Module 6.1 Wave Propagation on a Transmission Line (lossless case)

### Introduction:

本模組我們將探討無損傳輸線之入射波、反射波與駐波之時域行為，並藉由調整 toolbar 以觀察入射波與反射波之動態行為與合成。
Ex.1：負載阻抗為匹配時 ( $\left|\Gamma_L\right|$ = 0 )，反射波振幅將為 0，此時入射波與合成波相同！
Ex.2：當頻率越低時，可發現傳輸線的效應會越小，即傳輸線上不同位置所觀察到的振幅與相位變化越小。
Ex.3：當 $\left|\Gamma_L\right|$ = 0 時，入射波與反射波的振幅大小相同，可觀察到合成波為完全駐波。

### Formula:

1. $V_{total}(z,t)(V)$ : Total voltage waveform in time domain, defined by
$V_{total}(z,t) = \left|V_0^+(z)\right|cos(\omega t-\beta z+\varphi^+)$
$+ \left|V_0^-(z)\right|cos(\omega t+\beta z+\varphi^-)$
2. $V_{incident}(z,t)(V)$ : Incident voltage waveform in time domain, defined by
$V_{incident}(z,t) = \left|V_0^+(z)\right|cos(\omega t-\beta z+\varphi^+)$
3. $V_{reflected}(z,t)(V)$ : Reflected voltage waveform in time domain, defined by
$V_{reflected}(z,t) = \left|V_0^-(z)\right|cos(\omega t+\beta z+\varphi^-)$

### Parameters:

1. $\left|V_0^+\right|$ : Amplitude of the incident voltage wave at z=0, (V)
2. $\varphi^+$ : Phase angle of the complex voltage $V_0^+$, (rad)
3. $\left|\Gamma_L\right|$ : Amplitude of the reflection coefficient at z=0
4. $\theta$ : Phase angle of the reflection coefficient $\Gamma_L$, (rad)
5. $V_0^-$ : Reflected voltage wave at z=0, (V)
$V_0^- = V_0^+ \Gamma_L = \left|V_0^-\right|\angle\varphi^-$
6. $\beta$ : Phase cnstant, (rad/m)
7. $f$ : Operating frequency, (GHz)
8. $d$ : Length of the transmission line, value equal to 10 (cm)