Module 5.3 Bouncing Signals in 3 Sec. T.-Line w/ Pulse Source

Formula:

1. \(\Gamma_S\): 訊號源端的反射係數
    \(\Gamma_S = \frac{Z_S-Z_{01}}{Z_S+Z_{01}}\)
2. 反射係數
    \(\Gamma_{12} = \frac{Z_{02}-Z_{01}}{Z_{02}+Z_{01}}\)
    \(\Gamma_{21} = -\Gamma_{12}\)
    \(\Gamma_{23} = \frac{Z_L-Z_{03}}{Z_L+Z_{03}}\)
    \(\Gamma_{32} = -\Gamma_{23}\)
3. \(\Gamma_L\) : 負載端的反射係數
    \(\Gamma_L = \frac{Z_L-Z_{03}}{Z_L+Z_{03}}\)
4. \(h(t)\) : heavyside function
    \( \left\{ \begin{array}{rcl} h(t) = 0 \mathrm{,\quad for}\hspace{2mm} t < 0 \\ h(t) = 1 \mathrm{, \quad for}\hspace{2mm} t\geq 0 \end{array}\right.\)
5. \(V(z,t)\) :
    \(= \sum\limits_{n=0}^{\infty}{V_+ \left( \Gamma_S \Gamma_L \right)^n [h(-2nL+v_pt-z) + \Gamma_L \cdot h(v_pt+z-(2n+2)L)]}\)

Parameters:

1. \(V_0\) : Amplitude of DC voltage (V)
2. \(Z_S\) : Source impedance (Ω)
3. \(Z_L\) : Load impendance (Ω)
4. \(Z_{01}, Z_{02}, Z_{03}\) : Characteristic impendance of the transmission lines (Ω)
5. \(L_1, L_2, L_3\) : Length of the transmission lines (m)
6. \(v_p\) : The speed of electromagnetic wave in transmission line (m/s)