﻿ Module 4.1 Time varying uniform plane waves
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
total (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
n (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
n (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)