This study presents a planar helical electromagnetic bandgap (EBG) structure designed for integration with an equiangular spiral antenna operating at 2.5 GHz. An equivalent-circuit model is introduced, and the effects of the unit-cell width, substrate thickness, metallic-strip width, and interstrip gap on the electromagnetic response are investigated through full-wave parametric simulations. The optimized periodic structure is subsequently employed as a backing reflector for the spiral antenna and is compared with both an unbacked configuration and a perfect electric conductor (PEC) reflector. At 2.5 GHz, the EBG-backed antenna achieves a simulated gain of approximately 6.15 dBi, compared with 2.58 dBi for the unbacked antenna, while producing an axial-ratio response that is less strongly disturbed over the investigated frequency range than that of the PEC-backed configuration. The mean axial-ratio value over the investigated band is reduced from 2.22 for the PEC-backed case to 1.67 for the EBG-backed case. The results demonstrate that the proposed helical EBG structure provides a compact approach for controlling the radiation characteristics of spiral antennas in S-band electromagnetic and wireless systems.