﻿ Module 5.4 Bouncing Signal in a T.-Line System w Shunt/Series Discontinuity
Module 5.4 Bouncing Signal in a T.-Line System w Shunt/Series Discontinuity

### 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. $\Gamma_L$ : 負載端的反射係數
$\Gamma_L = \frac{Z_L-Z_{03}}{Z_L+Z_{03}}$
3. In the condition of Series :
$\Gamma_{13} = \frac{R+Z_{03}-Z_{01}}{R+Z_{03}+Z_{01}}$;    $\tau_{13} = (1+\Gamma_{13}) \times \frac{Z_{03}}{R+Z_{03}}$
$\Gamma_{31} = \frac{R+Z_{01}-Z_{03}}{R+Z_{01}+Z_{03}}$;    $\tau_{31} = (1+\Gamma_{31}) \times \frac{Z_{01}}{R+Z_{01}}$
4. In the condition of Shunt :
$Z_{1} = \frac{1}{R^{-1}+Z_{01}^{-1}}$;    $Z_{3} = \frac{1}{R^{-1}+Z_{03}^{-1}}$
$\Gamma_{13} = \frac{Z_{3}-Z_{01}}{Z_{3}+Z_{01}}$;      $\tau_{13} = 1+\Gamma_{13}$
$\Gamma_{31} = \frac{Z_{1}-Z_{03}}{Z_{1}+Z_{03}}$;      $\tau_{31} = 1+\Gamma_{31}$
5. $V(z,t)$
$V_1^+ = \frac{Z_{01}}{Z_{01}+Z_S}$;               $V_1^- = \frac{Z_{01}}{Z_{01}+Z_S} \times \tau_{13} \times \Gamma_L \times \tau_{31}$
$V_2^+ = \frac{Z_{01}}{Z_{01}+Z_S} \times \tau_{13}$;    $V_2^{++} = \frac{Z_{01}}{Z_{01}+Z_S} \times \Gamma_{13} \times \Gamma_S \times \tau_{13}$

### Parameters:

1. $Z_S$ : Source impedance (Ω)
2. $Z_L$ : Load impendance (Ω)
3. $Z_{01}, Z_{03}$ : Characteristic impendance of the transmission lines (Ω)
4. $L_1, L_3$ : Length of the transmission lines (m)
5. $R$ : 不連續處的串聯/並聯電阻 (Ω)
6. $C$ ：電磁波的傳遞速度 (m/s)