Unified Mitchell-Based Approximation for Efficient Logarithmic Conversion Circuit

This paper presents a novel method named the Unified Mitchell-based Approximation (UMA) to obtain an optimized Mitchell-based logarithmic conversion circuit for any desired conversion accuracy up to 14 bits. UMA is the first method that is able to obtain a conversion circuit when a specific accuracy is required. In this work, we studied and analyzed five design parameters and their impact on accuracy and hardware merits. We formulate the hardware model of the error correction circuit in the conversion circuit for performance evaluation. Given an accuracy requirement, the proposed method explores the design space of the five design parameters. As the design space is theoretically huge, we propose constraints for the range of the parameter values and develop a systematical search algorithm for exploring the design space. UMA is able to obtain an area-delay product optimized circuit for each of the conversion accuracies achieved by the existing Mitchell-based designs. Synthesis results in 90 nm CMOS technology show that the circuits obtained are comparable or better than the existing Mitchell-based designs with the same accuracy objective. Nine of the fifteen circuits obtained achieve better area-delay product by more than 50 percent. In addition, UMA is able to obtain circuits for any accuracy from 4 to 14 bits, while the best accuracy achieved by the existing Mitchell-based methods is less than 12 bits.