A translinear circuit for analogue function synthesis based on a Taylor series

A new circuit configuration is presented for synthesizing nonlinear functions. The proposed circuit is based on approximating the required function using a Taylor series. The terms of the resulting Taylor series are realized one-by-one, each in a separate building block, and the required function is the sum of the output currents of these blocks. The weights of the Taylor-series terms are controlled using current sources. The circuit is flexible and can synthesize any nonlinear function, to any degree of accuracy, once its Taylor-series approximation is obtained. The proposed circuit uses only bipolar transistors and current sources and is, therefore, very attractive for integration. Simulation results obtained from the synthesis of the ordinary Bessel functions J₀(x)and J₁(x), and the sine function sin(x) are presented.