EC-12.2 Transformers

What this is and why it exists

The transformer is the reason alternating current won the argument about how to distribute power.

It is also the simplest machine in this module, because nothing in it moves. That makes it the right place to meet magnetic coupling, referred impedances and the loss-and-efficiency reasoning that the rotating machines then reuse without re-explaining.

Everything in the next topic is easier because this one came first.

The vocabulary

• Turns ratio — the ratio of the numbers of turns on the two windings.
• Mutual flux — the magnetic flux that links both windings.
• Leakage flux — flux that links one winding only.
• Magnetising current — the current needed to establish the flux, drawn even with no load.
• Core loss — loss in the magnetic material, nearly independent of load.
• Copper loss — loss in the winding resistance, growing as the square of current.
• Regulation — the fall in output voltage from no load to full load.
• Open-circuit test — a test at rated voltage with the secondary unloaded.
• Short-circuit test — a test at rated current with the secondary shorted.

The mental model

Two windings on one magnetic core. A changing current in the first produces a changing flux, and that flux, passing through the second, induces a voltage in it.

The induced voltages are in the ratio of the numbers of turns. Energy is conserved, so the currents are in the inverse ratio. Those two sentences are the ideal transformer, and a surprising amount of practical work needs nothing more.

The most useful consequence is not the voltage change but the impedance change. A load on the secondary appears, from the primary, multiplied by the square of the turns ratio.

That single result makes a transformer a matching device. It is why a transformer appears in an audio output stage, in a measurement bridge, and at every stage of a power system. Getting the square right is the part people forget.

Now the practical model, which adds four elements to the ideal one, each corresponding to something physical.

Winding resistance is in series and causes copper loss and a voltage drop. Leakage reactance represents flux that links one winding only and therefore transfers no power. Magnetising inductance is in parallel and represents the current needed to establish the flux, drawn even when nothing is connected. And a parallel resistance represents core loss.

Two tests find all four, and the elegance of the pair is worth appreciating. The open-circuit test applies rated voltage with nothing connected to the secondary. Almost no current flows in the windings, so copper loss is negligible, and what is measured is the magnetising path and the core loss.

The short-circuit test applies enough voltage to drive rated current into a shorted secondary. That voltage is small, so the flux and therefore the core loss are negligible, and what is measured is the winding resistance and leakage.

Each test isolates one half of the model by making the other half negligible. That is a technique worth carrying beyond transformers.

Losses then give efficiency, and the shape of the efficiency curve is the part that matters in practice. Core loss is nearly constant, because the flux is set by the applied voltage rather than by the load. Copper loss grows as the square of the current.

Efficiency is highest at the load where the two are equal. That is usually well below the rated load. A transformer expected to run lightly most of the time is therefore not designed for peak efficiency at its rating.

Regulation is the last idea. The output voltage falls as load increases, because of the winding resistance and the leakage reactance. Expressed as a fraction of the rated voltage, that fall is what a supply agreement actually specifies. It decides whether equipment at the far end still works at full load.

What you should now be able to explain or do

• Derive the voltage and current ratios from the flux linking both windings.
• Refer an impedance across the turns ratio and explain why the square appears.
• Name the four elements of the practical equivalent circuit and what each represents.
• Explain how each of the two tests isolates half of that model.
• Say why efficiency peaks below rated load and what that means for sizing.
• Define regulation and say what it decides for equipment at the far end.

Check yourself