Question 2.2: BASIC SMITH CHART OPERATIONS A load impedance of 40 + j70 Ω ...
BASIC SMITH CHART OPERATIONS A load impedance of 40 + j70 Ω terminates a 100 Ω transmission line that is 0.3 λ long. Find the reflection coefficient at the load, the reflection coefficient at the input to the line, the input impedance, the standing wave ratio on the line, and the return loss.
The normalized load impedance is
\ z_{L}=\frac{Z_{L}}{Z_{0}} =0.4+j0.7,which can be plotted on the Smith chart as shown in Figure 2.11. By using a drawing compass and the voltage coefficient scale printed below the chart, one can read off the reflection coefficient magnitude at the load as |Γ| = 0.59. This same compass setting can then be applied to the standing wave ratio (SWR) scale to read SWR = 3.87 and to the return loss (RL) (in dB) scale to read RL = 4.6 dB.
Now draw a radial line through the load impedance point and read the angle of the reflection coefficient at the load from the outer scale of the chart as 104°.
Now draw an SWR circle through the load impedance point. Reading the reference position of the load on the wavelengths-toward-generator (WTG) scale gives a value of 0.106λ. Moving down the line 0.3 λ toward the generator brings us to 0.406λ on the WTG scale. Drawing a radial line at this position gives the normalized input impedance at the intersection with SWR circle of \ z_{in}= 0.365 −j0.611. Then the input impedance of the line is
The reflection coefficient at the input still has a magnitude of |Γ| = 0.59; the phase is read from the radial line at the phase scale as 248°.
