Some circuit design techniques for low-voltage analog functional elements using squaring circuits

This paper describes some novel circuit design techniques for analog integrated circuits operable on low voltage. These techniques make use of squaring circuits as fundamental circuit elements, which can be constructed easily in monolithic form to avoid processing difficulties. The following three circuit design techniques: the transistor-size unbalance technique, the bias offset technique, and the multitail technique, are applied to realize squaring circuits for deriving the inherent exponential law characteristic from a bipolar junction transistor (BJT) and the inherent square-law characteristic from an MOS field-effect transistor (MOSFET). Furthermore, dc transfer characteristics of the fundamental differential pairs, squaring circuits, and some analog functional elements such as OTAs, quarter-square multipliers, and logarithmic IF amplifiers, are verified with transistor arrays and discrete components on a breadboard or implemented with LSI