Difficulty: Easy
Correct Answer: Both A and R are correct and R is correct explanation of A
Explanation:
Introduction / Context:Matching in transmission lines eliminates reflections, maximizes power transfer, and ensures flat frequency response. Understanding why ZL = Z0 is fundamental in RF design.
Given Data / Assumptions:
Concept / Approach:When ZL = Z0, Γ = 0 and no power is reflected; all incident power is absorbed (and ideally delivered to the load). The definition of a matched termination is precisely that it equals Z0 and thus absorbs all incident power, providing the causal link from the Reason to the Assertion.
Step-by-Step Solution:
Set ZL = Z0 ⇒ Γ = 0.VSWR = (1 + |Γ|) / (1 − |Γ|) = 1 (perfect match).No standing waves form; all incident power is delivered to the matched load.Verification / Alternative check:Time-domain view: a wave reaching a matched load sees no discontinuity and thus no reflection; frequency-domain view: the impedance transformation along the line terminates in Z0 with flat response.
Why Other Options Are Wrong:
If R stated were false or unrelated, we would not obtain Γ = 0 or VSWR = 1.Only the given Reason directly explains why the Assertion holds in standard line theory.Common Pitfalls:
Confusing “maximum power transfer” Thevenin matching in lumped circuits with transmission-line matching; here, ZL must equal Z0 at the operating frequency.Final Answer:
Both A and R are correct and R is correct explanation of A
Discussion & Comments