An all-digital sigma-delta modulator (SDM) based RF synthesizer is presented. A multiplier-less architecture for the implementation of the band-pass SDM loop filter is proposed. Furthermore, this architecture enables the adjustment of the loop filter central frequency by exploiting homodyne up- and down-conversion. The RF synthesizer is comprised of a direct digital synthesizer (DDS) and the proposed multiplier-less single-bit band-pass SDM. Due to the simplicity of the synthesizer building blocks very high generated frequencies are possible. Modualtion is easily incorporated and as a test case its performance in a 32-QAM modulation scheme is presented.