AC maximum power transfer – Complex-conjugate matching Statement: In an AC circuit, power delivered to the load is maximized at the frequency where the load impedance is the complex conjugate of the source (output) impedance. Is this correct?

Introduction / Context:
Maximum power transfer is a cornerstone in RF, audio, and power electronics. In AC systems with reactance, matching is not just about magnitudes; the phase (reactive part) must be addressed via conjugation. This question confirms the complex-conjugate matching condition for peak power delivery.

Given Data / Assumptions:

• Linear AC circuit analyzed at a specific frequency using phasors.
• Source (output) impedance Zs = Rs + jXs, load impedance ZL = RL + jXL.
• Goal: maximize average power absorbed by the load.

Concept / Approach:

The average power to the load is maximized when ZL = Zs* (the complex conjugate of Zs). This cancels reactive parts (XL = −Xs) and matches resistive parts (RL = Rs), maximizing the magnitude of load voltage/current product that contributes to real power without reactive circulation.

Step-by-Step Solution:

Verification / Alternative check:

At the match: input seen by source is purely resistive; voltage standing wave ratio is minimized in transmission-line terms, confirming peak power transfer.

Why Other Options Are Wrong:

“False” and “must equal exactly (not conjugate)” ignore reactive cancellation. “True only for resistive sources” is unnecessary; the conjugate form explicitly covers reactive sources.

Common Pitfalls:

Matching magnitudes only; forgetting that reactive parts must cancel to avoid circulating reactive power and suboptimal real power absorption.

Final Answer:

True.