As per the Ranger Companion feature, you can add your proficiency bonus to your companion's AC.
I would like to know how to interpret this in terms of AC calculation.
Could I interpret as though my pet is getting a bonus to its base AC (Example: A PC wearing a shield). Or is this new number the new base AC?
In terms of formulas, let's take the Wolf:
AC = 13 (natural armor)
AC with Ranger Companion at level 3 = 15 (13[base] + 2[Prof])
The second interpretation would be that the wolf's new base AC simply 15.
The way the feature is worded makes me believe it's the former. The reason I ask this is to understand how this would interact with spells like Barkskin.
Barkskin states that your AC cannot be less than 16, meaning that if you choose to use Barkskin as the way you calculate your AC, it is now 16. You can choose to wear a shield on top of Barkskin, and receive the bonus as normal, meaning, it'd be 18 AC total.
Now let's go back to the Wolf. If the former interpretation is true, and I apply Barkskin to my wolf, that'd mean his base AC can now be 16 instead of 13, and in addition to this he receives a bonus to his armor class equal to my Proficiency bonus. Assuming level 3 ranger, that'd mean my wolf's armor class is now 18.
Otherwise, if the latter is true, then his AC is 16 while under barkskin but he does not receive the bonus because the latter interpretation states that the bonus is simply part of his base AC calculation instead of an additional amount of AC he gets because of the feature.