Synthesis of Static and Dynamic Translinear Circuits
10.1 Translinear Circuits: What Is In a Name?
In 1975, Barrie Gilbert proposed the word translinear to refer both to the remarkably consistent linear relationship that holds between the transconductance of the bipolar transistor and its collector current that extends over many decades and to a growing class of current-mode circuits that exploit this key property of the bipolar transistor as well as the intimate thermal contact and close matching of monolithically integrated devices . The translinear principle that he elucidated at that time states that, in a closed loop of base-emitter junctions comprising an equal number of clockwise facing and counterclockwise facing junctions,
where CW and CCW denote, respectively, the set of indices of clockwise facing junctions and the set of indices of counterclockwise facing junctions, Ij is the collector current flowing in the jth element, and Aj is the emitter area ratio of the jth element. This elegant circuit principle has 241 been the basis of a host of useful nonlinear circuits (e.g., wideband signal multipliers [2–7], frequency multipliers [8–11], array normalizers [12, 13], and vector-magnitude circuits [14–18]) that are utterly mysterious from the customary linear-circuit picture of ...