微波超低頻(VHF)和超高頻時金屬波導之全波分析

Abstract

電磁理論中的集膚效應(skin effect)中說明了電磁波所能傳遞到金屬內 部的深度只有集膚深度, 當頻率在10GHz時,金的集膚深度只有 0.76um, 而且一般的金屬厚度都遠大於這個深度也就是電磁波只會在在金屬表面, 並不會深入或穿透金屬層. 所以在處理馬克斯威爾方程式時, 可以做許多 的假設, 如導電係數無限大,金屬厚度無限薄. 但是,當我們需要去分析較 低頻, 尤其是當頻率低到使得集膚深度已經接近金屬厚度時, 前面的假設 已經不再成立. 這表示電磁波會遍佈於金屬甚至會穿透它. 此在相當低頻 的場論分析非得使用全波分析無法得到精確解. 本論文利用模展開全波分 析法完成在低頻時的分析並以此結果來設計一個時間延遲電路.另外, 我 們也探討導波管在高頻時金屬壁上的粗糙所造成的損耗.有限導電係數金 屬的表面粗糙會造成傳輸損耗的增加. 導波管寬面的金屬表面粗糙對傳輸 損耗之影響,已由陳鉅棟博士以一個簡化的例子完成. 但是考慮矩形導波 管大操作於TE10之模式, 此時的電流分布於整個金屬內壁. 因此窄面粗糙 的金屬壁所造成對傳輸損耗的影響必需被考慮到. 根據所考慮的金屬表面 粗糙模型, 可以知道在窄面的粗糙現象會比寬面的粗糙現象造成更大的傳 輸損耗之增加. By skin-effect, the electromagnetic field in the conductor decay by an amount 1/e or 36.8 % after traveling a distance of one skin depth. At microwave frequencies, for a good conductor, this distance is very small. Foe gold, ds= 0.76 mm. In general, the thickness of metal is far more than the skin depth. The result shows that most of current flow in a good conductor occurs in an extremely thin regon near the surface of conductor, and doesn't deep into the metal. At the other extreme of microwave frequency range, we discuss the increce of loss caused by the metal rough on inner surface of waveguide at high frrquency range. The surface roughness of finite conductivity metal of waveguide causes the increce of propagation loss. The effect of the rough on the wide wall surface had been done by Dr. C.-D. Chen. But in fact, the current distribution of TE10 mode, the mostly utilized mode of rectangular waveguide, distributes on the whole inner surface of waveguide. The influence on the increce of propagation loss caused by rough on narrow wall surface must be taken into consideration. By the model of roughness, the rough of narrow wall surfaces cause serious propagation loss than the wide wall surfaces.