As we know, all materials have electrical resistance, including the wire wrapped the core of a transformer to form its primary and secondary windings. The resistance in these windings is responsible for an average power loss, PI> that can be calculated in the usual way:
where R, and R. are the resistances of the primary and secondary windings, and Ip(rms) and Is(rms) are the effective values of the primary and secondary currents, respectively. Since the core is usually wound with copper wire, these losses are often called copper losses. In most transformers, copper losses are relatively small, typically on the order of 1% of the total power transferred.
A-transformer core itself has a certain inductance, so when flux in the core changes with time, as it does in normal transformer operation, electrical currents are induced in the core. If the core material is a conductor, such as the iron in an iron-core transformer, these currents may be large enough to cause noticeable power losses. The currents induced in a core this way are called eddy currents, and eddy current losses are losses caused by current flowing through the resistance of the core material. Eddy current losses increase as the frequency of the voltage applied to the transformer increases, because higher frequencies mean greater rates of change of flux, which in turn mean larger induced currents.
One popular construction method that is used to reduce eddy current losses is to assemble the core from laminated sheets. These laminations, or layers, are insulated from each other, so current flow is interrupted. Ferrite cores, which are from a special type of ceramic that has a small electrical conductivity but large permeability, are also used for that purpose.
Magnetism in ferromagnetic materials is attributable to the orientation of tiny magnetic domains. The magnetic fields produced by these domains align themselves with an externally applied magnetic field. In an inductor or transformer core, the external field is created by current flowing through the windings. When the current
is ac, as it is in a transformer, the external field is continually reversing direction, so the magnetic domains must also continually reverse their orientation. There is a type of inertia, or resistance to change.which is an inherent property of magnetic domains, and which requires energy to overcome. This energy must be supplied each time the orientation of a domain is changed, so energy is consumed in the core of a transformer as it responds to continually changing alternating current.
The energy consumed in that process is called hysteresis loss and is responsible for still another power loss in practical transformers. Hysteresis losses increase with the frequency of the applied voltage, because higher frequencies force the domains to reverse direction more often during a given interval of time.
The useful output power of a transformer is that which is delivered to its load, the input power is that which is delivered from a source to its primary side. Ihe efficiency of a transformer is defined the same way it is forother electrical divices:
Where PI is the sum of all the power losses in the transformer. Eddy current and hysteresis losses are usually grouped into a category called core losses, because they are both associated with the core. Thus, PI(totaJ) = Pcore + Pcopper’ Of course, the efficiency given-by (11-67) is always less than 1 and is often expressed as a percentage. Practical transformer efficiencies are generally quite high in comparison to other electrical and electronic devices, on the order of 90% to 98%.
The transformer shown in Figure 11-34 has a primary winding resistance of 0.5 and a secondary winding resistance of 0.1 . The power delivered to the load resistance is.48 Wand the effective value of the primary current is 0.4 A rms. If the core losses are 0.9 W, find the efficiency of the transformer.