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How much transmission line is needed between a load and a λ/4 matching section?


Nov 10, 2012
Nov 10, 2012
I am stumped with the following question and would appreciate it if someone could tell me if i'm on the right track or totally lost:

If a load of 100 + j50 is to be matched to a 50Ω transmission line using a λ/4 matching section, how much transmission line is needed between the load and the λ/4 matching section? 0.038λ

and what should the characteristic impedance of the matching section be? 82Ω

How I came up with the above answers:
First I started with normalizing the load, 2 +j, then using a Smith chart ploted the point 2 +j (this point is to the right and above the center point of the chart)
I draw a line from the center of the Smith chart through the point 2 +j to the edge of the chart. It hits the edge of the chart around 0.286λ. So then the λ/4 transformer is placed at 0.038λ from the load.
Now I draw a circle centered at the center of the chart with the point 2 + j on the circumference of the circle. It insects real line around 2.7 on the right side and 0.37 (= 1/2.7) on the left side. The λ/4 will need to match the 50Ω line to 135Ω (= 2.7*50Ω).
The impedance of the matching transformer is 82Ω (= √(50*135) ). Z λ/4 = √(R in * R out)

Thanks for the help guys and looking forward to the commments!