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This paper presents a low-cost beam-switching method for circularly-polarised (CP) patch antenna. By fabricating a switchable single feed circular patch antenna over a properly designed electronically tuneable high impedance ground plane, its radiation pattern can be steered. The feeding network in this design is also simplified. To demonstrate the concept, an antenna prototype with right hand circular polarisation (RHCP) at C band is developed, simulated and described in this paper. Using the electronically tuneable approach on both the antenna feed and high impedance ground plane the proposed antenna is able to cover 360° in azimuth at an elevation angle of 45° with an axial ratio lower than 3 dB. Furthermore, it reports a gain of 7.9 dBi at 4.8 GHz. The antenna is shown to be capable of achieving the beam-switching by tuning the high impedance surface electronically. The beam-switching is achieved without the use of array antenna, microwave phase shifters or beam-switching feed networks such as the Butler Matrix. Hence the proposed beam-switching CP antenna has compact size and low-cost, and is promising for small satellites applications.