Noise-shaping gradient descent-based online adaptation algorithms for digital calibration of analog circuits

Shantanu Chakrabartty, Ravi K. Shaga, Kenji Aono

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Analog circuits that are calibrated using digital-to-analog converters (DACs) use a digital signal processor-based algorithm for real-time adaptation and programming of system parameters. In this paper, we first show that this conventional framework for adaptation yields suboptimal calibration properties because of artifacts introduced by quantization noise. We then propose a novel online stochastic optimization algorithm called noise-shaping or ΣΔ gradient descent, which can shape the quantization noise out of the frequency regions spanning the parameter adaptation trajectories. As a result, the proposed algorithms demonstrate superior parameter search properties compared to floating-point gradient methods and better convergence properties than conventional quantized gradient-methods. In the second part of this paper, we apply the ΣΔ gradient descent algorithm to two examples of real-time digital calibration: 1) balancing and tracking of bias currents, and 2) frequency calibration of a band-pass Gm-C biquad filter biased in weak inversion. For each of these examples, the circuits have been prototyped in a 0.5-μ m complementary metal-oxide-semiconductor process, and we demonstrate that the proposed algorithm is able to find the optimal solution even in the presence of spurious local minima, which are introduced by the nonlinear and non-monotonic response of calibration DACs.

Original languageEnglish
Article number6416072
Pages (from-to)554-565
Number of pages12
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number4
StatePublished - 2013


  • Analog very-large-scale integration
  • digitally assisted analog circuits
  • noise-shaping
  • online learning
  • quantization
  • sigma-delta learning
  • stochastic optimization


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