Transformers are essential for power systems, allowing voltage levels to be changed efficiently. The ideal transformer model simplifies analysis by assuming perfect energy transfer between windings. This section explores the key principles and relationships that govern ideal transformer behavior.
Understanding ideal transformers is crucial for grasping real-world applications. We'll dive into voltage and current ratios, impedance transformation , and analysis techniques. These concepts form the foundation for working with more complex transformer circuits and power systems.
Assumptions and Basic Principles
Top images from around the web for Assumptions and Basic Principles Magnetic Flux, Induction, and Faraday’s Law | Boundless Physics View original
Is this image relevant?
Magnetic Flux, Induction, and Faraday’s Law | Boundless Physics View original
Is this image relevant?
1 of 3
Top images from around the web for Assumptions and Basic Principles Magnetic Flux, Induction, and Faraday’s Law | Boundless Physics View original
Is this image relevant?
Magnetic Flux, Induction, and Faraday’s Law | Boundless Physics View original
Is this image relevant?
1 of 3
Ideal transformer operates with perfect efficiency , no energy losses
Core permeability approaches infinity, resulting in negligible magnetizing current
Zero winding resistance eliminates copper losses
No flux leakage ensures all magnetic flux links both primary and secondary windings
Operates on principle of electromagnetic induction discovered by Faraday
Consists of two or more coils wound around a common ferromagnetic core
Primary coil connected to AC source induces voltage in secondary coil
Magnetic flux in core transfers energy between primary and secondary circuits
Voltage and Current Relationships
Turns ratio (N) defines relationship between primary and secondary windings
Voltage ratio directly proportional to turns ratio: V p V s = N p N s = N \frac{V_p}{V_s} = \frac{N_p}{N_s} = N V s V p = N s N p = N
Current ratio inversely proportional to turns ratio: I p I s = N s N p = 1 N \frac{I_p}{I_s} = \frac{N_s}{N_p} = \frac{1}{N} I s I p = N p N s = N 1
Step-up transformer increases voltage (N > 1), step-down decreases voltage (N < 1)
Ampere-turns balance maintains equilibrium between primary and secondary sides
Dot convention indicates relative polarity of windings (determines phase relationships)
Power Conservation Principle
Ideal transformer conserves power between primary and secondary sides
Input power equals output power: P p = P s P_p = P_s P p = P s
Power conservation expressed as: V p I p = V s I s V_p I_p = V_s I_s V p I p = V s I s
Apparent power (VA) remains constant across transformer
Power factor unaffected by ideal transformer
Reactive power (VAR) transfers between primary and secondary without losses
Efficiency of ideal transformer always 100% (real transformers approach 98-99%)
Transformer modifies impedance seen by source or load
Impedance transformation ratio proportional to square of turns ratio
Reflected impedance formula: Z r = N 2 Z L Z_r = N^2 Z_L Z r = N 2 Z L
Allows impedance matching between source and load for maximum power transfer
Useful in audio systems, RF circuits, and power distribution networks
Impedance transformation preserves complex nature of load (resistive and reactive components)
Can be used to step up or step down impedance based on application requirements
Analyzing Reflected Impedance
Reflected impedance represents load impedance as seen from primary side
Simplifies analysis by referring all circuit elements to one side of transformer
Enables use of series and parallel circuit analysis techniques
Maintains power relationships between primary and secondary circuits
Reflected current calculated using turns ratio: I r = I s N I_r = \frac{I_s}{N} I r = N I s
Reflected voltage determined by: V r = N V s V_r = N V_s V r = N V s
Useful for analyzing transformer circuits with complex loads or multiple windings
Phasor Diagram Representation
Graphical tool for visualizing voltage and current relationships in transformers
Represents magnitude and phase angle of electrical quantities as vectors
Primary and secondary voltages typically drawn in phase (ideal transformer)
Current phasors may lead or lag voltage phasors depending on load characteristics
Dot convention determines relative orientation of voltage phasors
Useful for analyzing power factor and phase relationships in transformer circuits
Helps visualize effects of non-ideal transformer characteristics (winding resistance, leakage inductance)
No-Load Condition Analysis
Represents transformer behavior when secondary winding open-circuited
Primary current consists only of magnetizing current (negligible in ideal case)
Secondary voltage induced but no current flows in secondary winding
Voltage ratio maintains turns ratio relationship: V s = V p N V_s = \frac{V_p}{N} V s = N V p
Core losses (hysteresis and eddy currents) become significant in real transformers
No-load test used to determine core losses and magnetizing current in practical transformers
Provides insight into transformer's magnetic circuit characteristics