Exponential Circuits

Abstract

Exponential circuits represent important building blocks for VLSI signal processing structures, telecommunication applications, medical equipments, hearing aid or disk drives. The exponential function can be obtained in bipolar technology from the exponential characteristic of the bipolar transistor. The nonzero value of the base current and the temperature dependence of the bipolar transistor parameters introduce relatively large errors in the computation of the exponential function. In CMOS technology, the exponential law is available only for the weak inversion operation of the MOS transistor. The great disadvantage of the circuits using MOS transistors in weak inversion is represented by their poor circuit frequency response, caused by the much smaller drain currents available for charging and discharging the parasite capacitances of the MOS transistors. Thus, circuits realized in CMOS technology that require a good frequency response can be designed using exclusively MOS transistors biased in saturation region. Because it exists a relative limited number of mathematical principles that are used for implementing the exponential circuits, the first part of the chapter is dedicated to the analysis of the mathematical relations representing the functional core of the designed circuits. In the second part of the chapter, starting from these elementary principles, there are analyzed and designed concrete exponential circuits, grouped following the mathematical principles they are based on.