7.1 Transformer theory and operation

Transformers are crucial devices that transfer electrical energy between circuits using electromagnetic induction. They're the backbone of power distribution systems, allowing efficient voltage changes for transmission and usage. This section dives into the theory behind transformers and their basic operation.

We'll explore how transformers work, from electromagnetic induction to core materials and winding configurations. Understanding these principles is key to grasping how transformers enable the widespread use of electricity in our modern world.

Transformer Principles

Electromagnetic Induction and Mutual Inductance

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• Electromagnetic induction generates voltage in a conductor when exposed to changing magnetic fields
• Mutual inductance occurs when two coils influence each other through their magnetic fields
• Changing current in one coil induces voltage in the nearby coil
• Strength of mutual inductance depends on coil proximity and orientation
• Transformer core materials (iron, ferrite) enhance magnetic coupling between coils

Flux Linkage and Faraday's Law

• Flux linkage measures the total magnetic field passing through a coil
• Calculated by multiplying the number of turns by the magnetic flux: $\lambda = N\Phi$
• Faraday's law states induced voltage is proportional to the rate of change of magnetic flux
• Expressed mathematically as: $e = -N\frac{d\Phi}{dt}$
• Negative sign indicates induced voltage opposes the change in magnetic flux (Lenz's law)
• Forms the basis for transformer operation and energy transfer between coils

Transformer Construction

Primary and Secondary Windings

• Primary winding receives input electrical energy
• Secondary winding delivers output electrical energy
• Windings consist of insulated copper wire coiled around the core
• Number of turns in each winding determines voltage transformation ratio
• Insulation between windings prevents direct electrical contact
• Winding configurations affect transformer efficiency and voltage regulation

Core Types and Materials

• Shell-type core encloses windings for better magnetic flux containment
• Core-type design has windings wrapped around central leg of core
• Laminated steel cores reduce eddy current losses in power transformers
• Ferrite cores used in high-frequency applications (radio, switching power supplies)
• Air cores employed in very high-frequency transformers (RF circuits)

Turns Ratio and Voltage Transformation

• Turns ratio (n) defined as the ratio of secondary to primary turns: $n = \frac{N_s}{N_p}$
• Voltage transformation follows the turns ratio: $\frac{V_s}{V_p} = \frac{N_s}{N_p} = n$
• Current transformation inversely proportional to turns ratio: $\frac{I_p}{I_s} = \frac{N_s}{N_p} = n$
• Ideal transformer conserves power: $P_p = P_s$ or $V_p I_p = V_s I_s$
• Practical transformers have slight power losses due to core losses and winding resistance

Transformer Types

Step-up Transformers

• Increase output voltage relative to input voltage
• Secondary winding has more turns than primary winding
• Used in power transmission to reduce current and minimize line losses
• Applications include boosting household voltage for high-voltage appliances (microwave ovens)
• Found in electronic circuits to increase AC voltage for specific components (fluorescent lamp ballasts)

Step-down Transformers

• Decrease output voltage relative to input voltage
• Primary winding has more turns than secondary winding
• Commonly used to reduce high transmission voltages to usable levels for consumers
• Employed in consumer electronics to lower AC voltage for device operation (phone chargers)
• Utilized in welding equipment to produce high current at low voltage for arc welding