Automata – What changes must be made in a Turing machine to be equivalent to a PDA, a DFA?

I think that to make a Turing machine have the same power as a DFA (by power I mean all the languages ‚Äč‚Äčthat a DFA can decide, so can the Turing machine), we just do not allow any use of the rewind or rewrite. You can only move to the right and read the string in the order in which it is presented.

To simulate a PDA, however, I'm not sure what restrictions we might apply. I was thinking about allowing the backlash, but not rewriting the tape can make a Turing machine have a power equivalent to a PDA, but I'm not sure it's a correct statement or how it would prove the equivalence of the two.