Fundamentals of DC Motors, Induction Machines, and BJT Transistors

DC Motor Speed-Torque Characteristics

• Graph Interpretation

  • Y-axis: Speed (N).
  • X-axis: Torque (T).
  • Shape: Linear downward slope (speed decreases as torque increases).

• Speed-Torque Formula

  N=V−IaRaϕN=ϕV−Ia​Ra​​,
  where I_a = armature current, R_a = armature resistance, ϕ = flux.

• Key Performance Points

  • At No Load: High speed, low torque.
  • At Full Load: Low speed, high torque (due to armature reaction).

• Applications

  Used in electric vehicles and cranes for variable speed control.

Working Principle of 3-Phase Induction Motor

• Stator Function

  • A 3-phase AC supply produces a Rotating Magnetic Field (RMF).
  • RMF Speed (Synchronous Speed, N_s): Ns=120fPNs​=P120f​.

• Rotor Operation

  • Conductors (aluminum bars) are cut by the RMF, inducing current (Faraday’s Law).
  • The induced current creates a rotor magnetic field, which interacts with the RMF to produce torque and rotation.

• Understanding Slip

  • Slip (s)=Ns−NrNsSlip (s)=Ns​−Nr​​, where N_r = rotor speed.

  • Example: For N_s = 1500 rpm and s = 4%, N_r = 1440 rpm.

Common Emitter BJT Characteristics

• Input Characteristics (Base-Emitter)

  • Graph: I_B vs V_BE.
  • Behavior: Exponential curve (similar to a diode).
  • Threshold Voltage: Approximately 0.7V for silicon.

• Output Characteristics (Collector-Emitter)

  • Graph: I_C vs V_CE for different values of I_B.

  • Operating Regions

    1. Active Region: IC=βIBIC​=β (linear amplification).
    2. Saturation Region: VCE≈0VCE​≈0 (switch ON).
    3. Cutoff Region: IC≈0IC​≈0 (switch OFF).

• Applications

  • Amplifiers: CE configuration is used for audio amplification.
  • Switches: Used in digital logic circuits.

DC Motor Construction and Operation

• Construction Components

  • Stator: Permanent magnets or electromagnets (field poles).
  • Rotor (Armature): Core with laminated steel, windings, and commutator.
  • Commutator: Reverses current direction to maintain continuous rotation.
  • Brushes: Conduct current to the commutator.

• Working Principle

  • Fleming’s Left-Hand Rule: Current in the armature combined with the magnetic field generates force, resulting in rotation.
  • Commutation: The commutator reverses the current every half-cycle to ensure continuous rotation in one direction.

• Torque Formula

  T=KϕIaT=K, where K = motor constant, ϕ = flux, I_a = armature current.