Calculate transformer
Calculate voltages, currents and impedance of a transformer
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%.
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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%.
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