An ARMA-Model-Based NTF Estimation on Continuous-Time <inline-formula> <tex-math notation="LaTeX">$\Delta\Sigma$</tex-math></inline-formula> Modulators

Abstract

In this brief, a noise transfer function (NTF) estimation algorithm is developed for continuous-time delta–sigma modulators. Different from previous methods, the proposed estimation method features an autoregressive-and-moving-average-model-based NTF approximation and low-cost computational resource. The NTF's zeros are derived by a spectral estimation on the quantization noise under the special situation, whereas the poles are obtained by a Feintuch-LMS adaptive filter with out-of-band tone injection. The proposed method could also track imprecise compensation effects on excess loop delay and finite gain and bandwidth. The parameter number of the method is only $2N+1$ for an $N$ th-order modulator. The simulation result shows that the proposed estimation method fits the modulator after compensation with less than $1.7\times10^{-6}V^{2}$ mean square error with $\pm 0.6$ -Vpp swing in a third-order modulator.