Figure 4.36: The output EMF from the brushes of commutation system (for a
In this circuit, R a and L a are the resistance and inductance of the armature
winding, respectively. The external voltage applied on the terminals of the
winding is V , while the back-EMF produced in the motor operation is E.The
dynamics of this equivalent circuit model of DC motor can be expressed as
V = i · R a + L a di
dt + E.
In the steady state, the input current is constant and the above equation
V = i · R a + E.
The conversion between the electro-magnetic power P em and the mechan-
ical power P me is possible because of the existence of the back-EMF. The
relationship between these two powers can be expressed as
P em = P me
E · I = T em · Ω.
Further explanation on conversion between P em and P me is given in sec-
One can easily deduce from equations 4.47 and 4.60 that,
T em = K t · I,
E = K e · Ω.
This implies that the torque constant (K t ) and back-EMF constant (K e )ofa
motor have the same magnitude when SI units are used.