I have a wordpress theme with a logo linking to a .pdf document.
To do exactly what you've asked you can make a small simple change...
However, without knowing why you need to refresh the page I can't say this is the best course of action. We need more information to be able to help you more appropriately.
Edit Not that you've explained why you need to reload the page (it goes blank when you click the link), you should change your previous code to this, in order to stop that happening...
var link = document.getElementById('logo'); link.href = "url_of_the_pdf"; link.target = "_blank";
Previously the output from
window.open() was being written to the page, which caused the current page contents to be deleted. This method changes the link so that it works correctly, and should resolve your previous problem.