When I calculate voltage drop at last sign I get wire sizes as large as 4/0 al is this correct?
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QUOTE=JDBrown;1512722]So, is the sketch below accurate (more or less)? How you figure your voltage drop really depends on how you decide to circuit the system. And that will depend on how you decide to figure your loads.
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The bare minimum Code requirement is going to be 13W per sign plus 180VA per receptacle. You'll need to verify the input power of your signs, as it's possible (even likely) that they use 13W lamps, but are rated for a bit higher input power due to ballast losses, power factor, etc. What you really need is the input amps or input VA of your signs (having one will allow you to calculate the other).
For the moment, though, let's assume 13W per sign at 100% power factor. You have 22 signs, and 22 duplex receptacles (1 at each sign location). (22 x 13) + (22 x 180) = 4246 VA total for your system. This is the minimum Code requirement, and probably about the load you can expect to have if they only plug in one rope light at each receptacle.
I don't think it would be a stretch to say this is going to be a continuous load (on for more than 3 hours at a time), so the maximum load you can put on your 20 amp circuit would be 16 amps, or 1920 VA. Knowing this, you will need a minimum of three 20 amp circuits. However, if you install all this on three 20 amp circuits, your customer is likely to end up tripping breakers if they plug in a lot of rope lights. I'm going to guess that they will want to plug a rope light into each receptacle, and they will want to daisy-chain together as many rope lights as they can. Based on my experience with regular ol' Christmas lights, that would mean 5 amps for each string or 10 amps at each duplex receptacle.
Unfortunately, since it's a continuous load, you would not be able to put two receptacles @10 amps each on a 20 amp circuit, so you would need a separate circuit for each receptacle. That seems a bit of overkill to me, so maybe you could assume they won't max out every string of rope lights and you'll be safe putting two receptacles to a circuit. Now you've got 11 circuits for receptacles plus one more circuit for the signs. The sign load is small enough that you'd probably be fine using one circuit for each location (2 duplex receptacles and 2 signs on one 20 amp circuit), cutting the total number of circuits to 10.
As you can see, you've still got some design decisions to make before it's time to start worrying about things like voltage drop and conductor sizes.[/QUOTE]