3. Transformers

3.2. Principle Operation of Transformers

By the End of This Section, You Will Understand:

  • ✅ The principle of operation of a transformer

  • ✅ How the output voltage relates to the secondary winding

  • ✅ How transformers are connected in circuits

  • ✅ What a centre-tapped transformer is and how it works

⚙️ 1. Principle of Operation of a Transformer

A transformer works on the principle of electromagnetic induction — specifically Faraday’s Law — which states:

A changing magnetic field in a coil of wire induces a voltage in another nearby coil.

Key points:

  • Only works with AC supply.

  • Primary winding receives AC input and generates a changing magnetic field.

  • This magnetic field passes through a magnetic core and cuts the secondary winding, inducing a voltage in it.

  • No electrical connection between the primary and secondary coils – power is transferred magnetically.

Faraday’s Law Formula:

e=−Ndϕdte = -N \frac{d\phi}{dt}

Where:

  • ee

    e: Induced EMF

  • NN

    N: Number of turns

  • dϕdt\frac{d\phi}{dt}

    dtdϕ​: Rate of change of magnetic flux

2. How Output Voltage Relates to the Secondary

The voltage induced in the secondary coil depends on:

  • The number of turns in both primary (

    NpN_p

    Np​) and secondary (

    NsN_s

    Ns​) windings.

  • The AC voltage applied to the primary coil.

Turns Ratio Formula:

VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}

Where:

  • VsV_s

    Vs​: Secondary voltage

  • VpV_p

    Vp​: Primary voltage

  • NsN_s

    Ns​: Number of turns in secondary

  • NpN_p

    Np​: Number of turns in primary

Results:

  • If

    Ns>NpN_s > N_p

    : It’s a Step-Up Transformer

  • If

    Ns<NpN_s < N_p

    : It’s a Step-Down Transformer

  • If

    Ns=NpN_s = N_p

    : Same voltage (isolation transformer)

3. How Transformers Are Connected

Transformers can be connected in different ways depending on the application:

a) Single-Phase Transformer Connection

  • Most basic type

  • Used in small electronics, domestic applications

b) Three-Phase Transformer Connections

Used in industrial and power systems:

  • Star-Star (Y-Y)

  • Delta-Delta (Δ-Δ)

  • Delta-Star (Δ-Y) – Common for transmission

  • Star-Delta (Y-Δ) – Common for motor starting

Why use different connections?

  • To manage phase shifts, load balancing, voltage levels, and fault handling.

4. Centre-Tapped Transformer

A centre-tapped transformer has a secondary winding with a tap in the middle, which divides the winding into two equal halves.

Structure:

less
|---------- Secondary Winding ----------| A CT B (+V_peak) (0V) (−V_peak)

  • The center tap (CT) is usually connected to ground or 0V reference.

  • Provides two equal and opposite voltages (e.g., +12V and −12V).

  • Common in dual power supplies for op-amps and analog circuits.

Example:

If the total secondary voltage is 24V (AC), then:

  • From A to CT: +12V

  • From B to CT: −12V

  • From A to B: 24V total

Summary Table

Topic Key Points
Principle of Operation Based on electromagnetic induction using AC
Voltage Relationship VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}
Transformer Connections Single-phase or Three-phase (Star, Delta)
Centre-Tapped Transformer Gives dual voltages from one secondary winding

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  • A labeled diagram of a centre-tapped transformer

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