Question:
When I print the paper space as a pdf in A3 size and then insert the pdf back to the paper space in another file, why the pdf file becomes very large?
Reason:
When there is no object in paper space, only viewport showing objects in model space, although the pdf file size is the same when you check in Acrobat Reader, such as "16.54 x 11.69 in", AutoCAD can not tell correctly its unit when it is imported with PDFATTACH command.
For example an A3 sheet size is 420 x 297 mm in your paper space. You need scale it down to "Scale: 0.029" to get "Width: 420" .
Solution:
Simply add a printable point at 0,0 in you paper space before printing it as a pdf file. Now AutoCAD can recognize its scale correctly.