__Basics of an ideal transformer__

__Basics of an ideal transformer__

Before discussing the characteristics of an ideal transformer need to understand the basics of an ideal transformer. The transformer is a device, which simply transfers electrical power from one circuit to another circuit while keeping the frequency and power constant and changing the voltage and current level. Depending upon the increase or decrease in voltage level at the output side, transformers can be named as a step-up transformer or step down transformer. In a step-up transformer, the output voltage will be step up by a specific ratio depending upon the construction of the transformer. Similarly, step down transformer decrease the output voltage by a specific ratio again depending upon the construction of the transformer. Both step up or step down transformers do not change the input frequency of the electrical signal and also keep the input and output power same by making the product of current and voltage same at input and output end, i.e.

The transformer is been made up of two coils i.e. primary coil (input side) and secondary coil (output side).

Input is been applied to the primary coil, which causes the production of a magnetic field in the surroundings of the primary coil. This magnetic field reaches secondary coil causing induction of current in secondary coil resulting voltage at the secondary coil. Output voltage induced in secondary coil depends upon the number of turns of the primary and secondary coil and can be found by using the formula:

__Characteristics of an Ideal transformer__

__Characteristics of an Ideal transformer__

An ideal transformer is not possible to design due to the limitations of materials used for the construction of a transformer. However, we can theoretically explain the characteristics of an ideal transformer. A few of the characteristics of an ideal transformer are been mentioned below.

**Zero resistance of coils**

The resistance of coils used for the construction of the transformer will be negligible.

**Zero reactance of coils**

Unlike actual copper coils, ideal transformers have zero reactance.

**No coper loss**

The ideal transformer does not have coper losses because both secondary and primary windings have no reactance or resistance.

**No hysteresis loss**

As in non-ideal coils, when current passes through a coil there is a phenomenon of magnetization and reversal of magnetization depending upon the current direction. There is always lag in magnetization direction and current cycle causing hysteresis loss. An ideal transformer, there is no phenomenon of hysteresis eliminating the loss due to hysteresis.

**No eddy current loss**

Eddy current is the current, which induces in a primary coil when the magnetic field produced due to the flow of current in the coil interacts with the turns of the same primary coil itself. The direction of this current will be in the opposite direction to the input current, causing loss due to opposition to the input. An ideal transformer there is no eddy current present in the primary coil as flux produced around the primary do not interact with the primary coil itself.

**No flux leakage**

An ideal transformer, there is no leakage of magnetic flux. All the flux generated due to the flow of current through the primary winding of the transformer is been directly linked to the secondary coil. No flux will be interacting with the primary winding or will interact with any other part of the transformer or outside space of the transformer eliminating any loss due to the leakage of flux.

**Infinite Permeability**

As there is no hysterias loss in an ideal transformer, so no additional magnetization current is required to produce flux in the primary coil. Thus, the ideal transformer has infinite permeability and the B-H curve will show a vertical line indicating no additional current requirement for the establishment of flux.

**No loss**

As ideal transformer does not have hysterias loss, eddy current loss or flux leakage, so it has no loss of power.

**100% Efficiency**

An ideal transformer has 100% efficiency; means power delivered at the output is equal to the input power. Therefore, there is no power loss or gain in an ideal transformer

**No frequency dependencies**

The ideal transformer does not affect the input frequency of the signal and provides the same frequency at the output. The ideal transformer works independently of frequency values and its working does not affect different frequency values.

Therefore, an ideal transformer is been made up of two resistance fewer coils with no core loss, eddy current loss and the magnetic field produced in the first coil having infinite permeability of magnetic flux linking with the second circuit.

There is no leakage of flux meaning that both the coils have no physical connection between them, but they have a complete link between both of them by means of magnetic flux. As magnetic flux of the primary coil is been completely transferred to the secondary coil.

In an ideal transformer, when alternating voltage Vp is applied to the primary winding of the transformer, peak flux Φ_{p }is induced in a primary coil having an Np number of turns. This flux Φ_{p} is been directly linked to the secondary coil where current is induced in the secondary coil and voltage Vs is produced in the secondary coil having a number of turns equal to Ns. For ideal transformer, emf (electromotive force) induced in secondary coil Vs can be given by:

From the relation above, it is clear that output voltage is directly dependent on a number of turns of primary and secondary coils. When the primary coil will have more number of turns, then the transformer will be stepping down. Similarly, the transformer will be step up in case of more turns in the secondary coil as compared to the primary coil.

In the case of an ideal transformer, when ends of secondary coils are been connected to the load and current I_{s} is been flowing through the load. As previously discussed that the material used for the construction of ideal transformer coils have infinite permeability. Therefore, it requires no additional excitation current for flux induction, and primary coil current I_{p} balances the current in secondary coil I_{s} by using the balancing relation:

From the discussion above it is clear that the ideal transformer can only be discussed theoretically for analysis purposes. However, the practical design of the ideal transformer is not possible due to the unavailability of ideal coil materials and leakage of flux and different losses.

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