1. What is the Transformer Turns Ratio to Impedance Formula?

The transformer impedance ratio formula describes the relationship between the turns ratio and impedance ratio in transformers. It states that the impedance ratio equals the square of the turns ratio, which is fundamental to transformer design and impedance matching applications.

2. How Does the Calculator Work?

The calculator uses the impedance ratio formula:

Where:

• Turns Ratio — Ratio of primary to secondary winding turns (unitless)
• Impedance Ratio — Ratio of primary to secondary impedance (unitless)

Explanation: This relationship arises from the fact that impedance transformation in a transformer is proportional to the square of the turns ratio due to the voltage and current transformation properties.

3. Importance of Impedance Ratio Calculation

Details: Accurate impedance ratio calculation is crucial for impedance matching in audio systems, RF applications, power distribution networks, and ensuring proper load matching for maximum power transfer.

4. Using the Calculator

Tips: Enter the turns ratio (a unitless value greater than 0). The calculator will compute the corresponding impedance ratio.

5. Frequently Asked Questions (FAQ)

Q1: Why is the impedance ratio squared?
A: The impedance ratio is squared because impedance is proportional to the square of the voltage ratio, and voltage ratio equals the turns ratio.

Q2: What are typical turns ratio values?
A: Turns ratios vary widely depending on application, from step-up ratios >1 to step-down ratios <1, with values ranging from fractions to hundreds.

Q3: Does this formula work for both ideal and real transformers?
A: This formula applies to ideal transformers. Real transformers have additional factors like leakage inductance and core losses that affect impedance transformation.

Q4: How is this used in audio transformer applications?
A: In audio systems, this formula helps match speaker impedance to amplifier output impedance for maximum power transfer and minimal distortion.

Q5: Can this formula be used for three-phase transformers?
A: Yes, the same fundamental relationship applies to three-phase transformers, though connection type (delta-wye, wye-delta) introduces additional √3 factors.