The paper presents a generalization of the Groszkowski’s result in differential oscillators, providing novel equations to describe the oscillation frequency dependence on the harmonic content. The effect of the common-mode oscillation is rigorously included. Moreover, an additional term, arising from the dependence of the transistor current on the drain voltage, which is dominant any time ohmic operation occurs, is disclosed here for the first time. This framework is applied to Van der Pol oscillators, both nMOS and CMOS, designed in a 28-nm bulk CMOS technology. The results correctly match the oscillation frequency dependence derived from detailed circuit simulations. The analysis shows that, when even harmonics are relevant, the classical Groszkowski’s result is not able to account for close-in phase noise performance. The novel theoretical framework fully justifies, instead, the simulation results and sheds new light on the flicker noise up-conversion mechanisms in the considered oscillator structures.

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Groszkowski 在差分振荡器拓扑中的结果的概括

本文介绍了 Groszkowski 在微分振荡器中的结果的概括，提供了新的方程来描述振荡频率对谐波含量的依赖性。共模振荡的影响严格包括在内。此外，这里首次公开了由晶体管电流对漏极电压的依赖性产生的附加项，该项在欧姆操作发生时占主导地位。该框架适用于采用 28 纳米体 CMOS 技术设计的 nMOS 和 CMOS 范德波尔振荡器。结果与从详细电路模拟得出的振荡频率相关性正确匹配。分析表明，当偶次谐波相关时，经典的 Groszkowski 的结果无法说明接近相位噪声性能。