Question
Which of these transmission line impedances would be suitable for constructing a quarter-wave Q section for matching a 100-ohm feed point impedance to a 50-ohm transmission line?
Answer Options
- A) 50 ohms
- B) 62 ohms
- C) 75 ohms
- D) 90 ohms
Correct Answer: C
Explanation
A Quarter-Wave Transformer (or Q Section) is a short length of transmission line, exactly one quarter wavelength long, used to match two different resistive impedances. The characteristic impedance of the Q section (Z_Q) is determined by the geometric mean (square root of the product) of the two impedances being matched (Z_1 and Z_2).
The formula for the characteristic impedance of the Q section is Z_Q = \sqrt{Z_1 Z_2}. For matching Z_1 = 100 \Omega to Z_2 = 50 \Omega, the required impedance is Z_Q = \sqrt{100 \Omega \times 50 \Omega} = \sqrt{5000} \approx 70.7 \Omega. Of the available standard transmission line impedances, 75 ohms (which is close to 70.7 \Omega) is the most suitable choice for constructing the Q section.
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