Transformer V/I/Z Reflection Calculator
Calculate voltage, current, and impedance reflections through an ideal transformer from primary to secondary (and back). Essential for audio output transformers, RF matching networks, and power supply design.
How to Use
- Enter the primary voltage V<sub>p</sub> (source side).
- Enter the target secondary voltage V<sub>s</sub> (load side).
- Enter the load current I<sub>s</sub> drawn by whatever is connected to the secondary.
- Optionally enter the secondary impedance Z<sub>s</sub> to see its reflected value on the primary side.
- Results: turns ratio, primary current, reflected primary impedance, power flow (conserved for ideal transformer).
Show Work
Formulas
History of the Transformer
The induction principle underlying every transformer was discovered by Michael Faraday in 1831, demonstrated with a simple iron-ring apparatus that had two coils wound on opposite sides. A changing current in the primary induced a voltage in the secondary — Faraday had built the first transformer, though he wasn\'t trying to. Joseph Henry made the same discovery independently about the same time.
The practical AC transformer arrived half a century later. Lucien Gaulard and John Gibbs patented a step-up/step-down system in London in 1882; William Stanley at Westinghouse improved and commercialized the design, demonstrating the first fully AC-powered town (Great Barrington, Massachusetts) in 1886. This system — stepping voltage up for transmission and down for distribution — settled the "War of the Currents" in favor of AC and made centralized electric utilities economically possible.
The impedance-reflection formulation Zp = n²·Zs comes from combining the voltage-ratio and current-ratio relationships. Oliver Heaviside had the full complex-impedance treatment worked out by 1893, and Charles Proteus Steinmetz\'s analysis extended it to three-phase transformers and unbalanced loads. Every modern power grid still runs on this math — transmission at 110–765 kV, distribution at 7–35 kV, customer delivery at 120–480 V, all connected through transformers obeying the same turns-ratio equations Faraday\'s experiments implied.
About This Calculator
Enter primary voltage, target secondary voltage, and load current on the secondary. The calculator returns the required turns ratio n = Vp/Vs, the resulting primary current Ip, and (if you supply a secondary load impedance) the reflected impedance seen on the primary side. Power is computed both sides and shown as conserved.
The math assumes ideal transformer behavior (no losses, infinite coupling). Real transformers have 1–5% efficiency loss and magnetizing current that draws even at no load. Use the Transformer Efficiency calculator for realistic loss modeling. Everything runs client-side; no values leave your browser.
Frequently Asked Questions
How ideal is "ideal"?
The ideal transformer model assumes 100% magnetic coupling between primary and secondary (no leakage flux), zero winding resistance, infinite core permeability (no magnetizing current), and no core loss. Real transformers deviate in all four: typical audio output transformers are 92–96% efficient; line-frequency power transformers are 95–99% efficient; RF baluns approach 98% within their bandwidth.
What does impedance reflection mean physically?
A load on the secondary "looks like" a different impedance on the primary, scaled by (N<sub>p</sub>/N<sub>s</sub>)². An 8Ω speaker behind a 10:1 step-down transformer appears as 800Ω on the primary — which is why tube amps use output transformers to match high-impedance plates to low-impedance speakers.
Autotransformer — does this math still apply?
The ratio math is the same: V<sub>p</sub>/V<sub>s</sub> = N<sub>p</sub>/N<sub>s</sub>. The difference is that primary and secondary share a winding rather than being isolated, which saves copper/core material for turns ratios near 1:1 but loses galvanic isolation. Common in variacs and utility tap-changing transformers.
Does this work for DC?
No — transformers only work for changing current (AC or pulsed DC). A DC transformer is a contradiction in terms because there\'s no changing flux to induce a voltage in the secondary. Modern "DC-DC converters" use switching to create AC through an internal transformer, then rectify the secondary output back to DC.
What about three-phase transformers?
Same turns ratio math per-phase. The connection topology (wye-wye, delta-delta, wye-delta, delta-wye) adds a √3 factor between phase and line voltages/currents, but each phase\'s transformer obeys the same equations shown here.
Common Use Cases
Tube Audio Output Transformer
Push-pull 6L6 output stage with 4kΩ plate-to-plate and 8Ω speaker needs a turns ratio of √(4000/8) ≈ 22:1 step-down. This is why guitar amp output transformers are large and heavy.
RF Impedance Matching
A 50Ω transmitter feeding a 300Ω folded dipole needs a 1:√6 ≈ 1:2.45 step-up matching transformer. Classic 4:1 balun does roughly this (50Ω unbalanced → 200Ω balanced).
Low-Voltage Wall Adapter
A transformer-based 12V adapter from 120V line uses a 10:1 step-down. Secondary current is 10× the primary current drawn, and the adapter must handle the load VA.
Isolation Transformer
1:1 ratio — same voltage on both sides, but the secondary is galvanically isolated from the primary. Essential for medical equipment safety and oscilloscope ground-loop mitigation.
Flyback SMPS Design
A buck-boost (flyback) converter transformer calculates reflected voltage: the primary sees V<sub>out</sub>·n plus V<sub>in</sub> during the switch-off period. Picking n sets the MOSFET voltage rating.
Last updated: