NEIEP Electrical Theory and Application 430 Practice Exam 2026 – Complete Study Resource

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How does a transformer reflect impedance and why is it important for design?

Z_in = a^2 Z_load

The key idea is that a transformer reflects impedance by the square of its turns ratio. For an ideal transformer, the voltage and current relate as Vp/Vs = a and Ip/Is = 1/a, where a = Np/Ns is the turns ratio. The impedance seen looking into the primary is Z_in = Vp/Ip. Substituting the relationships gives Z_in = (a Vs) / (Is / a) = a^2 (Vs/Is) = a^2 Z_load. So the load on the secondary appears at the primary as Z_load scaled by a^2.

This matters in design because it lets you match source impedance to the load by choosing the appropriate turns ratio, controlling voltage and current levels and maximizing power transfer. In real transformers, non-idealities like winding resistance and leakage inductance modify this, but the basic square-law reflection is the foundational idea.

Z_in = Z_load / a^2

Z_in = Z_load

Z_in = a Z_load

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