[Paper Review] Calibrating Control-Bounded ADCs

Hampus Malmberg, Till Mettler+3 more|arXiv (Cornell University)|Nov 12, 2022

Analog and Mixed-Signal Circuit Design4 citations

TL;DR

This paper proposes a digital filter calibration method for control-bounded analog-to-digital converters (CBADCs) to mitigate performance degradation from analog frontend component variations. By calibrating the digital estimation filter using recursive least squares (RLS), the method restores near-nominal performance in both behavioral and transistor-level simulations of a leapfrog frontend, achieving 80.4 dB SNDR after calibration despite 58.3 dB SNDR in the uncalibrated case.

ABSTRACT

The paper considers the calibration of control-bounded analog-to-digital converters. It is demonstrated that variations of the analog frontend can be addressed by calibrating the digital estimation filter. In simulations (both behavioral and transistor level) of a leapfrog analog frontend, the proposed calibration method restores essentially the nominal performance. Moreover, with digital-filter calibration in mind, the paper reformulates the design problem of control-bounded converters and thereby clarifies the role of sampling, desired filter shape, and nominal conversion error.

Motivation & Objective

• To address the sensitivity of CBADCs to analog frontend component variations.
• To demonstrate that digital estimation filter calibration can compensate for these variations.
• To reformulate the design problem of control-bounded converters to clarify the roles of sampling, filter shape, and nominal error.
• To validate the calibration method through both behavioral and transistor-level simulations.
• To show that calibration decouples analog design from digital estimation, enabling robust performance.

Proposed method

• The digital estimation filter coefficients hℓ are calibrated using recursive least squares (RLS) to minimize the calibration error ec[k].
• The calibration targets the filter coefficients hℓ that minimize the error between the estimated and actual signal transfer function.
• The reference signal s0[k] ∈ {±1} is used as a known excitation to excite the system and enable estimation of the filter response.
• The method leverages the relationship between the noise transfer function (NTF) and signal transfer function (STF) through the impulse response ˜gu(t).
• The calibration is applied to the discrete-time convolution of control signals sℓ[k], adjusting hℓ to compensate for variations in gℓ(t).
• The design reformulates CBADCs as a continuous-time filter design task, with sampling enforced by the digital estimator.

Experimental results

Research questions

• RQ1 Can digital filter calibration effectively compensate for analog frontend variations in CBADCs?
• RQ2 How does the calibration method affect the signal-to-noise-and-distortion ratio (SNDR) in the presence of component mismatches?
• RQ3 What is the role of sampling and the reference signal s0[k] in enabling calibration of the digital estimator?
• RQ4 How does the proposed calibration method compare to a fixed reference filter in terms of performance?
• RQ5 To what extent can calibration restore nominal performance in transistor-level implementations?

Key findings

• The calibrated digital filter restores performance to near-nominal levels in behavioral simulations of the leapfrog frontend.
• In transistor-level simulations, the calibrated filter achieved 80.4 dB SNDR, compared to 58.3 dB for the uncalibrated filter.
• The calibration error ec[k] can be made arbitrarily small using RLS-based adaptation.
• The method successfully compensates for component variations without requiring analog re-tuning.
• The calibration process decouples analog frontend design from digital estimation, enabling robust performance across process corners.
• The simulation results confirm that the digital estimator can effectively compensate for variations in the analog frontend through filter calibration.