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.

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

Determining the Noise and Signal Transfer Functions (NTF and STF) of a Continuous-Time Delta-Sigma Modulator (CTDSM) is an important aspect of the design verification process. In several practical CTDSM designs, like those with Switched Capacitor (SC) and Return-to-Open (RTO) feedback DACs, the loop filters are time varying, rendering traditional methods incorrect and/or time consuming. In this work, we exploit the linearity of the loop filter to determine the Signal and Noise Transfer Functions (NTF) of a modulator using time domain techniques that need far less simulation time than conventional methods.

Shanthi Pavan

Papers

Efficient estimation of noise and signal transfer functions of a continuous-time ΣΔ modulator