Transformer Turns Ratio Calculator
Voltage, current, and impedance transformation
Required Parameters
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Quick Answer
Turns ratio: n = Np/Ns = Vp/Vs = Is/Ip. A 10:1 transformer steps 240V down to 24V (or steps current up by 10×).
Design Notes
Ideal transformer equations assume 100% coupling and zero losses. Real transformers have copper losses (I²R), core losses (hysteresis + eddy currents), and leakage inductance. Efficiency ranges from 90-99% for power transformers. For impedance matching (e.g., audio), Z_reflected = n² × Z_load.
Common Mistakes
- 1
Forgetting that power is conserved — stepping voltage up means current steps down proportionally.
- 2
Ignoring magnetizing current, which flows even with no load and causes core heating.
- 3
Using a power transformer at frequencies other than its design frequency (e.g., 50Hz transformer at 60Hz or vice versa).
Knowledge Base
What is the transformer turns ratio formula?
Turns ratio n = Np/Ns = Vp/Vs = Is/Ip, where Np and Ns are primary and secondary turns, Vp and Vs are voltages, and Ip and Is are currents. A 10:1 transformer with 240V primary produces 24V secondary. Power is conserved: Vp×Ip ≈ Vs×Is (minus losses).
What is a step-down vs step-up transformer?
Step-down: more primary turns than secondary (Np > Ns), reduces voltage, increases current. Used in power supplies (240V→12V). Step-up: fewer primary turns (Np < Ns), increases voltage, decreases current. Used in ignition coils, CRT displays, and power transmission.
How does impedance transformation work?
Z_reflected = n² × Z_load. A transformer with 3:1 ratio connected to an 8Ω speaker presents 72Ω (9×8) to the amplifier. This is crucial in audio systems for matching amplifier output impedance to speaker impedance, and in RF systems for antenna matching.
What are transformer losses?
Copper losses: I²R heating in windings (proportional to current squared). Core losses: hysteresis (energy to magnetize/demagnetize core each cycle) and eddy currents (circulating currents in the core). Typical efficiency: small signal transformers 85-92%, power transformers 95-99%. Losses increase with frequency.
Can I use a transformer with DC?
No. Transformers require a changing magnetic flux (dΦ/dt) to induce voltage. DC creates a constant flux with no induced voltage, and the primary acts as a short circuit (only limited by winding resistance). However, you can transform DC by first converting it to AC (inverter), transforming, then rectifying back to DC — this is how switch-mode power supplies work.
What is the difference between isolation and autotransformers?
Isolation transformer: separate primary and secondary windings with no electrical connection, providing galvanic isolation (safety). Autotransformer: single winding with a tap, sharing a common connection — more efficient and smaller but NO isolation. Autotransformers (like variacs) are used where isolation isn't required.
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