First Demonstration of Power-Linear Regulator for Thermo-Optic Phase Tuning

This paper presents a power-linear regulator (PLR) using a voltage-squaring feedback loop designed for linear thermo-optic tuning. Nonlinear phase tuning occurs when conventional digital-to-analog converters (DACs) or low-dropout regulators (LDOs) are used to drive the thermo-optic phase shifter since the introduced phase change is proportional to the square of the voltage. The nonlinear phase tuning introduces the distortion and non-uniform resolution which degrades the system performance. We propose a PLR to achieve linear thermo-optic phase tuning, where the phase change is proportional to the input voltage. By adopting a voltage-squaring feedback loop, the output voltage is proportional to the square-root of the input voltage under fixed resistive heater and a linear mapping between the input voltage and phase change is established. This design is fabricated in a standard CMOS 65 nm process with an active area of 0.014 mm2. Under 2.5 V supply voltage, the proposed design achieves an input range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0\sim 1$ </tex-math></inline-formula> V and corresponding output range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0\sim 2$ </tex-math></inline-formula> V. The maximum delivered power is up to 40 mW while driving a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100~\Omega $ </tex-math></inline-formula> load. The measured power linearity error is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.5~\%$ </tex-math></inline-formula>. Additionally, the design demonstrates rapid transient behavior under a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100~\Omega $ </tex-math></inline-formula> load, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.2~\mu $ </tex-math></inline-formula>s rise time and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.7~\mu $ </tex-math></inline-formula>s fall time between 0 mW output power and 40 mW output power. The line regulation is 6 mV/V under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100~\Omega $ </tex-math></inline-formula> load. To the best of our knowledge, it is the first PLR demonstrated in the literature.