Continuous-Time Delta-Sigma Mo

The delta–sigma modulator, a single-bit oversampled analog signal encoder,was patented by Cutler in 1960 and described in the open literature by Inoseand Yasuda in 1962. It took unTIl the mid-1980s, specifically the publicaTIonof Candy’s widely-cited 1985 paper about the double integraTIon modulator,for the popularity of these modulators to take off. Since then, almost fifteenyears later, delta–sigma modulators have cornered the market in digital audioconverters (both analog-to-digital and digital-to-analog), and they are also usedto great advantage in lower-rate but sTIll higher-resolution applications such asinstrumentation and seismometers.Most modulators are implemented with a discrete-time loop filter usingcircuit techniques such as switched-capacitor, likely because it is easy to mapthe mathematics of modulators onto the implementation. Due to settling-timeconstraints in typical discrete-time implementations, the maximum clock rateis limited, and because delta–sigma circuits are necessarily oversampled, highresolution converters with only relatively narrow conversion bandwidths (up toa few hundred kilohertz) can be built. Ideally, resolution is determined onlyby the modulator loop filter and the oversampling ratio; if it were possible torelax the clock rate restrictions and thereby increase the clock rate, then for agiven oversampling ratio and loop filter, high-resolution converters with widerbandwidths (into the megahertz) could be built.One way to achieve higher clock rates is to build the loop filter portion out ofcontinuous-time circuits such as transconductors and integrators. The idea ofusing continuous-time filters in delta–sigma modulators is not particularly new:Adams’ seminal 1986 paper describes one of the first functional delta–sigmaaudio encoders that had a continuous-time loop filter built out of discrete opamps, resistors, and capacitors. However, since the mid-1990s, semiconductorprocesses have increased in speed to the point that it becomes possible tointegrate gigahertz-speed modulators. An example of an application wheresuch modulators are especially appealing is cellular radi an entire cellularband (tens of megahertz) could be digitized, possibly at the IF or RF, and thesignal details sorted out with digital signal processing.