Fractal Distribution of Antenna Array Elements for CubeSat Applications

Compact antenna design for CubeSats is severely constrained by a limited surface area, necessitating efficient space-sharing strategies. This study investigates a recursive fractal distribution algorithm using the similarity dimension parameter (Df) of the generating Iterated Function System (IFS) attractor to control element arrangement in X-band circular microstrip patch arrays (4×4 and 8×8). Using Ansys HFSS simulations, electromagnetic metrics—including gain, half-power beamwidth (HPBW), envelope correlation coefficient (ECC), maximum mutual coupling (Max|Sij|), and element input impedance (Zin)—were analyzed alongside the resulting available central space for payload integration. The results show that reducing Df from 2.0 to 1.3 on a 100×100mm substrate increases the maximum available central diameter from 12.4mm to 42.0mm (expanding its normalized area from 1.20% to 13.88%), providing sufficient space to accommodate an optical camera payload with a diameter of up to 36 mm. Concurrently, for the 8×8 array, gain decreases from 22.35dB to 20.27dB and HPBW narrows from 12.84° to 11.11°. Over the same range, the sidelobe level (SLL) degrades from −13.36 to −6.24dB, while maintaining a low ECC (≤0.0218) at Df=1.3. These findings demonstrate that fractal redistribution does not increase the total free area within the fixed antenna aperture, but instead redistributes it into a larger contiguous region, providing a controllable trade-off between electromagnetic performance and payload accommodation for small spacecraft platforms.