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A synchronous electric motor is an AC motor distinguished by a rotor spinning with coils passing magnets at the same rate as the alternating current and resulting magnetic field which drives it. Another way of saying this is that it has zero slip under usual operating conditions. Contrast this with an induction motor, which must slip in order to produce torque. They operate synchronously with line frequency. As with squirrel-cage induction motors, speed is determined by the number of pairs of poles and the line frequency. Synchronous motors are available in sub-fractional self-excited sizes to high-horsepower direct-current excited industrial sizes. In the fractional horsepower range, most synchronous motors are used where precise constant speed is required. In high-horsepower industrial sizes, the synchronous motor provides two important functions. First, it is a highly efficient means of converting ac energy to work. Second, it can operate at leading or unity power factor and thereby provide power-factor correction.
There are two major types of synchronous motors: non-excited and direct-current excited.
Non-excited motors are manufactured in reluctance and hysteresis designs, these motors employ a self-starting circuit and require no external excitation supply.
Reluctance designs have ratings that range from sub-fractional to about 30 hp. Sub-fractional horsepower motors have low torque, and are generally used for instrumentation applications. Moderate torque, integral horsepower motors use squirrel- cage construction with toothed rotors. When used with an adjustable frequency power supply, all motors in the drive system can be controlled at exactly the same speed. The power supply frequency determines motor operating speed.
Hysteresis motors are manufactured in sub-fractional horsepower ratings, primarily as servomotors and timing motors. More expensive than the reluctance type, hysteresis motors are used where precise constant speed is required.
DC-excited motors — Made in sizes larger than 1 hp, these motors require direct current supplied through slip rings for excitation. The direct current can be supplied from a separate source or from a dc generator directly connected to the motor shaft
Slip rings and brushes are used to conduct current to the rotor. The rotor poles connect to each other and move at the same speed - hence the name synchronous motor.
Synchronous motors fall under the category of synchronous machines which also includes the alternator (synchronous generator). These machines are commonly used in analog electric clocks, timers and other devices where correct time is required.
The speed of a synchronous motor is determined by the following formula:

where v is the speed of the rotor (in rpm), f is the frequency of the AC supply (in Hz) and n is the number of magnetic poles.