Separately-Excited DC Motor

Below we have the schematic diagram of a separately-excited DC motor and its equivalent circuit diagram.

In this type of motor, the field and armature circuits are separately excited, resulting in a high degree of controllability. Due to the need for two separate voltage sources, unless the extra cost is justified and/or the offered control flexibility is important, this type of motor is not commonly used.

The resistance $R_f$ in (b), is the combination of the field resistance and an adjustable resistance, which is used for speed control purposes.

The operation of this motor can be expressed as:

$$\begin{array}{rl}{I}_f& =\frac{V_f}{R_f}\\ \varphi & =\frac{N_f{I}_f}{\mathcal{R}}\end{array}$$

where $N_f$ is the number of turns of field winding and $\mathcal{R}$ is the magnetic reluctance.

Then:

$$\begin{array}{rl}{V}_a& =I_a{R}_a+E_c\\ E_c& =\frac{ZP}{2\pi a}\varphi {\omega }_m=\frac{ZP}{60a}\varphi n\\ {\tau }_m& =\frac{ZP}{2\pi a}\varphi I_a\end{array}$$