Understanding Transformer Basics: Principles, Types, and Equations

A transformer is an electronic device that converts alternating voltage from one value to another. It’s a fundamental component in many electrical systems.

It’s made up of two coils, known as the primary coil and the secondary coil. Crucially, these coils aren’t electrically connected. They are either arranged side-by-side or with one coil on top of the other. The coils are separated by air, iron-dust, or iron. The figure below shows various transformer symbols.

Image alt: transformer

Transformers operate on the principle of electromagnetic induction. When an AC voltage is applied to the primary coil, it creates a changing magnetic field. This field then passes through the secondary coil, which induces a changing voltage in that coil. According to Lenz’s Law, the induced voltage in the secondary coil will have the opposite polarity to the voltage in the primary coil.

Magnetic saturation of the core can occur in a transformer if too much current flows through it. Therefore, care needs to be taken, particularly when a DC component is present in the input signal.

Transformer Equation

The relationship between the voltages and the number of turns in the coils is described by the following equation:

Secondary a.c. voltage / primary a.c. voltage = Number of turns in secondary coil / Number of turns in primary coil

In symbols:

$V_s / V_p = N_s / N_p$

Where:

• $V_s$ is the secondary voltage.
• $V_p$ is the primary voltage.
• $N_s$ is the number of turns in the secondary coil.
• $N_p$ is the number of turns in the primary coil.

The ratio $N_s / N_p$ is called the turns ratio.

A transformer can have multiple secondary coils. These can be designed to either step up or step down the primary voltage, and a single transformer can have a combination of both.

In a perfect transformer, the power in the primary coil equals the power in the secondary coil:

Power in primary = power in secondary

OR

$V_p \times I_p = V_s \times I_s$

Where:

• $I_p$ is the primary current
• $I_s$ is the secondary current

Ideally, if $V_s$ is double $V_p$, then $I_s$ would be half of $I_p$. However, in reality, $I_s$ is always less than half of $I_p$ due to energy losses caused by:

• Resistance of the copper wire in the coils.
• Eddy currents in the core.
• The magnetic field not passing completely through the secondary coil (leakage flux).

Transformer Types

Transformers are categorized by their application and operating frequency. Some common types include:

• Main Transformers: These are typically used in power distribution systems. In the UK, they often operate at 50 Hz with a primary voltage of 240V AC. They may have secondary windings that step up or step down the voltage, or a combination of both.
• Audio Frequency Transformers: These are designed to transfer maximum power from an audio frequency output stage (like an amplifier) to the input of a loudspeaker.
• Radio Frequency Transformers: These often have adjustable iron-dust cores and are used in tuning circuits in radios. They are typically enclosed in shielding to prevent radiation from interfering with other circuits.