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Transformers

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Transformers

- The "simple transformer law" relates output voltage to input voltage and turns ratio. Investigate the importance of frequency and other parameters in determining the non-ideal behaviour of transformers.

Using the Kirchhoff's andFaraday’s laws

No magnetic hysteresis

We also need to separate running with load and free running, as it’s particular case.

Dependence of coefficient against frequency (with load)

- Measuring parameters of our transformer

A

Ohm’s law:

V

We used small DC voltages to measure the resistance of the winding

We will seek the solution of this equations in form:

~

V

theory

experiment

M(mutual inductance factor) depends on frequency because of depending µ on it

Diffusion flux

Inside flux

Dependence of coefficient against angle

- Describing all looses in the transformer

We measured steel losses using the chain (right).

A

V

V

~

r

h

Dependence ofdiffusionfluxagainst voltage

We can rebuild our chain using diffusion inductance

- Measuring and modeling hysteresis

If we know all the coefficients, we can have as a result of our model real hysteresis loop

- We are changing numbers of coil turns

A

V

V

~

We can imagine a real winding as system of coils, resistances and capacitors.

- Transformer coefficient depends on
- frequency because of the resistances of windings and the dependence of induction on frequency
- the load because of the resistance of the 2nd winding
- input voltage because of hysteresis mode
- turns number of the windings because of dependence M on it

Dependence ofsteel losses in the 2nd winding of voltage

Dependence of coefficient against frequency (with load)

Unideal transformer

Resistance of the winding

Losses of the flux

Losses in the core