Hence, \[ik_-\, \left[\psi_+(x_a) - \psi_-(x_a)\right] = ik_+\, \left[\psi_+(x_b) - \psi_-(x_b)\right].\] These two equations can be combined into a single matrix equation: \[\begin{bmatrix}1 & 1 \\ k...Hence, \[ik_-\, \left[\psi_+(x_a) - \psi_-(x_a)\right] = ik_+\, \left[\psi_+(x_b) - \psi_-(x_b)\right].\] These two equations can be combined into a single matrix equation: \[\begin{bmatrix}1 & 1 \\ k_- & - k_-\end{bmatrix}\begin{bmatrix}\psi_+(x_a) \\ \psi_-(x_a) \end{bmatrix} = \begin{bmatrix}1 & 1 \\ k_+ & - k_+\end{bmatrix} \begin{bmatrix}\psi_+(x_b) \\ \psi_-(x_b) \end{bmatrix}.\] After doing a matrix inversion, this becomes \[\Psi_b = \mathbf{M}_s(k_+,k_-) \, \Psi_a, \;\;\;\mathrm{where}\…
This page covers boundary value problems in transmission lines, emphasizing the uniqueness theorem and steps to resolve these issues through wave behavior and boundary conditions. It explains lossless...This page covers boundary value problems in transmission lines, emphasizing the uniqueness theorem and steps to resolve these issues through wave behavior and boundary conditions. It explains lossless TEM transmission lines and their wave equations, introduces reflection and transmission coefficients, and examines the behavior of standing waves and load impedance.
