In this guide
Every power supply you have ever opened contains a transformer, and every transformer obeys one beautifully simple rule: the ratio of voltages equals the ratio of turns. It sounds trivial — until your project needs 12V at 3A from a 230V mains transformer and you have to decide between a 15-0-15 and an 18-0-18 secondary, or your examiner asks why the turns ratio is 10:1 but the measured voltage ratio is 9.7:1.
This guide explains the turns ratio properly: the ideal law, why real transformers deviate from it, how current and impedance transform, tap changers, and the worked calculations you'll actually use.
The ideal law
For an ideal transformer with N₁ primary turns and N₂ secondary turns:
V₁/V₂ = N₁/N₂ = n (the turns ratio)
I₁/I₂ = N₂/N₁ = 1/n (current transforms inversely)
Z₁/Z₂ = (N₁/N₂)² = n² (impedance transforms as the square)
Power is conserved (minus losses): V₁I₁ ≈ V₂I₂.
The square-law for impedance is the one students forget and engineers use most: a transformer doesn't just change voltage, it changes the impedance the source sees. This is why transformers are used for impedance matching (audio, RF) and why a short circuit on the secondary looks like a small impedance on the primary — scaled by n².
Why real transformers deviate from the ideal
Measure a real 230V/12V transformer and you'll typically read 12.5–13V on no load. Three reasons:
- Regulation (voltage drop under load). Winding resistance and leakage reactance drop voltage as load current rises. A small 50VA transformer might have 10–15% regulation; a large distribution transformer 2–4%. Manufacturers deliberately wind the secondary slightly high so the full-load voltage lands on the nameplate value.
- Magnetizing current. A small no-load current flows to magnetize the core — it doesn't affect the ratio, but it's why the primary draws current with the secondary open.
- Losses. Copper loss (I²R in windings) and iron loss (hysteresis + eddy currents in the core) mean efficiency is 95–99% for distribution transformers, lower for tiny ones.
Note: The turns ratio is a property of the windings; the voltage ratio you measure includes regulation. If an examiner asks for the turns ratio, give N₁/N₂ from the winding data or the no-load voltage ratio — and mention regulation as the reason loaded measurements differ.
Worked examples
Example 1 — selecting a transformer for a linear power supply. You need a regulated 12V DC at up to 2A using a bridge rectifier and a 7812 regulator. The 7812 needs ~14.5V minimum at its input (12V + dropout + ripple headroom). After the bridge rectifier, Vdc ≈ Vsec(rms) × 1.414 − 1.4V (two diode drops). Solving: Vsec ≥ (14.5 + 1.4)/1.414 ≈ 11.2V rms at full load. With ~10% regulation on a small transformer, choose a 12-0-12 or 15-0-15, 36VA transformer (12V × 3A ≈ 36VA covers the 2A DC with rectifier crest factor). The 15V version runs the regulator hotter — calculate heatsink dissipation: (Vdc − 12) × 2A.
Example 2 — current on the primary. A 1kVA, 230V/24V transformer at full load: secondary current I₂ = 1000/24 ≈ 41.7A. Primary current I₁ = 1000/230 ≈ 4.35A (equivalently 41.7 × 24/230). Size the primary fuse/MCB for ~4.35A plus inrush margin — a slow (type D) characteristic or a time-delay fuse, because of magnetizing inrush.
Example 3 — impedance reflection. A 24V, 100W heater (R = 24²/100 = 5.76Ω) fed through a 230/24V transformer (n = 9.58) looks like R₁ = 5.76 × 9.58² ≈ 529Ω to the 230V mains. Mains current = 230/529 ≈ 0.435A, and 230 × 0.435 ≈ 100W. The transformer is transparent to power — it just rescales the V-I pair.
Example 4 — inrush current. At switch-on, if the core happens to be at residual magnetism opposing the first half-cycle, the core saturates and the primary draws a magnetizing inrush of 8–15× rated current for a few cycles. This is why transformer primaries need slow-blow fuses and why large transformers use point-on-wave switching or pre-insertion resistors. Your 1kVA example above can momentarily pull 40–60A — a fast 6A MCB will nuisance-trip.
Tap changers: adjusting the ratio in service
Real networks need voltage control, so distribution transformers carry off-circuit taps (typically ±2.5%, ±5% on the HV winding — adjusted de-energized with a tap switch), and large power transformers use on-load tap changers (OLTC) that shift taps without interrupting supply. Moving to a higher tap (more HV turns) lowers the secondary voltage, since V₂ = V₁ × N₂/N₁.
For student projects, the takeaway: if your site's mains runs chronically high (250V) or low (200V), a transformer with taps lets you correct it — and it's a legitimate viva talking point for any transformer-based project.
Three-phase transformer connections
| Connection | Voltage ratio | Notes |
|---|---|---|
| Dyn11 | V_LL(primary)/V_LL(secondary) = N₁/N₂ (with √3 factors) | Delta primary, star secondary with neutral — the standard distribution transformer; the "11" is the 30° phase shift (clock notation) |
| Yyn0 | Same magnitude, 0° shift | Needs a neutral on both sides; zero-sequence issues |
| Dyn (general) | Line ratio = turns ratio | Delta blocks triplen harmonics and zero-sequence — one reason it's the distribution favorite |
Worked check — Dyn11, 11kV/433V: turns ratio per phase = (11000/√3)/(433/√3) = 11000/433 ≈ 25.4. The √3 cancels because both sides are line-to-line — a handy simplification examiners love to test.
Instrument transformers: ratio as a measuring tool
Current transformers (CTs, e.g. 200/5A) and potential transformers (PTs, e.g. 11kV/110V) are transformers whose entire job is an accurate ratio. Two rules that differ from power transformers:
- A CT secondary must never be open-circuited under load — with the secondary open, all primary ampere-turns become magnetizing ampere-turns, the core saturates, and kilovolts appear across the secondary. Always short the secondary first.
- CT accuracy is specified at rated burden (the connected load in VA) — hang too much burden on it and the ratio error grows.
Warning: Transformer primaries connect to mains or HT. Inrush, stored energy, and (for CTs) open-secondary voltages are all genuinely dangerous. Do transformer wiring, tap changing and CT shorting de-energized and under supervision. Treat any 11kV-side work as restricted to qualified personnel — observe, don't touch.
Common mistakes
- Using the loaded voltage ratio as the turns ratio in calculations — correct for regulation first, or state your assumption.
- Forgetting the √3 in three-phase line vs phase quantities (though it cancels in Dyn line-ratio, it doesn't in star/delta current conversions).
- Sizing the primary fuse at rated current with a fast characteristic — inrush will trip it. Use slow-blow/time-delay.
- Ignoring VA derating for rectifier loads — a transformer feeding a capacitor-input rectifier should be rated ~1.5–1.6× the DC power because of harmonic crest factor.
- Assuming efficiency is constant — maximum efficiency occurs near the load where copper loss equals iron loss (typically 50–75% of full load), a standard exam derivation.
Where to go from here
- Transformer Architecture Explained for Students — the other transformer guide: construction, core types and losses in depth.
- Single-Phase vs Three-Phase Motors — where transformer secondaries usually end up.
- Three-Phase Wiring Basics — the supply side your transformer connects to.
- How to Use a Multimeter — verifying transformer voltages safely during testing.
- More machines topics in the Electrical branch hub.