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EMF Equation of a Transformer

Explore the step-by-step derivation of the transformer EMF equation using sinusoidal flux. Understand flux linkage, turn ratio, and the role of core flux density in voltage generation.

Edwiin
Field: Power switch
10Year<
China
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Background of Transformer EMF Equation Derivation

When a sinusoidal voltage is applied to the transformer's primary winding, an alternating flux ϕm is induced in the iron core. This sinusoidal flux links both primary and secondary windings, with its functional form described by a sine function.

Mathematical Derivation of Flux Rate of Change

The following outlines the derivation of the transformer's EMF equation, with defined parameters:

  • ϕm: Maximum flux (Weber)

  • f: Supply frequency (Hz)

  • N1: Number of primary turns

  • N2: Number of secondary turns

  • &Phi;: Flux per turn (Weber)

EMF Equation of a Transformer

EMF Equation of a Transformer

EMF Equation of a Transformer

EMF Equation of a Transformer

Turn Ratio and Flux Density Relation

The above equation is referred to as the turn ratio, where K denotes the transformation ratio.

Using the relation ϕm=Bm&times;Ai (where Ai is the iron core cross-sectional area and Bm is the maximum flux density), Equations (8) and (9) can also be expressed as:

EMF Equation of a Transformer

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