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Synchronous, Stepper and AC Motors Formulas and Equations

AC Machine Formulas & Equations for Stepper and Synchronous Motors

Following are the useful equations and AC motors formulas while designing and analyzing synchronous motors, stepper motors and other related AC machines.

Synchronous, Stepper and AC Motors Formulas and Equations

Synchronous Machine:

Speed of Synchronous Machine:

Synchronous machine are designed to be operated at synchronous speed, which is given by:
synchronous speed

  • is the synchronous speed
  • f is the line voltage frequency
  • P is the number of poles in a machine

Synchronous Motor:

Voltage Equation of Synchronous Motor:

V = Eb + Ia(Ra + jXs)


Resultant Voltage:

The difference between the voltage applied V and back EMF is known as resultant voltage ER

ER = V – Eb

ER = Ia(Ra + jXs)

Internal Angle:

It is the angle by which the armature current Ia lags behind the resultant voltage in armature ER, and it is given by;
Internal Angle in synchronous motor

Back EMF Generated:

E= KaφaNs


  • K= constant of the armature winding
  • φ= magnetic Flux per pole of the rotor
  • N= synchronous speed of the rotor

Related Posts:

Different Excitations:

  • E= V             Normal Excitation                            Lagging Power Factor
  • Eb < V             Under-Excitation                              Lagging Power Factor
  • Eb > V             Over- Excitation                                Leading Power Factor

Input Power:

The input power of synchronous motor is given by:
Input Power to synchronous motor

Φ is the angle between V and Ia

Mechanical Power In Rotor:

Mechanical power in rotor of synchronous motor

  • α is the load angle between E­& V
  • Φ is the angle between V & Ia
  • Tis gross torque produced
  • Nis the synchronous speed

Related Posts:

Stepper Motors Formulas

Step Angle:

Step Angle of stepper motor

  • β = step angle, the angle of rotation of the shaft with each pulse.
  • Ns = number of stator poles or teeth
  • Nr = number of rotor poles or teeth

Resolution Of Stepper Motor:

The number of steps required to complete one revolution, its given by;
Resolution of stepper motor
The higher the resolution, the higher the accuracy of the stepper motor.

Motor Speed:

Stepper Motor Speed


  • n = motor speed in revolution per second
  • f = stepping pulse frequency

Related Formulas and Equations Posts:

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