What Is an Ideal Transformer?

What Is an Ideal Transformer? . In this article, we will look into a special type of transformer known as the Ideal Transformer which is designed in ideal condition with no loss and 100% efficiency. We will discuss what is a transformer, ideal transformer. We will look into the working principle, properties, and equations of the ideal transformer. We will also look into an ideal transformer with load and with no load. In addition to these, we will also see the phasor diagram. Later, we will discuss the advantages, disadvantages, and applications of, the ideal transformer.

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What is a Transformer?

A transformer is a device that transfers electrical energy between two or more circuits. It is used for AC and is used for changing the voltage without changing the frequency. These types of transformers are known as step-up and step-down transformers. It uses the principle of electromagnetic induction for the transfer of energy. Transformers typically consist of two coils of wire these are known as primary and secondary windings.

Ideal Transformer

An Ideal Transformer is a type of imaginary transformer used as a theoretical approach to analyze the behavior of real transformers. This transformer does not have any loss of power, so the efficiency is 100%.In an Ideal Transformer, there is no leakage flux which means that the magnetic flux generated by the Primary winding will be linked with the secondary will have no loss. Also, an ideal transformer operates without magnetic saturation, maintaining linear magnetic properties regardless of the applied voltage or current.

The efficiency of an ideal transformer is 100% as the I²R loss and core loss of the transformer are zero. But in practical transformer, there are some losses that cannot be neglected. And hence, we cannot achieve 100% efficiency in a practical transformer.

Here, two coils are wound in the common magnetic core. The coil that is connected with the supply voltage V₁ is a primary winding and the coil that is connected with the load Z_L is a secondary winding.

As we have discussed in the properties of an ideal transformer that there are zero impedances in both windings. Therefore, the voltage induced in the primary winding is equal to the applied voltage V₁. Similarly, the voltage induced in secondary winding E₂ is the same as the secondary voltage V₂.

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To produce the required MMF and mutual flux Ф_M, the supply current I₁ is sufficient. This MMF is enough to overcome the demagnetizing effect of the secondary MMF as a result of load.

According to Lenz’s law, E₁ is equal and opposite to V₁.

E₁ = –V₁

The primary and secondary EMF is induced by the same mutual flux. Therefore, the E₁ and E₂ are in the same direction and opposite to the direction of V₁.

The magnetizing current I_μ produces mutual flux Ф_M in phase. And I_μ lags V₁ by 90˚. E₁ and E₂ are produced by mutual flux Ф_M and lags by 90˚. The secondary voltage V₂ is equal in magnitude to E₂ and is opposite to primary voltage V₁.

The below figure shows the phasor diagram of an ideal transformer.

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The transformation ratio (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)
• V₂ = Secondary Voltage
• I₁, I₂ = Current passes through the primary and secondary winding

From the above equation,

I₁T₁ = I₂T₂

According to the above equation, we can say that the demagnetizing ampere-turns (AT) of the secondary winding are equal and opposite to the magnetizing MMF of a primary winding of an ideal transformer.

E₁I₁ = E₂I₂

S₁ = S₂

According to the above equation, the apparent power (volt-amperes) drawn from the primary supply is equal to the apparent power transferred to the secondary without any loss in the ideal transformer.

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

Input Apparent Power = Output Apparent Power

Therefore, the KVA input of an ideal transformer is equal to the KVA output. This is not happening in the case of the practical transformer as there are some losses.

Properties of an Ideal Transformer

• The windings have very small or no resistance.
• As there is no resistance there will no loss.
• The efficiency will be 100%.
• There will be perfect coupling between the primary and secondary windings.
• There will no core loss from eddy currents and hysteresis loop.
• There will be no leakage flux.
• This is a perfect linear device.

Advantages of Ideal Transformer

• Ideal transformer is 100% efficient and thus have zero power wastage.
• They are easy to model, can be used to simplify and analyze complex transformer designs.
• They are useful in isolating the input and output circuits so as to avoid grounding.
• It can be used for power transformation like step up and step down transformers.

