"Let a person be told, as scripture teaches, that he was estranged from God by sin, an heir of wrath, exposed to the curse of eternal death, excluded from all hope of salvation, a complete alien from the blessing of God, the slave of Satan, captive under the yoke of sin; in time, doomed to horrible destruction, and already involved in it; that then Christ interposed, took the punishment upon himself, and bore what by the just judgement of God was impending over sinners; with his own blood expiated the sins which rendered them hateful to God, by this expiation satisfied and duly propitiated God the Father, by this intercession appeased his anger, on this basis founded peace between God and men, and by this tie secured the Divine benevolence toward them; will not these considerations move him the more deeply, the more strikingly they represent the greatness of the calamity from which he was delivered".
That's a good detailed explanation of PSA. If you notice it has some Ransom elements in it as we were slaves of Satan, and it has some of the modern idea that the love and mercy shown should induce us to respond (will not these considerations move him more deeply). But most importantly, I think it brings out the problem with using the early church fathers too much on this. They were developing this, as
@Martin Marprelate has generously provided evidence for with quotes, but for several well known reasons, they were most interested in the cosmic aspects of the atonement.
PSA is essential if you want to fully understand the role of your personal sinfulness and how it affects your relationship with God.
By the way, that's from Calvin, who for some reason is out of fashion now. I blame the Young Restless and Reformed. They were sometimes obnoxious, and have moved on now into woke politics for the most part. Calvin is surprisingly easy to read and on line for free or on your Kindle for a couple of bucks.