If we know the reflection coefficient, we can determine the characteristic impedance of the load by using a Smith Chart. The Smith Chart has circles of constant resistance and arcs of constant reactance. The relationship between reflection coefficient and characteristic impedance is shown in the diagram. At first glance, the Smith Chart appears complicated, but its elegance soon becomes obvious.
The Smith Chart can help us translate the reflection coefficient into impedance. First, measure the reflection coefficient with a network analyzer (or invent one of your own choosing). Place the reflection coefficient, by using either the mouse or the drop-down input boxes, at the desired value (real + imaginary) on the Smith Chart. Hit the Play button (triangle), and the program will display a circle with a radius equal to the reflection coefficient magnitude (constant VSWR circle). Notice that if you move the reflection coefficient anywhere on this circle, you can see from the waveform at the left that the SWR is the same, only its phase changes. (Phase values are not shown around the chart in this program; however, the phase is calculated and shown at the left side of the screen.)
Anmerkung: der komplexe Reflexionskoeffizient r(z) ist hier mit G (= Gamma) bezeichnet.
In general, only the horizontal line (diameter) is labeled with (normalized) resistance values and only the unit (outer) circle is labeled with (normalized) reactance values. To read the desired values, it is necessary to follow the appropriate circle of constant resistance to the diameter line, and to follow the appropriate arc of constant reactance to the unit circle. Hit Play again, and the program will display the constant-resistance circle and the constant-reactance arc for you. (The actual values are calculated and shown at the left side of the screen.)
Experiment with the simulator and see if you can predict the shape of the standing wave before you move the reflection coefficient
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Quelle: Firma Hewlett-Packard www.hp.com