A Low-voltage, Analog Power-law Function Generator

A new current-mode CMOS analog programmable arbitrary nonlinear function synthesizer

“…(1) Only one or two functions can be realized at a time; see for example [1] for a sine function generator realization, [3] where the realization of a Gaussian function generator is proposed, [7] for the inverse sine and the inverse cosine functions realizations, [8] for the realization of exponential and logarithmic functions, [10] where the realization of a tangent hyperbolic sigmoid is proposed, [13] where a triangular/trapezoidal function generator is presented, [14] where a sinh resistor is proposed for tanh linearization, [16] which presents a power law function generation, [17] where a Gaussian/triangular basis functions computation circuit is proposed, [19] for a fully differential tanh function realization, [23] which presents a realization for the hyperbolic tangent sigmoid function, [24] where radial basis function circuits are presented and [25] for the realization of an inverse sine function realization. (2) Recourse to the use of piecewise linear approximations to approximate the required nonlinear function; for example in [5,6,15,20,22], where piecewise linear approximations are used to approximate, and whence, realize several nonlinear functions.…”

“…It is worth mentioning here that while the use of rational functions may lead to better approximations than Taylor series approximations, the circuit realizations of the former are usually more complicated than those of the later. (4) Recourse to digital signal processing techniques; see for example in [4] where the target function is sampled in a grid and the sampled values are encoded in a set of digital words, [6] where look-up tables, or piecewise-constant interpolators, are used to store all the output voltages corresponding to every possible input voltage, [10] where a microcontroller is used to calculate the tanh(x) function approximation obtained using a Taylor series expansion for exp(2x), [18] where digital signal processing is used to find the coefficients of a suitable Taylor series approximation, and [23] where a piecewise linear approximation is used to approximate the tanh function and [16], BiMOS [24] or MOSFETs operating either in the weak inversion region; see for example [3,4,8,12,14,22], or the moderate inversion region [13]. Usually this is done to exploit to advantage the exponential current-voltage characteristics of the transistors.…”

“…(7) Extensive use of readily available integrated circuits; see for example [2] where a number of second-generation current conveyors are used for synthesizing nonlinear functions, [7] where a number of transconductors, squaring and square rooter circuits are used to realize the inverse sine function, [11] where a number of multipliers and amplifiers are used for calculating a particular function, [18] where a number of R-2R resistor ladders, a digital-to-analog converter, and a digital processor are used for performing Taylor-series function approximations. (8) Operation in voltage mode with input voltage and output voltage or mixed mode with voltages as the input or output and currents as the output or input; see for example [1,3,7,8,13,16,24]. Current-mode circuits with input current and output current are more attractive than their voltagemode counterparts.…”