Structured electronic design of high-pass ΣΔ converters and their application to cardiac signal acquisition

High-Pass <inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta$</tex-math> </inline-formula> Converter Design Using a State-Space Approach and Its Application to Cardiac Signal Acquisition

“…• Signal transfer function (STF): a high-pass filter characteristic with at least one pole, the location of which can be set independently; • Noise transfer function (NTF): a high-pass filter characteristic with all real zeros at the origin, leading to a 40 dB/dec slope in the signal band; Fig. 3 shows the design procedure proposed to develop the desired state-space based high-pass Σ∆ topologies [14]. Based on the resolution and the signal transfer requirements of the target application, the STF type, the order of the system and the state-space form can be chosen.…”

“…Note that the quantizer gain k q does not impact the location of the pole. This implies that the signal-dependent gain associated with k q and thus the momentary value of the input signal of the ADC [14] does not change the exact value of the location of the pole, unlike in the case of pseudo-resistors. The reader is referred to the Appendix for the derivation and the approximations made.…”

“…The row sum of the high-pass integrator is very low, and therefore, the sensitivity to finite DC gain, finite GBW and time-constant variation is marginal. But the row sums of the first and second integrator are quite large as compared to that of the high-pass integrator and hence they Figure 14: Top level circuit block diagram of the CT orthonormal HPΣ∆ modulator [14] suffer from larger sensitivities to integrator non-idealities. In general, the larger the row sum of the integrator, the larger the sensitivity to its non-idealities.…”

“…Further, the sensitivities to coefficient variations and to integrator non-idealities are described and evaluated in Section IV. Circuit design, simulation results and comparison with related prior art are explained in Section V. Finally, the Figure 3: Flowchart of the state-space based approach for Σ∆ topologies [14] conclusions are summarized in Section VI.…”

“…Integrator input referred thermal noise sources: (a) Orthonormal HPΣ∆; (b) Observable canonical HPΣ∆ topology[14] Frequency response of the IF-g(s) thermal noise transfer functions of the orthonormal HPΣ∆ topology[14] …”