A transformer is a clever, but very simplistic component. It’s job is to step up or down voltages. Doing so, the current changes accordingly to maintain the same power at both sides based on the P=IV equation.

Consisting of two separate coils, transformers operate on the principle of Electromagnetic Induction. Since there is no physical contact between the coils, only AC passes through while DC is blocked.

Electricity Basics

A bit about voltage & current

This might be very basic but it is important to understand. In conductors, like a copper wire, there are ‘free’ electrons floating around.

  • Voltage is a force that attracts electrons.
  • Current is the flow of electrons, measured in Amperes (A).

1A= 6 million million million electrons passing through a given cross section of a wire in 1 sec.

Once, when they figured this all out, they messed it up and got the direction of the current flow wrong. It has never been corrected, so we denote the flow of current from + to – and it is in opposite direction of the flow of electrons.

AC & DC

There are 2 types of currents:

  • Alternating Current (AC) and
  • Direct Current (DC)

When electricity is generated at power stations, it is in form of AC.

In the case of Direct Current, the electrons flow in one direction in the wire.

In the case of Alternating Current, the electrons fluctuate. They go back and forth in the wire 50 times a second.

Where are Transformers Used?

Electricity is distributed for long distances via transmission lines. Now, the flow of electrons generate heat which is a form of loss. This is because as they flow, they bump into the structure of the conductor wire, friction happens which results in heat.

To avoid this throughout the long transmission lines, a transformer steps up the voltage to hundred thousands of volts and another transformer steps it down just before the electricity arrives to the city.

While the voltage is super high, the current is at its minimum. This results in minimal losses.

Another example is the phone charger. In the wall we have 230V. The charger has a transformer in it that steps that 230V down to 5V.

Working Principle of Transformers

To understand the operation principle of a transformer there are 2 related theories to cover:

  • Magnetic field in a wire
  • Magnetic field in a coil
The direction of magnetic field caused by the current in a wire and in a coil.

Figure 1: Direction of magnetic field in a wire and a coil, induced by the flow of current. In the case of a wire, the magnetic flux direction can be easily found using our right hand where the thumb points to the direction of current flow, and the curved fingers to de direction of the flux.

Case of a Wire

When an electron passes through in a wire, it generates a magnetic field around it. This field has a direction. Based on the diagram above, we can determine this direction of the field using our right hand. Thumb points in the flow of current, while the curled fingers show the field.

Case of an Electromagnet

We take this wire and roll it up. We’ll end up having lots of wires next to each other, so this magnetic field gets stronger. While in the case of the wire the field rotates around, in the case of an electromagnet the field passes through the middle of the coil than turns back around in a loop.

An electromagnet is similar to a good old red & blue electromagnet. It has a North and a South pole. The magnetic flux always points from North to South outside of the coil. In the case of an Alternating Current, the current changes direction, thus, the North and South poles shift around.

Operation Principle of a Transformer

The only difference between a coil and a transformer, is that, in the transformer we have 2 coils. The coils never touch, they are isolated. The current flow in the primary coil induces a voltage in the secondary coil.

Construction of a Transformer: primary and secondary coils wrapped around a laminated iron core.

Figure 2: Basic construction of a transformer consisting of a primary and secondary windings. These coils are wrapped around a laminated iron core. Ip indicates the momentary primary current. The dotted green line shows the flux generated by the primary coil. We can also use the right hand to determine the direction of green the flux lines, although note, the green line shows the flux inside the coil, which is in opposite direction as it would be outside of a coil as in Figure 1. The aim of the core is to gather the lines coming out from the primary coil and transfer them into the secondary coil.

  • The primary and secondary coils are rolled around an iron core.
  • The core has high magnetic permeability, which means that it directs the primary coil’s filed across to the secondary winding.
  • AC is fed in the primary (DC can’t pass), so, the direction of the magnetic field that in the core will continuously change directions.
  • Based on the Law of Electromagnetic Induction, an Electromagnetic Force (EMF) will be generated.

