Research for High-Speed Wareform Measurement Algorithms

我们对波形采样技术中的超高速波形测量算法进行了研究，这些算法将成为下一代高速、高频信息通信系统中波形测量仪器的需求。我们得到了以下结果：（1）导出了波形采样系统中有限孔径时间效应的显式公式。在波形采样系统中，理想情况下采样应该瞬时执行，然而它需要一些时间（称为“孔径时间”），并且这种有限的孔径时间降低了波形采样精度。我们推导了有限孔径时间与采样精度之间的关系，并通过数值模拟证实了这一结果。(2)本文导出了波形采样系统中孔径抖动效应的显式公式。在实际的波形采样系统中，采样时钟的上升沿会发生波动，这种波动称为“孔径抖动”，这种孔径抖动会降低波形采样精度。我们推导了孔径抖动与采样精度之间的关系，并通过数值模拟和实验证实了这一结果。(3)我们已经推导出新的算法来评估采样电路的性能。(4)我们推导出明确的公式动态功耗的跟踪/保持电路。(5)我们推导出了时间交错AD转换器系统中通道失配效应（如失调、增益、时序、带宽、线性度）的显式公式。(6)我们推导出了用于测量仪器中产生各种波形的DA转换器中采样抖动效应的显式公式。

We have performed the research for ultra-high-speed waveform measurement algorithms which are especially used for waveform sampling technology, and these algorithms will be required in next generation waveform measurement instruments for high-speed and high-frequency information and communication systems. We have obtained the following results :(1) We have derived explicit formulas for finite aperture time effects in waveform sampling systems. In waveform sampling systems, ideally the sampling should be performed instantaneously, however it takes some time (which is called "aperture time") and this finite aperture time degrades the waveform sampling accuracy. We have derived the relationship between finite aperture time and sampling accuracy, and we have confirmed this result by numerical simulation.(2) We have derived explicit formulas for aperture jitter effects in waveform sampling systems. In actual waveform sampling systems, the rising edge of the sampling clock fluctuates, which is called "aperture jitter", and this aperture jitter degrades the waveform sampling accuracy. We have derived the relationship between aperture jitter and sampling accuracy, and we have confirmed this result by numerical simulation as well as experiments.(3) We have derived new algorithms to evaluate the performance of the sampling circuits.(4) We have derived explicit formulas for dynamic power dissipation of track/hold circuits.(5) We have derived explicit formulas for channel mismatch effects (such as offset, gain, timing, bandwidth, linearity) in time-interleaved AD converter systems.(6) We have derived explicit formulas for the sampling jitter effects in DA converters which are used in measurement instruments to generate various waveforms.