Minimum-phase calibration of sampling oscilloscopes
Minimum-phase calibration of sampling oscilloscopes
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DOI：
10.1109/tmtt.2006.879167
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发表时间：
2006-08
影响因子：
4.3
通讯作者：
A. Dienstfrey;P. Hale;D. Keenan;Tracy S. Clement;Dylan F. Williams
中科院分区：
文献类型：
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作者：
A. Dienstfrey;P. Hale;D. Keenan;Tracy S. Clement;Dylan F. Williams
我们描述了一种算法，用于确定一个线性时不变的响应函数的最小相位从其幅度。该过程是基于Kramers-Kronig关系与所需相位响应的辅助直接测量相结合。我们证明，截断的希尔伯特变换引起估计相位的大误差，但这些误差可以近似使用少量的基函数。作为一个例子，我们得到了最小相位校准的采样示波器在频域中。该结果取决于通过电光采样（EOS）技术结合扫频正弦校准程序获得的数据。EOS技术在宽带宽上产生幅度和相位信息，但从直流到约1 GHz的不确定性估计已降级。正弦扫描过程仅返回示波器响应函数的幅度，但可以在约1 MHz至几GHz的精细频率网格上执行。由此产生的最小相位校准范围从直流到110 GHz的频率，并可追溯到基本单位。作为我们分析的一部分，确定了示波器响应函数在两种测量所共有的频率处的最小相位特性的有效性。提供了完整的不确定性分析
We describe an algorithm for determining the minimum phase of a linear time-invariant response function from its magnitude. The procedure is based on Kramers-Kronig relations in combination with auxiliary direct measurements of the desired phase response. We demonstrate that truncation of the Hilbert transform gives rise to large errors in estimated phase, but that these errors may be approximated using a small number of basis functions. As an example, we obtain a minimum-phase calibration of a sampling oscilloscope in the frequency domain. This result rests on data obtained by an electrooptic sampling (EOS) technique in combination with a swept-sine calibration procedure. The EOS technique yields magnitude and phase information over a broad bandwidth, yet has degraded uncertainty estimates from dc to approximately 1 GHz. The swept-sine procedure returns only the magnitude of the oscilloscope response function, yet may be performed on a fine frequency grid from about 1 MHz to several gigahertz. The resulting minimum-phase calibration spans frequencies from dc to 110 GHz, and is traceable to fundamental units. The validity of the minimum-phase character of the oscilloscope response function at frequencies common to both measurements is determined as part of our analysis. A full uncertainty analysis is provided