Replacing Hard Drive and avoiding full Time Machine Backup

I am planning to replace my hard drive with one with a greater capacity.

Some time ago, after a defragmenting catastrophe, I performed a Time Machine restore after which Time Machine did a full backup - thus using up a huge chunk of my Time Machine backup drive. This seems a little pointless, doesn't it? In simple terms, after restoring drive A from drive B, a copy of drive A is made on drive B - thus duplicating the data from which the restoration was made.

I realise that Time Machine is much more sophisticated than that but I know from consulting Backup Loupe how much data is backed up and it was >120GB and the space available on my Time Machine backup drive decreased accordingly.

So, if I now want to change my hard drive I anticipate that a similar performance will take place. Is there a way to avoid this?