This transformer design reference covers the main equations and design checks used to analyze simple AC transformers. Students need this cheat sheet to connect voltage, current, turns ratio, power transfer, losses, and efficiency in one organized place. It is useful for circuit analysis, engineering design projects, and troubleshooting transformer behavior.
The focus is on practical formulas that can be applied to ideal and real transformers.
The core idea is that a transformer changes AC voltage by electromagnetic induction, using a primary coil, secondary coil, and magnetic core. For an ideal transformer, the voltage ratio equals the turns ratio, while the current ratio changes in the opposite direction. Real transformers include winding resistance, core losses, leakage flux, heat limits, and voltage regulation.
Good design balances electrical performance, safety margin, insulation, core size, and efficiency.
Key Facts
- For an ideal transformer, Vs / Vp = Ns / Np, where V is voltage and N is the number of turns.
- For an ideal transformer, Ip / Is = Ns / Np, so current changes inversely with the turns ratio.
- Ideal power transfer is Pp = Ps, so Vp Ip = Vs Is when losses are ignored.
- The apparent power rating is S = V I, measured in volt-amperes, and it helps set winding and thermal limits.
- Transformer efficiency is efficiency = Pout / Pin x 100%, where Pin includes output power plus losses.
- Copper loss in a winding is Pcu = I^2 R, so heating increases rapidly as current increases.
- Voltage regulation can be estimated as regulation = (Vno-load - Vfull-load) / Vfull-load x 100%.
- The reflected impedance is Zp = (Np / Ns)^2 Zs, which lets a load on one side be analyzed from the other side.
Vocabulary
- Primary winding
- The coil connected to the input AC source of a transformer.
- Secondary winding
- The coil connected to the output load of a transformer.
- Turns ratio
- The ratio of the number of turns in the secondary coil to the number of turns in the primary coil.
- Core loss
- Power lost in the magnetic core due to hysteresis and eddy currents.
- Copper loss
- Power lost as heat in the transformer windings because the wire has electrical resistance.
- Voltage regulation
- The percent change in secondary voltage from no load to full load.
Common Mistakes to Avoid
- Using the turns ratio backward, which gives the wrong secondary voltage. Always match Vs / Vp with Ns / Np.
- Assuming current increases when voltage increases, which is wrong for an ideal transformer. If voltage steps up, current steps down for the same power.
- Ignoring VA rating, which can lead to overheating even when the voltage ratio is correct. Check S = V I against the transformer rating.
- Treating efficiency as 100% for real transformers, which ignores copper loss, core loss, and stray losses. Use efficiency = Pout / Pin x 100% for practical designs.
- Using DC formulas for transformer operation, which is wrong because transformers require changing magnetic flux. A basic transformer does not operate normally from steady DC.
Practice Questions
- 1 A transformer has Np = 500 turns, Ns = 100 turns, and Vp = 120 V. Find the secondary voltage.
- 2 An ideal transformer delivers 24 V at 5 A to a load. If the primary voltage is 120 V, find the primary current.
- 3 A transformer has a no-load secondary voltage of 13.2 V and a full-load secondary voltage of 12.0 V. Calculate the percent voltage regulation.
- 4 Explain why a step-up transformer must have lower secondary current than primary current when losses are ignored.