load-reflects-by-turns-ratio-squared - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

A load-reflects-by-turns-ratio-squared scan maps the secondary load back to the primary with R_p = R_s * (N_p / N_s)^2, so the source sees a turns-squared equivalent rather than a copied load value. The arithmetic is exact only for the stated load resistances, turns counts, voltages, currents, powers, and rows in the ideal transformer, perfect-coupling, no-magnetizing-current model. Real transformers add winding resistance, leakage inductance, core loss, magnetizing current, load tolerance, probe/calibration limits, finite precision, and measurement uncertainty.

The input equivalent load is a checked turns-squared ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Reflected load uses the square of the turns ratio

The secondary load is cited through the transformer source. The primary equivalent is not a copied caption.

R_p=R_s\left({N_p\over N_s}\right)^{2}

A larger secondary load reflects to a larger primary load

The turns ratio stays fixed while the secondary resistance changes.

\begin{array}{c|c|c|c}R_s&R_p&I_s&I_{p,\text{load}}\\3\ \text{ohm}&12\ \text{ohm}&2\ \text{A}&1\ \text{A}\\6\ \text{ohm}&24\ \text{ohm}&1\ \text{A}&\tfrac{1}{2}\ \text{A}\\12\ \text{ohm}&48\ \text{ohm}&\tfrac{1}{2}\ \text{A}&\tfrac{1}{4}\ \text{A}\\\end{array}

A load reflects by the turns ratio squared

The primary-side equivalent is checked against the cited transformer row, not merely against matching numbers.

R_p=R_s\left({N_p\over N_s}\right)^{2}=3\ \text{ohm}\left({4\over2}\right)^{2}=12\ \text{ohm}