A 15-MHz Bandwidth 1-0 MASH $\Sigma \Delta $ ADC With Nonlinear Memory Error Calibration Achieving 85-dBc SFDR

Abstract

A 1-0 MASH ΣΔ analog-to-digital converter (ADC) demonstrates a digital linearization technique for the first time treating integrator distortion with memory and capacitor mismatch errors. A two-tap sequential polynomial derived from an output-referred error analysis accurately models the non-ideality of a first-order modulator. The model parameters are extracted by correlating various moments of the ADC digital output with a one-bit pseudorandom noise (PN) superimposed on the input, largely reducing the circuit overhead associated with the nonlinear calibration. The prototype ADC employing amplifiers with a gain of roughly 30 dB measures an 85-dBc spurious-free dynamic range (SFDR) and a 67-dB signal-to-noise and distortion ratio (SNDR) for a 1.1- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm V} _{\rm PP} $</tex></formula> ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$-$</tex></formula> 1-dBFS), 4.99-MHz sinusoidal input at 240 MHz sampling clock (8× OSR) with a 7.5-msec calibration time. For a 1.1- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm V} _{\rm PP}$</tex></formula> two-tone input at 14.9 MHz and 15.1 MHz, the third-order intermodulation product (IM3) after calibration is 87.1 dBc, which is over 30 dB better than that without calibration. The core ADC consumes 37 mW from a 1.25-V supply and occupies 0.28 mm 2 in a 65-nm CMOS low-leakage digital process in which the transistor threshold voltages are around 0.5 V.