How does a Transformer work ?

What is a transformer and how does it work?

A transformer is an electrical apparatus designed to convert alternating current from one voltage to another. It can be designed to "step up" or "step down" voltages and works on the magnetic induction principle. A transformer has no moving parts and is a completely static solid state device, which insures,

under normal operating conditions, a long and trouble-free life. It consists, in

its simplest form, of two or more coils of insulated wire wound on a laminated steel core. When voltage is introduced to one coil, called the primary, it magnetizes the iron core. A voltage is then induced in the other coil, called the

secondary or output coil. The change of voltage (or voltage ratio) between the primary and secondary depends on the turns ratio of the two coils.

Ideal transformer equations

By Faraday's law of induction

V_\text{S} = -N_\text{S} \frac{\mathrm{d}\Phi}{\mathrm{d}t}

V_\text{P} = -N_\text{P} \frac{\mathrm{d}\Phi}{\mathrm{d}t}

Combining ratio of

Turns ratio

=\frac{V_\text{P}}{V_\text{S}} = \frac{-N_\text{P}}{-N_\text{S}}=a

for step-down transformers, a > 1

for step-up transformers, a < 1

By law of Conservation of Energy, apparent, real and reactive power are each conserved in the input and output

S=I_\text{P} V_\text{P} = I_\text{S} V_\text{S}

Combining (3) & (4) with this endnote^[b] yields the ideal transformer identity

\frac{V_\text{P}}{V_\text{S}} = \frac{I_\text{S}}{I_\text{P}}=\frac{N_\text{P}}{N_\text{S}}=\sqrt{\frac{L_\text{P}}{L_\text{S}}}=a

By Ohm's Law and ideal transformer identity

Z_\text{L}=\frac{V_\text{S}}{I_\text{S}}

. . . (6)

Apparent load impedance Z'_L (Z_L referred to the primary)

Z'_\text{L} = \frac{V_\text{P}}{I_\text{P}}=\frac{aV_\text{S}}{I_\text{S}/a}=a^2\frac{V_\text{S}}{I_\text{S}}=a^2{Z_\text{L}}

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