A Study of the Lock Range of Injection-Locked CMOS Active-Inductor Oscillators Using a Linear Control System Approach

Abstract

This brief investigates the lock range of injection-locked <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> oscillators using a linear control system approach. It explores the intrinsic relation between the lock range of injection-locked <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> oscillators and the injection-induced variation of the impedance of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> tank. We show that injection-locked active-inductor <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> oscillators exhibit a larger lock range, as compared with their passive counterparts. We further show that the large lock range of injection-locked active-inductor oscillators is due to both the low quality factor and the large injection-induced variation of the inductance of active inductors. These findings are validated using an injection-locked passive <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> oscillator and an injection-locked active-inductor <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> oscillator designed in IBM 0.13- μm 1.2-V CMOS technology.