# What is an Ideal transformer? | Elementary Theory of Ideal Transformer

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### Ideal Transformer Definition:

#### If the secondary is not loaded the energy stored in the magnetic ﬁeld ﬁnds its way back to the source as the ﬂux collapses.If the secondary winding is connected to a load then part of the power from the source is delivered to the load through the magnetic ﬁeld as a link.The medium does not absorb and lose any energy. Power is required to create the ﬁeld and not to maintain the same.As the winding losses can be made very small by proper choice of material, the ideal eﬃciency of a transformer approaches 100%.The large magnetizing current requirement is a major deterrent.However, if now a piece of magnetic material is introduced to form the magnetic circuit Figure(b) the situation changes dramatically.These can be enumerated as below. #### Mutual Induction in the air core #### 6.As the medium is made of a conducting material eddy currents are induced in the same and produces losses. These are called ‘eddy current losses’. To minimize the eddy current losses the steel core is required to be in the form of a stack of insulated laminations.

From the above, it is seen that the introduction of the magnetic core to carry the ﬂux introduced two more losses.Fortunately, the losses due to hysteresis and eddy current for the available grades of steel is very small at power frequencies.Also, the copper losses in the winding due to magnetization current is reduced to an almost insigniﬁcant fraction of the full load losses. Hence steel core is used in power transformers.

#### As a current I0 amp is passed through the primary winding of T1 turns it sets up an mmf of I0T1 ampere which is, in turn, sets up a ﬂux φ through the core.Since the reluctance of the iron path given by R = l/µA is zero as µ → ∞, a vanishingly small value of current I0 is enough to setup a ﬂux which is ﬁnite. As I0 establishes the ﬁeld inside the transformer it is called the magnetizing current of the transformer. #### Thus the RMS primary induced emf is #### Here ψ1peak is the peak value of the ﬂux linkages of the primary.The same mutual ﬂux links the secondary winding.However, the magnitude of the ﬂux linkages will be ψ2peak = T2φm.The induced emf in the secondary can be similarly obtained as, #### which yields the voltage ratio as  #### So far, an unloaded ideal transformer is considered.If now a load impedance ZL is connected across the terminals of the secondary winding a load current ﬂows as marked in Figure(c) above.This load current produces a demagnetizing MMF and the ﬂux tends to collapse.However, this is detected by the primary immediately as both E2 and E1 tend to collapse.The current drawn from supply increases up to a point the ﬂux in the core is restored back to its original value.The demagnetizing MMF produced by the secondary is neutralized by additional magnetizing MMF produces by the primary leaving the mmf and ﬂux in the core as in the case of no-load.Thus the transformer operates under constant induced emf mode.Thus, #### If the reference directions for the two currents are chosen as in the Figure above, then the above equation can be written in phasor form as, #### Thus voltage and current transformation ratio are inverses of one another.If an impedance of ZL is connected across the secondary, #### The input impedance under such conditions is READ HERE  Transformer - Definition, Types, Working Principle, Diagram