System Optimization: High-Frequency Buck Converter With 3-D In-Package Air-Core Inductor

In this work, we present the analytical model of buck converter with 3-D in-package air-core inductor (
$150~\mu \text{m}$
thick). To optimize the power efficiency at a targeted power density, models including 3-D inductor and power switches are developed. Compared to 3-D electromagnetic (EM) simulation, the proposed inductor model has a modeling error within 12% for the inductance calculation. With the proposed design methodology, an inductor with
$Q$
-factor up to 35 at 300 MHz is achieved. From the system aspect, the loss breakdown in the integrated power converter is investigated. A 0.5 ratio buck converter can reach 88.5% efficiency at 1–5 W/mm
²
based on the optimized inductor designs, with output voltage ranging from 0.7 to 0.9 V and based on 28 nm CMOS.