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In this equation $\tilde {V}(z)$ is the total voltage anywhere on the line (at any point z), $\tilde {I}(z)$ is the total current anywhere on the line (at any point z), $\tilde {V_0}^+$ and $\tilde {V_0}^-$ are the phasors of forward and reflected voltage waves at the load (where z=0), and $\tilde {I_0}^+$ and $\tilde {I_0}^-$ are the phasors of forward and reflected current wave at the load (where z=0).These voltages and currents are also phasors and have a constant magnitude and phase in a specific circuit, for example $\tilde {V_0}^+=|\tilde {V_0}^+| e^\Phi =4e^{25^0}$, and $\tilde {I_0}^+=|\tilde {I_0}^+| e^\Phi =5e^{-40^0}$. We can get the time-domain expression for the current and voltage on the transmission line by multiplying the phasor of the voltage and current with $e^{j \omega t}$ and taking the real part of it.

If the signs of the $\omega t$ and $\beta z$ terms are oposite the wave moves in the forward $+z$ direction. If the signs of $\omega t$ and $\beta z$ are the same, the wave moves in the $-z$ direction.

In the next several sections, we will look at how to find the constants $\beta$, $\tilde {V}_0^+$, $\tilde {V}_0^-$, $\tilde {I}_0^+$, $\tilde {I}_0^-$. In order to find the constants, we will introduce the concepts of transmission line impedance $Z_0$, reflection coefficient $\Gamma (z)$, input impedance $Z_{in}$.

In the following simulation, we have three waves as a function of distance z. One is fixed $\cos (\beta z +0^0)$ with a constant phase of $0^0$, and for the other two signals the phase can be changed manually by changing the slider t that represents time. In the simulation, $\beta =1$ and $\omega =1$. This simulation is realistic only if time moves forward from 0 to 5. Observe how phase change $\omega t$ as the time increases from 0 to 5, then answer the question below.

The sign in front of $\beta z$ and $\omega t$ is opposite for the forward going wave.

True False