Module 5.1 Bouncing Signal in T. Line w/ DC Source

### Formula:

1. $\Gamma_S$: 訊號源端的反射係數
$\Gamma_S = \frac{Z_S-Z_0}{Z_S+Z_0}$
2. $\Gamma_L$ : 負載端的反射係數
$\Gamma_L = \frac{Z_L-Z_0}{Z_L+Z_0}$
3. $h(t)$ : heavyside function
$\left\{ \begin{array}{rcl} h(t) = 0 \mathrm{,\quad for}\hspace{2mm} t < 0 \\ h(t) = 1 \mathrm{, \quad for}\hspace{2mm} t\geq 0 \end{array}\right.$
4. $V(z,t)$ :
$= \sum\limits_{n=0}^{\infty}{V_+ \cdot \left( \Gamma_S \Gamma_L \right)^n [h(-2nL+v_pt-z) + \Gamma_L \cdot h(v_pt+z-(2n+2)L)]}$

### Parameters:

1. $V_0$ : Amplitude of DC voltage (V)
2. $Z_S$ : Source impedance (Ω)
3. $Z_L$ : Load impendance (Ω)
4. $Z_0$ : Characteristic impendance of the transmission line (Ω)
5. $L$ : Length of the transmission line (m)
6. $v_p$ : The speed of electromagnetic wave in transmission line (m/s)