A little question

Hi, here, I have a question when reading the EBNF part of the book.

> A pushdown automaton is a finite state machine with a stack

Did you assume that the size of the stack is infinite?

Let's say you have a finite state machine with a stack size of N(an integer).

> Any context-free grammar can be implemented by a pushdown automaton (PDA)

Is this argument still true?