Created some drawing to help you understand, that modern SAM missiles are rather an endgame (semi active) guided ballistic missiles, than anything else.

Here are some classic SAM designs...



... and here are the modern SAM's. (Patriot/S-300/-400)



oops the upper one is a SCUD ballistic missile. biggrin

Usual flight path of the Patriot/S-300/-400 missiles is a ballistic one:

Hpasp
Free SAM Simulator, "Realistic to the Switch"
(U-2 over Sverdlovsk, B-52's over Hanoi, F-4 Phantoms over the Sinai, F-16's and the F-117A Stealth bomber over the Balkans.)
http://sites.google.com/site/samsimulator1972/home

Book from the author - Soviet Nuclear Weapons in Hungary 1961-1991
https://sites.google.com/view/nuclear-weapons-in-hungary/
thumbsup