Assertion (A): A half-wavelength (λ/2) transmission line section can be used as a 1:1 transformer to present the load directly at the input. Reason (R): For a lossless line, the input impedance of a half-wavelength section equals the load impedance (Z_in = Z_L) because the impedance repeats every λ/2. Choose the correct option evaluating A and R.

Introduction:Transmission-line sections are often used as impedance transformers. A special case is a half-wavelength (λ/2) section, which repeats impedances seen at its load end. This question checks whether λ/2 can act as a 1:1 transformer and why.

Given Data / Assumptions:

• Lossless or low-loss uniform line
• Electrical length = λ/2 at the frequency of interest
• Characteristic impedance Z0 is real

Concept / Approach:The general input impedance of a line is Z_in = Z0 * (Z_L + j Z0 tan(βl)) / (Z0 + j Z_L tan(βl)). For l = λ/2, βl = π, and tan(π) = 0, simplifying Z_in to Z_L. Hence, a λ/2 line repeats the load impedance at its input, acting as a 1:1 transformer.

Step-by-Step Solution:

Verification / Alternative check:On a Smith chart, a λ/2 rotation returns any impedance point to itself, confirming Z_in = Z_L at λ/2.

Why Other Options Are Wrong:

• B: R is the correct causal explanation, not incidental.
• C: R is not wrong; it is the core principle.
• D: A is not wrong; λ/2 repetition is standard theory.

Common Pitfalls:Applying λ/2 behavior off-frequency (where electrical length ≠ λ/2); ignoring losses which slightly perturb equality in real lines.

Final Answer:Both A and R are correct and R is correct explanation of A