A 0.016 mm2 12 b $\Delta \Sigma $ SAR With 14 fJ/conv. for Ultra Low Power Biosensor Arrays

The instrumentation systems for implantable brain–machine interfaces represent one of the most demanding applications for ultra low-power analogue-to-digital-converters (ADC) to date. To address this challenge, this paper proposes a <inline-formula> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula>SAR topology for very large sensor arrays that allows an exceptional reduction in silicon footprint by using a continuous time 0–2MASH topology. This configuration uses a specialized FIR window to decimate the <inline-formula> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula> modulator output and reject mismatch errors from the SAR quantizer, which mitigates the overhead from dynamic element matching techniques commonly used to achieve high precision. A fully differential prototype was fabricated using <inline-formula> <tex-math notation="LaTeX">$0.18\,\mu $ </tex-math></inline-formula>m CMOS to demonstrate 10.8 ENOB precision with a 0.016 mm² silicon footprint. Moreover, a 14fJ/conv figure-of-merit can be achieved, while resolving signals with the maximum input amplitude of ±1.2 Vpp sampled at 200 kS/s. The ADC topology exhibits a number of promising characteristics for both high speed and ultra low-power systems due to the reduced complexity, switching noise, sampling load, and oversampling ratio, which are critical parameters for many sensor applications.