Mutual impedance formula between two arbitrary antenna elements

The mutual impedance formula between two arbitrary antenna elements is constructed based on the Fourier analysis in angle dependence and the appropriate choosing of the expansion functions in distance dependence. The unknown coefficients in the formula are obtained through solving simultaneous equations based on numerical sampling by using a full-wave solver or based on the measured data. This formula is applicable to arbitrary types of antenna elements. The two elements could be the same or different. The accuracy of this trained formula is observable by comparing the training set and the testing set. It is therefore controllable. This formula is not only useful in the analysis of the mutual impedance between two isolated elements but also will be useful in array problems where the mutual coupling effect should be taken into account in a finite array environment. The validity of the proposed formula is confirmed through comparisons between the results from this formula and those from the full-wave commercial software.