I was reading about the Barding rule on page 155 of the PHB, and I was just curious if a Beastmaster Ranger could armor up their companion? If so, how would that stack with the Ranger's proficiency bonus added to their companion's AC?
Barding. Barding is armor designed to protect an animal’s head, neck, chest, and body. Any type of armor shown on the Armor table in this chapter can be purchased as barding. The cost is four times the equivalent armor made for humanoids, and it weighs twice as much.
If you look at that description of Barding from the PHB, it can be reasoned that any animal can wear Barding, regardless of the animal's exact purpose. I figure this because it says "armor designed to protect an animal's head, neck, chest, and body." It does not specify anything about the animal itself.
The armour does not add to the animal's natural AC, but rather it provides an alternative way to calculate the animal's AC (you choose whichever you prefer).
As for the bonus to AC that the animal companion gets by being a beast master ranger's companion: that stacks with the armor, because it is a special bonus to AC, and usually bonuses will stack.
Hope that helped!
Yes, but keep in mind Encumbrance
Keep in mind that barding has twice the weight. Hence full plate barding would require 130 pounds. If playing with Encumbrance (PH 176) then 13 strength for a large creature (such as riding horse or war horse), or 26 strength for a medium creature would be required not to slow down by 10 feet. This means most ranger companions will be restricted to Breastplate Barding (14 + Dex mod+ ranger's proficiency bonus).
If trying to put Full Plate Barding on your companion and also looking to mount your beast companion as small creature such as a halfling of 40 pounds with 30 pounds of gear (just Breastplate is 20 pounds (PH 145)), this would put 200 pounds on the poor mount. Which is easily more than 10 times the starting Strength of most companions leading to it being heavily encumbered. If ever finding a belt of giant's strength and attune your companion to it this might be possible, but in general you'll have to go with a lower weight barding.
This balances out the potential exploits of putting full-plate barding on tiny size familiars or making beast companions AC too high since they get +2 AC initially then later +6 AC when player reaches level 17 from Ranger's Companion (PH 93).