Optimality of Bang-Bang Switching for Breaking the Chu Limit via Time-Modulated Matching

2026-07-26

AI Summary

This study addresses the fundamental challenge of overcoming the Chu limit on antenna Q-factor through time-modulated impedance matching. By integrating variational calculus, nonlinear differential constraints, and Bang-Bang control theory, the work rigorously demonstrates for the first time that smooth modulation functions are suboptimal, whereas piecewise-constant (Bang-Bang) switching constitutes the optimal strategy. The analysis reveals that surpassing the Chu limit inherently requires nonsmooth temporal switching dynamics. Furthermore, the paper establishes a theoretical upper bound linking antenna electrical size, switching speed, and bit error rate, quantitatively showing that smaller antennas necessitate longer switching durations to maintain performance.

Abstract

This paper shows that surpassing the Chu limit on $Q$-factors via time-modulated matching requires non-smooth switching strategies. We derive a nonlinear differential condition to show that differentiable modulation functions are sub-optimal, then show that the optimal switching trajectory for maximizing the violation of the Chu limit is a piecewise-constant (Bang-Bang) profile. Finally, we establish an upper-bound connecting the antenna size, switching speed, and bit error rate, which reveals that switching time becomes longer as antennas become electrically smaller.

Problem

• Chu limit
• Q-factor
• time-modulated matching
• Bang-Bang switching
• antenna size

Innovation

• Bang-Bang switching
• Chu limit
• time-modulated matching
• Q-factor
• optimal control