Input-Independent and Power-Efficient Time-Interleaved ADC Calibration Using Adaptive Kuramoto Synchronization

Timing skew is a critical bottleneck in high-speed Time-Interleaved (TI) Analog-to-Digital Converters (ADCs) that severely degrades dynamic range. This paper presents a mathematically rigorous, data-driven synchronization framework for calibrating effective sampling timing in TI-ADCs based on the Kuramoto oscillator model. Conventional clock-alignment methods often fail to capture signal-path mismatches, such as sampling switch aperture delay, while correlation-based techniques suffer from signal-dependent “blind-spot” regions. Overcoming this fundamental limitation without analog complexity is achieved via a fully digital feedback loop where each sub-ADC channel is modeled as a coupled oscillator following discrete-time Kuramoto dynamics. Unlike traditional approaches that rely on auxiliary analog phase detectors, the proposed scheme utilizes the ADC outputs to estimate and correct the effective sampling instants directly. A Lyapunov-based stability analysis proves that global phase synchronization is guaranteed when the adaptive coupling strength exceeds a critical value Kc. Theoretical results show that the system ensures exponential convergence of phase alignment, driving the total inter-channel timing error toward zero without relying on input-signal statistics. Behavioral MATLAB R2025a simulations of a 12-bit, 4-channel, 10 GS/s TI ADC confirm the analytical predictions. The proposed Kuramoto-based calibration achieves a residual skew reduction of over 99% and an SFDR improvement of 55.12 dB compared to correlation-based methods, even at blind-spot input frequencies, while adaptively reducing digital control power through dynamic coupling adjustment. The study demonstrates that data-driven, synchronization-based calibration provides an input-independent, energy-efficient, and mathematically verifiable solution for system-level timing correction in TI ADCs.