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Theory of Operation

Author: 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. 17-1. Schematic Transformer Diagram

Fig. 17-1 (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 Φm and also produces in the air around the primary coil a very small leakage flux which is neligibly small compared to Φm. The flux Φm produces a counter electromotive force E1 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 N1 turns and the secondary coil has N2 turns and N1 = N2, then Φm will also generate a voltage E2 in the secondary coil; E2 will equal E1 because both coils have the same number of turns. The number of volts generated per turn of N1 and N2 will be the same because Φm is common to both coils. The voltage E2 is then proportional to N2 and can be made any desired value by proper choice of secondary turns N2. The ratio of input voltage to output voltage is then

ee_101-192.png (17-1)

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 I2 flows in Nz turns and a load circuit, as shown in Fig. 17-1 (b), a magnetomotive force mmF2, which is proportional to N2I2, is produced in the secondary coil. By Lenz's Law, mmF2 is in opposition to Φm and tends to reduce Φm. Also, mmF2 produces a flux ΦL2 in the air paths around the secondary coil, and ΦL2 generates a voltage -ez = L2 dI2/dt which is subtractive from E2. Furthermore, the slight reduction of Φm reduces , and so an additional primary component of current I'1 appears in the primary coil turns N1. A magnetomotive force mmfi is produced in the primary coil by N1I1 and produces a leakage flux ΦL1 in the air paths around the primary coil. This flux in turn generates a voltage in the primary coil.


The current I1 is the vector sum of Ie and I'1. The counter voltages - E1 and - E2 cause reactance drops I1X1 and 72X2 in the primary coil and secondary coil, respectively. The fluxes ΦL1 and ΦL2 are called leakage fluxes because each links only the coil that produces it and leaks around the other instead of linking it as does Φm. 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 volt-ampere input is equal to the volt-ampere 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.

(1) An excellent and thorough introduction to electronic transformers can be found in R. Lee's book "Electronic Transformers".

Last Update: 2011-02-23