Following are permissions /roles are assigned to User / Operator :
At SQL Server instance following roles are to assigned:
dbcreator public
Using Selected Database following roles are to assigned:
db_backupoperator db_denydatareader public
As a result user / operator created has minimal permissions for database access and can create backup. For downloading the script visit following link, http://gallery.technet.microsoft.com/Create-Minimum-Rights-4d746f7d