Versuchen Sie dies, Sie können das Format zip in gz ändern, wenn Sie möchten :)
$this->load->dbutil();
$prefs = array(
'format' => 'zip',
'filename' => 'my_db_backup.sql'
);
$backup =& $this->dbutil->backup($prefs);
$db_name = 'backup-on-'. date("Y-m-d-H-i-s") .'.zip';
$save = 'pathtobkfolder/'.$db_name;
$this->load->helper('file');
write_file($save, $backup);
$this->load->helper('download');
force_download($db_name, $backup);