Synchronous Motor Back EMF Explained

In a synchronous motor, the back electromotive force (back EMF), often denoted as $E_b$, is a voltage generated within the stator windings. This voltage arises due to the relative motion between the stator conductors and the rotating magnetic field produced by the rotor's field winding. It effectively opposes the applied stator voltage.

Factors Influencing Back EMF Magnitude

The magnitude of the back EMF ($E_b$) in any rotating electrical machine is fundamentally related to the strength of the magnetic field and the speed of rotation. According to Faraday's law of electromagnetic induction, the induced EMF is proportional to the rate of change of magnetic flux linkage. For a synchronous motor, this relationship can be conceptually understood as:

$$E_b \propto \Phi \times N$$

Where:

• $\Phi$ represents the magnetic field flux per pole, determined by the rotor's magnetic field strength.
• $N$ represents the speed of rotation (in revolutions per unit time).

Let's analyze how the given options relate to these factors:

Analyzing the Options for Back EMF Dependence

1. Speed of the motor: In a synchronous motor operating under normal conditions, the speed ($N$) is constant. It is synchronized with the supply frequency ($f$) and the number of poles ($P$) of the motor, following the synchronous speed formula $N_s = \frac{120f}{P}$. Since the speed is fixed and determined by the system, it doesn't act as a variable parameter that the motor adjusts to change the back EMF magnitude during operation. While speed is a component in the basic EMF equation, it's not the primary *control* variable for $E_b$ magnitude in a synchronous motor.

2. D.C. excitation only: The magnetic field flux ($\Phi$) in a synchronous motor is primarily generated by the direct current (DC) flowing through the rotor's field winding. The strength of this magnetic field is directly proportional to the magnitude of the DC excitation current. By adjusting the DC excitation current, the operator can directly control the rotor's magnetic field strength ($\Phi$). Consequently, increasing the DC excitation strengthens the field, leading to a higher back EMF ($E_b$), while decreasing the excitation weakens the field and reduces $E_b$. This makes DC excitation the principal method for controlling the back EMF magnitude.

3. Load on the motor: The mechanical load applied to the synchronous motor influences the torque it produces and affects the angle between the applied voltage and the back EMF (the torque angle, $\delta$). It also affects the armature current ($I_a$) and the power factor. While the load condition impacts the relationship between terminal voltage ($V$) and back EMF ($E_b$) (e.g., $V \approx E_b - I_a Z_a$), the load itself does not directly set or control the magnitude of the back EMF generated by the rotating field system. The back EMF is established by the excitation level and synchronous speed.

4. Both the speed and rotor flux: While the rotor flux ($\Phi$) is critical and is indeed controlled via DC excitation, the speed ($N$) of a synchronous motor is fixed at the synchronous speed. Therefore, stating that the back EMF depends on 'both speed and rotor flux' as if both are independently varied is misleading in the context of operational control. The rotor flux is controlled by DC excitation, and the speed is predetermined by the supply frequency.

Conclusion on Back EMF Dependence

Based on the analysis, the magnitude of the back EMF ($E_b$) generated in a synchronous motor is directly influenced and controlled by the strength of the rotor's magnetic field. This field strength is, in turn, directly managed by adjusting the level of DC excitation supplied to the rotor field winding. Hence, the back EMF magnitude depends on DC excitation only.