Why must the cross section grow as the cable length increases?
Voltage drop is directly proportional to cable length. If you double the distance, the drop at the same cross section doubles as well; to keep the drop constant you have to double the cross section. In a 12V system a 3% budget is only 0.36 V, so this effect is felt very quickly.
Looking at the formula the relationship is clear: ΔV = 2 x L x I x ρ / A. The drop is directly proportional to length and current and inversely proportional to cross section. Also, L is not just the one-way distance between the driver and the motor; the factor of 2 represents the total path of the outgoing and returning conductors.
Practical consequences:
- A cross section that is sufficient at 3 metres creates twice the drop at 6 metres; to hit the same 3% target you have to double the cross section.
- Reducing the current serves the same purpose. For the same power, moving to 24V halves the current and lets you go twice the distance with the same cross section.
- As the cable gets longer the cost rises quickly along with the cross section; it is often more economical to bring the driver closer to the motor and cover the long distance with a low-current control line.
This last item is important: keeping the thick arm that carries the motor power short and covering the long distance with the IN1-IN5 inputs of the KS250, the A-E input lines of the PT500 or with an RF remote control solves both the cross section and the voltage drop problem. Temperature must not be forgotten either: at 90-105 °C the resistance of copper rises by 27-33% compared with nominal.
The full topic: DC Motor Driver Selection Guide