信号发生器输出幅度平坦度测量中的非线性与相关性问题研究

Research on the Nonlinearity and Interdependency in the Measurement of the Output Amplitude Flatness of Signal Generators

摘要:

针对评价信号发生器输出特性的一项重要指标——信号发生器输出幅度平坦度,介绍了输出幅度平坦度的测量方法,并且针对其不同的计算公式建立了测量的数学模型;由于该数学模型是非线性模型,并且由于输入量之间可能存在相关性,所以在进行测量不确定度分析的过程中必须考虑在合成标准不确定度时是否需要加入数学模型按泰勒级数展开后所得方差的高阶项以及表征相关性的协方差项；根据高阶项对合成标准不确定度整体的贡献大小判断是否可以忽略；同时比较了通过实验方法得到相关系数与相关系数直接取0或取1时对应扩展不确定度的大小；最后针对幅度平坦度的测量提出有效避免处理相关问题的方法,并对环境温度、供电电源以及阻抗匹配等影响信号发生器幅度平坦度测量不确定度的实际操作问题给出具有实用价值的参考意见。

Abstract:

The output amplitude flatness of signal generators is an important technical index to evaluate the output property of a signal generator. In this paper, the measurement method of output amplitude flatness is introduced, and measurement mathematical models are proposed according to different formulas. Because of the nonlinearity of the mathematical models and the possible interdependency between different input variables, it must be considered whether the higher-order items and the covariance items in the Taylor series expansion should be taken into account in the combined standard uncertainty in the process of the measurement uncertainty analysis. It is analyzed whether the higher-order items could be ignored according to their contributions to the combined standard uncertainty. And the expanded uncertainties are compared when the correlation coefficient is evaluated at different values-‘0’, ‘1’ and the experimentally decided value, respectively. In the end, a valid method is proposed to avoid working on the covariance items in the measurement of the output amplitude flatness,and some practical suggestions are offered on how to deal with the problems that are the influences of environment temperature and power supply and impedance matching on the measurement uncertainty of the output amplitude flatness of signal generator.