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)