10. Inductors

• Inductors


  • Coils
  • Chokes
• Basic Inductor


  • Coil of wire
  • 3D field
  • Field of each coil adds to form a strong magnetic field

  
• Faraday's Law


  Vind = N dF/dt
• Self inductance (L)


  • Measure of a coil's ability to establish an induced voltage as a result of a change in its current
  • Unit is Henry (H)

  
• Current through inductor


  Magnetic field

  
• Change in current


  Magnetic field changes

  
• Induced voltage via self inductance


  Opposes the change in current

  
• Lenz's Law


  When the current through a coil changes, an induced voltage is created as a result of the changing magnetic field and the direction of the induced voltage is such that it always opposes the change in current

  
• Induced voltage


  Depends on L and di/dt

  
• Energy Storage


  • Stores energy in the magnetic field created by the current
• Physical characteristics of inductors

  • Cross sectional area A
  • Core material (magnetic or non-magnetic)
  • Number of turns (N)
  • D.C. resistance or winding resistance (Rw)
  • Winding Capacitance (Cw)
• Inductors in Series


  LT = L1 + L2 + L3 + ... = LN
• Parallel Inductors


  Total inductance < smallest inductance
• Inductors in D.C. Circuits

  • No induced voltage when current is constant
  • Inductor appears as short to D.C.

  
• Time Constant


  • t = L/R
  • Inductors action opposes a change in current
  • Current cannot change instantaneously
• Energising and De-energising Inductors

  1. Exponential increase and decrease in current

  2. Time constant t = L/R
• Induced voltage in the Series RL Circuit

  • Prevents current from changing instantaneously
  • L acts as open circuit to non-changing current

  
• Voltage in RL circuit as inductor de-energises

  • Induced voltage opposes change in steady state current
  • All energy stored in inductor in magnetic field is dissipated

  
• Instantaneous VL when SW1 is closed = 25V, after 5t VL = 0V
• Instantaneous VL when SW1 opens and SW2 closes = 208V, after 5t VL = 0V
• Exponential Formulae


  For increasing and decreasing current in inductors
• Current and voltage in inductor

  • Current lags inductor voltage by 90°
  • Faster the rate of change of current the larger the induced voltage VL
• Inductive Reactance (XL)


  • Opposition to sinusoidal current
  • Increases with frequency
• In AC circuits with inductors, current lags voltage by 90°
• Ohm's Law in AC circuits with inductors

  R replaced by XL
• Power in an inductor

  • Instantaneous power p=vi
  • True power ideally 0, practically (Irms)^2 * Rw
  • Reactive power Pr=VrmsIrms=Vrms^2/XL
• Quality Factor (Q) of a coil

  Q = XL/Rw
• Inductor Applications


  • Power supply filter
  • RF choke
  • Tuned circuits
• Testing Inductors


  Ohmmeter - open reads infinity, good reads Rw, shorted windings reads lower Rw