Analog Approximation of Functions Using Generalized Polynomials

Abstract

We describe a new constructive method of approximation of analogue functions in CMOS. The method relies on the theories of Bürmann expansion and interpolation using Lagrange generalized polynomials: any real differentiable function can be synthesized in a unique way as a linear combination of the powers tanhn(x). We give the exact formulas for the coefficients involved in the linear combination. SPICE simulations confirm the method through a linear (linearized transconductor), squaring, cube, exponential and bump circuit four-quadrant function approximator.