基于保角变换的微小电容标准建模与设计  

Modeling and design of small capacitance standards based on conformal mapping

作　　者：吴晓媛 杨雁[2] 贺青[2] 迟宗涛[1] Wu Xiaoyuan;Yang Yan;He Qing;Chi Zongtao(School of Electronic Information,Qingdao University,Qingdao 266000,China;National Institute of Metrology,Beijing 100029,China)

机构地区：[1]青岛大学电子信息学院,青岛266000 [2]中国计量科学研究院,北京100029

出　　处：《仪器仪表学报》2019年第9期116-123,共8页Chinese Journal of Scientific Instrument

基　　金：国家自然科学基金(51877202,51377150);国家重点研发计划NQI专项(2016YFF0200105)资助

摘　　要：在可编程电容器中,亚皮法量级的微小电容单元因受边缘效应等杂散电容的影响较大,难以实现准确、稳定的微小电容标准。本文给出了一种基于Kelvin等电位保护电极的微小电容单元实现方法,该方法将影响小电容单元的杂散电容限定为中心电极与保护电极之间因边缘效应而产生的杂散电容。并对此结构建立了等效微小电容单元解析模型,给出了一种通过保角变换分析杂散电容变化的算法,发现在电极厚度以及间距一定的情况下,中心电极与保护电极之间的气隙是杂散电容的主要影响量。基于此,分析气隙变化对杂散电容和主电极电容值的影响,同时结合有限元分析软件Ansoft Maxwell验证,确定微小电容单元的最佳气隙区间,进而准确实现微小电容标准的设计。经测试,在可编程熔融石英电容器中,亚pF量级实际微小电容单元电容值与设计微小电容单元电容值一致性良好。In the programmable capacitor,due to the influence of stray capacitance generated by the edge effects,it is difficult to achieve accurate and stable small capacitance standards of sub-pF and below.In this paper,a method of implementing a small capacitance standards based on Kelvin equipotential protection electrode is proposed,so that the stray capacitance affecting the small capacitance is limited to the stray capacitance generated by the edge effect between the center electrode and the guard electrode.The analytical model of equivalent small capacitance standard is established,and the algorithm for analyzing the variation of stray capacitance is proposed by conformal mapping.It is found that the air gap between the center electrode and the guard electrode is the main influencing factor of stray capacitance when both the electrode thickness and the distance between the electrode plates are determined.Combined with the finite element analysis software Ansoft Maxwell to verify the optimal air gap between the main electrode and the guard electrode,and the small capacitance standards will be realized.It has been tested that in the programmable fused silica capacitor,the actual small capacitor capacitance value of the sub-pF level is basically the same as the design small capacitor capacitance value.

关 键 词：交流阻抗 电容标准 保角变换 边缘效应 有限元分析 

分 类 号：TB99[一般工业技术—计量学]