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The trade-offs in terms of performance and size of an axial-mode helical antenna for satellite communications are investigated. The antenna size is reduced by using a backfire bifilar helical antenna (BBHA) combined with a dielectric core. The antenna is designed using Ansoft's HFSS and the results are verified experimentally. A size reduction of 70% is achieved. The gain at 2.4 GHz is 2.6 dBic with an axial ratio bandwidth of 400 MHz. The half power bandwidth is 80 degrees and the antenna return loss is below -10 dB between 2.2 GHz to 2.6 GHz. A two-element dielectric-loaded BBHA array is simulated using HFSS and results are compared with a single dielectric-loaded BBHA.