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Theory of OperationAuthor: E.E. Kimberly Transformers operate on the principle of mutual inductance described in Chapter 5. Those used for unusual purposes sometimes have air cores, but almost all have iron cores because of the advantages of smaller size, lower cost, and higher efficiency.^{(1)}
Fig. 171 (a) shows a simple transformer having two coils on an iron core. An alternating voltage V applied to one coil, called the primary, will cause a current Ie, called the exciting current, to flow as in an ordinary inductance coil. The exciting current produces the mutual flux Φ_{m} and also produces in the air around the primary coil a very small leakage flux which is neligibly small compared to Φ_{m}. The flux Φ_{m} produces a counter electromotive force E_{1} which would be equal and opposite to V if there were no resistance and no other flux linking the primary coil. If the primary coil has N_{1} turns and the secondary coil has N_{2} turns and N_{1} = N_{2}, then Φ_{m} will also generate a voltage E_{2} in the secondary coil; E_{2} will equal E_{1} because both coils have the same number of turns. The number of volts generated per turn of N_{1} and N_{2} will be the same because Φ_{m} is common to both coils. The voltage E_{2} is then proportional to N_{2} and can be made any desired value by proper choice of secondary turns N_{2}. The ratio of input voltage to output voltage is then
(171) When a load is connected to the secondary coil, the resistances and leakage fluxes of both coils modify the actual ratio of primary voltage to secondary terminal voltage because they cause a leakage impedance voltage drop. When a current I_{2} flows in Nz turns and a load circuit, as shown in Fig. 171 (b), a magnetomotive force mmF_{2}, which is proportional to N_{2}I_{2}, is produced in the secondary coil. By Lenz's Law, mmF_{2} is in opposition to Φ_{m} and tends to reduce Φ_{m}. Also, mmF_{2} produces a flux Φ_{L2} in the air paths around the secondary coil, and Φ_{L2} generates a voltage ez = L_{2} dI_{2}/dt which is subtractive from E_{2}. Furthermore, the slight reduction of Φ_{m} reduces , and so an additional primary component of current I'1 appears in the primary coil turns N_{1}. A magnetomotive force mmfi is produced in the primary coil by N_{1}I_{1} and produces a leakage flux Φ_{L1} in the air paths around the primary coil. This flux in turn generates a voltage in the primary coil. The current I_{1} is the vector sum of Ie and I'1. The counter voltages  E_{1} and  E_{2} cause reactance drops I_{1}X_{1} and 72X_{2} in the primary coil and secondary coil, respectively. The fluxes Φ_{L1} and Φ_{L2} are called leakage fluxes because each links only the coil that produces it and leaks around the other instead of linking it as does Φ_{m}. The leakage fluxes are not actually distinguishable one from the other in the transformer but are separated in theory for the purpose of analysis. The transformer serves not only to transform voltages from one level to another but also to isolate one circuit from all others when necessary. The voltage and power losses are so small in most transformers that, for most practical purposes, it can be said that the voltampere input is equal to the voltampere output. Unless the leakage impedances are unusually large, the power factor on the primary side is about the same as that on the loaded secondary side.


Home Transformers Theory of Operation 