<p>In this paper, the efficiency and the quality factor (Q) of an infinitesimal loop antenna with the circumference of 0.01λ enclosed in a µ-negative (MNG) shell of 0.023λ diameter is investigated. It is demonstrated that an MNG shell can be designed to produce an electrically small system with a matched input impedance leading to total efficiency approaching unity. Simulation results show that the fractional bandwidth of significantly better than Chu limit can be obtained, especially if the material is regarded dispersionless. The calculated Q of the antenna with LL model, M model, and Z model MNG are 74.5%, 55.9%, and 37.5% of those predicted by Chu limit, respectively.</p>