Symbolic computation of SNR for variational analysis of sigma-delta modulator

Signal-to-noise ratio (SNR) is an important design metric for switched-capacitor sigma-delta modulators (SC-SDMs). In an automatic synthesis environment, fast SNR computation is of paramount importance. So far the main SNR computation method has been behavioral simulation. Other less accurate methods are based on empirical formulas. These methods could not contribute too much to the enhancement of synthesis efficiency. In this work a highly efficient and purely symbolic SNR computation method is proposed. The difficulty in the computation of noise power (requiring integration of a rational function) is overcome by Taylor polynomial approximation. Together with a symbolic loop-transfer analysis tool, the SNR can be computed fully symbolically. This novel computation method is applied to variational SC-SDM analysis. The effectiveness and efficiency are compared to behavioral Monte Carlo simulation results.