As a magnetic confinement configuration for electron-positron pair-plasmas, the APEX collaboration [T. S. Pedersen et al., New J. Phys. 14, 035010 (2012)] plans to construct a compact levitated dipole experiment with a high-temperature superconducting coil. In order to realize stable levitation of the dipole field coil, a simple feedback-controlled levitation system was constructed with conventional analog circuits. We report the properties of a prototype levitation system using a permanent magnet and compare its behavior to predictions from a stability analysis. We also present a practical review needed for the construction of a compact levitated dipole trap system based on the work of Morikawa et al. [Teion Kogaku, J. Cryo. Soc. Jpn. 39, 209 (2004)]. Numerical orbit analysis suggests improved confinement properties of charged particles in a dipole field trap by replacing the permanent magnet with a levitated superconducting coil magnet. Such a compact dipole field configuration is potentially applicable to the confinement of various charged particles including positrons and electrons.