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Ideal Transformer · Voltage-Current Transformation and Impedance Transformation

Transformer with adjustable turns ratio \(n = N_2/N_1\) | Side-by-side display of primary and secondary voltage/current waveforms
Verify \(V_2/V_1 = n\), \(I_2/I_1 = 1/n\), and the impedance transformation \(Z_{in} = Z_L / n^2\)

Transformer Parameters

2.0
0.1 (Step-down)5.0 (Step-up)

\(n > 1\): Step-up transformer

100 V
10 V250 V
50 Hz
40 Hz60 Hz
500 Ω
10 Ω5000 Ω

Theoretical Relations

\(V_2 = n \cdot V_1\) — V
\(I_2 = I_1 / n\) — A
\(Z_{in} = R_L / n^2\) — Ω

Actual Values (RMS)

\(V_1\)
—
\(V_2\)
—
\(I_1\)
—
\(I_2\)
—
\(P_{in}\)
—
\(P_{out}\)
—
\(Z_{in}\) (Reflected Impedance)
—

Voltage Waveforms · \(v_1(t)\) and \(v_2(t)\)

\(V_2/V_1 = n\)
🔵 Primary voltage \(v_1(t)\)  |  🔴 Secondary voltage \(v_2(t)\)  |  Ideal transformer voltages are in phase, amplitude ratio = \(n\)

Current Waveforms · \(i_1(t)\) and \(i_2(t)\)

\(I_1/I_2 = n\)
🟢 Primary current \(i_1(t)\)  |  🟠 Secondary current \(i_2(t)\)  |  Ideal transformer currents are in phase, amplitude ratio = \(1/n\)

Relation Verification

\(V_2 / V_1 = n\) —
\(I_1 / I_2 = n\) —
\(P_{out} = P_{in}\) —

📐 Ideal Transformer Theory

\(V_2/V_1 = N_2/N_1 = n\)
\(I_2/I_1 = N_1/N_2 = 1/n\)
\(Z_{in} = V_1/I_1 = Z_L / n^2\) (reflected impedance)
Ideal transformer has no loss: \(P_{in} = P_{out}\)

⚡ Characteristics and Key Observations

• Ideal transformer maintains constant power; voltage and current transformations are reciprocals.
• \(n > 1\) step-up: secondary voltage increases, current decreases.
• \(n < 1\) step-down: secondary voltage decreases, current increases.
• Reflected impedance \(Z_{in}\) depends on load \(R_L\) and turns ratio \(n\).