A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer's core, which induces a varying electromotive force (EMF) across any other coils wound around the same core. Electrical energy can be transferred between separate coils without a metallic (conductive) connection between the two circuits. Faraday's law of induction, discovered in 1831, describes the induced voltage effect in any coil due to a changing magnetic flux encircled by the coil. Transformers are used to change AC voltage levels, such transformers being termed step-up or step-down type to increase or decrease voltage level, respectively. Transformers can also be used to provide galvanic isolation between circuits as well as to couple stages of signal-processing circuits. Since the invention of the first constant-potential transformer in 1885, transformers have become essential for the transmission, distribution, and utilization of alternating current electric power. A wide range of transformer designs is encountered in electronic and electric power applications. Transformers range in size from RF transformers less than a cubic centimeter in volume, to units weighing hundreds of tons used to interconnect the power grid. Principles Ideal transformer equations By Faraday's law of induction: where is the instantaneous voltage, is the number of turns in a winding, dΦ/dt is the derivative of the magnetic flux Φ through one turn of the winding over time (t), and subscripts P and S denotes primary and secondary. Combining the ratio of eq. 1 & eq. 2: where for a step-up transformer a < 1 and for a step-down transformer a > 1. By the law of conservation of energy, apparent, real and reactive power are each conserved in the input and output: where is apparent power and is current. Combining Eq. 3 & Eq. 4 with this endnote gives the ideal transformer identity: where is winding self-inductance. By Ohm's law and ideal transformer identity: where is the load impedance of the secondary circuit & is the apparent load or driving point impedance of the primary circuit, the superscript denoting referred to the primary. Ideal transformer An ideal transformer is linear, lossless and perfectly coupled. Perfect coupling implies infinitely high core magnetic permeability and winding inductance and zero net magnetomotive force (i.e. ipnp − isns = 0). A varying current in the transformer's primary winding