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<inline-formula><tex-math notation="LaTeX"> $\Sigma \Delta$</tex-math></inline-formula>) topologies with high linearity, targeting high accuracy of the high-pass cut-off frequency. Intermediate functions are evaluated mathematically to compare the proposed HP<inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta$</tex-math></inline-formula> 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 HP<inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta$</tex-math></inline-formula> modulator is designed to be implemented in 0.18 <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>m CMOS technology, is tested with real prerecorded ECG signals.