Analysis and Synthesis of Static Translinear Circuits

This report describes the class of static translinear circuits, which are capable of accurately implementing a wide range of static nonlinear relationships in the current signal domain, such as products, quotients, fixed power-law relationships, vector magnitude, and rational functions. After a brief historical account of the emergence of the class of translinear circuits, we examine the representation of information in translinear circuits and systems. Then, we describe the translinear principle and its application to the analysis and synthesis of translinear-loop circuits, illustrating the processes with several example circuits. We then describe the operation and implementation of a translinear-circuit primitive called the multiple-input translinear element (MITE). From such elements, we build MITE networks, a class of low-voltage translinear circuits that is equivalent to the class of translinear-loop circuits. We describe intuitively the operation of MITE networks. We also describe how to analyze and synthesize such circuits, illustrating these processes with several example circuits. 1 Translinear Circuits: What’s in a Name? I ¦ n 1975, Barrie Gilbert coined the word translinear to describe a class of circuits whose large-signal behavior hinges on the extraordinarily precise exponential current–voltage characteristic of the bipolar transistor and the intimate thermal contact and close matching of monolithically integrated devices [1]. The functions performed by these fundamentally large-signal circuits—including multiplication [2–7], wideband signal amplification [3,8], and various power-law relationships [9]— were utterly incomprehensible from the customary linear-circuit picture of the bipolar transistor