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 ∆Σ modulators. Different from previous methods, the proposed estimation method features an ARMA model based NTF approximation and lowcost computational resource. The NTF's zeros are derived by a spectral estimation on the quantization noise under the special situation, while the poles are obtained by a Feintuch-LMS adaptive filter with out-of-band tone injection. The proposed method also could 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. Simulation result shows the proposed estimation method fits modulator after compensation with less than 1.7 × 10 −6 V 2 mean square error with ±0.6Vpp swing in a third-order modulator.