Transformer Turns Ratio Calculator

Understanding Transformer Turns Ratio

The transformer turns ratio is the fundamental relationship that governs how transformers convert voltage and current levels. Understanding this ratio is essential for transformer design, selection, and analysis in power systems, electronics, and electrical engineering applications.

What is Turns Ratio?

The turns ratio (n) is the ratio of the number of turns in the secondary winding to the primary winding:

• N₁: Number of turns in primary winding
• N₂: Number of turns in secondary winding
• n > 1: Step-up transformer (increases voltage)
• n < 1: Step-down transformer (decreases voltage)
• n = 1: Isolation transformer (same voltage)

Fundamental Transformer Relationships

Ideal transformers follow these relationships:

• $$\rac{V_2}{V_1} = \rac{N_2}{N_1} = n$$
  (Voltage Ratio)
• $$\rac{I_2}{I_1} = \rac{N_1}{N_2} = \rac{1}{n}$$
  (Current Ratio)
• $$P_1 = P_2$$
  (Power Conservation, assuming 100% efficiency)
• $$Z_2 = Z_1 \ imes n^2$$
  (Impedance Transformation)

Step-Up vs Step-Down Transformers

Step-Up Transformer (n > 1):

• Secondary voltage higher than primary voltage
• Secondary current lower than primary current
• Used in power transmission to reduce I²R losses
• Example: 120V to 240V for appliances

Step-Down Transformer (n < 1):

• Secondary voltage lower than primary voltage
• Secondary current higher than primary current
• Used in power supplies and distribution
• Example: 240V to 12V for electronics

How to Use This Calculator

1. Enter primary winding parameters (voltage, current, or turns)
2. Enter secondary winding parameters (any known values)
3. The calculator computes all remaining values
4. View turns ratio and transformer type (step-up/down)
5. See impedance transformation if applicable

Example Calculations

Practical Applications

• Power Distribution: Stepping voltage up for transmission, down for distribution
• Isolation: Electrical isolation while maintaining voltage levels
• Impedance Matching: Matching source and load impedances for maximum power transfer
• Voltage Conversion: Adapting equipment to different voltage standards
• Current Transformers: Measuring high currents safely

Transformer Efficiency Considerations

Real transformers have losses that reduce efficiency:

• Copper Losses: I²R losses in windings (load-dependent)
• Core Losses: Hysteresis and eddy current losses (constant)
• Typical Efficiency: 95-99% for power transformers
• Small transformers: 85-95% efficiency

Frequently Asked Questions