Design and implementation of an approximate full adder and its use in FIR filters

Abstract: Implementation of the polyphase decomposed FIR filter structure involves two steps; the generation of the partial products and the efficient reduction of the generated partial products. The partial products are generated by a constant multiplication of the filter coefficients with the input data and the reduction of the partial products is done by building a pipelined adder tree using FAs and HAs. To improve the speed and to reduce the complexity of the reduction tree a4:2 counter is introduced into the reduction tree. The reduction tree is designed using a bit-level optimized ILP problem which has the objective function to minimize the overall cost of the hardware used. For this purpose the layout design for a 4:2 counter has been developed and the cost function has been derived by comparing the complexity of the design against a standard FA design. The layout design for a 4:2 counter is implemented in a 65nm process using static CMOS logic style and DPL style. The average power consumption drawn from a 1V power supply, for the static CMOS design was found to be 16.8μWand for the DPL style it was 12.51μW. The worst case rise or fall time for the DPL logic was 350ps and for the static CMOS logic design it was found to be 260ps. The usage of the 4:2 counter in the reduction tree infused errors into the filter response, but it helped to reduce the number of pipeline stages and also to improve the speed of the partial product reduction.