Homework Help: Smith Chart problem

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1. Apr 25, 2017

maearnie

1. The problem statement, all variables and given/known data
An antenna is modeled by a 40ohm resistor in parallel with a capacitor with Xc = -j25. The antenna is fed
by a lossless 50ohm signal line 0.15 wavelengths long. Use a Smith Chart to find the input impedance to
the transmission line.

2. Relevant equations

3. The attempt at a solution
The solution is in the attached file but i dont understand it after obtaining the admittance.

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2. Apr 26, 2017

tech99

This is how the person worked it out. First the parallel R and Xc can be expressed as admittances, by simply taking the reciprocal of each. Then they are normalised by dividing by 0.02, which is the value at the centre of the chart (it is the Zo of the line, 50 Ohms or 1/50=0.02 Siemens). Plot the normalised admittance, then notice the VSWR, which is the radial distance, and we rotate around the chart at this radius towards the generator for a distance of 0.15 lambda. This point gives the admittance at the generator, and we travel across the chart to the opposite point to obtain the normalised impedance at the generator. Multiply R and X by 50 to obtain the required values.
But I think the following is easier:
Find the normalised values of the parallel R and Xc by dividing each by 50.
Find their reciprocals, which gives you normalised admittance.
Plot the point and then travel diametrically across the chart and mark the normalised impedance of the load.
Note the VSWR at this point - the radius.
Rotate around the chart at this radius towards the generator for 0.15 lambda and this point gives you the normalised input impedance of the line.
Multiply the normalsed impedance values by 50 to obtain the actual values.

3. Apr 26, 2017

maearnie

Thank you very much!!! i was wondering why they multiplied 50 instead of multiplying it. hahaha