TMC5130A DATASHEET (Rev. 1.14 / 2017-MAY-15)
55
With rising motor velocity, the motor generates an increasing back EMF voltage. The back EMF voltage
is proportional to the motor velocity. It reduces the PWM voltage effective at the coil resistance and
thus current decreases. The TMC5130A provides a second velocity dependent factor (PWM_GRAD) to
compensate for this. The overall effective PWM amplitude (PWM_SCALE) in this mode automatically is
calculated in dependence of the microstep frequency as:
푓
ꢒ푇ꢓꢊ
푃ꢏꢐ_푆퐶ꢎꢑ퐸 = 푃ꢏꢐ_ꢎꢐ푃ꢑ + 푃ꢏꢐ_퐺푅ꢎ퐷 ∗ ꢀ56 ∗
푓
ꢋ퐿퐾
With fSTEP being the microstep frequency for 256 microstep resolution equivalent
and fCLK the clock frequency supplied to the driver or the actual internal frequency
As a first approximation, the back EMF subtracts from the supply voltage and thus the effective current
amplitude decreases. This way, a first approximation for PWM_GRAD setting can be calculated:
푉
푓
∗ ꢃ.46
ꢋ퐿퐾
푃ꢏꢐ_퐺푅ꢎ퐷 = 퐶퐵ꢓ푀퐹
[
] ∗ ꢀ휋 ∗
푟푎푑
푠
푉푀 ∗ ꢐ푆푃푅
CBEMF is the back EMF constant of the motor in Volts per radian/second.
MSPR is the number of microsteps per rotation, e.g. 51200 = 256µsteps multiplied by 200 fullsteps for
a 1.8° motor.
Motor current
PWM scaling
PWM reaches
(PWM_STATUS)
max. amplitude
255
D
A
R
G
Constant motor
RMS current
_
M
W
P
Nominal current
(e.g. sine wave RMS)
PWM_AMPL
0
0
VPWMMAX
Velocity
Figure 7.5 Velocity based PWM scaling (pwm_autoscale=0)
Hint
The values for PWM_AMPL and PWM_GRAD can easily be optimized by tracing the motor current with
a current probe on the oscilloscope. It is not even necessary to calculate the formulas if you carefully
start with a low setting for both.
UNDERSTANDING THE BACK EMF CONSTANT OF A MOTOR
The back EMF constant is the voltage a motor generates when turned with a certain velocity. Often
motor datasheets do not specify this value, as it can be deducted from motor torque and coil current
rating. Within SI units, the numeric value of the back EMF constant CBEMF has the same numeric value
as the numeric value of the torque constant. For example, a motor with a torque constant of 1 Nm/A
would have a CBEMF of 1V/rad/s. Turning such a motor with 1 rps (1 rps = 1 revolution per second =
6.28 rad/s) generates a back EMF voltage of 6.28V. Thus, the back EMF constant can be calculated as:
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