Design and implementation of novel FPGA based time-interleaved variable centre-frequency digital Sigma-Delta modulators

Abstract

Multiresolution analog-to-digital converters (MRADC) are usually used in Time Domain ElectroMagnetic Interference (TDEMI) measuring systems for very fast signal sampling with a sufficient dynamic range. The properties of the spectrum measured by the TDEMI system influenced by imperfections in the MRADC are analyzed in this paper. Errors are caused by imperfect matching of the offset and gain and phase of the circuits used in parallel input channels typical for the MRADC. For deep analyses of MRADC behavior, a precise mathematical model has been created using the concept of additive error pulses. Furthermore, a dedicated process of the identification of discrepancy parameters from experimental data is proposed. Identified parameters enter the expressions of the model and enable side to side comparison of experimental and theoretical results.Novel, multi-path, time-interleaved digital sigma-delta modulators that can operate at any arbitrary frequency from DC to Nyquist are designed, analysed and synthesized in this study. Dual- and quadruple-path fourth-order Butterworth, Chebyshev, Inverse Chebyshev and Elliptical based digital sigma-delta modulators, which offer designers the flexibility of specifying the centre-frequency, pass-band/stop-band attenuation as well as the signal bandwidth are presented. These topologies are compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity to non-idealities. Detailed simulations performed at the behavioural-level in MATLAB are compared with the experimental results of the FPGA implementation of the designed modulators. The signal-to-noise ratios between the simulated and empirical results are shown to be different by not more than 3-5 dBs. Furthermore, this paper presents the mathematical modelling and evaluation of the tones caused by the finite wordlengths of these digital multi-path sigma-delta modulators when excited by sinusoidal input signals.