Question

You are a microwave engineer for Verizon, and is responsible for

the planning of the antenna system on the base station tower.
You have two antenna designs at hand to choose from, one with the
impedance of Zant1 = 150 + j75 Ω, and the other with the impedance
of Zant2 = 75 + j150 Ω. The transmission line between the ground
station and the antenna on the tower has the characteristic impedance
of 75 Ω.

a) Please mark and label both antennas’ impedance on the
smith chart. (Hint: Normalize the impedance first)

Answer 1

To mark and label the impedance on the Smith chart, first normalize the impedance by dividing it by the characteristic impedance of the transmission line. Then, plot the normalized impedances on the Smith chart using the real and imaginary axes.

Step-by-step explanation:

To mark and label both antennas' impedance on the Smith chart, we first need to normalize the impedance. Normalizing the impedance means dividing the impedance by the characteristic impedance of the transmission line. In this case, the characteristic impedance is 75 Ω. So, for the first antenna, the normalized impedance is Zant1_normalized = (150 + j75) / 75 = 2 + j1. For the second antenna, the normalized impedance is Zant2_normalized = (75 + j150) / 75 = 1 + j2.

Now, we can mark and label these normalized impedances on the Smith chart. The Smith chart represents the complex impedance of a device as a point on a polar coordinate system. The horizontal axis represents the real part of the impedance, and the vertical axis represents the imaginary part.