Assertion–Reason (Impedance Matching with Stubs): Impedance matching on a transmission line can be achieved using reactive stubs. Reason: A double-stub tuner is specifically used for impedance matching when the signal frequency varies widely.

Introduction:
Single- and double-stub tuners are classic tools for impedance matching on RF transmission lines. This question asks whether stubs accomplish matching and whether double-stub tuners are the solution for signals with varying frequency.

Given Data / Assumptions:

• Lossless or low-loss lines for conceptual clarity.
• Reactive stubs (short- or open-circuited) provide controllable susceptance/ reactance.
• Double-stub tuners allow position-fixed matching using two adjustable stubs at specified spacings.

Concept / Approach:

Stubs can transform impedances by adding a controlled reactive element that cancels the load’s reactive part and transforms the resistive part to match Z0. A double-stub arrangement is helpful when the load position is not adjustable or unknown; however, like most lumped/distributed matching networks, a double-stub solution is inherently narrowband. It is not “specifically for varying frequency”; instead, it enables matching at a chosen frequency (or narrow band) when the stub locations are constrained.

Step-by-Step Solution:

Verification / Alternative check:

Smith-chart constructions show single-stub solutions at specific positions; adding a second stub relaxes position constraints while remaining frequency-sensitive.

Why Other Options Are Wrong:

• Options a, b: misstate the explanatory role of R.
• Option d: claims A is wrong, contradicting standard practice.
• Option e: both are not wrong; A is correct.

Common Pitfalls:

Assuming “more stubs = broadband.” Broadband behavior requires multi-section transformers or wideband networks, not simply adding a second narrowband stub.

Final Answer:

A is correct but R is wrong