flux-turns-voltage-three-row-scan - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

Transformer winding voltage comes from turns multiplying the shared flux-change rate, so both windings cite the same magnetic source. The flux-rate rows are exact ideal-coupling ledgers; real cores have finite permeability, leakage flux, hysteresis, eddy-current loss, winding resistance, saturation, and measurement tolerance.

Shared flux-rate rows make winding voltage proportional to turns. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Winding voltage is turns times shared flux rate

The flux change and interval stay fixed. Each winding multiplies the same rate by its turns.

V=N{\Delta\Phi\over\Delta t}

Three turn-pair rows scan the shared flux relation

The same flux-rate source feeds both winding voltage labels.

\begin{array}{c|c|c|c|c}N_p&N_s&\Delta\Phi/\Delta t&V_p&V_s\\2&1&1\ \text{V}&2\ \text{V}&1\ \text{V}\\4&2&1\ \text{V}&4\ \text{V}&2\ \text{V}\\6&3&1\ \text{V}&6\ \text{V}&3\ \text{V}\\\end{array}

The final flux row cites one shared source

One flux-change source and one interval generate both winding voltage labels.

6\cdot1\ \text{V}=6\ \text{V}\quad;\quad3\cdot1\ \text{V}=3\ \text{V}