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Transformer Principles

Transformers are passive devices for transforming voltage and current.

Transformers are extremely efficient machines, with 95 percent efficiency being commonplace and 99 percent efficiency being achievable. There is almost no upper limit to their power-handling capability, and the lower limit is only set by the allowable no-load loss.

Transformers and inductors perform fundamental circuit functions and they are a necessary component in electrical systems as diverse as distribution terminals for multi megawatt power generating stations to hand-held radio transceivers operating on a fraction of a watt.

Transformers are the heaviest, largest, and often most expensive of circuit components and the geometry of the magnetic circuit is three-dimensional - this property places a fundamental restraint on reducing transformer size. The properties of available materials limit weight reduction and the high cost of transformers is due to the impracticability of standardisation, the materials needed, and the processes inherent in their manufacture.

Transformers are indispensable for voltage transformation in power applications their ability to isolate circuits and to alter ground conventions can often be matched in no other convenient manner. They are needed in frequency selective circuits whose operation depends on the response o~ inductances. They are extremely rugged nad capable of withstanding severe environmental conditions. 

 

The transformer is based on two principles: first, that an electric current can produce a magnetic field (electromagnetism), and, second that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). Changing the current in the primary coil changes the magnetic flux that is developed. The changing magnetic flux induces a voltage in the secondary coil.

An ideal transformer is shown in the above diagram. Current passing through the primary coil creates a magnetic field. The primary and secondary coils are wrapped around a core of high magnetic permeability, such as iron, so that most of the magnetic flux passes through both the primary and secondary coils.

Induction law

The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that:

V_text{s} = N_text{s} frac{mathrm{d}Phi}{mathrm{d}t},

where Vs is the instantaneous voltage, Ns is the number of turns in the secondary coil and Φ is the magnetic flux through one turn of the coil. If the turns of the coil are oriented perpendicular to the magnetic field lines, the flux is the product of the magnetic flux density B and the area A through which it cuts. The area is constant, being equal to the cross-sectional area of the transformer core, whereas the magnetic field varies with time according to the excitation of the primary. Since the same magnetic flux passes through both the primary and secondary coils in an ideal transformer, the instantaneous voltage across the primary winding equals

V_text{p} = N_text{p} frac{mathrm{d}Phi}{mathrm{d}t}.

Taking the ratio of the two equations for Vs and Vp gives the basic equation for stepping up or stepping down the voltage

frac{V_text{s}}{V_text{p}} = frac{N_text{s}}{N_text{p}}.