Time machine fails backup

Question

Can anyone advise me?
I use Time Machine to backup. All has been well the backups were flawless until recently when I decided that I needed to encrypt my sensitive work and personal files placing them into an encrypted Apple Disk Image on my hard disk. Ever since then at some stage Time Machine had decided that there is insufficient disk space and the backup fails.
When it first began to fail I increased the backup disk space and began a fresh start backup.
The backup disk is now 1 TB and the total amount on my hard disk to be backed up to backup is 183 gb which includes the disk image which is 40 gb.
The only change has been the creation of the disk image otherwise everything else is the same. Would it be better to have a number of disk image files and spread the encrypted material across smaller dmgs?

Answer 1

Thank you for your response which is very helpful. I have changed the dmg to a sparse bundle and Time Machine appears to be handling the backup better.
Initially I was confused about the difference between a sparse image and a sparse bundle but read in https://discussions.apple.com/thread/2001162?start=0&tstart=0 what the difference is and see that the sparse bundle appears to have been developed by Apple for exactly my kind of problem.
You say that "… be aware that disk image files are not backed up at all while the image is mounted."
I do not wish to disagree but when I was backing up the vanilla dmg and also last night backing the sparse bundle dmg the back up has worked and did work on the mounted disk. In my case the disc is always mounted as it contains the bulk of the files I work on. Perhaps I have misunderstood what you were saying.
Thank you again for your response.