A heuristic finite frequency H-infinity filtering technique with application to cascaded 2-1 sigma-delta modulators

Due to limited accuracy of the modern fabrication technologies, cascaded sigma-delta modulators could suffer from finite amplifier gain and capacitor mismatch. Unfortunately, these non-ideal analog components cause inevitable mismatch of the analog circuits and digital noise cancellation filters; consequently it leads to a poor signal-to-noise ratio (SNR). In this paper, the SNR performance enhancement problem is formulated as a robust H-infinity filtering problem in finite frequency domain. Specifically, we propose a heuristic finite impulse response (FIR) filter design that deals with the problem by treating the non-ideality as parametric uncertainty in the integrators´ pole and zero of the modulators. In contrast with the existing approaches, the proposed design is a direct approach which directly adjusts the gain responses of the noise transfer function to yield high-order noise shaping by searching the coefficients of FIR filters via solving linear matrix inequality (LMI) feasibility problems. We have confirmed the validity of the proposed method via simulations of a cascaded 2-1 modulator with 2% deviation in the analog integrators. Simulation results show that the modulator matched by the proposed filter achieves better SNR performance than that matched by the conventional one.