# Calculate transformer

Calculate voltages, currents and impedance of a transformer

## Transformer online calculator

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. For mains transformers and transformers with a closed iron core, k is around 99%. In the case of coupled air-cored coils of belt filters, k is only about 50%.

### Calculate transformer

 Eingabe Number of turns N1 Number of turns N2 Primary voltage Secondary voltage mV V kV Primary current Secondary current mA A kA Coupling factor % Decimal places 0 1 2 3 4 6 8 10 Resultat Primary voltage Secondary voltage Primary current Secondary current Primary impedance Secondary impedance

## Formulas for calculating the translation

### 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 coils of belt filters only about 50%.

#### Voltage transmission

The ratio of the secondary voltage to the primary voltage is proportional to the ratio of secondary turns and the primary turns of the transformer.

$$\displaystyle ü=\frac{U_1}{U_2}=\frac{N_1}{N_2}$$    ⇒    $$\displaystyle U_2=\frac{U_1 · N_2}{N_1}$$    ⇒    $$\displaystyle U_1=\frac{U_2 · N_1}{N_2}$$
U1 = Primary voltage [V]
U2 = Secondary voltage [V]
N = Number of turns

#### Current ratio

The ratio of the secondary current to the primary current is inversely proportional to the number of secondary turns and the primary turns of the transformer.

$$\displaystyle \frac{I_2}{I_1}=\frac{N_1}{N_2}$$    ⇒    $$\displaystyle I_2=\frac{I_1 · N_1}{N_2}$$    ⇒    $$\displaystyle I_1=\frac{I_2 · N_2}{N_1}$$

#### Impedance translation

The secondary impedance is related to the primary impedance like the square of the translation factor.

$$\displaystyle Z_1=ü^2 · Z_2 = \left( \frac{N_1}{N_2}\right)^2 · Z_2$$
Z1 = Input impedance (Primary impedance) [Ω]
Z2 = Output impedance (Secondary impedance) [Ω]
ü = Voltage transmission factor [1]

### Realer Transformator

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):

The secondary voltage is calculated taking into account the coupling factor according to the formula:

$$\displaystyle U_2= U_1 · \frac{N_2}{N_1} · k$$
U1 =Primary voltage [V]
U2 = Secondary voltage [V]
N1 = Number of turns (primary side)
N2 = Number of turns (secondary side)
k = Coupling factor (magnetic efficiency)

For mains transformers and transformers with a closed iron core, k is around 99%. With coupled air coils of belt filters only about 50%.