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Spectral Impact of Mismatches in Interleaved ADCs

Jérémy Guichemerre, Robert Reutemann, Thomas Burger, Christoph Studer

Abstract

Interleaved ADCs are critical for applications requiring multi-gigasample per second (GS/s) rates, but their performance is often limited by offset, gain, and timing skew mismatches across the sub-ADCs. We propose exact but compact expressions that describe the impact of each of those non-idealities on the output spectrum. We derive the distribution of the power of the induced spurs and replicas, critical for yield-oriented derivation of sub-ADC specifications. Finally, we provide a practical example in which calibration step sizes are derived under the constraint of a target production yield.

Spectral Impact of Mismatches in Interleaved ADCs

Abstract

Interleaved ADCs are critical for applications requiring multi-gigasample per second (GS/s) rates, but their performance is often limited by offset, gain, and timing skew mismatches across the sub-ADCs. We propose exact but compact expressions that describe the impact of each of those non-idealities on the output spectrum. We derive the distribution of the power of the induced spurs and replicas, critical for yield-oriented derivation of sub-ADC specifications. Finally, we provide a practical example in which calibration step sizes are derived under the constraint of a target production yield.

Paper Structure

This paper contains 17 sections, 1 theorem, 21 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Contributions
  3. Limitations of Prior Art
  4. Notation
  5. Ideal Interleaving and Mismatches
  6. Ideal Interleaving
  7. Offset
  8. Gain Mismatch
  9. Timing Skew
  10. Spur-Level Statistics
  11. CDF of Offset Spurs
  12. CDF of Gain-Mismatch Replicas
  13. CDF of Skew Replicas
  14. Combined CDF for Maximum Spur Constraints
  15. Case of a Uniform Distribution
  16. ...and 2 more sections

Key Result

Lemma 1

Let $\mathbf{x}\xspace$ be a vector of even length $N$ containing realizations of i.i.d. zero-mean real-valued Gaussian random variables, each of variance $\sigma^2$. Then, the entries of its DFT $\tilde{\mathbf{x}\xspace}=\mathbf{F}\xspace\mathbf{x}\xspace$ are distributed as follows: where the entries in eq:3_lemma are mutually independent, and ${\tilde{x}_k = \tilde{x}_{N-k}^*}$ for $k=N/2+1,\

Figures (4)

  • Figure 1: (a) Conceptual block-diagram of an interleaved ADC, (b) example of an ideally sampled single-sided output spectrum and DFT of a mismatch sequence for a $4\times$ interleaved ADC. (c), (d), and (e) show the impact of the mismatch sequence of (b) in the case of offset, gain mismatch, and timing skew, respectively.
  • Figure 2: Complementary CDF (CCDF) of the squared magnitude of DFT entries for i.i.d. uniform sequences (various $N$) normalized to unit variance of the magnitude, compared with the Gaussian case. Already at $N=16$, the Gaussian approximation is accurate within $1$ dB at $10^{-4}$ probability.
  • Figure 3: Offset calibration step size that ensures the strongest offset spur remains below a specified power limit with $99\%$ probability in a $12$-bit $16\times$ interleaved ADC. Note that $\textnormal{LSB}=2^{1-B}$ for a $B$-bit ADC.
  • Figure 4: Gain and sampling instant calibration step size that ensures the strongest replica remains below a specified power limit relative to the input signal with $99\%$ probability in a $12$-bit $16\times$ interleaved ADC.

Theorems & Definitions (1)

  • Lemma 1