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Tutorial on Gilbert mixers Mar 1, 2005 12:00 PM Barrie Gilbert
The recent article concerning active mixers (see “Comparing active Gilbert mixers integrated in standard SiGe process — Part I” by N Rodriguez, E Hernandez et al., January RF Design, page 50) refers to the widely used four-transistor core called a “Gilbert cell.” This has been the practice for almost four decades, and it probably won't change now. Since the name used for a basic circuit topology is no more than its commonly recognized label, one can serve as well as any other. This is also a classic case of typecasting, of the sort suffered by a Brokaw, a Darlington or a Widlar. Admittedly, it has been gratifying to affirm, in all those elevator encounters with entry-level engineers, “Yes, that's me.” Still, I am bound to wonder whether this fortuitous discovery of one of the industry's basic circuits is perceived as my most useful — or, gasp, sole! — contribution to the noble analog art. That wouldn't be much to brag about, as the net worth of a lifetime. However, in teaching the basics of active mixers during lectures, and in comments from the floor at many conferences, I've strenuously tried to give the credit for first describing this cell to a certain H. E. Jones. Although he and I independently discovered this way of alternating the polarity of a current-mode signal, he documented this invention first. During the examination phase of an early patent application of mine, which included this core and several elaborations, Jones's prior use of the idea was cited as relevant prior art[1], and was so recognized in the issued (Tektronix) patent. Necessarily, those claims relating to this core, appearing in the original application, had to be removed. The prior obscurity of Jones' patent was probably due, at least in part, to its title and the relatively less central role played by the core in his application, which concerned a specific embodiment of synchronous-demodulation principles. And the subsequent use of the description “Gilbert mixer” — more accurately applied to the completed structure, which comprises this core, its voltage-to-current converter, and the all-important local oscillator driver stage — can perhaps be attributed to my subsequent enthusiastic evangelizing of this and similar basic circuits (although related more analog multiplication than frequency-translation) at every opportunity, in numerous papers and elsewhere. Some of today's young designers are making remarkable strides in advancing the performance of monolithic mixers. They understand that while the dusty, classic vignettes may provide a suitable point of departure, they fall short of being the satisfying final destination sought by the adventurous inventor, who will be compelled to break away from the everyday; to courageously seek the untrodden path; to apply stubborn tenacity and unflagging persistence when faced with the frustrations inherent in nature's fundamentals, never for a moment doubting that there are countless ways to implement the crucial frequency-translation function, beyond goading the tired old workhorses of yesteryear into going the extra mile. Still, there remains the prospect of clever colorful variations, yet to be composed, devised, invented or discovered, that will be founded firmly and four-squarely on these same venerable themes. However achieved, further improvements in raw performance must boil down to persuading intermodulation and noise to keep their distance and, contrary to their nature, be less obnoxious and mutually exclusive. This can only happen by accounting for numerous concurrent and co-dependent non-linear mechanisms, using simulation studies in which the reliability of all the device models has been meticulously benchmarked by prior calibration, and with close attention to the design of experiments. Simple, first-order analyses of “real” mixer behavior are all but irrelevant in addressing these perplexing issues. Even the occasional brave attempts at meaningfully comprehensive non-linear mathematical analyses remain powerless to illuminate the deeply intertwined consequences of dynamic carrier-transport in active devices, far less point toward appropriate remedies. The active mixer, an analog circuit of but two or three few key parts, offers the most compelling example of how a rudimentary function, of the sort that be may expressed in a short line of DSP code, can pose intriguing design challenges of profound depth and substance. Our comprehension of the darker side of its elusive character is as unsatisfactory today as when it was first devised and pressed into service by the visionary creator of the superhet receiver. Perhaps it is time to call any implementation of this indispensable element an “Armstrong device.”
Barrie Gilbert,
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