Disadvantages of Ideal Transformer

• This case is only theoretically possible and isn’t true in real world or practical applications.
• As it has no loss, so analysis of loss conditions can’t be done.
• Ideal transformers has a limited frequency range and it can’t be used to study the behavior of large frequencies.
• It is assumed to have perfect coupling but in reality there is leakage flux which reduces the efficiency.

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Applications of Ideal Transformer

• Ideal transformers are used to analyze the behavior of the practical transformer, as there is no loss and leakage of flux it easier to analyze.
• Ideal transformers are used for analysis of step-up and step-down transformer’s performance. Thus they are used for voltage transformation.
• This type of transformer are used to transmitting electricity at long ranges by stepping up the voltage of the transformer.
• It is used for coupling of signals which is used in audio and telecommunications.
• They are used of isolation of circuits to prevent it from grounding.
• The conversion ratio is used for voltage regulation in transformers.

Practical Transformer

An ideal transformer is explained with some assumptions. These assumptions are not valid for the practical transformer. Because, in an ideal transformer, we have assumed windings with zero resistance and core has infinite permeability. This is not possible as all windings have resistance and core material is not available with infinite permeability.

Therefore, in a practical transformer, we need to consider the winding resistance and leakage reactance.

Winding Resistance

In a practical or actual transformer, there is always some resistance in the primary and secondary winding. The effect of winging resistance considers by adding resistance in series with each winding. The equivalent circuit of the transformer after adding resistance is shown in the figure below.

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As the resistance is added to the circuit, there are some amounts of voltage drop that occur in the circuit. Therefore, the induced EMF in the windings is not the same as the voltage. So, we cannot assume secondary terminal voltage V₂ is equal to E₂ and supply voltage V₁ is equal to E₁.

The secondary terminal voltage V₂ is less than the secondary induced EMF E₂ by an amount of secondary voltage drop I₂R₂.

V₂ = E₂ – I₂R₂

Similarly, primary induced EMF E₁ is equal to the vector difference of supply voltage V₁ and primary voltage drop I₁R₁.

E₁ = V₁ – I₁R₁

Leakage Reactance

For an ideal transformer, we have assumed that the flux produced by the primary winding links both the primary and secondary windings. But in the case of the actual transformer, not all produced flux is available in the magnetic core. There are some amounts of flux diverted to the non-ferromagnetic material surrounding medium. And also, the core has finite permeability. So, this small amount of flux that flows in the external path is known as primary leakage flux. It is denoted by Ф_L1.

The secondary current I₂ produces a flux Ф₂ that opposes the main flux Ф_M. A portion of this is flux is diverted to the surrounding medium. This leakage flux is called secondary leakage flux Ф_L2. The remaining flux only links the secondary turns and induces EMF E_L2 in the secondary winding.

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Therefore, the flux that passes completely through the core and links both windings is called mutual flux Ф_M. The typical diagram of fluxes in a transformer is shown in the figure below.

Due to the leakage flux Ф_L1 and Ф_L2, the induced EMF E_L1 and E_L2 are different from induced EMF E₁ and E₂ caused by the mutual flux Ф_M. The effect of leakage flux is considered by adding an inductance in series with each winding. It is added in such a way that, the voltage drops in each series inductances (X₁ and X₂) are equal to that produced by the leakage fluxes. The representation of leakage reactance is shown in the figure below.

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Where,

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

The reactances added in the above circuit are a fictional quantity introduced as a convenience to represent primary and secondary leakage flux.

Ideal Transformer – FAQs

Which law is used in Transformer?

Faraday’s law of electromagnetic induction is used in the working principle of the transformer. According to this law, the induced EMF is equal to the rate of change of the magnetic flux in the circuit

What is rating in transformer?

Rating species the maximum power that the transformer can handle. It is given in kVA(Kilovolt-amperes).

What is the efficiency of a transformer?

The ratio of output power to input power is known as efficiency of the transformer.

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