Backend systems for radio telescopes have tended to be designed specifically for the particular RF and IF frequencies and digitization bandwidth of the particular project. As analogue-to-digital conversion technology advances, it is becoming feasible and cost effective to develop receivers using wideband digitization with a common architecture. This project lead by the Oxford Experimental Radio Cosmology Group aims to design and develop a common receiver – down-conversion and digital backend – for a number of different telescopes. A down-conversion architecture using a single heterodyne step with IQ mixers and a baseband IF presents a common IF signal to the digitiser from a variety of RF signal sources. The Xilinx RF System-on-Chip device (RFSoC), which has RF ADCs integrated with and FPGA and processors, was selected as the platform for the backend. In this paper, the system architecture of the RFSoC-based digital backend, including the down-conversion circuit interfacing the existing electronics and RFSoC ADCs, will be described. We have performed a comprehensive performance characterization of the RFSoC ADCs, and the test results address concerns about the interleaved spurs, dynamic range, intermodulation distortion and long-term stability. We have successfully developed a real-sampling PFB-based spectrometer on the RFSoC platform and we are currently working on the IQ sampling PFB-based spectrometer. The latest test results for the IQ sampling spectrometer and the future development plan will be discussed in this paper. Applications of the common receiver system will include the CBASS-South telescope, the Goonhilly-3 29-m telescope, the Tulancingo 32-m telescope, and the Redshift Receiver on the Large Millimetre Telescope where the existing IF signal band is comparable to the RF band on the other systems.