Adaptive digital correction of analog errors in MASH ADCs. I. Off-line and blind on-line calibration

Abstract

Abstract-Cascaded delta-sigma (MASH) modulators for higher order oversampled analog-to-digital conversion rely on precise matching of contributions from different quantizers to cancel lower order quantization noise from intermediate delta-sigma stages. This first part of the paper studies the effect of analog imperfections in the implementation, such as finite gain of the amplifiers and capacitor ratio mismatch, and presents algorithms and architectures for digital correction of such analog imperfections, as well as gain and spectral distortion in the signal transfer function. Digital correction is implemented by linear finite-impulse response (FIR) filters, of which the coefficients are determined through adaptive off-line or on-line calibration. Of particular interest is an on-line "blind" calibration technique, that uses no reference and operates directly on the digital output during conversion, with the only requirement on the unknown input signal that its spectrum be bandlimited. Behavioral simulations on dual-quantization oversampled converters demonstrate near-perfect adaptive correction and significant improvements in signal-to-quantization-noise performance over the uncalibrated case, using as few as 5 FIR coefficients. An alternative on-line adaptation technique using test signal injection and experimental results from silicon are presented in the second part, in a companion paper [1].

Ein Unscented Kalman Filter zur Schätzung von Schaltungsnichtidealitäten eines zeitkontinuierlichen Sigma-Delta Wandlers mit impliziter Dezimation

“…Buhmann (buhmann@imtek.de) ne Offline Methode, um verschiedene Nichtidealitäten, wie z.B. endliche Bandbreite, Variation der Filterkoeffizienten und Verstärkung, wie auch spektrale Störung, zu schätzen (Cauwenberghs and Temes, 2000;Balestrieri et al, 2004). Hierzu wird der Eingang zum Wandler unterbrochen und durch ein bekanntes analoges Signal ersetzt.…”

“…Diese zusätzli-che Anforderung an die Kalibrierungsmethode führt direkt zu der zweiten Gruppe, welche eine online Korrektur des ADCs ermöglichen. Bei diesen Verfahren wird ein bekanntes breitbandiges Signal dem eigentlichen Eingangssignalüber-lagert (Cauwenberghs and Temes, 2000). Die Fehler des ADCs werden dann durch eine mathematische Korrelation der Eingang und Ausgangssignals geschätzt.…”

Robust Filter Design for Sigma-Delta Modulators with One-Bit Quantizer and Analog Mismatch

“…But (7) is derived assuming perfect analog components. It is known that the modulator is, however, sensitive to imperfections in the analog components (Norsworthy et al, 1997), (Cauwenberghs et al, 2000). For example, two common sources of error are finite amplifier gain and mismatch in capacitor values, which are manifested as uncertainties in the gains and poles of the integrators (Norsworthy et al, 1997), (Gani, 2005).…”

“…However, like the inevitable mismatch of the analog components, the non-ideality of multi-bit quantization causes signal distortion and degrades the performance of the modulators. Recently, there are some research works presenting different digital techniques for correcting errors in mash ADC's, such as adaptive filter approach (Cauwenberghs et al, 2000), (Kiss et al, 2000), robust control approach (Gani, 2005), (Yang et al, 2006), and the other techniques (Leger et al, 2004), (Siragusa et al, 2000), (Plekhanov et al, 2003), (Yu, Shiang-Hwua, 2006). Stability analysis and design of a single-stage modulator using sliding mode control approach has been addressed in (Plekhanov et al, 2003), (Yu, Shiang-Hwua, 2006).…”

Extended frequency-band-decomposition sigma–delta A/D converter

“…Many sigma-delta topologies need a digital calibration. For example, the mismatch effects in MASH topologies could be reduced by using an on-line or an off-line calibration [6] or a background coefficient estimation [7]. The non-linearities induced in the DAC of multi-bit modulators can also be reduced by the use of calibration [8], [9].…”