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

$\Gamma_S$ : 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.

$V(z,t)$

$V_1^+ = \frac{Z_{01}}{Z_{01}+Z_S}$ ;

$V_1^- = \frac{Z_{01}}{Z_{01}+Z_S} \times \tau_{13} \times \Gamma_L \times \tau_{31}$

$V_2^+ = \frac{Z_{01}}{Z_{01}+Z_S} \times \tau_{13}$ ;

$V_2^{++} = \frac{Z_{01}}{Z_{01}+Z_S} \times \Gamma_{13} \times \Gamma_S \times \tau_{13}$