Optimal common-centroid-based unit capacitor placements for yield enhancement of switched-capacitor circuits

Abstract

Yield is defined as the probability that the circuit under consideration meets with the design specification within the tolerance. Placement with higher correlation coefficients has fewer mismatches and lower variation of capacitor ratio, thus achieving higher yield performance. This study presents a new optimization criterion that quickly determines if the placement is optimal. The optimization criterion leads to the development of the concepts of C-entries and partitioned subarrays which can significantly reduce the searching space for finding the optimal/near-optimal placements on a sufficiently large array size.

PACES: A Partition-Centering-Based Symmetry Placement for Binary-Weighted Unit Capacitor Arrays

“…, where SCi and SCk are the sum of total self-correlation coefficients of Ci and Ck, and SCik is the sum of the cross-correlation coefficient [11,21]. However, in many applications, multiple capacitors are taking into account to the placement.…”

“…However, it had been shown that the placement with larger overall correlation coefficient L is not a sufficient criteria [21,22] and thus the Monte-Carlo simulation [23] is conducted to evaluate the random mismatch for simulating the statistical fluctuation.…”

“…4. The placement with high degree of dispersion has endorsed in better linearity performance [21,22]. Given the N-bit SAR ADC and placement array, the capacitance C0 and C1 contain one unit capacitor are placed at the central of the array to alleviate the systematic mismatch.…”

“…Given the N-bit SAR ADC and placement array, the capacitance C0 and C1 contain one unit capacitor are placed at the central of the array to alleviate the systematic mismatch. In addition to the systematic mismatch, for the random mismatch, the capacitance C0 and C1 located at center array also achieve the minimum variance of LSB ratio [21]. Moreover, the capacitance CN is placed as the chessboard-like placement meets the coincidence, dispersion and symmetry of the common-centroid rules [4] and has been shown to obtain the minimum variation of MSB ratio [21,22].…”

“…To reduce the placement generation time while maintaining a low ratio mismatch M and high overall correlation coefficient L, the diagonal weighting method [16] was presented. However, several counterexamples have shown that a placement with a low ratio mismatch M and high overall correlation coefficient L may not exhibit high performance [21,22].…”