The impedance matching network shown in the figure is to match a lossless line having characteristic impedance \( Z_0 = 50 \, \Omega \) with a load impedance \( Z_L \). A quarter-wave line having a characteristic impedance \( Z_1 = 75 \, \Omega \) is connected to \( Z_L \). Two stubs having characteristic impedance of \( 75 \, \Omega \) each are connected to this quarter-wave line. One is a short-circuited (S.C.) stub of length \( 0.25 \lambda \) connected across PQ and the other one is an open-circuited (O.C.) stub of length \( 0.5 \lambda \) connected across RS. The impedance matching is achieved when the real part of \( Z_L \) is:
The impedance matching network shown in the figure is to match a lossless line having characteristic impedance \( Z_0 = 50 \, \Omega \) with a load impedance \( Z_L \). A quarter-wave line having a characteristic impedance \( Z_1 = 75 \, \Omega \) is connected to \( Z_L \). Two stubs having characteristic impedance of \( 75 \, \Omega \) each are connected to this quarter-wave line. One is a short-circuited (S.C.) stub of length \( 0.25 \lambda \) connected across PQ and the other one is an open-circuited (O.C.) stub of length \( 0.5 \lambda \) connected across RS. The impedance matching is achieved when the real part of \( Z_L \) is:
Show Hint
- 112.5 \( \Omega \)
- 75.0 \( \Omega \)
- 50.0 \( \Omega \)
- 33.3 \( \Omega \)
The Correct Option is A
Solution and Explanation
The relationship between the load impedance \( Z_L \) and the characteristic impedance \( Z_1 \) of the quarter-wave line is given by: \[ Z_L = Z_1 \left( \frac{Z_0}{Z_1} \right) = 75 \times 1.5 = 112.5 \, \Omega. \] Step 2: Conclusion.
For the impedance matching to be achieved, the real part of \( Z_L \) must be \( 112.5 \, \Omega \). Final Answer: \[ \boxed{112.5 \, \Omega}. \]
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