I don't know what mistake you made last time. But from my experience, if a big company wants to hire you, they don't care too much about the salary range. Small company will, because they have a tight budget.
If I were you, I will focus on my skills and qualifications. Tell them how much do you earn.More importantly, tell them why should they hire you and why should they pay you that much.
If you are not sure how much you would ask, just say I believe that they will give you a fair salary package and you are open to any negotiation.
That is all.