An 8.5 mW Continuous-Time $\Delta \Sigma$ Modulator With 25 MHz Bandwidth Using Digital Background DAC Linearization to Achieve 63.5 dB SNDR and 81 dB SFDR

This paper presents a third order, single-loop, continuous-time ΔΣ modulator with an internal 4-bit quantizer. The modulator is sampled at 500 MHz, and features an oversampling ratio of only 10. Therefore, DAC linearization by dynamic element matching is ineffective, and the DAC nonlinearities are not corrected within the ΔΣ modulator loop but in the subsequent digital circuit. The unit element mismatches are digitally estimated based on a correlation, and correction factors are thus derived. Moreover, in order to achieve a low-power operation, all amplifiers are compensated for finite gain-bandwidth related non-idealities. In the presented work, this compensation includes the fast proportional loop, which is used to compensate for excess loop delay. The presented ΔΣ modulator has been realized in a 1.2 V, 90 nm CMOS process and achieves an SNDR of 63.5 dB and an SFDR of 81 dB within a 25 MHz bandwidth. The modulator occupies an active die area of only 0.15 mm² and has a power consumption of 8 mW, with an additional 0.02 mm² and 0.42 mW estimated for the digital DAC correction logic. The overall modulator achieves a figure of merit of 138 fJ/conv.