Why am I having a such a bad time with my barbarian? He gets hit so often with the -1 AC and medium armor. What are the barbarians in your group doing differently? Did they go more Dex and Con focus than Str? Are the barbarians in your campaign tearing it up? The champion seems much more durable. And the Ranger archer dealing damage from range seems to do better a lot of the time. Maybe it is unlucky rolls.
If you have a martial that stays at range, that just means the monsters are that much more likely to target you instead.
And it's a natural instinct for many GMs to play the monsters "smart" which in this case means "avoiding the hard target", the Champion.
If so, your party might be imbalanced in the area of sharing incoming damage.
I strongly believe every martial must take on the very essential task of: soaking (or negating*) damage.
*) it's almost impossible to build a character that doesn't take damage. The monsters are simply too dangerous.
If the fourth character is a squishie I can definitely understand your pain - not only do you compare your defense with the best defender of the game, you don't get much help in the most important task either: causing damage. After all, when all monsters are dead, you don't need a high AC...
Champions and ranged fighters have both considerably lower DPS than you do. Your allies need to, at a minimum, realize it is in their interest to keep you standing to output your impressive DPS even though it means inconveniencing themselves.
In contrast, the five-man party I'm GMing feature one barbarian, one fighter, one ranger - all melee warriors. The barbarian might take a bit more damage than the other two, but is also doing huge amounts of damage herself. If she's at risk of going down, she can rely on two allies to step up.
And of course, the impressive healing power of the Cleric. (Only the fifth character, a Wizard, feels like it is playing in junior league)
My suggestion would be to have the archer character understand the necessity to stay close to enemies and divert some of the damage you're currently soaking onto his or her own body.
After all, in a game with "free" healing, taking damage is not a problem. Only taking too much damage in too short time is.
Bottom line is: it might not be entirely your fault your character is taking so much damage...!
Regards