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)