Winding Ratios
Part of Power Transmission
How the ratio of turns in a transformer’s primary and secondary windings determines output voltage, current, and impedance.
Why This Matters
A transformer is a machine for changing voltage. Its only adjustable parameter — the one that determines everything about its electrical behavior — is the ratio of turns in its two windings. Get the ratio right and you have exactly the step-up or step-down ratio you need. Get it wrong and you either over-voltage your load or transmit at too low a voltage to be useful.
Understanding winding ratios lets you do three things. First, design a transformer from scratch for any voltage conversion you need. Second, rewind an existing transformer core for a different application. Third, diagnose whether a scavenged transformer is suitable for your purpose before you wire it into a system. The math is simple — a ratio problem — but its implications flow through every aspect of transformer construction.
The Fundamental Relationship
A transformer works by mutual induction. AC current in the primary winding creates a changing magnetic flux in the core. That changing flux passes through the secondary winding and induces a voltage in it. The induced voltage is proportional to the number of turns the flux passes through.
If the primary has N_p turns and the secondary has N_s turns, the voltage ratio is:
V_s / V_p = N_s / N_p
Rearranging:
V_s = V_p × (N_s / N_p)
This equation is exact for an ideal transformer (one with no losses). Real transformers deviate slightly, but for well-made designs the error is under 2-3%.
Step-up transformer: More secondary turns than primary turns → secondary voltage is higher than primary voltage.
Step-down transformer: Fewer secondary turns than primary turns → secondary voltage is lower than primary voltage.
Isolation transformer: Same turns on both sides (1:1 ratio) → same voltage, but galvanic isolation between circuits. Used for safety and noise rejection.
Current Follows the Inverse Ratio
Power cannot be created by a transformer. Input power (nearly) equals output power:
P_in = P_out
V_p × I_p = V_s × I_s
Rearranging:
I_s / I_p = V_p / V_s = N_p / N_s
Current transforms by the inverse of the voltage ratio. If voltage steps up by 10, current steps down by 10.
This is the crucial insight for transmission line design. A 10:1 step-up transformer reduces current to 1/10th of its original value. Since I²R losses depend on current squared, a 10:1 current reduction means 100:1 reduction in transmission losses.
Summary of transformation ratios:
| Ratio (N_s : N_p) | Effect on Voltage | Effect on Current |
|---|---|---|
| 2:1 (step up) | ×2 | ÷2 |
| 5:1 (step up) | ×5 | ÷5 |
| 10:1 (step up) | ×10 | ÷10 |
| 1:1 (isolation) | ×1 | ×1 |
| 1:2 (step down) | ÷2 | ×2 |
| 1:10 (step down) | ÷10 | ×10 |
Calculating Turns for a Target Voltage
Given: You have a generator producing 24V AC. You want to transmit at 240V. How many turns on the secondary if the primary has 50 turns?
V_s / V_p = N_s / N_p
240 / 24 = N_s / 50
10 = N_s / 50
N_s = 500 turns
Given: You want to step 240V transmission voltage back down to 12V for battery charging. Primary (transmission side) has 400 turns. How many secondary turns?
V_s / V_p = N_s / N_p
12 / 240 = N_s / 400
0.05 = N_s / 400
N_s = 20 turns
A secondary of only 20 turns — far fewer than the primary. This is normal for large step-down ratios.
Volts Per Turn: The Design Parameter
When designing a transformer from scratch (or rewinding a core), you cannot simply choose any number of turns for the primary. The core has a maximum flux capacity — adding too few turns causes it to saturate (the core cannot handle the magnetic field and the transformer draws excessive current and distorts).
The relationship is:
Volts per turn = V_p / N_p = (approximately) 4.44 × f × B_max × A_core
f = frequency (Hz)
B_max = maximum flux density (Tesla) — about 1.2T for silicon steel, 1.6T for good electrical steel
A_core = cross-sectional area of the core (m²)
This formula tells you the minimum number of turns for the primary given your core size and frequency. Use it to determine N_p, then calculate N_s from the turns ratio.
Practical shortcut for salvage transformers: A transformer already has N_p set. Measure the primary turns-per-volt by winding a test secondary. Wind exactly 10 turns on the core, energize the primary from your AC source, and measure the secondary output voltage. Then:
Volts per turn = V_test / 10
Turns needed for target voltage = V_target / (volts per turn)
This is the most reliable method when dealing with a core of unknown specification. You measure what the core actually produces rather than calculating from material properties.
Winding Sequence and Coupling
The coupling between primary and secondary depends on how they are wound. For best coupling:
- Both windings should be on the same core leg
- Secondary should be wound directly over the primary (with insulation between)
- Concentric winding (one over the other) gives better coupling than windings on separate legs of an E-I core
Effect on performance: Poor coupling (windings far apart, not concentric) causes increased leakage inductance. Leakage inductance acts like a series inductor on the output — it causes voltage to droop under load and creates worse regulation. A well-wound transformer with concentric coils maintains near-constant output voltage from no-load to full-load.
