Transformer Impedance Matching

Zin = (Np/Ns)² · Zload

Quick answer

This calculator solves Zin = (Np / Ns)² × Zload for Reflected Impedance. With Primary Turns 0.5, Secondary Turns 1.1, Load Impedance 1.03 kΩ, the result is 0.2128 kΩ. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Reflected Impedance (Ω)
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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 — Primary turns
  • Ns — 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.

Symbols and units

Symbol Meaning Default unit Accepted units
Zin Reflected Impedance Ω mΩ, Ω, kΩ, MΩ
Np Primary Turns — —
Ns Secondary Turns — —
Zload Load Impedance Ω mΩ, Ω, kΩ, MΩ

Step by step

  1. 1. What you know: Primary Turns 0.5, Secondary Turns 1.1, Load Impedance 1.03 kΩ
  2. 2. The relation: Zin = (Np / Ns)² × Zload
  3. 3. Substitute: Np = 0.5, Ns = 1.1, Zload = 1.03 kΩ
  4. 4. Result: Reflected Impedance = 0.2128 kΩ

Nearest standard component values

Series Nearest value Error
E12 0.22 kΩ 3.4%
E24 0.22 kΩ 3.4%

Worked examples

Minimum range

Given: Primary Turns 0.025, Secondary Turns 0.055, Load Impedance 2.2 Ω

Result: Reflected Impedance = 0.4545 Ω

Low range

Given: Primary Turns 0.25, Secondary Turns 0.55, Load Impedance 22 Ω

Result: Reflected Impedance = 4.545 Ω

Typical

Given: Primary Turns 0.5, Secondary Turns 1.1, Load Impedance 1.03 kΩ

Result: Reflected Impedance = 0.2128 kΩ

High range

Given: Primary Turns 0.8, Secondary Turns 1.76, Load Impedance 10.3 kΩ

Result: Reflected Impedance = 2.128 kΩ

Maximum range

Given: Primary Turns 8, Secondary Turns 17.6, Load Impedance 103 kΩ

Result: Reflected Impedance = 21.28 kΩ

Solving for each variable

Solve for Reflected Impedance

Primary Turns 0.025, Secondary Turns 0.055, Load Impedance 2.2 Ω → 0.4545 Ω

Solve for Load Impedance

Reflected Impedance 1 Ω, Primary Turns 0.025, Secondary Turns 0.055 → 4.84 Ω

Solve for Primary Turns

Reflected Impedance 1 Ω, Secondary Turns 0.055, Load Impedance 2.2 Ω → 0.03708

Solve for Secondary Turns

Reflected Impedance 1 Ω, Primary Turns 0.025, Load Impedance 2.2 Ω → 0.03708

How Reflected Impedance changes with Primary Turns

Primary Turns (input) Reflected Impedance (result)
0.05 2.128 Ω
0.125 13.3 Ω
0.25 53.2 Ω
0.375 119.7 Ω
0.5 0.2128 kΩ
0.75 0.4788 kΩ
1 0.8512 kΩ
2 3.405 kΩ
3.5 10.43 kΩ
5 21.28 kΩ

The same result in other units

Unit Value
mΩ 212800
Ω 212.8
kΩ 0.2128
MΩ 0.0002128

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Frequently asked questions

How do you calculate Transformer Impedance Matching?

Use Zin = (Np / Ns)² × Zload. With Primary Turns 0.5, Secondary Turns 1.1, Load Impedance 1.03 kΩ, Reflected Impedance works out to 0.2128 kΩ.

What is the formula for Transformer Impedance Matching?

The formula is Zin = (Np / Ns)² × Zload. A transformer reflects the load impedance back to the primary scaled by the square of the turns ratio.

How do you find Load Impedance when you know the other values?

Rearrange for Load Impedance: with Reflected Impedance 1 Ω, Primary Turns 0.025, Secondary Turns 0.055, Load Impedance is 4.84 Ω.

How do you find Primary Turns when you know the other values?

Rearrange for Primary Turns: with Reflected Impedance 1 Ω, Secondary Turns 0.055, Load Impedance 2.2 Ω, Primary Turns is 0.03708.

What units does Transformer Impedance Matching use?

Reflected Impedance is shown in mΩ, Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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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