In the following we will consider (and plot) the complex-plane. A Smith chart is developed by examining the load where the impedance must be matched. Or, it is defined mathematically as the 1-port scattering parameter s or s 11. 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. The complex reflection coefficients R(,) of a filmsubstrate system for the parallel. The Smith chart is a polar plot of the complex reflection coefficient (also called gamma and symbolized by ). 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. I'm not sure what you mean by "assuming the TL impedance is real". On Smith Chart, decreasing the phase of the reflection.
is a polar plot of complex reflection overlaid on top of the Smith chart. The input reflection coefficient angle will be decreased by twice the electrical length of the line. Otherwise if the reflection coefficient, \$\Gamma=-j\$, it would indicate a purely capacitive load. youre plotting S11 / S22 - theyre reflection coefficients (smith chart shows. In plotting - complex reflection coefficient, along real and imaginary. Henceforth, using the picture above, if the reflection coefficient, \$\Gamma=j\$, it would mean that the transmission has a purely inductive load. Smith Chart - complex reflection coefficient, in polar form, arbitrary impedance. 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): the center of the chart and the constant reflection coefficient circle, read zL -j0:425. Forgive me for my knowledge of transmission lines and microwave circuits is very minuscule.