The Multiple-input Translinear Element: a Versatile Circuit Element

We define the multiple-input translinear element (MITE), a versatile circuit primitive from which we can construct lowvoltage translinear circuits and log-domain filters. A K-input MITE produces an output current that is exponential in a weighted sum of its K input voltages. We briefly discuss six MITE implementations and show experimental data from two of these six that we have fabricated in a 2–μm double-poly CMOS process available through MOSIS. 1. TRANSLINEAR CIRCUIT ELEMENTS In 1975, Barrie Gilbert [1] coined the word translinear to describe a class of nonlinear circuits whose operation is based on the exponential current–voltage relationship of the bipolar transistor. The word translinear derives from a contraction of one way of expressing the exponential current–voltage relationship of the bipolar—that is, the bipolar's transconductance is linear in the current flowing into its collector terminal. The subthreshold MOS transistor also has an exponential current–voltage relationship [2], so we can count it as a translinear device. Notwithstanding some limitations of the subthreshold MOS transistor compared to the bipolar transistor from the standpoint of translinear-circuit implementation [2, 3], the subthreshold MOS transistor has some unique properties that enable us to implement certain translinear circuits with fewer transistors or with lower supply-voltage requirements than we could using bipolar transistors [3–5]. In this paper, we define a new translinear circuit primitive called the multiple-input translinear element (MITE). A Kinput MITE has K different transconducances, each of which i s linear in the MITE's output current. From these elements, we can construct MITE networks [6], a class of translinear network circuits that can embody product-of-power-law relationships in the current signal domain. For a given productof-power-law relationship, a MITE network implementation will often require fewer transistors and permit a lower powersupply voltage than would a corresponding translinear loop implementation. From MITEs, we can also make log-domain filters [7], a class of filters in the current signal domain that are large-signal linear yet comprise only grounded capacitors, current sources, and translinear (i.e., highly nonlinear) devices. 2. THE MULTIPLE-INPUT TRANSLINEAR ELEMENT We depict a circuit symbol for an ideal MITE in Fig. 1; the MITE sums K input voltages, V1 through VK , scaled, respectively, by dimensionless positive coefficients, w1 through wK . The MITE then generates a current, I, that is exponential in this weighted sum. We assume that we have the ability to control the values of the weighting coefficients proportionally, so we can make accurate ratios of weighting coefficients.