瞬变电磁法圆形线圈自感计算

摘要

在瞬变电磁法(TEM)中,圆形回线的自感参数用于局部导体晚期瞬变电磁场的等效计算、接收线圈固有过渡过程计算、关断时间的计算以及瞬变电磁仪器研制等.目前,在瞬变电磁法教科书中,圆形线圈自感计算均使用近似公式.这里根据毕奥-萨伐尔定律推导出单匝圆形线圈磁感应强度及自感的积分表达式,利用MATLAB软件进行数值计算.结果表明,目前使用的自感近似公式,在用于计算半径为0.5m和1 m的圆形接收回线自感时,误差分别为-18.978％和- 26.542％.用于计算发射回线的自感时,当回线半径从2.821 0 m～112.837 9 m时,自感近似公式的误差从-35.84％～-55.65％,且单匝正方形回线与等面积单匝圆形回线的自感值之间存在5.12％ ～8.11％的偏差.%In Transient electromagnetic methods ( TEM), the self-inductance coefficient of circular loop has been applied to the equivalent method calculation of transient electromagnetic field late induced by partial conductive ore bodies, the calculation of natural transient process for receiving coil, the turn-off time calculation and the developing of TEM instruments. But there are several approximate formulas in current TEM textbooks. This paper has deduced the integral formula of the magnetic induction density and the self-inductance coefficient for circular loop in single - tum according to blot-savart law, and then do numerical calculation with the mathematical software MATLAB. There is a large margin for the error when using the existing approximate formulas in current literatures; For Rx - loop, the error is - 18. 978% at least; ForTx-loop,the error is - 35. 84 %～ -55. 65% ; thecomparison indicates that the deviations between the single - turn circular loop and the equal area of single -turn square loop in inductance values is 5. 12% ～ 8.11%.