The transformer is one of the simplest of electrical devices. Its basic design, materials, and principles have changed little over the last one hundred years, yet transformer designs and materials continue to be improved. Transformers are essential in high voltage power transmission providing an economical means of transmitting power over large distances. The simplicity, reliability, and economy of conversion of voltages by transformers was the principal factor in the selection of alternating current power transmission in the "War of Currents" in the late 1880's. In electronic circuitry, new methods of circuit design have replaced some of the applications of transformers, but electronic technology has also developed new transformer designs and applications. Transformers come in a range of sizes from a thumbnail-sized coupling transformer hidden inside a stage microphone to gigawatt units used to interconnect large portions of national power grids, all operating with the same basic principles and with many similarities in their parts. Transformers alone cannot do the following:
• Convert DC to AC or vice versa
• Change the voltage or current of DC
• Change the AC supply frequency.
However, transformers are components of the systems that perform all these functions.
The transformer may be considered as a simple two-wheel 'gearbox' for electrical voltage and current. The primary winding is analogous to the input shaft and the secondary winding to the output shaft. In this comparison, current is equivalent to shaft speed, voltage to shaft torque. In a gearbox, mechanical power (speed multiplied by torque) is constant (neglecting losses) and is equivalent to electrical power (voltage multiplied by current) which is also constant. The gear ratio is equivalent to the transformer step-up or step-down ratio. A step-up transformer acts analogously to a reduction gear (in which mechanical power is transferred from a small, rapidly rotating gear to a large, slowly rotating gear): it trades current (speed) for voltage (torque), by transferring power from a primary coil to a secondary coil having more turns. A step-down transformer acts analogously to a multiplier gear (in which mechanical power is transferred from a large gear to a small gear): it trades voltage (torque) for current (speed), by transferring power from a primary coil to a secondary coil having fewer turns.
Flux coupling laws
A simple transformer consists of two electrical conductors called the primary winding and the secondary winding. If a time-varying voltage [pic]is applied to the primary winding of [pic]turns, a current will flow in it producing a magnetomotive force (MMF). Just as an electromotive force (EMF) drives current around an electric circuit, so MMF drives magnetic flux through a magnetic circuit. The primary MMF produces a varying magnetic flux [pic]in the core (shaded grey), and induces a back electromotive force (EMF) in opposition to [pic]. In accordance with Faraday's Law, the voltage induced across the primary winding is proportional to the rate of change of flux : [pic]
Similarly, the voltage induced across the secondary winding is: [pic]
With perfect flux coupling, the flux in the secondary winding will be equal to that in the primary winding, and so we can equate [pic]and [pic]. It thus follows that: [pic]
Hence in an ideal transformer, the ratio of the primary and secondary voltages is equal to the ratio of the number of turns in their windings, or alternatively, the voltage per turn is the same for both windings. This leads to the most common use of the transformer: to convert electrical energy at one voltage to energy at a different voltage by means of windings with different numbers of turns. The EMF in the secondary winding, if connected to an electrical circuit, will cause current to flow in the secondary circuit. The...