How to Calculate Transformer Ratios
Learn how to calculate transformer turns ratio, voltage ratio, current ratio, and impedance transformation. Includes step-up, step-down, and isolation transformer examples.
How Transformers Work
A transformer transfers AC electrical energy between two circuits through electromagnetic induction. The primary winding is connected to the input voltage; the changing magnetic flux it creates in the iron core induces a voltage in the secondary winding. The ratio of the number of turns in each winding determines how voltage and current are transformed. Transformers only work with AC — a DC input creates a constant magnetic field that induces no secondary voltage.
The Turns Ratio Formula
The fundamental transformer equation relates turns to voltages: Vp/Vs = Np/Ns = n, where Vp and Vs are the primary and secondary voltages, and Np and Ns are the number of turns. This ratio n is called the turns ratio. A transformer with 1,000 primary turns and 100 secondary turns has a turns ratio of 10:1, so an input of 120 V AC produces an output of 12 V AC. Rearranging: Vs = Vp × (Ns/Np).
Current Transformation
An ideal transformer conserves power (Pin = Pout), so if voltage is stepped down, current is stepped up by the same ratio: Ip/Is = Ns/Np = 1/n. A 10:1 step-down transformer with 1 A primary current delivers 10 A to the secondary. In practice, transformer efficiency is 95–99% for well-designed units, so Is = (Ip × Np × η) / Ns, where η is efficiency. This inverse relationship between voltage and current is why high-voltage transmission lines carry low current — reducing resistive losses (P = I²R) over long distances.
Step-Up and Step-Down Configurations
A step-up transformer (Ns > Np) increases voltage and decreases current; a step-down transformer (Ns < Np) decreases voltage and increases current. Mains power adapters are step-down transformers — a 230 V to 12 V adapter has a ratio of approximately 19.2:1. Audio output transformers are often step-down units matching a high-impedance tube amplifier output to a low-impedance speaker. Step-up transformers appear in high-voltage test equipment, CRT televisions (flyback transformers), and inverters.
Impedance Transformation
A transformer also transforms impedance by the square of the turns ratio: Zp = n² × Zs, where Zp is the impedance seen at the primary and Zs is the load impedance at the secondary. A 4 Ω speaker connected to a transformer with a 10:1 turns ratio appears as 4 × 10² = 400 Ω at the primary. This impedance matching is critical in RF circuits and audio amplifiers to maximize power transfer — maximum power transfers when source and load impedances are matched.
Calculating a Center-Tapped Transformer
A center-tapped transformer has a secondary with a tap at the midpoint, providing two equal secondary voltages. If the full secondary is 24 V, each half delivers 12 V relative to the center tap. This configuration is used in full-wave rectifier circuits: each half of the secondary alternately conducts through a diode, producing DC with ripple at twice the input frequency. The center tap becomes the DC negative rail, and the transformer rating must handle the full secondary current even though each half only conducts for half a cycle.
Transformer Core Losses and Efficiency
Real transformers suffer two types of core loss. Hysteresis loss occurs because energy is needed to repeatedly remagnetize the core material; it is proportional to frequency and is minimized with grain-oriented silicon steel or ferrite cores. Eddy current loss is caused by circulating currents induced in the core; it is minimized by laminating the core into thin sheets insulated from each other. Copper losses (I²R in the winding resistance) add to these. Together, they set the efficiency: η = Pout / Pin = Pout / (Pout + P_core + P_copper).
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