Transformer Turns Ratio & Ideal Model
The transformer turns ratio refers to the ratio of the number of windings in the primary coil to the number of windings in the secondary coil of a transformer. This ratio determines how voltage and current are transformed between the two coils. In the ideal transformer model, energy losses are neglected, and the input power equals the output power, allowing for a direct relationship between voltage, current, and turns ratio, following the equations Vp/Vs = Np/Ns and Ip/Is = Ns/Np.
Transformer Turns Ratio & Ideal Model
The transformer turns ratio refers to the ratio of the number of windings in the primary coil to the number of windings in the secondary coil of a transformer. This ratio determines how voltage and current are transformed between the two coils. In the ideal transformer model, energy losses are neglected, and the input power equals the output power, allowing for a direct relationship between voltage, current, and turns ratio, following the equations Vp/Vs = Np/Ns and Ip/Is = Ns/Np.
💡 Key Takeaways
- Understand how the transformer turns ratio determines the voltage and current scaling between primary and secondary.
- Learn the ideal transformer model and its assumptions (perfect coupling, negligible magnetizing current, no core losses).
- Use the turns ratio to relate voltages, currents, and impedances across windings (V1/V2 = N1/N2, I1/I2 = N2/N1, Z_in = a^2 Z_load).
- Recognize practical limitations and when the ideal model breaks down (leakage inductance, winding resistance, core losses, saturation).
❓ Frequently Asked Questions
What is the transformer turns ratio?
The turns ratio (a) is Np/Ns, the primary turns divided by the secondary turns. It sets voltage and current transformation: Vs = Vp / a, Is = Ip × a, and Pp = Ps in an ideal transformer.
What does the ideal transformer model assume?
It assumes perfect coupling (k = 1), zero winding resistance, and no core losses. Under this model, Vp/Vs = Np/Ns, Ip/Is = Ns/Np, and power is conserved (Pp = Ps).
How can you tell if the transformer will step up or step down based on turns?
If Np > Ns (a > 1) it steps down the voltage (Vp > Vs). If Np < Ns (a < 1) it steps up the voltage (Vs > Vp).
How do you reflect an impedance from the secondary to the primary?
The primary sees Z_in = (Np/Ns)^2 × Z_L. This lets you analyze the circuit as if the primary were connected to an impedance scaled by the square of the turns ratio.
What is the power relationship in an ideal transformer?
In an ideal transformer, Pp = Vs × Is = Vp × Ip; input power equals output power (no losses).