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Where \$r\$ is your resistance, \$j\$ is your imaginary number \$\sqrt\$ and \$x\$ is your reactance which is your "resistance" of your capacitance or inductance, so to speak. Remember that your formula for impedance is: If the impedance was only real and not complex, it would mean your transmission line would be purely resistive with no indication of induction or capacitance. From the load to the source we walk clockwise on a circle of constant VSWR centered at the normalized Z 1 (1.41. The normalized load (compared to the 50 ohm line) has a value of 2, and therefore it is the starting point of our analysis. I'm not sure what you mean by "assuming the TL impedance is real". This can be better understood if we see the Smith Chart of the input impedance of the transformer (Fig 5). Otherwise if the reflection coefficient, \$\Gamma=-j\$, it would indicate a purely capacitive load. Henceforth, using the picture above, if the reflection coefficient, \$\Gamma=j\$, it would mean that the transmission has a purely inductive load. If you had to cut horizontal line across the middle of this circle in half, you would see that top half would be a more inductive load and the bottom half being a more capacitive load. real axis, you can basically determine real and imaginary components of the impedance. Wikipedia has a very good image of how the Smith Chart is organized (for impedance): Forgive me for my knowledge of transmission lines and microwave circuits is very minuscule.
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