Revisiting this 2014 thread in 2019
As this thread tells you, just changing your base (unarmored) AC is of very little help, since every character with a better AC than simply 10 + Dex replaces this formula for something else. In short: improving the formula to 11 + Dex does not help much since it gets replaced for most characters.
Not even giving you "natural armor" is of substantial benefit. Note how even a Lizardfolk's Natural Armor ability (AC = 13 + Dex) only helps a very limited selection of characters except on the very lowest levels. A Lizardfolk Monk replaces her AC calculation and thus has no use for her ability (assuming a Wisdom of 16 or better). A Lizardfolk Draconian Sorcerer replaces her AC calculation. A Lizardfolk in armor replaces her AC calculation.
To be sure, 13 + Dex is still good enough to benefit some characters through much of their careers (wizards and circle druids?), just not nearly as many as you'd believe. And that's effectively a +3 Amulet!
So the only benefit that gives a consistent bonus is by giving an AC bonus. However, in 5E there are no different types of AC bonuses. So a +1 AC amulet of natural armor would be
identical to a Ring of Protection (except, I suppose, the different name allowing you to stack both for +2).
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However, there is, I believe, a useful implementation that tries to replicate the intention behind the d20 amulet:
Your Dexterity modifier counts as one higher for the purposes of calculating AC.
Now, you benefit equally if you wear no armor or leather armor. You benefit if you're a monk using Unarmored Defense or a Wizard using Mage Armor. However, to benefit if you're using medium armor (such as a Breastplate) you need to have a middling Dexterity score. And you wouldn't benefit at all if you wear heavy armor.
This makes the item consistent with how 5E treats natural armor. That is, the more artificial armor you wear the less you gain from natural armor.
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There is, of course, a much simpler implementation: you gain +1 AC.
The difference here is that unlike the Ring of Protection there's no attunement requirement. This makes the item very powerful - much more than a mere +1 Amulet of Natural Armor in d20 (despite the identical mechanism).
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Finally, you could experiment with replicating the
Barkskin spell. However, that spell suffers terribly by a mismatch between the spell's name, history and expected effect on one hand, and the spell's actual 5E mechanism on the other. I would recommend against this option myself.