High-Pass $\Sigma \Delta$ Converter Design Using a State-Space Approach and Its Application to Cardiac Signal Acquisition

Cardiac signal acquisition with high linearity and accuracy of the high-pass cut-off frequency imposes a challenge on the implementation of the analog preprocessing and the analog-to-digital converter. This paper describes a state-space-based methodology for designing high-pass sigma-delta (HP ΣΔ) topologies with high linearity, targeting high accuracy of the high-pass cut-off frequency. Intermediate functions are evaluated mathematically to compare the proposed HPΣΔ topologies with respect to dynamic range. A sensitivity performance analysis of the noise transfer function with respect to integrator nonidealities and coefficient variations is also described. Finally, to illustrate the design approach, an orthonormal HPΣΔ modulator is designed to be implemented in 0.18 μm CMOS technology, is tested with real prerecorded ECG signals.