Module 4.1 Time varying uniform plane waves

Introduction:

    本模組探討均勻平面波的電場在自由空間中時域的變化情形。
    Ex：空間中有兩面電流屏幕 \(J_{s1}\) 和 \(J_{s2}\)，電流密度振幅相等。\(J_{s1}\) 在XY平面上與\(J_{s2}\)相距0.25 \(\lambda\) ( z = 0.25\(\lambda\) )，又 \(J_{s1}\) 初始相位領先 \(J_{s2}\) 相位 0.5 \(\pi\)，其輻射特性為
     +z 的 endfire 場型圖，-z方向為 null 場型圖。

Formula:

1. Etotal (z,t) (V/m) : Total eletrical field due to three infinite plane parallel current sheets, defined by
     Êtotal (z,t) \( = \frac{\eta_{0} J_{s1} }{ 2 }cos[\omega (t-\frac{z -d_{1} }{ c })] x̂ + \frac{\eta_{0} J_{s2} }{ 2 }cos[\omega (t-\frac{z -d_{2} }{ c })] x̂ + \frac{\eta_{0} J_{s3} }{ 2 }cos[\omega (t-\frac{z -d_{3} }{ c })] x̂ \)
2. E (z,t) (V/m) : Eletrical field due to a infinite plane current sheet, defined by
     Ên (z,t) \( = \frac{\eta_{0} J_{sn} }{ 2 }cos[\omega (t-\frac{z -d_{n} }{ c })] x̂, \) (n = 1, 2, 3)
3. J (t) (A/m) : A infinite plane current sheet, defined by
     Ĵn (z,t) \( = \ -J_{sn} cos[\omega (t-\phi_{n})] x̂, z = a_{n}, \) (n = 1, 2, 3)

Parameters:

1.   \(J_s\) : Amplitude of the surface current density, (A/m)
2.   \(\phi\)   : Phase angle of the surface current density, (rad),
3.   \(f\)   : Operating frequency, (GHz),
4.   \(d\)   : Location of the surface current density from zero, (\(\lambda\)),
5.   \(\eta_{0}\) : Instrnsic impdance of the free space, (\(\Omega\))
6.   \(c\)    : Speed of light, (m/s)