It helps to be clear on the distinction between the antagonist and the source of conflict, and to understand the structural implications for stories where they are one and the same, and stories where they are distinct.
The antagonist opposes the protagonist by acting against him or her. In order to show and understand the conflict that drives the story, the antagonist must be introduced at about the same time as the protagonist.
The source of conflict is the person or agency that causes the antagonist to act against the protagonist, either directly through some sort of motivation (the bad guy sends his henchmen), or indirectly by creating the conditions that force the protagonist and the antagonist to compete (they must fight to the death in the arena).
|Emperor Palpatine (Wikipedia)|
You might argue that the source of conflict is the ultimate antagonist because many stories end only when the protagonist finally manages to destroy the source of conflict. If you want to think in terms of major and minor antagonists, that's fine.
But it's important to be clear on the distinction between the character who actively opposes your protagonists and the reason that character opposes the protagonist. The Emperor Palpatine was the source of conflict and Star Wars didn't end until he was destroyed, but it was Darth Vader who most actively opposed Luke and Han.
Deren blogs daily at The Laws of Making.