Capacitor for Inrush Current from Motors

I will be controlling 5 motors at 12vdc, 300mA each using relays. I know I should use a capacitor to mitigate the inrush current, but I haven't been able to find out what value capacitor I might need. Also, should I put a capacitor between the power supply and the relays (1 cap for all 5 relays) or is it mandatory that I put one between each relay-motor? Also, people have mentioned using diodes with the capacitors. Any help with is greatly appreciated.

It is not so simple.

Is 300 mA the stall current for the motors, or the running current? There may be a concern if the stall current is much greater, especially if they are all switched on at once. One advantage of using a microcontroller, is that you can arrange it so they do not all start at once.

The next question is - what sort of power supply is it? What ratings?

Is it being used to power the Arduino as well? Or the relays?

How long is the wiring from one part to another?

Now, what do you mean by "using diodes with the capacitors"?

You need a diode ("pointing") from the collector (drain) of the NPN (N-channel) transistor (FET) switching the relay, to the supply voltage for that relay to suppress inductive "kickback" - I mention that it goes between those points rather than saying it goes across the relay because while diagrammatically the same, the diode needs to be in this position to most effectively suppress the inductive "kickback".

Try to estimate either the starting current, or the voltage drop, when you connect the motor.

If your motor is physically obstructed from turning, the high stall current may persist for quite a while, and a capacitor won't help much. On the other hand, if the motor is immediately able to start turning, the duration of the stall current will be shorter.

A capacitor is only going to be able to supply additional starting current, if it is "charged up" before the relay closes the circuit to the motor. Therefore the capacitor must be on the upstream side of the relay. Having the capacitor on the motor side of the relay would make the startup current problem even worse, because when you close the relay, you would also be providing current to charge up the capacitor. Although, you would still want a small capacitor on the motor side to help with runtime electrical noise from the motor.

You can then ffigure out how many coulombs of extra starting current you need. Suppose you want 1 amp of extra current for 0.1 seconds. That is 0.1 coulombs of electric charge. Now suppose you expect the supply voltage to droop by 1 volt, and not more, when you start the motor. A charged up capacitor which is 0.1 farads will deliver 0.1 coulombs of charge when it's voltage reduces one volt. Thats how a farad is defined. That's a rather large capacitor but it illustrates the concept mathematically.

To mitigate inrush current you need a soft-start circuit, usually a resistor
that connects first before being bypassed once the receiving circuit's capacitance
has charged up. Capacitors are usually responsible for in-rush current as they
pull lots of current for a step-change in voltage.

Here the idea is to limit stall current's effects on the supply voltage? In which case
you want to supply all the inrush current from a capacitor, not really mitigate it. You need to
know how long it takes to spin up the motors, since that's the timeframe for the capacitor
to provide current - calculate the charge needed, then C = Q/dV where dV is the largest
drop in supply voltage you can tolerate.

I believe 300mA is the running current. They start up just about immediately as far as I can tell.
I read that when motors are switched on by a relay, the inrush current can damage or shorten the life of the relay. I'm also concerned with electrical feedback back to the power supply from the motors. These motors will be supplied power from a buck converter hooked up to an 18.5 volt 3.5A power supply. One or two other buck converters will be connected to this power supply, and although I don't think it will be a problem, I don't want any electrical noise messing with or damaging the buck converters. I assume that the inrush current could also potentially damage the buck converter (rated at 3A, motors will pull 1.5A). Would I be treating both of these issues (relay damage and electrical noise) by putting the capacitor between the relay and the motor? If so, what value might I need, or will I need to use two different value caps on each to treat the different problems?

MarkT:
To mitigate inrush current you need a soft-start circuit, usually a resistor
that connects first before being bypassed once the receiving circuit's capacitance
has charged up. Capacitors are usually responsible for in-rush current as they
pull lots of current for a step-change in voltage.

How might this look? I'm having a hard time understanding how the resistor is located in the circuit relative to the capacitor.

d_vee:
I believe 300mA is the running current. They start up just about immediately as far as I can tell.

And in order to start up "immediately", they need to draw extra current, which is the "inrush" or "stall" current and will be many times the running current.

d_vee:
I read that when motors are switched on by a relay, the inrush current can damage or shorten the life of the relay.

I suspect your relays are rated at more than 1 amp (if they are not, then you should perhaps re-think your design), and the stall current is not likely to be much more than that, so this will not be a concern.

d_vee:
I'm also concerned with electrical feedback back to the power supply from the motors. These motors will be supplied power from a buck converter hooked up to an 18.5 volt 3.5A power supply. One or two other buck converters will be connected to this power supply, and although I don't think it will be a problem, I don't want any electrical noise messing with or damaging the buck converters.

The buck converters will incorporate an output capacitor to take care of this.

d_vee:
I assume that the inrush current could also potentially damage the buck converter (rated at 3A, motors will pull 1.5A).

If briefly overloaded, it will probably just fail to hold the voltage for the duration of the overload.

d_vee:
Would I be treating both of these issues (relay damage and electrical noise) by putting the capacitor between the relay and the motor? If so, what value might I need, or will I need to use two different value caps on each to treat the different problems?

If you mean putting a capacitor across the motor terminals after the relay, as has previously been pointed out, this is exactly what you must not do (apart from an 0.1µF capacitor to suppress noise) as it would make the problem much worse as the relay then has to switch not only the motor inrush current, but the much higher initial charging current of the capacitor.

What is most important, is to control the relays with an Arduino so that no two motors are switched on within a reasonable starting time (100 ms) of each other.