Power transfer via transformers — matching condition: Is maximum power transfer obtained when the primary winding’s impedance equals the secondary winding’s impedance, regardless of source and load, or when the load reflected to the primary matches the source (Thevenin) impedance?

Introduction / Context:
Transformers are used to match impedances between a source and a load. The classic maximum power transfer theorem states that a load receives maximum power when it equals the complex conjugate of the source’s Thevenin impedance (for purely resistive sources, equal resistance). In transformer-coupled systems, this condition is met when the load, reflected to the primary through the turns ratio, matches the source impedance—not when the primary and secondary impedances are arbitrarily made equal to each other.

Given Data / Assumptions:

• Linear, ideal transformer model for first-order reasoning.
• Source characterized by a Thevenin impedance Z_S and Thevenin voltage V_S.
• Load Z_L connected to the transformer secondary.

Concept / Approach:
Reflected impedance: Z_reflected_to_primary = (N_P/N_S)^2 * Z_L. Maximum power transfer condition: Z_reflected_to_primary ≈ Z_S (or Z_S* for complex matching). Therefore, the engineering task is to choose the turns ratio such that the load, when reflected, equals the source impedance. Simply equating “primary impedance” and “secondary impedance” is meaningless because they exist on different sides and are related by the square of the turns ratio; equality between them does not guarantee matching to the source.

Step-by-Step Solution:

Verification / Alternative check:
Example: source 50 Ω, load 200 Ω. Choose N_P/N_S = sqrt(50/200) = 1/2 so that the 200 Ω load reflects as 50 Ω; maximum transfer occurs. Primary and secondary impedances are not “equal” in absolute terms; they are related by the square of turns ratio.

Why Other Options Are Wrong:
“Correct” contradicts the theorem. Conditions like 1:1 transformers, resonance, or ideal sources do not change the fundamental matching requirement.

Common Pitfalls:
Assuming equal impedances on both windings ensures maximum power. The correct condition is source matching to the load as seen through the transformer.

Final Answer:
Incorrect