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Physical limitations based only on antenna volume, form factor and material parameters are applied to electrically small antennas in the form of single dipoles. The upper bound on the gain-bandwidth product is solely determined by the polarisability matrix that characterises the antenna when it is immersed in a uniform applied static field. The polarisability, and hence the bandwidth, is increased by loading the dipole arms close to their ends. The half-power impedance bandwidth is increased from 5 to 13% by moving the coils from the centre to the ends of the dipole arms. The introduction of a stub-matching further improves the bandwidth but the physical limit is not reached. Finally, a dual-resonance dipole antenna is analysed. It is observed that a second resonance hardly reduces the bandwidth of the first resonance if the resonances are separated more than 1.7 times in frequency.