Question

A lossless transmission line of length l=0.4? is terminated with a complex load impedance Z_L=60+j50 ? and characteristic impedance (Z_0=50 ?). Use Smith Chart to find: The VSWR on the line; The reflection coefficient at the load and its phase angle; The load admittance of the line Y_L in S; The input impedance of the line in ?; The distance to the first voltage minimum from the load in ?; and The distance to the first voltage maximum from the load in ?. By calculation only, verify the following parameters in Q3 part(a): The input impedance of the line in ?. The distance to the first voltage minimum from the load in ?. The distance to the first voltage maximum from the load in ?.

Answer 1

A lossless transmission line of length l=0.4 is terminated with a complex load impedance Z_L=60+j50 and characteristic impedance Z_o= 50

Normalized impedance

Point z_L( 1.2, 1.0) is plotted on Smith Chart.

Reflection coefficient is read from the chart.

At that point SWR, S = 2.5

Load admittance

Y_L=1/(Z_L) = 0.0098 - j0.0081

Input impedance Z_in is away from Load point Z_L along the wavelength to generator scale.

Load point Z_L is at  .

Z_in is at

The first voltage maximum occurs at SWR.

Hence the distance from load is at