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An original determination of the maximum phase shift range obtained for an array of N coupled oscillators
Analog Integrated Circuits and Signal Processing ( IF 1.4 ) Pub Date : 2021-01-07 , DOI: 10.1007/s10470-020-01791-x
Kaouthar Djemel , Rahma Aloulou , David Cordeau , Hassene Mnif , Jean-Marie Paillot , Dorra Mellouli , Mourad Loulou

This paper presents an original approach, using a harmonic balance optimization method, allowing to predict the maximum phase shift range that can be practically obtained for an array of N coupled oscillators. Indeed, unlike what is predicted by the theory, the proposed analysis allows to show that the maximum value of the phase shift decreases by increasing the number N of coupled oscillators in the array. Hence, this method allows to find an empirical limit of the phase shift obtained between two adjacent oscillators which tends to ± 180°/N. The results obtained with the proposed method are compared with the measurement results of an array made of two and four coupled voltage controlled oscillators (VCOs) implemented in the QUBiC4X 0.25 µm BiCMOS SiGe:C process of NXP semiconductors. These measurement results confirmed that the maximum measured phase shift range is close to ± 180°/2 and ± 180°/4 for arrays made of two and four coupled VCOs respectively.



中文翻译:

对N个耦合振荡器阵列获得的最大相移范围的原始确定

本文提出了一种使用谐波平衡优化方法的原始方法,可以预测N耦合振荡器阵列实际可获得的最大相移范围。实际上,与该理论所预测的不同,所提出的分析允许显示通过增加阵列中耦合振荡器的数量N来减小相移的最大值。因此,该方法允许找到两个相邻振荡器之间获得的相移的经验极限,该极限趋于±180°/ N。将该方法获得的结果与由NXP半导体的QUBiC4X 0.25 µm BiCMOS SiGe:C工艺实现的由两个和四个耦合压控振荡器(VCO)组成的阵列的测量结果进行了比较。

更新日期:2021-01-08
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