Transaction log entries are only purged on checkpoint if you are running in simple recovery mode. If you are in simple recovery mode, you cannot run log backups at all.
In full recovery mode transaction log entries are only removed from the log after a log backup.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability