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.
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Key facts
Category
Math & Numbers
Input types
select, number
Output type
json
Sample coverage
4
API ready
Yes
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.
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
1Select the transfer direction, choosing either Secondary to Primary (toPrimary) or Primary to Secondary (toSecondary).
2Input the source impedance value in ohms, and provide the turns ratio directly or enter the primary and secondary turn counts.
3The calculator computes the turns ratio (a = N₁/N₂) and applies the reflection formula (Z' = a²·Z or Z' = Z/a²).
4The 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.
Examples
1. Reflecting Speaker Impedance to an Audio Amplifier
Audio Equipment Designer
Background
An engineer is designing a tube amplifier and needs to match an 8-ohm speaker load to the primary side of an output transformer with a turns ratio of 10.
Problem
Determine the reflected impedance seen by the amplifier's output tube to ensure proper impedance matching.
How to use
Set the direction to 'Secondary → Primary', enter the turns ratio (a) as 10, and set the impedance (Z) to 8 ohms.
direction: "toPrimary", a: 10, Z: 8
Outcome
The reflected impedance is calculated as 800 ohms, with a reflected admittance of 0.00125 S.
2. Power Grid Impedance Reflection using Turn Counts
Electrical Grid Analyst
Background
A grid analyst needs to refer a secondary load impedance of 4 ohms back to the primary side of a step-down transformer with 1000 primary turns and 250 secondary turns.
Problem
Calculate the equivalent primary impedance without manually computing the turns ratio first.
How to use
FAQ
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.