Formula & Calculator
Transformer Turns Ratio
Relates the primary and secondary voltages of a transformer to its winding turns ratio.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| V₁ | Primary winding RMS voltage | V |
| V₂ | Secondary winding RMS voltage | V |
| N₁ | Number of turns in primary winding | dimensionless |
| N₂ | Number of turns in secondary winding | dimensionless |
| a | Turns ratio (a = N₁/N₂ = V₁/V₂) | dimensionless |
What it means
The turns ratio of a transformer is defined as the ratio of the number of turns in the primary winding to the number of turns in the secondary winding. For an ideal transformer, the voltage ratio equals the turns ratio: V₁/V₂ = N₁/N₂. This relationship is derived from Faraday’s law of induction. The turns ratio determines whether the transformer steps up (N₂ > N₁) or steps down (N₂ < N₁) the voltage. It also determines the current ratio: I₁/I₂ = N₂/N₁ (inverse). The turns ratio is a critical parameter for selecting a transformer for a specific application, such as power supplies, audio amplifiers, or impedance matching. Example: A transformer with N₁=1000 turns and N₂=200 turns, with V₁=230V, gives V₂ = 230 * (200/1000) = 46V. This is a step‑down transformer with a turns ratio of 5:1.
Worked example
Transformer Turns Ratio – Practical Example
Real‑World| Parameter | Value |
|---|---|
| N₁ | 500 |
| N₂ | 100 |
| V₁ | 240 V |
| Formula | V₁/V₂ = N₁/N₂ |
Common mistakes
- Voltage ratio: V₁/V₂ = N₁/N₂ – for an ideal transformer.
- Current ratio: I₁/I₂ = N₂/N₁ – inversely proportional.
- Polarity: Dot convention must be observed for phase relations.
- Step‑up: If N₂ > N₁, the voltage is stepped up (V₂ > V₁).
- Leakage: Real transformers have leakage inductance and losses – the ratio holds approximately.
Applications
The transformer turns ratio V₁/V₂ = N₁/N₂ relates the primary and secondary voltages to their respective turns. This determines whether a transformer steps up or steps down voltage. Engineers use this ratio to design power transformers for transmission and distribution, to adapt voltages for electronic equipment, and to design isolation transformers. The ratio is also used to calculate the current ratio (I₁/I₂ = N₂/N₁). By selecting the appropriate turns ratio, professionals can match the voltage requirements of the load with the available supply. This formula is fundamental to transformer design and application.
- Power transformer design for grid and industrial use
- Voltage conversion for electronic devices (wall adapters)
- Isolation transformers for safety and noise reduction
- Impedance matching with audio transformers
- Educational foundation of transformer operation