Question On "Improvement Patents"

Such an 'improvement' patent application will be no more or no less than a normal patent application. The only difference is that there is a piece of prior art (your first patent) that may or may not be held against you. Further, your first patent may not only be regarded as prior art (if and how will depend on the publication data of the patent application and the filing data of your new application) but it will also prevent you to be allowed claims that overlap with the claims that have been granted already. This is called the prohibition of 'statutory type double patenting'. If claims would overlap, the solution would be to file a so-called terminal disclaimer in the newer patent which would set the expiry date of the ne patent equal to the expiry date of the earlier patent.