SQL Server - Sudden log autogrowth after database backup
I wanted to clear this in a comment but there is no room to do this, so I post it as the answer.

While the the key point of what happens is right, i.e. the  full backup cause the log to grow, this explanation below given by Ste Bov is completely wrong:


  When you start a full backup that is the new point in time that the
  tLog backups will work from, but they cant work until that backup is
  complete, so during this time the transaction log grows, once the full
  backup is complete you now have a new point in time and the tLog
  backups will now be able to actually release the data from the
  transaction log and it will return to its normal usage levels


Fisrt of all full backup will NOT make "the new point in time that the
 tLog backups will work from", yes it creates a new recovery point, but the next log backup will start exaclty from the point where the previous log backup was stopped (this point in the log file, last_LSN, is written to the backup and can be seen using RESTORE HEADERONLY, or by querying msdb..backupset)

Second, starting with SQL Server 2005, concurrent log and full backups are possible, you can prove it yourself. What happens instead is that the log backup cannot clear the log when it finishes if there is a full/differential backup running concurrently. That is because diff/full backup need to write out the "active portion"* of the log in order to get a database in consistent stay when restored.

*to be precise, it's not an "active portion", but all the log records from 
MIN(LSN of last checkpoint, LSN of oldest active transaction) to the LSN at which the data read portion of a backup ends

So the log should be large enough to be able to accomodate all the activity that is logged for the whole duration of the full backup.

More on this here:

Concurrent log and full backups by Randal

More on how much transaction log a full backup includes by Randal