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Back EMF & Internal Resistance
This page has a description of what “Back EMF” is, how it occurs, and what it means for a motor and controller.
A speed controller varies the motor speed by varying the voltage fed to the motor. So what happens to this voltage at the motor? Back EMF.
When voltage is applied to a motor, it rotates. This “applied voltage” is either the battery or the voltage fed to the motor by the speed controller. It is shown in the diagram, above as Vs. As it rotates, the armature cuts the magnetic field, and a conductor moving in a magnetic field generates a voltage. So the moving armature acts as a generator and generates a voltage (a ‘back emf’).
A simple explanation.…
When an electric motor is first switched on, the rotor is stationary, so there is no back electromotive force (back EMF) opposing the supply voltage. At this point, the motor behaves almost like a simple resistor, and a very large stall current can flow—often many times higher than the motor’s normal operating current.
As the motor begins to spin and approaches its maximum RPM, it generates increasing back EMF. This back EMF effectively reduces the voltage across the motor windings, which in turn limits the current to a safe, steady level.
Allowing the motor to reach (or get close to) its maximum RPM is therefore important because it ensures sufficient back EMF is produced to keep current under control. If the motor is prevented from accelerating— e.g. by excessive load or incorrect gearing — it cannot generate this opposing voltage, and high stall currents will persist. This can lead to overheating, reduced efficiency, and potential damage to both the motor and its controller.
A technical explanation….
If the source voltage (output from the controller) is Vs and the back emf voltage if Vb then we can say Vs = Vb + IR where I is the current the motor is drawing and R is the motor’s resistance. If the motor is lightly loaded the current is small, then the IR bit in the equation is small and the motors speed will be high so that Vb is very nearly equal to Vs. If the motor loading increases the current it draws will increase, so the IR bit gets bigger and (if we keep Vs constant) the motor must slow down a bit so Vb drops by the amount IR has increased.
In most applications, the driver is operating the speed control so will automatically increase the speed to compensate for the greater load.
For example, a typical motor might have a resistance, R, of 50 milliohms (i.e. 0.1 amps). If we feed 24v to the motor, which is lightly loaded, so only drawing, say 2 amps, then Vs = Vb + IR becomes 24 = Vb + 0.05 x 2 the IR term is only 0.1 volts. Now if we load the motor so it is taking 30 amps, the IR term becomes (30 * 0.05) – or 1.5v. The motor speed will drop by 6.25%, not a huge amount.
However, if the motor’s full speed is limited to 1/4 full speed, the effect is somewhat more noticeable. 1/4 full speed will mean a maximum of 6v on the motor, using the figures above. But this full speed restriction will not alter the I or the R in our equation. So the IR drop will still be 1.5v. 1.5v is 25% of 6v which is significant.
Thermal effects
Motor armatures are wound with copper wire. As copper heats up, its resistance rises. The IR voltage drop we have discussed above is lost as heat. Heat is current squared times resistance, so I2R. So a loaded motor gets hot. It is this heating that limits the continuous current the motor can handle.
However, there is a lot of copper, and a lot of iron, in a motor. It takes quite a long time for all this metal to actually heat up – maybe 15 minutes or more, so for short periods, the motor can absorb a significant amount of heat, and it is usually quite safe to run the motor at as much as 3 or 4 times its continuous rating for a minute or so.
Clearly this timing is dependent on the motor design, and a close eye should be kept on the motor temperature as overheating can cause the magnets to permanently weaken [the Curie effect].
IR Compensation
Some motor controllers have IR compensation. In this, the controller measures the motor current and as this increases, automatically raises the output voltage to partially offset the IR drop in the motor. Properly set up, this can be very effective. Wrongly set, however, it causes the motor speed to vary and be unstable. Therefore, it is not incorporated in 4QD controllers because of the difficulty in setting it correctly. However, in Oct 2025 we introduced a variation of IR compensation that adjusts the low voltage warning levels as the current increases. This is in version 2.5.4 and later of the Pro-100 / 160 / 360 controllers.