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Turns Ratio Formula:
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The impedance to turns ratio equation calculates the transformer turns ratio based on the impedance ratio between primary and secondary windings. This relationship is fundamental in transformer design and analysis, particularly in impedance matching applications.
The calculator uses the turns ratio equation:
Where:
Explanation: The square root relationship comes from the fact that impedance is proportional to the square of the turns ratio in an ideal transformer.
Details: Accurate turns ratio calculation is crucial for transformer design, impedance matching in audio and RF systems, power distribution networks, and ensuring proper voltage transformation in electrical systems.
Tips: Enter both primary and secondary impedance values in ohms. Both values must be positive and greater than zero for accurate calculation.
Q1: Why is there a square root in the formula?
A: The square root exists because impedance is proportional to the square of the turns ratio (Z ∝ N²), so to find the turns ratio from impedance, we take the square root of the impedance ratio.
Q2: What are typical turns ratio values?
A: Turns ratio values vary widely depending on application, from step-up ratios >1 to step-down ratios <1, with values ranging from fractions to hundreds or more.
Q3: Does this formula work for all transformer types?
A: This formula applies to ideal transformers. Real transformers may have additional factors to consider, but this provides a good approximation for most practical purposes.
Q4: What if I have multiple windings?
A: For transformers with multiple secondary windings, calculate each turns ratio separately relative to the primary winding.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the given formula. Accuracy depends on the precision of your impedance measurements and how closely the transformer approximates ideal behavior.