This work introduces an accurate linearized model and phase noise spectral analysis of digital bang-bang PLLs, that includes both the reference and the digitally-controlled oscillator (DCO) noise contributions. A time-domain analysis of bang-bang PLLs is leveraged to derive closed-form expressions for the integrated jitter, leading to a precise estimation of the binary phase detector (BPD) equivalent gain. The theoretical predictions differ by less than 1% from the simulation results obtained using a behavioral model, in all typical cases: dominant reference noise, dominant DCO noise, and comparable contributions. An accurate discrete-time model that takes into account the time-variant effect arising from the multirate nature of a digital phase-locked loop (DPLL) is used, along with the provided estimation of the jitter, to predict the output and input-referred phase noise spectra. An excellent match with the simulated spectra is achieved for all the different operating conditions.

中文翻译：

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Bang-Bang 数字 PLL 的综合相位噪声分析


这项工作介绍了数字 Bang-Bang PLL 的精确线性化模型和相位噪声频谱分析，其中包括参考噪声和数控振荡器 (DCO) 噪声贡献。利用 Bang-Bang PLL 的时域分析来导出积分抖动的封闭式表达式，从而精确估计二进制相位检测器 (BPD) 等效增益。在所有典型情况下，理论预测与使用行为模型获得的模拟结果相差不到 1%：主要参考噪声、主要 DCO 噪声和可比贡献。使用精确的离散时间模型，该模型考虑了数字锁相环 (DPLL) 的多速率特性所产生的时变效应，并结合提供的抖动估计来预测输出和输入参考相位噪声谱。对于所有不同的操作条件，都实现了与模拟光谱的完美匹配。