If the secondary winding is a part of a closed circuit, current will flow. Just to be clear, electrons don’t jump from primary to secondary. They are all along the wires and they just start to fluctuate back and forth due to the EMF.

Faraday’s Law of Electromagnetic Induction states that if a wire is placed in a changing magnetic field and EMF will be generated.

Why don’t Transformers work with DC ?

As the Law of Electromagnetic Induction states above, the wire has to be in a changing magnetic field in order for the EMF to be induced.

The magnetic field is only changing when it shifts the North and South polarity. If we had a direct current, the N & S poles would be fixed, thus, no field movement, resulting in no EMF induced.

Transformer Formulas

Turns Ratio

The way to control the voltage at the secondary side of the Transformer, is to have a different amount of turn of the copper wire than the primary.

Based on the formula below, the more turns we have at the secondary side compare to the primary, the higher the voltage will be induced.

Transformer symbol and general equations for primary & secondary voltages, current and winding turns.

Figure 3: General symbol for transformers and related equations. Note, the voltage transferred from primary to secondary side is proportional to the number of winding turns (N), whereas, the current is inversely proportional.

Where:

  • Ip: primary current
  • Is: secondary current
  • Vp: primary voltage
  • Vs: secondary voltage
  • Np: number of turns in primary winding
  • Ns: number of turns in secondary winding

The Resistance Equation of the Secondary Side

Let’s derive an equation for the secondary resistance in terms of the primary side turns as well as the primary voltage and current.

Derivation for the secondary side's resistance equation in terms of primary voltage, current and winding turn for transformers.

Transformer Equivalent Circuit

 The equivalent circuit for transformers.

Figure 4: The equivalent circuit for transformers. The various resistors and inductors symbolise the losses happening in the coils as well as the core.

Where:

  • Rp: primary winding resistance
  • Rs: secondary winding resistance
  • Re: Eddy Current losses
  • jXp: primary winding reactance
  • jXs: secondary winding reactance
  • jXm: magnetising flux

Simplified Equivalent Circuit

To simplify our calculations, we sum up the primary resistance and reactance with the secondary side’s. We do this by using the resistance equation from above.

This equation expresses the secondary side’s resistance in terms of the primary’s voltage and current. Essentially, it is what the secondary side sees through the coils. We can use this to add up with the secondary’s resistance & reactance.

The Simplified Equivalent Transformer Circuit

Figure 5: The simplified equivalent transformer circuit where the primary side’s resistance and reactance are summed up with the secondary side’s.

Resistance & Impedance of the Winding

A coil is said to have an impedance. Impedance consists of two parts: resistance(R) and reactance(jX). Reactance happens when the voltage and current are not in phase. Why does this happen in a coil?

As the magnetic field rotates, the changing magnetic field will induce a so called Back EMF that opposes the current flow. So it will stay behind and it is said to lag the voltage. When this happens, we have reactance. The resistive part of the impedance is the natural resistance of copper.

Back EMF in a coil due to change of magnetic field

Figure 6: The image shows the direction of magnetic flux in a coil induced by the current. Having an alternating current, the changing magnetic field will cut the coil. For the duration of this change, a back EMF will be induced that opposes the current flow. This causes a 90° current lag compared to the voltage.

Eddy Current Losses

As we mentioned, there is a magnetic flux travelling through the iron core from the primary to the secondary. The iron is a conductor with free electrons, so this magnetic field naturally tries to move these electrons.

By exciting the electrons, energy is transferred, which will be dissipated as heat. This is loss of magnetic energy. To prevent this, the core is made up of thin laminated sheets that are insulated from one another.

This way the core still drives the flux from the primary side to the secondary, but the lamination prevents the flow of current.

See this video for a visual demonstration.

 

Transformer Efficiency

There are 2 types of losses in a transformer:

  • Copper loss – due to I^2*R losses
  • Iron loss – due to Eddy Current
Efficiency equation for transformers