By S. Hussain Ather
Updated March 24, 2022
Fotokot197/iStock/GettyImages
Transformers are the heart of modern power distribution, converting alternating current (AC) to the voltages required by home appliances and industrial equipment. The key to their operation is the turns ratio – the proportion of coil turns in the primary winding compared to the secondary winding. Understanding this ratio is essential for designing efficient, reliable transformer systems.
The transformer turns ratio, denoted as TR, is calculated by dividing the number of turns in the primary winding (NP) by the number of turns in the secondary winding (NS):
TR = \frac{N_P}{N_S}
This ratio is directly proportional to the voltage ratio:
TR = \frac{V_P}{V_S}
Here, VP is the primary voltage and VS is the secondary voltage. The primary winding is the energized coil that induces a magnetic field; the secondary winding is the unenergized coil that receives the induced voltage.
For ideal transformers, the phase angles of the primary and secondary currents are equal (ΦP = ΦS), ensuring synchronous operation.
Because the input waveform is sinusoidal, the turns ratio directly dictates how the voltage changes as current passes from primary to secondary. Note that the term “ratio” in this context actually represents a fraction; for example, a 5:10 winding ratio equals a fraction of 1/2, halving the input voltage.
Depending on whether the secondary voltage is higher or lower than the primary, the transformer acts as a step‑up or step‑down device. A transformer with identical voltage on both sides is known as an impedance transformer, used to match circuit impedances or isolate sections.
At its core, a transformer consists of two coils wound around a ferromagnetic core. The core, often laminated to reduce eddy currents, provides a common magnetic path that links the primary and secondary windings. Insulated, thin metal sheets in the core reduce resistance and improve efficiency.
Energy losses arise from non‑ideal magnetic flux coupling and eddy currents. Modern transformers mitigate these losses through careful core design and material selection, achieving efficiencies above 95%.
When an AC voltage is applied to the primary coil, it generates a time‑varying magnetic field. The rate of change of magnetic flux (dΦ/dt) induces an electromotive force (EMF) in both windings, as described by Faraday’s Law:
V = N \frac{dΦ}{dt}
Because the magnetic flux linking both windings is essentially the same, the induced EMFs are directly proportional to their respective turn counts, leading back to the turns ratio equation.
Magnetic flux itself can be expressed as:
Φ = B A \cos\theta
For a simple solenoid, this simplifies to Φ = N B A where B is magnetic field strength and A is core cross‑sectional area.
Power plants generate electricity as DC or low‑frequency AC, which is converted to high‑frequency AC for transmission. Transformers step this voltage up for efficient long‑distance delivery and step it down for safe residential use. Along the way, distribution grids employ buses and circuit breakers to manage load and protect infrastructure.
Transformer efficiency is calculated as:
η = \frac{P_O}{P_I}
where PO is output power and PI is input power. The magnetizing current – required to establish the core’s magnetic field – is typically small relative to the load current, contributing to the high efficiency of modern designs.
Mutual inductance describes how a change in current in one winding induces a voltage in the other. When a load is applied to the secondary, the primary must increase its current to maintain the magnetic flux, as expressed in the primary voltage equation:
V_P = I_P R_1 + L_1 \frac{ΔI_P}{Δt} - M \frac{ΔI_S}{Δt}
Similarly, the secondary voltage satisfies:
V_S = I_S R_2 + L_2 \frac{ΔI_S}{Δt} + M \frac{ΔI_P}{Δt}
Here, M = \sqrt{L_1 L_2} is the mutual inductance between the coils.
These equations illustrate how load changes on the secondary influence the primary current, a critical consideration in transformer design and protection.
