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High Accuracy Exponential Function Generator for Analog Signal Processing

C. Popa
University Politehnica of Bucharest, RO

Keywords:
exponential function, Taylor series, analog signal processing

Abstract:
A new CMOS current-mode pseudo-exponential circuit based on the superior-order Taylor series expansion will be presented. The advantage of the circuit with respect to the previous reported similar ones is the smaller value of the limited expansion error obtained by using a superior-order approximation of the exponential function. Because of the circuit modularity and of the small silicon area consumption, the total error could be very easily reduced by increasing the number of terms from the previous expansion. The circuit presents the important advantage of the independence of the output current on technological parameters. The frequency response is improved due to the strong inversion operation of all MOS transistors and to the current-mode operation of the circuit. In order to evaluate the total error of the circuit core, the second-order effects will be taken into account, resulting an additional error summed to the error caused by the neglecting of the superior-order terms from the exponential function Taylor series expansion. The circuit area is relatively small due to the exclusively utilization of MOS transistors (all resistors have been removed from the circuit). The SPICE simulation of the squarer behavior confirms the theoretical estimated results.

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