√x circuit based on a novel, back-gate-using multiplier

Translinear circuits using subthreshold floating-gate MOS transistors

“…In [5]- [7], the authors present current-mode circuits with various power-law transfer characteristics, in which the logging and antilogging are done through the exponential current/voltage relationship of the bipolar transistor, whereas the weighted summation is accomplished via a resistive divider. In [8], van der Gevel and Kuenen present a one-quadrant current multiplier, in which the logging and antilogging are done through the exponential current/voltage relationship of the subthreshold MOS transistor, whereas the weighted summation is accomplished via the capacitive divider formed between the MOS transistor's gate and its back-gate (i.e., substrate). In this paper, we describe a family of multiple-input, multiple-output current-mode circuits that also embodies this general principle.…”

“…Consequently, the question of the relationship between translinear circuits and the family of the circuits just described arises naturally. Indeed, the circuits presented in this paper and the circuits of [5]- [8] are translinear circuits if the class of translinear circuits is extended to include circuits with loops that have voltage drops across elements that do not have exponential current/voltage relationships. We can analyze these circuits by applying the reformulated translinear principle of Hart [ 11].…”

Translinear circuits in subthreshold MOS

“…This circuit was proposed and its function experimentally demonstrated in [29]. The operation of the circuit can be understood by noting that a single transistor (M4) can perform a single quadrant multiplication because the voltages on the gate and bulk control the current in a multiplicative fashion (see Equation 4).…”

“…The actual currents in the four MOSFETs M1 ,M2,M3,M4, can be written as a function ofthepsicurrents: In the original implementation [29] it was suggested that to improve accuracy, the voltage on the local substrate (n-well) of devices M3 and Ma should be set at a value close to that of node B, the local substrate of of devices M2 and M4. This is indeed necessary, as the bulk voltage determines x of all transistors, which V IBD ~" " Vdd "1"" #i i. :!7,, [,, Fig.…”

A class AB CMOS square-rooting circuit

“…In addition, two approaches have been reported on the realization of a square-root function using MOS transistors. The ® rst approach is based on the use of weak inverted MOS transistors (van der Gevel and Kuenen 1994). This approach obtains low power consumption and low voltage operation.…”