Well not twice. For each extra shield the unit that you're upgrading costs, it takes two gold per shield to upgrade in vanilla/PTW; it costs three in conquests.
Example:
A warrior costs 10 shields. A swordsman costs 30 shields. That's 20 extra shields. In vanilla/PTW, the upgrade would cost 40 gold (20 extra shields * 2 gold per shield). In conquests, the upgrade would cost 60 gold (20 extra shields * 3 gold per shield).