The Smith chart shown below is an impedance chart generated using Keysight ADS s

Question

The Smith chart shown below is an impedance chart generated using Keysight ADS software. The point labeled "A" is the load impedance connected to a lossless transmission line of a certain length. The point labeled "B" is the input impedance looking into the transmission line. Both "A" and "B" lie on a circle of constant part of which is shown. The system impedance is 75 ohms. Which value below represents the best estimate for the load impedance (point "A") in ohms? Z_L = 40 Ohm Z_L = 75 Ohm Z_L = 20 Ohm Z_L = 30 Ohm

Explanation / Answer

here point A lies on reactance zero circle so the load A is pure resistive and since it is lies on a circle whose value is less than 0.5

0.5 corresponds to 0.5*75 =37.5ohm

so value 40ohm and 75 ohm is not correct

and value 20ohm corresponds to 20/75=0.266 in smith chart which is close to zero resistance circle

and moreover by looking at impedance B which is approximately close to 1+j*1 circle assuming the point B is located at 0.9+j*0.9 so the impedance will be (0.9+j*0.9)*75=67.5+j*67.5 so the corresponding magnitude of reflection coefficient will be 0.43 so the best value will be

option ZL=30ohm which corresponds to magnitude of reflection coefficient 0.42 and resistance circle 0.4

since both A and B is at constant reflection circle

hence Zl=30ohm is the best answer and moreover magnitude of reflection coefficient doesnot change with frequency because the load is resistive

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