman. Analog Dialogue 36, Part 1 (2002), pp. 3-5. Archives: find it in Volume 36, Part 1 (Jan-Jun), 2002.

Dan Sheingold [dan.sheingold@analog.com]

 

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Scott Wayne [scott.wayne@analog.com]

 


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