Transformers:
The Power of Induction.

A transformer has at least two windings linked by a changing magnetic field. The input winding is the primary; the output winding is the secondary. Their electric circuits can be separate, although both share magnetic flux in a common core or path.

A changing magnetic flux induces voltage: e = −N·dΦ/dt for an ideal winding. More turns produce more induced voltage for the same changing flux. The minus sign expresses Lenz’s law: induced effects oppose the change producing them.

For an ideal transformer driven with an appropriate AC waveform, Vs/Vp = Ns/Np. Double the secondary turns, double its RMS voltage in this model. Fewer secondary turns step the voltage down. Voltage ratio alone does not tell you the available current or the insulation rating.

In an ideal loaded transformer, Vp·Ip = Vs·Is for RMS values with the simplified resistive-load assumptions used here. Current ratio is inverse to turns ratio: Is/Ip = Np/Ns. A higher voltage does not mean free extra power; it generally means lower available output current for the same input power.

Winding resistance causes heating; the core has hysteresis and eddy-current losses; flux leakage and magnetizing current affect behavior. Efficiency η = Pout/Pin is less than 100%. An unloaded real transformer still draws some current. This course models an ideal voltage ratio and estimates input power from an adjustable efficiency; it is not a device design tool.

An ordinary transformer does not transfer continuous power from steady DC. A switching power converter can chop DC into a changing waveform for a suitable transformer. Applying DC to a winding not designed for it can overheat or saturate the core. The ideal waveform display in the workbench assumes sinusoidal AC; it does not predict saturation or switch transients.

Core material, cross-section, winding design, insulation, and frequency set safe operating limits. An isolation transformer can have electrically separated windings, but an autotransformer shares a winding and does not provide isolation. The relative winding polarity (dot convention) determines whether connected secondary voltages aid or oppose.

An ignition coil uses magnetically coupled windings, but real ignition action involves charging magnetic energy and rapidly interrupting primary current to create a transient high voltage. It cannot be accurately predicted by applying the workbench’s steady sinusoidal transformer ratio to a constant 12 V battery.

Examples include high-frequency transformers inside certain isolated DC–DC converters or onboard chargers, inductive coupling in some communications or sensor arrangements, and transformers in service/test equipment. Vehicle architecture varies: not every DC–DC converter uses a transformer, and many are non-isolated.

Before condemning a transformer, verify the specified input type, switching/AC command, protection status, output load, connectors, and applicable OEM procedure. A continuity check can reveal an open winding, but normal winding resistance cannot rule out shorted turns, insulation faults, weak drive, or loaded-voltage problems.