利用等效磁流法做平面近場轉換遠場

Abstract

本論文探討平面近場電場轉換遠場場型，方法為等效磁流法。利用等效原理與映像法理論將天線等效成磁流源，等效磁流面必須包圍住待測天線，所得到的等效磁流就可以用來決定遠場場型。在一定的近似下，不論待測天線的形狀為何，等效磁流法皆能得到相當正確的遠場場型。經由適當的推導可得到一個包含等效磁流的積分方程式，再利用動差法，並配合共軛梯度法，就可以得到等效磁流解，遠場場型就可以獲得。再進一步，利用特殊的塊狀托普利斯矩陣結構，就可以使用二維的快速傅利葉轉換來加速共軛梯度法並大大的減少計算時間和儲存容量。最後利用極短電偶極陣列天線與隨機的極短電偶極所求得的遠場場型來和精確的遠場場型做比較，以驗証等效磁流法的可行性

n this thesis, we discuss the planar near field to far field transformation using equivalent magnetic current approach. Utilizing equivalence principle and image theory to replace antenna with equivalent magnetic currents, the equivalent magnetic current plane has to encompass the antenna under test. The equivalent magnetic currents are used to determine far field pattern. Under certain approximations, the equivalent magnetic current approach can produce correct far field pattern regardless of the shape of the antenna under test. From proper derivations, an electric field integral equation contains equivalent magnetic currents is developed. The equivalent magnetic currents obtained by method of moments and conjugate gradient method determine the far field pattern. Furthermore, utilizing the special structure of block Toeplitz matrix, two-dimensional fast Fourier transform is used to accelerate the conjugate gradient method and drastically reduces the computation time and storage requirements. Finally, far field patterns of the infinitesimal short dipole arrays and random infinitesimal short dipole sources are compared with analytic far field patterns to prove the equivalent magnetic current approach works fine in near field to far field transformation.