Provided herein are new compact and miniature oxygen concentrator apparatus, as well as methods incorporating use of the apparatus. The apparatus and methods utilize selected cycle times, adsorbent specifications and novel conditions to produce a fast Pressure Swing Adsorption (“PSA”) system. The oxygen concentrator apparatus and methods herein have significant utility in the fields of biotechnology, engineering, and medicine. A particularly advantageous use of this invention is as a “snap on” portable oxygen concentrator, where piped compressed air is already available such as in civil and military hospitals, ambulances, air craft cabins, mobile fish tanks, etc. Those embodiments eliminate the need for dedicated moving machinery (blower, compressor, vacuum pump) normally associated with a conventional PSA oxygen concentrator.