Engineering
Ideal AC transformer: voltage ratio and reflected resistive load
Calculate step-down / step-up transformer turns ratio a = Np / Ns, secondary voltage Vs = Vp / a, current Is = Vs / ZL, and reflected primary impedance Zp = a^2 * ZL.
Why transformer voltage scales with a—while reflected impedance scales with a^2!
This exercise uses an ideal transformer with positive integer winding counts and a purely resistive secondary load. Voltages and currents are RMS magnitudes; winding polarity and phase are not represented. With a=Np/Ns, Vs=Vp/a and Is=a×Ip.
The load reflected to the primary is a²×Rload. For the resistive load used here, real power is Vs²/Rload. A complex load needs phasor calculations and power-factor treatment; do not interpret voltage times current as real watts for an arbitrary impedance.
The ideal equations omit winding resistance, leakage, magnetizing current, core losses, saturation and frequency limitations. This is a numerical exercise, not a winding, insulation or mains-wiring design. The step-up example gives a high voltage mathematically and does not establish safe operating ratings.
| Transformer Parameter | Cell | Step-Down Example | Electrical Output |
|---|---|---|---|
| Primary Np & Secondary Ns | B2 = 1,200, B3 = 100 | Turns ratio a = 12:1 | Step-Down (a > 1) |
| Primary Voltage Vp | B4 = 240 V RMS | Vs = 240 / 12 | 20 V RMS Secondary |
| Load Resistance ZL | B5 = 8 Ohms | Is = 20 / 8 = 2.50 A | Power P = 20 * 2.5 = 50 W |
| Reflected Primary Impedance | (B2 / B3)^2 * B5 | 12^2 * 8 = 144 * 8 | Zp = 1,152 Ohms (Ip = 0.2083 A) |
Secondary RMS Voltage Vs = Vp * (Ns / Np)
The example 1200:100 ratio produces 20 V RMS from 240 V RMS. Swapping to 100:500 produces 1200 V RMS in the ideal calculation.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(B2<=0,B3<=0,B2<>INT(B2),B3<>INT(B3),B4<0,B5<=0),"Invalid inputs",ROUND(B4 * (B3 / B2), 2)))Reflected Primary Impedance Zp = (Np / Ns)^2 * ZL (Ohms)
Squares the turns ratio before multiplying by secondary load impedance B5.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(B2<=0,B3<=0,B2<>INT(B2),B3<>INT(B3),B4<0,B5<=0),"Invalid inputs",ROUND(((B2 / B3) ^ 2) * B5, 2)))Try the example
Use the original values or change them to test your understanding.