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