11. Transformers

• Transformers


  Devices that transfer electrical energy from one circuit to another through electromagnetic induction
• Class Test


  2013
• Class Test


  1. Friday Week 8: 26th April

  2. T0.03 (usual lecture theatre)

  3. 08:30 start – prompt

  4. 09:30 finish

  5. 25 multiple choice questions
• Topics covered


  • Mutual inductance
  • Operation and Construction
  • Step up, step down transformers
  • Resistive load, reflected loads
  • Impedance matching
  • Isolation
  • Practical transformer
  • Types of transformer
  • Troubleshooting
• Mutual inductance


  Changing electromagnetic field due to current in one coil induces voltage in second coil

  
• Mutual inductance (Lm)


  • Measure of how much voltage is induced in coil 2 as a result of changing current in coil 1
  • Formula: Lm = k√(L1*L2), where k is the coefficient of coupling

  
• Coefficient of coupling (k)

  Ratio of lines of flux produced by coil 1 linking coil 2 to total flux produced by coil 1

  
• Factors affecting coefficient of coupling (k)

  • Physical closeness of coils
  • Core material
  • Construction and shape of cores
• Basic transformer


  Consists of input winding, output winding, and a common core (air, iron, or ferrite)

  
• Transformer cores


  • Air and ferrite: higher frequency
  • Iron: audio

  
• Turns ratio (n)


  Ratio of number of turns in secondary winding to number of turns in primary winding
• Step up and step down transformers

  Ratio of secondary voltage to primary voltage is equal to the ratio of number of turns in secondary to number of turns in primary

  
• A.C. transmission and distribution is eased by step up and step down transformation
• Full load efficiency of transformers is typically 97% to 98%
• Transformers are used to transfer power from low power to electronic circuits
• Ferromagnetic core


  Increases magnetic flux linkage, but causes power transfer losses
• At full load, input power is approximately equal to output power
• For step up transformers

  Secondary current (Is) is less than primary current (Ip)
• For step down transformers

  Secondary current (Is) is greater than primary current (Ip)

  
• In an ideal transformer, primary power equals secondary power
• Reflected load


  Load connected to the secondary winding appears to have a different resistance when viewed from the primary winding
• Impedance matching


  Matching the source and load impedances to maximize power transfer

  
• Impedance matching example


  • Matching a 300Ω antenna to a 75Ω system using a transformer
• Determining transformer turns ratio for impedance matching


  If amplifier has 800Ω internal resistance and 8Ω speaker, what is the turns ratio to provide maximum power transfer?

  
• Transformer isolation


  Transformer isolates the secondary circuit from any DC in the primary, and allows induced voltage in the secondary from changing current in the primary

  
• Transformer isolation prevents shocks and provides power line isolation
• Non-ideal transformer characteristics


  • Winding resistance
  • Core losses (heating, hysteresis, eddy currents)
  • Magnetic flux leakage
  • Winding capacitance

  
• Transformer rating


  Specified in volt-amperes (VA), primary/secondary voltage, and operating frequency

  
• Transformer efficiency (η)


  Ratio of output power to input power, typically >95%
• Tapped transformers


  Have taps on the secondary winding at points other than the center, allowing minor adjustments to the turns ratio
• Tapped transformer applications


  • A.C. to D.C. conversion using a center-tapped secondary
  • Utility pole transformers with multiple taps to accommodate line voltage variations
• Multiple winding transformers


  Have multiple secondary windings on a common core to provide different stepped up or stepped down voltages
• Autotransformers


  Have one winding that serves as both the primary and secondary, with desired turns ratios provided by taps, no electrical isolation
• Determining input and output power for an autotransformer


  Assign arbitrary current directions, use Kirchhoff's law to find currents, and calculate input and output power