If you break your log backup chain by switching a database into simple recovery or by executing BACKUP LOG WITH NO_LOG and WITH TRUNCATE_ONLY, there is a misconception that you then have to do a full backup in order to get your transaction log backups to run again. This is incorrect. Once you switch your recovery model back to full you only have to do a differential backup in order to restore the chain.
See Paul Randal’s blog post for more information (and an example script to demonstrate this).
Sql Server Powershell 