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# Transformers - EE201 Transformers Oct 9 2007 The inductance...

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EE201 Transformers Oct. 9, 2007 Denard Lynch Page 1 of 7 The inductance we have studied previously is correctly know as the self inductance of a coil, commonly called just inductance . Mutual inductance is the inductive effect (the reaction to a changing flux predicted by Faraday’s Law) in one coil due to the flux created in another . (Refer to notes on mutual inductance in previous notes on “Inductance”.) This mutual inductance is used to advantage in a device called a transformer, which is used extensively in the electrical and electronics industries. A transformer is a device in which two coils are deliberately arranged so that the flux from one coil is maximally coupled to a second coil, usually on the same core. Assume for the moment that there is a flux established in one of two closely coupled coils, Φ p , then the voltage induced in this coil, e p , is given by: e p = N p d Φ p dt = L p di p dt Similarly, the voltage induced in the second coil would be: e s = N s d Φ s dt If we define a coefficient of coupling, k , as k = Φ s Φ p , where Φ p is the originally induced flux and Φ s is the portion of the flux which couples the second coil. Clearly Φ s can never be greater than Φ p , so k max 1. Modern transformers are “tightly coupled”, with k 1. Most of the useful formulas describing transformer behaviour are developed here assuming that k = 1, but they could easily be modified to reflect the performance of a “loosely coupled” coil ( k < 1). The first useful operational formula: if k = 1, Φ p = Φ s = Φ e p = N s d Φ dt , and e s = N s d Φ dt and e p e s = N p N s , where N s N p is called the turns ratio, n therefore, e s = ne p (1) Note that a turns ratio, n > 1 is called a step-up transformer, a turns ratio < 1 is called a step-down transformer, and an n = 1 is called an isolation transformer. While the voltage depends on changing flux, the flux depends only on the current (Ampere’s Law for magnetic circuits).

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EE201 Transformers Oct. 9, 2007 Denard Lynch Page 2 of 7 Recall = NI = Φℜ or Φ = NI . The primary flux: Φ p = N p I p p , and the secondary flux must be: Φ s = N s I s s . Since we have assumed k = 1, Φ p = Φ s = Φ , and since they are wound on the same core, p = s .
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