将电容量值和互感量值溯源到由量子化霍尔电阻保存的电阻基准量值，是当今国际计量界的研究热点之一。在电阻－电容量值的传递方面，长期以来无法解决准确实现90°相角的问题，被迫采用传统的电桥方法。而电桥方法中阻抗的定义不完善，实施难度很大，操作极为复杂。电阻－互感量值的传递，因为互感频率特性的影响，以交流电桥方法无法准确得到直流状态下的互感值。能得到电感直流状态值的伏秒法，因不能准确测量感应面积，使得传递准确度一直徘徊不前。本论文工作回归问题本质，灵活地应用精密电磁测量的精髓——“补偿法”，针对电容和互感量值较难溯源的若干问题进行了研究。 分析了传统电阻－电容量值传递方法的固有缺陷，提出了一种标准电压补偿方法。通过构建一个相位可准确改变且幅值稳定的标准电压作为交流补偿器，使得该方法定义完善、操作简单。自主研制出一台基于主从三处理器协调工作的信号源，其中引入DDS技术，成功解决了准确实现90°相角的问题。采用光纤进行数模隔离和同步通信，实现了各路输出信号之间电气上的完全独立，解决了商用信号源不能满足的幅度与相位无依赖的问题。 结合同轴扼流圈理论、开尔文内臂方法和数字瓦格纳支路技巧，建立了一套用于电阻－电容量值传递的自动化测量装置，较完善地实现了阻抗的四端对定义。提出了一种基于查找表技术的自动平衡方法，使电阻－电容量值传递商业化成为可能。该装置对电阻－电容量值传递的测量不确定度可小到0.5ppm。 分析了互感线圈的分布参数模型，理论上证明了以伏秒法可得到其直流状态下的互感值。提出了一种标准面积补偿方法，通过构建同步标准补偿面积，只需测量面积残差，便巧妙地解决了感应面积难以准确测量的问题。研究了实现标准面积补偿法的若干关键技术难题，其中包括同步测量信号的产生、恒流源的构建、采样电阻的制作及其负载系数的测量、时间脉宽的测量、电压和面积的测量等。 建立了一套用于电阻－互感量值传递的自动化测量装置。采用该装置对实验室制造的340mH互感线圈进行了测量，不确定度可小到0.22μH/H，相对国外互感测量的最好准确度水平至少提高了一个数量级，为我国建立量子质量基准打下了坚实基础。还采用低频交流外推法，对用于电阻－互感量值传递的标准面积补偿法提供了有效的旁证。
The establishment of traceable system from capacitance and mutual inductance value to the resistance value derived from the quantized Hall resistance has become the focus in the international metrology area. The conventional AC bridge method with the imperfect four-terminal pair (4TP) definition, the complicated operation and the extremely difficult implementation is employed for resistance-capactitance comparisons due to the accuracy limitation of the quadrature phase. Besides, the accuracy of the mutual inductance measurement can not be ulteriorly improved on account of the unwanted effect of distributed parameters in the AC bridge method and the accuracy limitation of the induced area measurement in the DC method. Aiming at solving these problems, the essence of the precise measurement named compensation method is flexibly applied to the traceable system. The problems of conventional bridges for resistance-capacitance comparisons are deeply analyzed. A new digital compensation method with perfect 4TP definition and simple operation is proposed, in which a standard voltage with accurate phase-shift and stable amplitude is used as a compensator. A signal source based on the master-slaver structure with three processors is developed，in which the direct digital frequency synthesis (DDS) technique is employed to realize the accurate quadrature phase. And the unique property with no dependence between the amplitude and the relative phase is achieved through the complete isolation and the strict synchronization using optical fibers. In combination with the coaxial chock theory, Kelvin arm method and digital Wagner branch skill, a new setup for resistance-capacitance comparisons with a good 4TP definition is constructed. A novel balance technique based on the lookup table is proposed, thus the automated comparisons could be achieved. Experimental results indicate that the relative uncertainty for R-C comparisons with 0.5ppm is obtained. The distributed parameter circuit of the real mutual inductance is modeled and the V.s method to get the DC value of mutual inductance is theoretically proved. A new compensation method with a standard area is proposed, in which only the residual area between the induced voltage of the mutual inductor and a synchronously generated standard square wave is observed. Therefore, the accuracy requirement for the digital integrator is considerably decreased. In addition, several key technologies of this compensation method are discussed, including the synchronized signal generation, the current source design, the sampling resistance development and the load effect measurement, the time interval measurement, the voltage measurement and the area measurement. An automatic setup for the mutual inductance measurement is constructed. A lab-made 340mH mutual inductance is measured and the relative uncertainty is estimated to be 0.22μH/H. The accuracy compared with the traditional method is increased by more than one order of magnitude, and the confidence to redefine the kilogram by the Joule balance is greatly increased. Besides, an AC extrapolation method based on the previous standard voltage is employed. Experimental results demonstrate that these two approaches are in good agreement. It is strongly proved that the measurement result of the compensation method with the standard area is reliable.
