reflected-load-three-row-scan - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

A transformer reflects a secondary load into the primary by the square of the turns ratio, so the source sees a different effective resistance. The rows are exact ideal-transformer ledgers; real reflected loads shift with winding resistance, leakage inductance, core loss, magnetizing current, frequency, and measurement uncertainty.

Secondary load rows scan reflected resistance and primary load current. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Secondary load reflects through the turns ratio squared

The transformer row fixes the turns ratio, then the load row computes the primary equivalent.

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

Three load rows scan resistance, current, and reflected load

The turns ratio stays fixed while the secondary load 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}

The reflected resistance is downstream of the transformer source

The accepted row binds load resistance, turns ratio, and primary load current.

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