Tapped Windings for Multiple Voltages
A single winding can provide multiple voltage taps by bringing out a lead at intermediate points. This is the same principle as the center-tap used in split-phase distribution.
Example: Multi-tap secondary
You wind a secondary of 300 turns for 300V total, but bring out leads at turns 50, 100, 150, 200, 250, and 300:
- Tap at 50 turns: 50V
- Tap at 100 turns: 100V
- Tap at 150 turns: 150V (center tap — useful for balanced supplies)
- Tap at 200 turns: 200V
- Tap at 250 turns: 250V
- Tap at 300 turns: 300V
The same core and winding provides any voltage from 50V to 300V by selecting the tap. This is how bench power transformers and autotransformers provide multiple output voltages.
Voltage regulation between taps is independent. Under load, the tap that carries current will exhibit voltage drop proportional to its series resistance. Unloaded taps will remain at their no-load voltage.
Autotransformer: One Winding, Both Roles
A conventional transformer has electrically isolated primary and secondary windings. An autotransformer uses a single winding with a tap, where part of the winding serves as the primary and the whole (or a different portion) serves as the secondary.
Autotransformer for 240V → 120V step-down:
┌────────────────────────────────────────┐
│ ←──── 200 turns (primary input) ───→ │
│ ←── 100 turns ─→ │
│ A B C │
│ ↑ ↑ ↑ │
│ 240V 120V 0V (common) │
The 240V input connects across all 200 turns (A to C). The 120V output is taken from the center 100 turns (B to C). The B-C portion of the winding serves both as part of the primary and as the secondary.
Advantages: Smaller, lighter, cheaper than an equivalent two-winding transformer. More efficient (less copper, less flux, less loss).
Disadvantage: No isolation between primary and secondary. Any fault on the primary can appear directly on the secondary. Use only where isolation is not required (voltage adjustment, not safety separation).
Autotransformers are excellent for small voltage corrections — for example, stepping 220V equipment up to 240V, or compensating for a transmission line with excessive voltage drop. They are not suitable as a safety barrier between high and low voltage sections of a system.
Rewinding a Salvaged Transformer
Salvage transformers are valuable because the core lamination is already done. The two most common sources:
Microwave oven transformers (MOTs): Large E-I cores capable of hundreds of watts. Primary typically 200-250 turns of fairly thin wire for 120V or 240V. Secondary is usually a high-voltage winding (2,000V) used by the magnetron — remove this and wind your own secondary.
To rewind:
- Remove the original secondary by cutting or unwinding the wire. Leave the primary intact if it matches your source voltage.
- Count the primary turns (or measure turns-per-volt with the test secondary method above).
- Calculate the required secondary turns for your target voltage.
- Wind the secondary over the primary, separated by insulation layers.
- Use wire gauged for the expected secondary current (see below).
Procedure for large step-down secondaries (e.g., 240V to 12V): The 12V secondary will carry 20× the primary current for the same power. At 500W, the secondary carries 41.7A. This requires 8 AWG wire or heavier. Winding 41.7A-rated wire (which is thick and stiff) on a microwave transformer core is physically challenging — consider winding multiple thinner wires in parallel instead. Four 14 AWG wires in parallel carry the same current as one 8 AWG wire and are far easier to wind.
Wire Gauge for Each Winding
The primary winding carries primary current; the secondary carries secondary current. Wire in each winding must be rated for its respective current.
Current density guideline: For a transformer with natural air cooling, keep current density below 3-4 A/mm² of wire cross-section. This ensures acceptable temperature rise.
| Current (A) | Minimum wire cross-section (mm²) | Approximate AWG |
|---|---|---|
| 0.5 | 0.17 | 24 AWG |
| 1 | 0.33 | 22 AWG |
| 2 | 0.67 | 20 AWG |
| 5 | 1.67 | 16 AWG |
| 10 | 3.33 | 12 AWG |
| 20 | 6.67 | 8 AWG |
| 40 | 13.3 | 6 AWG |
Use magnet wire (enameled copper wire) — the thin enamel insulation allows many turns to fit in the window space. Bare wire requires bulky insulation and fills the core window far too quickly.
Testing a Wound Transformer
Before putting a transformer under load, test these four parameters:
-
Open-circuit voltage — Measure V_s with no load. Should match your calculated secondary voltage within 2%. If significantly low, count turns again; you may have miscounted or poorly coupled the windings.
-
Turns ratio check — Divide measured V_s by measured V_p. This is your actual turns ratio. Compare to the design ratio.
-
No-load current — Measure primary current with no load on secondary. It should be a small fraction of rated current (typically 5-10%). High no-load current indicates core saturation — too few primary turns for your source voltage. Add more primary turns.
-
Temperature check under load — Apply full rated load and run for 30 minutes. Check core and winding temperature. Warm is acceptable (40-60°C above ambient). Hot to the touch (over 80°C) indicates excessive losses — check core lamination quality and winding resistance.