Coefficients synthesis method for high-order bandpass sigma-delta modulators

This paper is the first to realize automatic coefficient synthesis of high-order modulators used in bandpass sigma-delta analog-to-digital converters (ADCs). To begin with, the initial noise transfer functions (NTFs) of bandpass sigma-delta modulators (BPSDMs) are taken from inverse-Chebyshev bandreject filter functions with stopband attenuation equal to the required value. New semi-empirical stability constraints are then used to examine the initial NTFs such that only stable NTFs remain. Tradeoffs among chip area, power consumption, and performance are made to further select a most appropriate NTF from those stable NTFs. The NTF(z) is then fitted to BPSDM structures and their corresponding coefficients can be easily obtained. Feedforward and cascade-of-resonator structures with orders of 6, 8 and 10, are used as examples in this paper. Thus coefficients of stable BPSDMs which meet the required specifications can be automatically generated by a computer program implemented in accordance with the synthesis method. Two design examples that can be applied on communication systems are given.