An Asynchronous Geometric Sequence Array-Based Binary Search Digital Low-Dropout Regulator for $O$(log$n$)-Complexity Coarse Searching Operations

This article presents a coarse search scheme for digital low-dropout regulators (DLDOs) that enables an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O$</tex-math></inline-formula>(log <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula>)-complexity of coarse searching operations. To address the effectiveness of the searching algorithm, the proposed DLDO conducts asynchronous coarse searching using the proposed binary search scheme and synchronous fine searching using a fixed-precision linear searching scheme. The chip was fabricated using a 28-nm process, and the proposed DLDO was designed to cover an output voltage (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_{\text{OUT}}$</tex-math></inline-formula>) of 0.45–0.95 V with an input voltage (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_{\text{IN}}$</tex-math></inline-formula>) of 0.5–1 V. The proposed DLDO regulates the output with a wide load range from 15 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Omega$</tex-math></inline-formula> to 450 k<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Omega$</tex-math></inline-formula> at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_{\text{OUT}}$</tex-math></inline-formula> = 0.45 V and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_{\text{IN}}$</tex-math></inline-formula> = 0.5 V condition. Compared with the conventional binary search scheme, the proposed DLDO achieves an average coarse searching time improvement of 3.7 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>s for light-to-heavy load-transition and 32 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>s for heavy-to-light load-transition.