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.
Understanding Transformer Design Reference
The magnetic core has a limit. Each cycle of the supply creates changing magnetic flux in the core, and that flux must stay below the saturation level of the material. If the primary is connected to a voltage that is too high, or to a frequency that is too low, the flux becomes too large.
The core then saturates. Primary current can rise sharply even with no useful load connected. This can overheat the winding, trip protection, or damage insulation.
Designers therefore choose enough core area and enough primary turns for the lowest intended frequency. A transformer made for fifty hertz should not be used directly on a much lower frequency supply at its rated voltage.
Core loss has two main causes. Hysteresis loss occurs because the magnetic domains in the steel repeatedly change direction. Eddy current loss occurs because changing flux induces circulating currents inside the core itself.
Thin insulated laminations reduce eddy currents by breaking up their path. Ferrite cores are common at high frequencies because their electrical resistance is much higher than steel. Core loss can occur even when the secondary is open, so a transformer may feel warm while doing little external work.
Winding loss behaves differently because it grows with load current. Resistance increases as copper gets hotter, creating a feedback effect in which heat causes more resistance and more heating.
A load does not always use electrical power in the same way. A heater mostly converts input power to heat, so its power factor is close to one. Motors, chargers, and some lighting circuits can draw current that is out of step with voltage.
Their volt-ampere demand may be much larger than the watts they consume. This matters because winding heating depends mainly on current, not just useful watts. A transformer must be rated for the required volt-amperes.
Its internal winding resistance and leakage magnetic field create an internal voltage drop under load. Loads with poor power factor can produce a larger drop, which is why a measured secondary voltage may differ from the label value.
A practical design check starts with the load voltage, load current, supply frequency, and required isolation level. The designer then selects a core, calculates a safe volts per turn value, and chooses winding turns. Wire size must carry the expected current without excessive temperature rise.
The coil window must physically fit the copper, insulation layers, tape, and spacing. Insulation is not optional. Primary and secondary windings need adequate separation to prevent a dangerous fault path.
Testing should include no load current, secondary voltage at full load, temperature after extended operation, and insulation checks. Measurements near mains supplies require proper probes, fuses, enclosed terminals, and trained supervision.