Dan - you need to use either the Special Direct Mode or Direct Mode 0 as these cards (if you are using Mifare Classic) are not 100% ISO14443A compliant. So for the auth and read/write of blocks and sectors, you do need to either use the SDM or DM0...please see attached for details mainly around using the DM0 for these cards. (this covers the TRF7960/-60A and the TRF7964A/TRF7970A.
(Please visit the site to view this file)
If you are using Mifare DESFire EV1 or Plus cards, then you don't need to drop the TRF7970A into DM0 or SDM mode, you can use Direct Mode 2 (this is default mode).