【作者】 李红莲；

【导师】 张钟华； 李小亭；

【作者基本信息】 河北大学 ， 等离子体物理， 2005， 硕士

【摘要】 量子化霍尔电阻比实物标准更稳定、更准确,对实际应用是非常有价值的。因此国际计量委员会推荐各国实验室统一启用量子化霍尔电阻自然基准。我国的直流量子化霍尔电阻标准已取得了可喜的成果,但交流量子化霍尔电阻标准还未建立。为了适应我国加入WTO以后,鉴定结果国际互认的要求,从直流量子化霍尔电阻标准导出交流电阻标准从而完成交直流电阻标准转换的工作已迫在眉睫。为此,中国计量院张钟华院士提出了新型的可计算电阻——镯环型可计算电阻,它克服了经典的同轴型和回线型AC/DC可计算电阻的阻值范围窄、端部电磁场不易计算、稳定性较差等缺点。 本论文以镯环型可计算电阻为研究对象,针对影响此种类型可计算电阻AC/DC转换时精确度的电感问题,运用了复变函数法求解二维场问题,由对数复函数建立了其磁场分布的数学模型。通过计算模型中矢量磁位(?)的值,确定了镯环型线圈近似为离散分布的无限长直导线时其附近磁场的分布,结合由模型所得的磁场分布图,在对离散分布的无限长直导线外部磁场的特点进行分析的基础上,提出了分界磁力线的概念并确定了该磁力线的位置进而计算出漏磁通,并将所得结果应用于具体的数值算例进行了验证。为了对镯环型线圈附近的磁场进行较为精确的计算,进一步分析了电流流向相反的两层导线情形下导线内部磁场的分布特点,得到了导线内部磁力线形状与单层情况时相同,仍然为椭圆的结论,并给出了椭圆的长短轴之比。在对双层导线外部的磁场进行讨论时发现此种情况下同样存在分界磁力线,并通过分析描述了它的特点。同时又采用了不同的方法来验证分界磁力线结果的正确性,得出公共磁通在电流均匀分布和离散分布时相等的结论。最终得到了电流离散化后增加的漏电感,从而给出实际电感与电流均匀分布时电感的差别。 本工作完成了交直流电阻标准转换中电感这一影响因素的分析,它是以直流电阻标准为基础来建立交流标准工作中不可缺少的一部分。同时采用的计算方法和所得结论对漏磁通和漏电感的计算具有相应的参考价值。更多还原

【Abstract】 The quantum Hall resistance is valuable in practical applications for its superiority over object standard in accuracy and stability, thus CIPM has given an international recommended value of the quantum Hall resistance for the values of resistance unity. The natural standard of DC quantum Hall resistance been completed in China. However, the AC resistance standard has not been set up yet. In order to keep consistency with international units after joining the WTO, it is urgent to accomplish the transform of AC/DC quantum Hall resistance standard. Therefore, a new kind of calculable resistor with toroid shape is proposed by Prof. Zhang Zhonghua NIM. With this design it is possible to get better result than the traditional calculable resistors.This paper describes the inductance of calculable resistor of toroid design which influences the transform of AC/DC quantum Hall resistances standard. Theoretical models were built based on the complex logarithm transform function. Using this model, the vectormagnetic potential A of long straight current-carrying wires with discrete distribution iscalculated and the value of A at any point is gained by numerical calculations. Thus, the distribution of magnetic field can be obtained, demonstrating the relation of the field and the wires. It also displays the distribution of main magnetic flux and the leakage flux. Furthermore, the equations of boundary magnetic field line and the position of the boundary on the axis can be calculated theoretically on the model. Because the high precision is required in this work, it remains to be discussed the magnetic field of the double layer lines which carryreverse current. Two conclusions are drawn. The first one is that the lines of A in the double lines inner magnetic are ellipses. The other is the ratio of long axis and short one is related with R and d. These results are the same as the single turns’. Discussing the external magnetic field of wires, boundary magnetic field lines are also given. By analyzing the model and its figure, their characteristics are given. Another method is utilized to validate the result of the equations of magnetic-curve boundary and the same results are present. According to the results, the leakage inductance of the current with discrete distribution is computed and then the distinction between the practical inductance and the perfect one is presented.The analysis of the leakage inductance, which influences the transform of AC/DCquantum Hall resistance standard, is indispensable in building the AC quantum Hall resistance standard which based on the AC calculable resistor standard. Therefore, the method of calculation and the conclusion in this paper can give a reference for valuing leakage flux and inductance in engineering electromagnetic更多还原