Loading [MathJax]/jax/output/HTML-CSS/jax.js
Module 4.3 Bouncing Signals in 3 Sec. T.-Line w/ Pulse Source
  • cm
    {Z_{01}} =
    40Ω
    {L_1} =
    600m
    {Z_{02}} =
    25Ω
    {L_2} =
    1200m
    {Z_{03}} =
    100Ω
    {L_3} =
    600m
    z = 0
    z = L
    Z_S
    \delta (t)
    \Gamma_L =
    0.00
    \Gamma_S =
    0.11
    ZL
    Load
    0
    L1
    L1+L2
    L1+L2+L3
  • t
    =
    0.00μs
    V(t)
    =
    0.00
    V
    V(t)
    =
    0.00
    V
    V(t)
    =
    0.00
    V
    1000
    1500
    500
    2000
    0
    2500
    0.5
    1
    0
    1.5
Z_S = (Ω)
Z_L = (Ω)
Z_{01} = (Ω)
Z_{02} = (Ω)
Z_{03} = (Ω)
L_1 = (m)
L_2 = (m)
L_3 = (m)
V_p = 10^{8} (m/s)

Formula:

1. \Gamma_S: Source reflection coefficient
    \Gamma_S = \frac{Z_S-Z_{01}}{Z_S+Z_{01}}
2. Reflection coefficients at different interfaces
    \Gamma_{12} = \frac{Z_{02}-Z_{01}}{Z_{02}+Z_{01}}
    \Gamma_{21} = -\Gamma_{12}
    \Gamma_{23} = \frac{Z_L-Z_{03}}{Z_L+Z_{03}}
    \Gamma_{32} = -\Gamma_{23}
3. \Gamma_L : Load reflection coefficient
    \Gamma_L = \frac{Z_L-Z_{03}}{Z_L+Z_{03}}
4. 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.
5. V(z,t) :
    = \sum\limits_{n=0}^{\infty}{V_+ \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_{01}, Z_{02}, Z_{03} : Characteristic impendance of the transmission lines (Ω)
5. L_1, L_2, L_3 : Length of the transmission lines (m)
6. V_p : Speed of electromagnetic wave in the transmission line (m/s)