When designing a transformer, you want to make sure that it is efficient. There are fundamental principles that you need to know: the amount of windings, the core losses, and the flux.

Magnetomotive force (mmf) in a transformer is the current in a coil of wire wrapped around a core, which produces a magnetic flux in the core. As Ohm’s Law is defined as V= IR, the relationship for mmf is defined as F  = Ni, where “F ” is the symbol for mmf, “N” is the symbol for number of turns of wire in coil and “i” is the symbol for current. The measurement for mmf is in ampere-turns.

The relationship between the mmf and the flux in the core is defined as: Φ = F/R, where R is the total reluctance in the core. The reluctance is the counterpart of electrical resistance. It obeys the same rules as resistances in an electric circuit. 

Determining the polarity of a mmf source in a magnetic circuit using the right-hand rule.

A winding of N turns of wire is wrapped around one leg of the core, which is comprised of iron or certain other similar metals (collectively called ferromagnetic materials). The current passing within the path of I_net is then Ni. Since the coil of wire cuts the path of I_net N times, losses occur.

Transformer losses are divided into losses in the windings, termed copper loss, and those in the magnetic circuit, termed iron loss. Losses in the transformer arise from:

Winding resistance is the result of current flowing through the windings causes resistive heating of the conductors. At higher frequencies, skin effect and proximity effect create additional winding resistance and losses.

Hysteresis losses result each time the magnetic field is reversed. A small amount of energy is lost due to hysteresis within the core. For a given core material, the loss is proportional to the frequency, and is a function of the peak flux density to which it is subjected. These losses also produce heat within the core of the transformer.

Eddy currents losses occur when ferromagnetic materials are used. Ferromagnetic materials are good conductors, and a solid core made from such a material also constitutes a single short-circuited turn throughout its entire length. Eddy currents, therefore circulate within the core in a plane normal to the flux, and are responsible for resistive heating of the core material. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness.

Magnetostriction an effect in the magnetic flux in a ferromagnetic material, such as the core, which causes it to physically expand and contract slightly with each cycle of the magnetic field. This produces the buzzing sound commonly associated with transformers, and in turn causes losses due to frictional heating in susceptible cores.

Mechanical losses, in addition to magnetostriction, are the alternating magnetic field that causes fluctuating electromagnetic forces (emf) between the primary and secondary windings. These losses incite vibrations within nearby metalwork, adding to the buzzing noise, and consuming a small amount of power.

Stray losses are leakage inductance. It is, by itself, largely lossless, since energy supplied to its magnetic fields is returned to the supply with the next half-cycle. However, any leakage flux that intercepts nearby conductive materials such as the transformer’s support structure will give rise to eddy currents and be converted to heat. There are also radiative losses due to the oscillating magnetic field, but these are usually small.

When winding copper around the core, it is expected that losses will occur. The series resistance accounts for the Copper (I²R) losses. Hysteresis and Eddy current losses are losses that are accounted for by the resistor R_c. As previously stated, both Hysteresis and Eddy current losses cause heating in the core material, and both losses must be considered in the design of any machine or transformer. Since both losses occur within the metal of the core, they are usually combined and called core losses.

For the purpose of this article, I will give you a simple explanation of eddy current loss. In a transformer we supply alternating current in the primary, this alternating current produces an alternating magnetizing flux in the core. As this flux links with secondary winding there will be induced voltage in secondary, resulting in current to flow through the load connected with it. Some of the alternating fluxes of transformer may also link with other conducting parts like a steel core or an iron body of transformer. As the alternating flux links with these parts of transformer, there would be a locally induced emf. Due to these emfs there would be currents, which will circulate locally at that parts of the transformer. These circulating current will not contribute in output of the transformer and dissipated as heat. As the transformer is loaded it produces heat. When it heats, I²R losses occur. The amount of heat produced is dependent upon how much load is on the transformer. The higher the load, the more heat is produced. This type of energy loss is called eddy current loss of transformer.

Where V_p, I_p and N_p relate to the primary side of the transformer. V_s, N_s, and I_s relate to the secondary side of the transformer.

Transformer designers cannot change the current portion of the I²R losses, which are determined by the load requirements. They can only change the resistance part of the I²R losses by using a material that has a low resistance per cross-sectional area without adding significantly to the cost of the transformer. Most transformer designers have found copper the best conductor considering the weight, size, cost and resistance of the conductor. Designers can also reduce the resistance of the conductor by increasing the cross-sectional area of the conductor.

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