(Solved): Derive equations for future voltage and current along transmission line (leap frog method) and apply ...

behavior of electrical signals along a transmission line. It is commonly used to analyze and design high-frequency and highspeed digital circuits. The equation is a partial differential equation that relates the voltage and current along the transmission line. The general form of the transmission line equation is: $\begin{array}{l}{?}^2\mathrm{V}(\mathrm{z},\mathrm{t})/?{\mathrm{z}}^2=(\mathrm{R}/\mathrm{L})?\mathrm{V}(\mathrm{z},\mathrm{t})/?\mathrm{t}+(\mathrm{G}/\mathrm{C}){?}^2\mathrm{V}(\mathrm{z},\mathrm{t})/\\ ?{\mathrm{t}}^2\end{array}$ where: - $\mathrm{V}(\mathrm{z},\mathrm{t})$ is the voltage along the transmission line at position $z$ and time $t$. - $\mathrm{R}$ is the resistance per unit length of the transmission line. - $L$ is the inductance per unit length of the transmission line. - $G$ is the conductance per unit length of the transmission line.