February 22, 2025

Transformers

A transformer transfers electrical energy between circuits using electromagnetic induction. Two coils wound around a shared magnetic core — AC in one, AC out the other, with the voltage ratio determined by the turns ratio. No moving parts, high efficiency, and the ability to provide electrical isolation between circuits. Transformers are why AC won over DC for power distribution, and why they're still in every mains-powered device.

How They Work

AC in the primary coil creates a changing magnetic flux in the core. That changing flux induces a voltage in the secondary coil. The ratio of voltages equals the ratio of turns:

V_p / V_s = N_p / N_s

V_p = primary voltage
V_s = secondary voltage
N_p = number of turns in primary
N_s = number of turns in secondary

Power is conserved (assuming ideal transformer, no losses):

V_p × I_p = V_s × I_s

Therefore: I_p / I_s = N_s / N_p

Step up voltage, step down current — and vice versa. If you step voltage up 10×, current drops 10×. This is the principle that makes long-distance power transmission practical: high voltage, low current, low resistive losses.

Example Calculations

Step-down transformer:
Primary: 120V AC, 200 turns
Secondary: 100 turns

V_s = V_p × (N_s / N_p)
V_s = 120V × (100/200) = 60V

If secondary current = 2A:
Primary current = I_s × (N_s/N_p) = 2A × (100/200) = 1A

Types

  • Step-down — more primary turns than secondary. Used in power supplies to reduce mains voltage to something useful. The transformer in a wall wart is a step-down transformer.
  • Step-up — more secondary turns than primary. Used in power transmission, CRT televisions (high-voltage supply), ignition coils.
  • Isolation transformer — 1:1 turns ratio. No voltage change, but provides galvanic isolation between primary and secondary. Used in medical equipment, lab bench setups, and anywhere you need to break ground loops or protect against shock.
  • Autotransformer — a single winding with taps. Primary and secondary share part of the winding. Smaller and cheaper than a separate-winding transformer for the same power, but no isolation. Variacs (variable autotransformers) use this principle.
  • Current transformer (CT) — a toroidal transformer where the primary is a conductor passing through the centre. Used for measuring large AC currents safely — the secondary current is proportional to the primary but at a safe level.

Real Transformers — Non-Ideal Behaviour

Ideal transformers don't exist. Real ones have:

  • Copper loss — resistance in the windings dissipates power as heat (I²R). More current, more heat.
  • Core loss — hysteresis and eddy current losses in the core material. Eddy currents are why transformer cores are laminated rather than solid iron.
  • Leakage inductance — not all flux from the primary links to the secondary. This leakage inductance causes voltage regulation issues under load.
  • Magnetising current — the primary draws some current even with no load, to maintain the core flux.

Good power transformer efficiency is typically 95–99%. Small signal transformers (audio, RF) are optimised for frequency response rather than efficiency.

Impedance Transformation

A transformer doesn't just transform voltage and current — it transforms impedance. The impedance seen looking into the primary equals the secondary impedance multiplied by the turns ratio squared:

Z_primary = Z_secondary × (N_p / N_s)²

This is used in audio for impedance matching — connecting a low-impedance speaker to a high-impedance amplifier output stage. Valve (tube) amplifiers use output transformers specifically for this reason.