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Concept
Transformer
Summary
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer's core, which induces a varying electromotive force (EMF) across any other coils wound around the same core. Electrical energy can be transferred between separate coils without a metallic (conductive) connection between the two circuits. Faraday's law of induction, discovered in 1831, describes the induced voltage effect in any coil due to a changing magnetic flux encircled by the coil.
Transformers are used to change AC voltage levels, such transformers being termed step-up or step-down type to increase or decrease voltage level, respectively. Transformers can also be used to provide galvanic isolation between circuits as well as to couple stages of signal-processing circuits. Since the invention of the first constant-potential transformer in 1885, transformers have become essential for the transmission, distribution, and utilization of alternating current electric power. A wide range of transformer designs is encountered in electronic and electric power applications. Transformers range in size from RF transformers less than a cubic centimeter in volume, to units weighing hundreds of tons used to interconnect the power grid.
Ideal transformer equations
By Faraday's law of induction:
where is the instantaneous voltage, is the number of turns in a winding, dΦ/dt is the derivative of the magnetic flux Φ through one turn of the winding over time (t), and subscripts P and S denotes primary and secondary.
Combining the ratio of eq. 1 & eq. 2:
where for a step-up transformer a < 1 and for a step-down transformer a > 1.
By the law of conservation of energy, apparent, real and reactive power are each conserved in the input and output:
where is apparent power and is current.
Combining Eq. 3 & Eq. 4 with this endnote gives the ideal transformer identity:
where is winding self-inductance.
Official source
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