Transformer Ratios, Losses, Cooling and Ratings

Transformer Principles, Efficiency & Cooling Classifications

A transformer is a static electromagnetic device that transfers alternating current electrical energy from one circuit to another at the same frequency through mutual electromagnetic induction, altering voltage and current levels proportionally.

The Ideal Transformer Relationship

An ideal transformer consists of two isolated windings wound on a common high-permeability laminated ferromagnetic core. The primary winding connects to the AC input source, while the secondary winding connects to the load. Neglecting internal losses:

Where:

• $V_p, V_s$ = Primary and secondary RMS terminal voltages
• $N_p, N_s$ = Number of turns in primary and secondary coils
• $I_p, I_s$ = Primary and secondary currents
• $a$ = Turns ratio

Fundamental Rule of Conservation of Energy: A step-up transformer increases voltage while proportionally reducing current; a step-down transformer decreases voltage while proportionally increasing current. Total apparent power remains constant: $S_p = V_p \cdot I_p = V_s \cdot I_s = S_s$.

Transformer Losses & Efficiency

Because transformers have zero moving parts or bearings, their operating efficiencies are high, often exceeding $98\%$. Internal energy losses are categorized into two primary forms:

1. Copper Losses ($I^2R$ Losses): Resistive heat generated by load currents flowing through the primary and secondary copper windings. Copper losses vary with the square of the connected electrical load current ($P_{\text{cu}} \propto I^2$).
2. Iron (Core) Losses: Losses that occur continuously in the magnetic core whenever the transformer is energized, at the applied voltage and frequency, with load-related changes and other losses considered:
   • Hysteresis Loss: Energy expended overcoming internal molecular friction as magnetic domains reverse alignment 120 times per second under $60\text{ Hz}$ AC. Minimized by constructing the core from grain-oriented silicon alloy steel.
   • Eddy Current Loss: Circulating electrical currents induced inside the conductive core iron itself by the alternating magnetic flux. Minimized by constructing the core from thin, stacked sheets of silicon steel (laminations), insulated from each other by a microscopic layer of baked varnish or oxide film. The laminations break up the circular conductive loops, raising electrical resistance and slashing eddy current heating.

Transformer Cooling Classifications

Internal heat generated by copper and core losses must be dissipated to prevent thermal breakdown of winding insulation. Transformers are classified by their cooling mechanisms under IEEE/CSA standards:

Turns-ratio example and operating limits

An ideal single-phase transformer has 1,000 primary turns and 100 secondary turns. With 600 V applied to its rated primary, the ideal secondary voltage is 60 V. If the secondary supplies 20 A, its apparent load is 1,200 VA and ideal primary current is 2 A. The frequency is unchanged. Real input includes magnetizing current and losses, so exact equality of input and output real power is an idealization.

Do not connect a transformer designed for AC directly to steady DC. Without alternating flux and the intended inductive impedance, current can become excessive and overheat the winding. Rated frequency, voltage, kVA, cooling condition and insulation limits all matter. An autotransformer shares part of a winding between circuits and does not provide the same electrical separation as a separate-winding transformer. Instrument transformers serve measurement/protection duties and have their own secondary safety requirements.

Source notes

Official scope and technical references checked 2026-10-17: Reference 1; Reference 2. Archived DOE handbooks are used for physical principles, not current Canadian legal requirements.