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Solved Problems-7

Problem-7
A 50-ohm line feeds an inductive load ZL = 35 + j35 ohms. Design a double-stub tuner to match this load to the line (make use of a Smith chart).
Solution
The normalised load admittance is given as,
 
Description: Description: 101658.png
 
Steps of Design
 
(a) Since the distance between the first stub and the load is not given, we assume that the first stub is located at the load.We locate the point of load admittance on the chart, say the point A.

(b) Also, as the distance between the stubs is not mentioned, we assume it to be Description: Description: 101676.png. Therefore, the auxiliary circle is drawn as shown in Smith chart.
Description: Description: 101667.png
Designing a double-stub tuner
 
(c) This auxiliary circle intersects the constant conductance circle (with conductance of 0.7142) at the point B. Hence, the first stub is located at the point B where the normalised admittance as read from the chart is,
 
Description: Description: 101689.png
 
(d) The first stub must contribute to a susceptance of (j0.7142 – j0.49) = j0.224. The +0.224 constant susceptance circle intersects the rim of the chart at 0.036λ.
 
So, the length of the first stub as measured from the short-circuit admittance point (extreme left-hand point on the chart) is given as,
Description: Description: 101698.png
 
(e) Now, we draw a circle with centre at O and radius equal to OA. This circle cuts the unitary conductance circle at the point C. The second stub is located at the point C.

(f) The portion of the line between the stubs changes the admittance at the point A to the point C. The normalised admittance at the point C without the second stub as measured from the chart is (1 + j0.65). For perfect matching, the second stub must eliminate the imaginary component of this admittance, i.e. the second stub must provide a susceptance of –j0.65. This [–j0.65] circle cuts the rim of the chart at 0.408λ.
 
So, the length of the second stub as measured from the short circuit admittance point (extreme left-hand point on the chart) is given as,
 
Description: Description: 101708.png
 
Hence, the complete specifications of the double stub are as given:
  • Length of first stub located at load, Lstub1 = 0.286λ
  • Length of second stub, Lstub2 = 0.158λ
  • Distance between stubs = Description: Description: 101715.png




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