Self-Coupling and Mutual Pulling in Phase-Locked Loops
Self-Coupling and Mutual Pulling in Phase-Locked Loops
复制标题
锁相环中的自耦合和互牵引
DOI：
10.1109/tcsi.2022.3155517
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Tsutomu Yoshimura
中科院分区：
文献类型：
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作者：
Tsutomu Yoshimura
本文研究了锁相环中振子耦合的影响。特别地，基于非线性微分方程对自耦合和互耦合系统进行了数值分析，并与同步条件下的线性近似模型的结果进行了比较。分析表明，在给定耦合强度下，使用参考时钟的耦合比使用自耦合引起的锁相环不稳定性更大。结果表明，在同步条件下，单锁相环中互耦的相位误差与参考时钟耦合的相位误差表现相同，互耦的噪声灵敏度是参考时钟耦合的两倍。此外，准同步条件下互耦的相位误差很大程度上取决于两个锁相环的频差与锁相环带宽之间的关系。我们采用0.18标准CMOS工艺设计并制作了测试电路进行理论验证。从测量结果来看，调整两个锁相环之间的时序差可以有效地缓解同步条件下的相互耦合。此外，我们在测试电路中实现了两个振荡器之间的互注入，并验证了它们的有效性。所提出的方法将有助于实现锁相环之间的相互耦合的紧凑和有效的消除。
The influence of coupling of oscillators in phase-locked loops (PLLs) was studied here. Particularly, numerical analyses based on nonlinear differential equations of the self- and mutual coupling systems were performed and compared with the results of the linear approximation model under synchronous conditions. The analysis revealed that coupling using the reference clock caused greater PLL instability than that caused by self-coupling for a given coupling strength. This shows that the phase error of mutual coupling exhibits the same behavior as that of reference-clock coupling in the single PLL under synchronous conditions, and the noise sensitivity of mutual coupling is twice that of the reference-clock coupling. In addition, the phase error of mutual coupling in the quasi-synchronous condition strongly depends on the relationship between the frequency difference of the two PLLs and the PLL bandwidth. We designed and fabricated the test circuits for theoretical verification using the 0.18-standard CMOS process. From the measurements, adjustment of the timing difference between the two PLLs is effective in mitigating mutual coupling under synchronous conditions. Moreover, we implemented mutual injections between two oscillators in the test circuit and confirmed their effectiveness. The proposed methods will be useful for achieving the compact and effective cancellation of the mutual coupling between PLLs.