This paper presents a single loop, third order continuous time ΔΣ modulator with an internal 4 bit quantizer sampled at 500 MHz with only an oversampling ratio of 10. Since multi-bit operation commonly suffers from DAC non-linearities, and dynamic element matching is ineffective at low oversampling, an alternative auxiliary DAC linearization is proposed for ΔΣ modulators. The unit element mismatches are digitally estimated based on a cross correlation of a binary test signal with the modulator output and represent the measured DNL of DAC1. The corresponding INL is calculated and stored in an 15×8 lookup-table which is applied to the 8 bit auxiliary DAC to linearize DAC1. Moreover, a design centering approach for amplifier finite gain bandwidth compensation within the loop filter is presented which allows for large bandwidth mismatch with negligible effect on loop filter stability. This results in a robust architecture over temperature, supply, and excess loop delay variations. The presented ΔΣ modulator achieves an SNDR of 67.5 dB, DR of 72 dB, and SFDR of 79 dB over a 25 MHz bandwidth and is implemented in a 1.2 V, 90 nm CMOS process. The modulator occupies an active area of 0.19 mm<sup>2</sup> and has a power consumption of 8.5 mW. It achieves a figure of merit of 88 fJ/conv-step which is one of the best published for multi-bit ΔΣ modulators.
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