Smith Chart Question Inductive Reactance

[binhexoctdec]

Hello,

I'm a little new to Smith Charts and have been having difficulty trying answer this particular question below.

Homework Statement

The problem states there is a 12.5 m long, 100 Ω lossless transmission line terminated with a load impedance Zl = 50 + j110 Ω. The line is operating with a wavelength of λ = 10 m.

The question is split into parts but the particular part I'm having difficulty with is asking for the shortest distance (d) from the load to the location on the line where the line impedance has it's highest inductive reactance. It also asks for the line impedance at that point.

Homework Equations

The Attempt at a Solution

I went through the process of normalizing Zl and drawing the circle of constant reflection coefficient magnitude to answer the previous parts of the question but in this case I am stumped.

I know that distance (d) = (X - 0.141)*λ , where X is some wavelength value towards the generator and λ = 10 m. The 0.141 value is the wavelength value of the normalized Zl toward the generator. I guess the question comes down to how to obtain X?

Any help would be appreciated. Thanks.

 

[LightHero]

The highest inductive reactance in the load will be at the point where the load impedance is closest to the jω axis. In this case, that point is at 50 + j100 Ω. Therefore, X = 0.1, and d = (0.1 - 0.141)*10 m = -4 m. The line impedance at this point would be equal to the normalized load impedance, which is 50 + j110 Ω.