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Example: Calculate the input impedance at z = -0.14 m on a transmission line with 050[ ]Z=Ω40[ ]jΩ that is connected to a load impedance of , assuming 70LZ=−2[1/m]βπ=. Solution: Step 1: Calculate the normalized load impedance: (70 40) / 50 1.4 0.8zj=− =−jStep 2: Locate the load impedance on the Smith Chart (A) (Because the imaginary part is negative, the location is on the lower half of the Smith Chart). rΓ1.4 A 0.8Step 3: Find the distance reading (0.312) rΓ1.4 A 0.8 0.312Step 4: Calculate the electrical distance of movement (Note: in this example, the wavelength is 1m). / 0.14 /1 0.140.14 0.312 0.452lλ==+= Step 5: Rotate the load impedance on the constant Γ-circle (in clockwise direction) for an electrical distance of 0.14 (Point B on the chart) rΓRead “r” here, it is the VSWR. In this example, the value is VSWR= 2.1 B A 0.8 0.452 0.312 0.14Step 6: Read the normalized impedance representing this point (negative sign for the imaginary part because it is on the the lower part of the chart for impedance). 0.52 0.22Bzj=− Un-normalize it to get the input impedance. 050 (0.52 0.22) 26 11[ ]BBZZz j j=×=× − =− Ω rΓ0.52 Analytical calculation: 000tan( )(0.14)tan( )70 40 50 tan(2 0.14)5050 (70 40) tan(2 0.14)50 (0.512 0.233)25.6 11.6[ ]LLZjZ lZZZjZ ljjjjjjββππ+−=+−+ ×=+− ×=× −=− Ω B


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