current-scale-keeps-power-ideal - Electronic Circuits XIII & XIV: Power Supplies and Switching Energy Step by Step

A current-scale-keeps-power-ideal scan holds the voltage ratio fixed and varies the secondary current across three rows, checking that the primary current rises through the inverse turns ratio so P_in = P_out closes row by row. The arithmetic is exact only for the stated currents, voltages, powers, turns counts, and rows in the ideal lossless, perfectly coupled transformer model. Real supplies add winding resistance, leakage flux, diode forward variation, ripple, heating, probe/calibration limits, finite precision, and measurement uncertainty.

The ideal transformer current scale keeps input and output power equal. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Ideal power starts from the same voltage ratio

The checked secondary voltage is 8 V. The current scale is chosen so input power and output power close to the same value.

I_p=I_s{N_s \over N_p}

Every scanned current closes the same input-output ledger

Increasing secondary current raises both side powers together; the ideal transformer does not create an extra power row.

\begin{array}{c|c|c|c}I_s&I_p&P_{\text{out}}&P_{\text{in}}\\3\ \text{A}&1\ \text{A}&24\ \text{W}&24\ \text{W}\\6\ \text{A}&2\ \text{A}&48\ \text{W}&48\ \text{W}\\9\ \text{A}&3\ \text{A}&72\ \text{W}&72\ \text{W}\\\end{array}

Ideal current scale keeps power equal

The load side carries 3 A. The ideal transformer current scale makes the primary carry 1 A.

8\ \text{V}\cdot3\ \text{A}=24\ \text{W}=24\ \text{W}