An ARMA-Model-Based NTF Estimation on Continuous-Time $\Delta\Sigma$ Modulators

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 Nth-order modulator. The simulation result shows that the proposed estimation method fits the modulator after compensation with less than 1.7 × 10
^-6
V
²
mean square error with ±0.6-Vpp swing in a third-order modulator.