Electronic – Back EMF protection on bidirectional DC motor controller

You can think of the motor as behaving like a resistor connected to a generator (the latter corresponding to the back EMF). It produces a torque that is proportional to the current through the resistor.

The higher the difference between the back EMF and the input voltage, the higher the current. The higher the current, the higher the torque.

If the motor is stalled, the entire input voltage appears across the resistor and a lot of torque is produced. Since it only takes a bit of torque to overcome losses such as bearing friction and windage and magnetic losses when there is no load, the motor spins up until the back EMF is almost equal to the input voltage and the torque has dropped until the motor is no longer accelerating significantly. The current resulting from the remaining difference (multiplied by the input voltage) gives you the power consumption with no load. Efficiency is zero, of course, with no load since it is producing zero output power at the shaft.

The losses in the copper windings are the current squared times the resistance (which is the winding resistance) aka \$I^2R\$ losses.

If the windings had zero resistance the back EMF would always be equal to the input voltage, (even under load) since any difference would allow infinite current to flow, generating infinite torque.

You probably already know the answer but the layout is confusing you.

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1 and 2. Motor arranged in H-bridge configuration but without limit switches.

If you had been asked to create a reversible motor with electronic control you would have created the H-bridge as shown in Figure 1. We can rearrange this as shown in figure two. Switch SW1A and SW1B are two poles of the same switch.

Now we just have to add in the limit switches.

^{simulate this circuit}

Figure 3. H-bridge with limit switches.

Figure 3 shows the status when the system is at the reverse limit and SW1 has just been thrown to the FWD position.

The snubber diodes are always in circuit and always pointing the right direction.