# Transformer Impedance Transfer Calculator

Reflect an impedance through an ideal transformer: Z' = a²·Z, where a = N₁/N₂. Supports secondary→primary and primary→secondary directions; a can be given directly or derived from N₁/N₂. Also returns admittance Y and reflected admittance.

> Canonical page: https://elysiatools.com/en/tools/transformer-impedance-transfer

- **Category:** Math & Numbers

- **Keywords:** transformer impedance, impedance reflection, reflected impedance, Z' = a²·Z, turns ratio, ideal transformer, circuit analysis, electrical engineering

## Overview

The Transformer Impedance Transfer Calculator allows you to quickly calculate the reflected impedance and admittance across an ideal transformer. By inputting the source impedance and either the direct turns ratio or the specific number of primary and secondary turns, you can instantly determine the equivalent impedance and admittance as seen from either the primary or secondary side.

## Inputs

- **Direction** (select)
- **Turns Ratio a (N₁/N₂)** (number): Direct turns ratio. If omitted, derived from N₁/N₂ below.
- **Primary Turns N₁** (number): Used to derive a when a is not given directly.
- **Secondary Turns N₂** (number): Used to derive a when a is not given directly.
- **Impedance Z (Ω)** (number): Impedance on the source side (secondary for toPrimary, primary for toSecondary).
- **Decimal Places** (number)

## When to use

- When designing impedance matching networks in RF or audio circuits using coupling transformers.
- When analyzing power distribution systems to refer load impedances back to the primary high-voltage side.
- When solving electrical engineering homework or verifying circuit simulations involving ideal transformers.

## How it works

- Select the transfer direction, choosing either Secondary to Primary (toPrimary) or Primary to Secondary (toSecondary).
- Input the source impedance value in ohms, and provide the turns ratio directly or enter the primary and secondary turn counts.
- The calculator computes the turns ratio (a = N₁/N₂) and applies the reflection formula (Z' = a²·Z or Z' = Z/a²).
- The tool outputs the reflected impedance, the source admittance, and the reflected admittance rounded to your specified decimal places.

## Use cases

- Calculating the reflected load impedance of a loudspeaker connected to an audio amplifier through an output transformer.
- Determining the equivalent impedance of a distribution grid load as seen from the high-voltage transmission line.
- Verifying theoretical calculations for electrical engineering coursework and laboratory experiments.

## Frequently asked questions

### What formula is used to reflect impedance from the secondary to the primary side?

The formula is Z' = a²·Z, where a is the turns ratio (N₁/N₂) and Z is the secondary impedance.

### Can I calculate the reflected impedance if I do not know the turns ratio directly?

Yes, you can enter the primary turns (N₁) and secondary turns (N₂) to automatically derive the turns ratio.

### How does the calculator handle admittance?

It calculates the source admittance as Y = 1/Z and reflects it using the inverse square of the turns ratio.

### What is the difference between primary-to-secondary and secondary-to-primary reflection?

Secondary-to-primary multiplies the impedance by a², whereas primary-to-secondary divides the impedance by a².

### Does this calculator account for non-ideal transformer losses?

No, this calculator assumes an ideal transformer with no winding resistance, core losses, or leakage inductance.

## Related tools

- [Three-Phase Short-Circuit Current Calculator (IEC 60909)](https://elysiatools.com/en/tools/short-circuit-current-calculator): Estimate the three-phase symmetric short-circuit current using the IEC 60909 far-from-generator method: I"_k = c·U_n/(√3·|Z|) and i_p = κ·√2·I"_k with κ = 1.02 + 0.98·e^(−3R/X). Source impedance is the series sum of transformer and line R/X.
- [Dimensional Analysis Unit Cancellation Tutor](https://elysiatools.com/en/tools/dimensional-analysis-unit-cancellation-tutor): Step-by-step factor-label unit cancellation with inverted-factor diagnosis and optional student-answer checking.
- [Perfect Number Checker](https://elysiatools.com/en/tools/perfect-number-checker): σ(n) = 2n ⟺ perfect. Factorization-based σ(n), proper-divisor sum, deficient/perfect/abundant classification, abundancy index, Euclid–Euler form. n ≤ 10¹².
- [PERT Network Analyzer (Expected Duration & Variance)](https://elysiatools.com/en/tools/pert-network-analyzer): Three-point PERT estimates: te and σ² per activity, critical path, expected project duration and variance, and normal completion probability for a target time.
- [Polynomial Regression Calculator](https://elysiatools.com/en/tools/polynomial-regression-calculator): Fit a polynomial least-squares curve to paired numeric data and inspect coefficients, R squared, and predictions
- [Prime Factorization Calculator](https://elysiatools.com/en/tools/prime-factorization): Factor any integer into its prime factors with detailed analysis and mathematical properties.
- [Absolute Value Calculator](https://elysiatools.com/en/tools/absolute-value-calculator): Calculate the absolute value of positive, negative, or decimal numbers and explain the sign relationship
- [Air Changes per Hour (ACH, n = Q/V)](https://elysiatools.com/en/tools/air-changes-per-hour): Compute the air change rate (ACH / n) of a room from the outdoor supply airflow Q and the room volume V: n = Q/V (1/h). Three modes: solve ACH (given Q and V), solve airflow (given n and V), or solve volume (given n and Q). Flow in m³/s/m³/h/CFM, volume in m³/ft³/L. Also reports the well-mixed single-zone purge time to reach a target residual fraction ε (default 1%): t = −ln(ε)/n hours.

## Samples

- [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion
- [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion
- [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion
- [Web Image Processing Rust Samples](https://elysiatools.com/en/samples/web-image-processing-rust): Web Rust image processing examples including image read/save, scaling, and format conversion