Electrical Time Constant (L/R)
It is the time it takes for the current in the motor winding to reach approximately 63 percent of its final value after the voltage is applied, and it is found from the ratio of inductance to resistance. For 2 mH and 0.5 Ω this time is 4 ms; it is the fundamental quantity that must be compared with the PWM period.
The current reaches its final value in about five time constants. For a 4 ms winding that means 20 ms. The period of 20 kHz PWM, on the other hand, is only 50 µs; that is, the current cannot come anywhere near its final value within one period, it only takes a small step. This is exactly why the current ripple stays small.
The general rule can be summarised as follows: the smaller the PWM period is compared with the electrical time constant, the smoother the current. When the ratio is typically kept below one tenth, the ripple stays at an acceptable level. When the period approaches the time constant, the current falls to zero at every pulse and starts rising again; this discontinuous conduction condition means torque oscillation and heating.
The same quantity also affects the current limit and the current-sensing termination behaviour. If the time constant is large the current reaches the threshold more slowly and the protection response is somewhat delayed. For this reason, when setting the current threshold both the real running current and the settling time of the current must be taken into account.
The context in which this term is used: DC Motor Driver Selection Guide