How do you calculate Transformer Impedance Matching?

Use the formula Zin = (Np / Ns)² × Zload. A transformer reflects the load impedance back to the primary scaled by the square of the turns ratio. Enter the values you know in the calculator above and it solves for the remaining variable.

What is the formula for Transformer Impedance Matching?

The Transformer Impedance Matching formula is Zin = (Np / Ns)² × Zload, where Zin—Impedance seen at the primary (Ω); Np, Ns—Primary/secondary turns; Zload—Actual load impedance on the secondary (Ω).

What does Zin mean in the Transformer Impedance Matching formula?

Zin is Impedance seen at the primary (Ω).

Transformer Impedance Matching

Zin = (Np/Ns)² · Zload

Calculator

Reflected Impedance

Primary Turns

Secondary Turns

Load Impedance

Result

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Formula

Zin = (Np / Ns)² × Zload

Description

A transformer reflects the load impedance back to the primary scaled by the square of the turns ratio. This lets a transformer match a source to a load for maximum power transfer—for example matching a low-impedance loudspeaker to a high-impedance amplifier output stage, or matching antenna feedlines. Choosing the turns ratio sets the impedance transformation.

Variables

Zin — Impedance seen at the primary (Ω)
Np, Ns — Primary/secondary turns
Zload — Actual load impedance on the secondary (Ω)

Practical Notes

Classic example: an 8 Ω speaker matched to a 5 kΩ tube plate load needs a turns ratio of √(5000/8) ≈ 25:1. Impedance matching maximizes power transfer but not efficiency.

Related Concepts

All Magnetics & Transformers formulas →

Transformer EMF Equation Transformer VA Rating Transformer Voltage Regulation Transformer Current Ratio Transformer Copper Loss Transformer Iron (Core) Loss Transformer Turns-per-Volt Transformer Impedance Matching

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