Reflected load through a transformer — magnitude comparison: Is the equivalent (reflected) load seen at the primary always larger than the actual load connected to the secondary?

Introduction / Context:The concept of reflected impedance allows us to analyze a transformer-coupled load from the source side. Designers choose turns ratios to “transform” impedances to desired levels. It is a common misconception that the reflected load is always larger than the physical load; the truth depends entirely on the turns ratio.

Given Data / Assumptions:

• Ideal transformer with turns ratio a = Np/Ns.
• Load Z_L is connected across the secondary.
• Reflected impedance seen at the primary is Z_in = a^2 * Z_L.

Concept / Approach:Because Z_in = (Np/Ns)^2 * Z_L, the input impedance scales by the square of the turns ratio. If Np > Ns (step-down voltage), a > 1 and Z_in > Z_L. If Np < Ns (step-up voltage), a < 1 and Z_in < Z_L. Therefore, the reflected load can be larger, equal, or smaller, depending on the chosen ratio.

Step-by-Step Solution:

Verification / Alternative check:Example: Np = 100, Ns = 200 ⇒ a = 0.5. For Z_L = 100 Ω, Z_in = 0.25 * 100 = 25 Ω, clearly smaller than Z_L.

Why Other Options Are Wrong:“Correct” contradicts the square-law scaling. Statements limited to specific frequencies ignore that the impedance transformation is frequency-independent in the ideal model (though Z_L itself may be frequency-dependent).

Common Pitfalls:Forgetting the square on the turns ratio and assuming a linear scaling; mixing up primary and secondary labeling when applying a^2.

Final Answer:Incorrect