 # Difference Between Ideal and Real or Practical Transformer

## What is the Difference Between Ideal Transformer & Practical or Real Transformer?

An ideal transformer is a theoretical model of a practical transformer without losses. In short:

• Transformer + 0% losses = Ideal Transformer
• Transformer + Losses = Practical Transformer

Let’s discuss what is the main difference between them. ### What is an Ideal Transformer?

An ideal transformer is no more but an imaginary like a theoretical model which doesn’t exist in real life with practical applications. It has zero losses at all having 100% efficiency which is only used to represent the current and voltage transformation ratio of the practical transformer while analyzing circuits related to it.

The ideal transformer has the following assumptions

• There are no losses in the transformer (Leakage, ohmic, iron core (I2R as eddy current & hysteresis losses) etc.
• There is no leakage flux or leakage inductance.
• 100% efficient e.g. Input = Output.
• The core permeability is infinite.

The schematic diagram of the ideal iron-core transformer is shown in the figure below. According to Lenz’s law, E1 is equal and opposite to V1.

E1 = –V1

The below figure shows the phasor diagram of an ideal transformer. The transformation ratio also known as turns ratio “a” for an ideal transformer is defined as below equations. Where,

• a = Transformation ratio
• T1, T2 = Number of turns in primary and secondary winding
• E1, E2 = Induced EMF
• V1 = Supply voltage (primary voltage)
• V= Secondary Voltage
• I1, I2 = Current passes through the primary and secondary winding

From the above equations, we get

I1T1 = I2T2

similarly;

E1I1 = E2I2

Hence:

S1 = S2

In other words; the input apparent power is equal to the output apparent power.

Input Apparent Power = Output Apparent Power

Keep in mind that ideal transformer doesn’t exist in real life applications and these assumptions are only applicable to an ideal transformer and all of the above mentioned points are not valid for practical transformers.

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### What is a Real Transformer?

If we relax these assumptions (mentioned and applicable only for the ideal transformer above) one by one, we will arrive at the model of a practical or real transformer. In other words, losses occur in a real or practical transformer (aka practical transformer or actual transformer). Let’s consider a practical transformer having winding resistance and leakage reactance as follow:

Winding Resistance

The equivalent circuit of the transformer after adding resistance in the circuit is shown in the figure below. Due to the voltage drop because of added resistances, this way, the secondary terminal voltage V2 is less than the secondary induced EMF E2 by an amount of secondary voltage drop I2R2 as V2 ≠ E2 and supply voltage V1≠E1. Therefore;

V2 = E2 – I2R2 Same is the case for primary induced EMF E1 is equal to the vector difference of supply voltage V1 and primary voltage drop I1R1.

E1 = V1 – I1R1

Leakage Reactance

The flux generated in the winding of actual transformer passes completely through the core and links both windings is called mutual flux ФM. The typical diagram of fluxes in a transformer is shown in the figure for real transformer above.

Due to the leakage flux ФL1 and ФL2, the induced EMF EL1 and EL2 are different from induced EMF E1 and E2 caused by the mutual flux ФM. The representation of leakage reactance (X1 and X2) is shown in the figure below. Where,

• X1 = Primary leakage reactance
• X2 = Secondary leakage reactance

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### Key Differences between Ideal & Real Transformers

The following table shows the main differences between an ideal & Real transformer.

 Characteristics Ideal Transformer Practical / Real Transformer Existence Imaginary – Doesn’t exist. Exists in real life for practical applications Efficiency = 100% > 100% Losses No Yes Inductive Material Pure Inductive Material Pure 2 Set of Inductive Materials I2R losses No Yes iron loss & Core losses No Yes Core Permeability μC Infinite (∞) Finite Core Reluctance Zero Lower Leakage Flux ΦC & Reactance No Yes Ohmic Resistance drop No Yes Condition Ideal Practical Applications Not practical uses, but only to analyze circuits to represent the current & voltage transformation ratios. Practically used in real life applications such as step-up or step-down the level of current or voltage for utilization.

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