## Transformers

### What is transformer?

In electronics, a transformer is a device that transfers electrical energy from one circuit to another through electromagnetic induction. It consists of two or more coils of wire, which are wound around a common magnetic core. When an alternating current flows through one coil (called the primary), it creates a changing magnetic field around the coil. This changing magnetic field induces a voltage in the other coil (called the secondary), which is connected to a load.

Transformers are used for a variety of purposes in electronics, including stepping up or stepping down the voltage of an AC power supply, isolating one part of a circuit from another, matching impedances between circuits, and providing galvanic isolation to protect against electrical noise and interference. They are commonly found in power supplies, audio equipment, and communication systems, among other applications. Transformers are essential components in many electronic devices and have played a critical role in the development of modern electronics.

#### Electrical symbol of Transformer

The electrical symbol for a transformer is two coils of wire with a common core, as shown below: The coil with the zigzag line represents the primary winding, and the coil with the parallel lines represents the secondary winding. The dot on the coils indicates the relative polarity of the windings, where the end of the coil with the dot has a positive voltage relative to the other end. The common core connects the two coils magnetically and is often depicted as a straight line connecting the two coils.

### Formula

The formula for transformer is:

$$\frac{V_{1}}{V_{2}}=\frac{N_{1}}{N_{2}}$$

where $V_{1}$ and $V_{2}$ are the voltages in the primary and secondary coils, respectively, and $N_{1}$ and $N_{2}$ are the number of turns in the primary and secondary coils, respectively.

#### Transformer Ratio

The ratio of a transformer refers to the relationship between the number of turns in the primary winding to the number of turns in the secondary winding. It is denoted by the symbol "a" and is expressed as:

a = Np/Ns

where Np is the number of turns in the primary winding and Ns is the number of turns in the secondary winding.

The transformer ratio is an important factor that determines the voltage and current levels in the secondary winding relative to the primary winding. In an ideal transformer, the ratio of the voltages in the primary and secondary windings is equal to the ratio of the number of turns in the respective windings. Thus, if the transformer has a voltage ratio of 2:1, this means that the secondary voltage is half that of the primary voltage.

The ratio of a transformer also determines its impedance ratio, which is the ratio of the impedance seen by the primary winding to the impedance seen by the secondary winding. The impedance ratio is also equal to the square of the turns ratio:

Impedance ratio = (Np/Ns)^2

Knowing the transformer ratio is important for determining the voltage and current levels in a transformer, as well as its impedance ratio and overall performance characteristics.

#### Efficiency of a Transformer

The efficiency of a transformer is defined as the ratio of output power to input power, expressed as a percentage. It is a measure of how much power is actually delivered to the load compared to the total power consumed by the transformer.

The formula for efficiency of a transformer is:

$$\eta = \frac{\text{Output power}}{\text{Input power}} \times 100\%$$

where $\eta$ is the efficiency, and the output power and input power are measured in watts.

In terms of voltage and current, the efficiency formula can be expressed as:

$$\eta = \frac{V_{out}I_{out}}{V_{in}I_{in}} \times 100\%$$

where $V_{in}$ and $I_{in}$ are the input voltage and current, and $V_{out}$ and $I_{out}$ are the output voltage and current.

The efficiency of a transformer with power loss can be calculated using the following formula

$$\eta = \frac{P_\text{out}}{P_\text{in}} = \frac{(V_\text{out} - I_\text{out}R_{loss}) I_\text{out}}{(V_\text{in} - I_\text{in}R_{loss}) I_\text{in}} \times 100\%$$

where:

• $\eta$ is the efficiency of the transformer
• $P_{out}$ is the output power
• $P_{in}$ is the input power
• $V_{out}$ is the output voltage
• $I_{out}$ is the output current
• $V_{in}$ is the input voltage
• $I_{in}$ is the input current
• $R_{loss}$ is the resistance of the transformer's windings, which causes power loss due to heating.

Note that the term $I_{out}R_{loss}$ represents the power loss in the output winding, while $I_{in}R_{loss}$ represents the power loss in the input winding. The efficiency of the transformer is affected by these power losses, which result in a lower output power than the input power.

### Types of Transformer

There are several types of transformers, classified based on their design, application, and construction. Some of the most common types of transformers include:

1. Power transformers: These are used to step up or step down voltage levels in power transmission and distribution systems.

2. Distribution transformers: These transformers are used for the final voltage transformation from the transmission level to the level required by the consumer.

3. Autotransformers: An autotransformer has a single winding with a tap that allows the transformer to function as both a step-up and step-down transformer.

4. Isolation transformers: These are designed to isolate the input and output circuits, providing electrical safety and reducing noise and interference.

5. Instrument transformers: These are used to measure current and voltage levels in high-voltage circuits, and to provide signals for protection and metering.

6. Toroidal transformers: These have a donut-shaped core and are commonly used in audio equipment due to their low magnetic interference.

7. Step-up transformers: These increase voltage levels from the input to the output.

8. Step-down transformers: These decrease voltage levels from the input to the output.

9. Three-phase transformers: These are used in three-phase power systems to step up or step down voltage levels.

10. Pulse transformers: These are used to transmit short duration pulses or signals, typically in digital circuits or telecommunications.