The article provides analytical expressions for the electromagnetic fields generated by a lightning return stroke characterized by a channel-base current with arbitrary time waveform, in presence of either a perfectly conducting or a lossy ground, assuming the transmission line model for the current along the channel. In this second case, a time-domain analytical expression for the Cooray–Rubinstein formula is presented. The main idea that leads to the derivation of analytical formulas consists of dividing the channel into intervals in which the distance between the field source point and the observation point can be approximated with a linear function of the time, and of the spatial coordinates of both points. In the companion aticle, a detailed comparison is proposed with the classical (numerical) approach highlighting an excellent agreement both at close and far distances, considering all the values of practical interest for the ground conductivity. Moreover, the method guarantees a meaningful improvement in computational performance.

中文翻译：

---

具有任意通道基电流的雷电电磁场的解析表达式—第一部分：理论

本文提供了由雷电回击产生的电磁场的解析表达式，该雷击的特征是具有理想时间的通道基电流，在存在理想导电或有损耗接地的情况下，假设沿着通道的电流具有传输线模型。在第二种情况下，给出了Cooray–Rubinstein公式的时域解析表达式。导致得出分析公式的主要思想是将通道划分为多个间隔，在这些间隔中，场源点和观测点之间的距离可以用时间以及两个点的空间坐标的线性函数来近似。在同伴阁楼中 考虑到地面电导率的所有实际价值，建议采用经典（数值）方法进行详细比较，以突出在近距离和远距离都具有出色的一致性。此外，该方法保证了计算性能的有意义的改进。