5.3 Transformer principles and equivalent circuits

Transformers are the unsung heroes of power systems, letting us zap electricity across vast distances and into our homes. They're like voltage shape-shifters, using magnetic magic to boost or drop voltage levels as needed. Pretty cool, right?

But transformers aren't perfect. They've got some energy-draining quirks like core losses and copper losses. Understanding these hiccups helps us build better transformers and keep our power systems humming along smoothly.

Transformer Basics

Core Components and Operation

• Ideal transformer consists of two or more coils of wire wound around a common magnetic core
• Primary winding receives input electrical energy and creates a changing magnetic field
• Secondary winding interacts with the changing magnetic field to produce output electrical energy
• Turns ratio defines the relationship between primary and secondary voltages and currents
• Turns ratio calculated by dividing the number of turns in the secondary winding by the number of turns in the primary winding
• Voltage ratio equals turns ratio in an ideal transformer ($V_s / V_p = N_s / N_p$)
• Current ratio inversely proportional to turns ratio ($I_s / I_p = N_p / N_s$)

Electromagnetic Principles

• Transformer operation based on Faraday's law of electromagnetic induction
• Changing current in primary winding induces a changing magnetic flux in the core
• Changing magnetic flux in the core induces a voltage in the secondary winding
• Mutual inductance between primary and secondary windings enables energy transfer
• Magnetic core typically made of ferromagnetic materials (iron, silicon steel) to enhance flux linkage
• Core shape can be designed as shell-type or core-type to optimize magnetic circuit

Transformer Losses

Core Losses

• Hysteresis losses occur due to the energy required to realign magnetic domains in the core material
• Eddy current losses result from circulating currents induced in the core by the changing magnetic field
• Core losses collectively referred to as iron losses or no-load losses
• Minimized by using laminated core construction and high-resistivity core materials (silicon steel)
• Core loss increases with frequency and flux density

Copper Losses and Efficiency

• Copper losses (I²R losses) occur due to the resistance of the transformer windings
• Winding resistance causes power dissipation as heat when current flows through the conductors
• Copper losses increase with the square of the current ($P_{copper} = I^2R$)
• Transformer efficiency calculated as the ratio of output power to input power ($\eta = P_{out} / P_{in} \times 100\%$)
• Efficiency affected by both core and copper losses
• Typical transformer efficiencies range from 95% to 99% for large power transformers

Transformer Equivalent Circuit

Modeling Transformer Behavior

• Equivalent circuit represents the transformer's electrical characteristics
• Magnetizing inductance models the magnetization of the core
• Leakage inductance represents the magnetic flux that does not link both windings
• Core losses modeled as a resistance in parallel with the magnetizing inductance
• Winding resistances included to account for copper losses
• Ideal transformer included to represent the turns ratio

Impedance Transformation

• Transformer can be used to match impedances between source and load
• Impedance transformation ratio equals the square of the turns ratio ($Z_s / Z_p = (N_s / N_p)^2$)
• Useful for maximizing power transfer in electrical systems
• Impedance matching improves efficiency in power transmission and audio systems

Transformer Applications

Voltage Manipulation and Power Distribution

• Step-up transformers increase voltage for efficient long-distance power transmission
• Step-down transformers reduce voltage for safe distribution to end-users
• Distribution transformers convert medium voltage to low voltage for residential and commercial use
• Instrument transformers provide isolated, scaled-down voltages and currents for measurement and protection devices

Specialized Transformer Types

• Autotransformers use a single winding for both primary and secondary, offering compact design and higher efficiency for small voltage changes
• Isolation transformers provide electrical isolation between primary and secondary circuits for safety and noise reduction
• Three-phase transformers used in industrial power systems and large-scale power distribution
• Pulse transformers designed for transmitting short-duration pulses in digital circuits and power electronics