8.1.1. Operating principle of a transformer

Transformers are stationary electrical machines which transmit energy from systems with certain current and voltage values into systems with generally different current and voltage values but with identical frequency.

Two separate windings are on the same iron core.

Following connection to alternating voltage U₁ there is a standstill current I₀. The magnetomotive force Q = I₀ · N₁ generates a magnetic alternating flow (F₁) in the iron core.

The input and output winding of an alternating voltage are induced in accordance with the induction law. A self-induction voltage U₁₀ arises in the input winding. It is counter-positioned in accordance with Lenz’s law on applied voltage. During idling operation - because of mutual induction - there arises the output voltage U₂₀ which is simultaneously the terminal voltage U₂.

U_1~ ® I_0~ ® Q_0~ ® F_1~ ® U_20~

The value of the induced voltage is derived from the following equation:

	max. flow density
AFe	limb cross-section
U0	induction voltage
f	frequency
N	number of turns

The induction voltage increases along with the number of turns, the magnetic flow density in the iron core, the iron cross-section and the frequency.

Example:

Which maximum flow density occurs in an iron core of 16 cm² cross-section when a voltage of 380 V (50 Hz) is applied to the primary coil with 980 turns?

Given: A_Fe = 16 cm²; N₁ = 980; U₁ = 380 V; f = 50 Hz

Sought:

Solution:

» 1.09 V · s · m^-2

» 1.09 T

The iron core evidences a maximum flow density of 1.09 T.