Calculate Transformer

Calculate voltages, currents and impedance of a transformer

Transformer Calculator

Transformer Calculation

This function can be used to calculate the voltages, currents and impedance of a transformer for a given impedance. A coupling factor of 100% (ideal transformer) is preset.

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Results
Primary voltage:
Secondary voltage:
Primary current:
Secondary current:
Primary impedance:
Secondary impedance:

Transformer & Parameters

≡≡||≡≡
Transformer
N₁ : N₂
Fundamentals

A transformer transfers electrical energy from the primary to the secondary side through magnetic coupling. The turns ratio determines voltage and current.

Coupling Factor
Ideal transformer: k = 100%
Mains transformer: k ≈ 99%
Air core coils: k ≈ 50%

Example Calculations

Practical Calculation Examples

Example 1: Mains Transformer 230V/12V

Given: N₁ = 2300, N₂ = 120, U₁ = 230V, k = 99%

\[ü = \frac{N_1}{N_2} = \frac{2300}{120} = 19.17\]
\[U_2 = U_1 \cdot \frac{N_2}{N_1} \cdot k = 230 \cdot \frac{120}{2300} \cdot 0.99 = 11.9V\]
\[I_1 = I_2 \cdot \frac{N_2}{N_1} = I_2 \cdot \frac{1}{19.17} = 0.052 \cdot I_2\]
Typical mains transformer with iron core
Example 2: Audio Transformer

Given: N₁ = 1000, N₂ = 100, Z₂ = 8Ω, k = 98%

\[ü = \frac{N_1}{N_2} = \frac{1000}{100} = 10\]
\[Z_1 = ü^2 \cdot Z_2 = 10^2 \cdot 8 = 800Ω\]
At U₁ = 10V: \[U_2 = \frac{10}{10} \cdot 0.98 = 0.98V\]
Impedance matching for audio amplifier
Example 3: RF Transformer

Given: N₁ = 20, N₂ = 5, U₁ = 5V, k = 60%

\[ü = \frac{N_1}{N_2} = \frac{20}{5} = 4\]
\[U_2 = U_1 \cdot \frac{N_2}{N_1} \cdot k = 5 \cdot \frac{5}{20} \cdot 0.6 = 0.75V\]
\[Z_1 = ü^2 \cdot Z_2 = 16 \cdot Z_2\]
Air core coils with lower coupling
Transformer Characteristics
Turns Ratio:
ü > 1: Step-down transformer
ü = 1: Isolation transformer
ü < 1: Step-up transformer
Power: P₁ ≈ P₂ (lossless)
Applications:
Mains: 230V → 12V
Audio: Impedance matching
RF: Balun, transformers
Measurement: Current/voltage transformers

Formulas for Calculating the Transformation

Ideal Transformer

With the ideal transformer, there are no losses. Magnetic coupling k = 1. For mains transformers and transformers with a closed iron core, k is around 99%. With coupled air core coils of band filters only about 50%.

Voltage Transformation
\[ü = \frac{U_1}{U_2} = \frac{N_1}{N_2}\]
\[U_2 = \frac{U_1 \cdot N_2}{N_1}\]

Voltages behave like turns ratios

Current Transformation
\[\frac{I_2}{I_1} = \frac{N_1}{N_2}\]
\[I_2 = \frac{I_1 \cdot N_1}{N_2}\]

Currents behave inversely to turns ratios

Impedance Transformation
\[Z_1 = ü^2 \cdot Z_2\]
\[Z_1 = \left(\frac{N_1}{N_2}\right)^2 \cdot Z_2\]

Impedances behave like the square of the transformation ratio

Real Transformer

The real transformer deviates from the ideal transformer due to the copper resistance, the leakage flux, magnetization curve, etc. For a real transformer, k < 1 (leakage flux).

Real Transformer with Coupling Factor
\[U_2 = U_1 \cdot \frac{N_2}{N_1} \cdot k\]

The secondary voltage is calculated taking into account the coupling factor k.

Practical Applications

Mains Transformers
  • Voltage adaptation
  • Galvanic isolation
  • Safety extra-low voltage
  • Power electronics
Audio Transformers
  • Impedance matching
  • Ground loop isolation
  • Tube amplifiers
  • Balancing
RF Transformers
  • Balun (balanced/unbalanced)
  • Impedance transformation
  • Band filters
  • Antenna matching

Parameter Legend

Primary Side
U₁ = Primary voltage [V]
I₁ = Primary current [A]
N₁ = Primary turns
Z₁ = Primary impedance [Ω]
Secondary Side
U₂ = Secondary voltage [V]
I₂ = Secondary current [A]
N₂ = Secondary turns
Z₂ = Secondary impedance [Ω]
ü = Transformation ratio
k = Coupling factor

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