Module 5.5 TDR Simulator

Formula:

1. \(T_1 = L_1 / v_p ;  T_2 = L_3 / v_p\)
2. \(\Gamma_L\) : 負載端的反射係數 (Load reflection coefficient)
    \(\Gamma_L = \frac{Z_L-Z_{03}}{Z_L+Z_{03}}\)
3. 電阻串聯時 (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. 電阻並聯時 (In the condition of Shunt) :
    \(Z_{1} = \frac{1}{R^{-1}+Z_{01}^{-1}}\);     \(Z_{3} = \frac{1}{R^{-1}+Z_{03}^{-1}}\)
    \(\Gamma_{13} = \frac{Z_{3}-Z_{01}}{Z_{3}+Z_{01}}\);       \(\tau_{13} = 1+\Gamma_{13}\)
    \(\Gamma_{31} = \frac{Z_{1}-Z_{03}}{Z_{1}+Z_{03}}\);       \(\tau_{31} = 1+\Gamma_{31}\)

Parameters:

1. \(Z_L\) : 負載阻抗 (Load impedance) (Ω)
2. \(Z_{01}, Z_{03}\) : 傳輸線特徵阻抗 (Characteristic impedances of the transmission lines) (Ω)
3. \(L_1, L_3\) : 傳輸線長度 (Lengths of the transmission lines) (m)
4. \(R\) : 不連續處的串聯/並聯電阻 (Series/shunt resistance at discontinuity) (Ω)
5. \(v_p\) :電磁波的傳遞速度 (Speed of EM wave in the transmission line) (m/s)