Spurs-Free Single-Bit-Output All-Digital Frequency Synthesizers With Forward and Feedback Spurs and Noise Cancellation

All-digital frequency synthesis architectures with phase and polar Σ-Δ modulation feedback loops are introduced as a means to overcome the inherent spectral-quality limitations of forward-dithered all-digital frequency synthesizers represented by the family of pulse direct digital synthesizers. The spectrum of dithered pulse direct digital synthesizers is derived first, with and without modulation, as well as that of their variations with multiple dithered paths and with colored dithering resulting in lower noise level. The limited dynamic range achieved by forward-dithered all-digital frequency synthesizers motivates the introduction of phase and polar Σ-Δ modulation feedback loop architectures which are modeled and analyzed to derive their noise transfer functions. Extensive MATLAB simulation illustrates the suppressed near-in noise and the high spurs-free dynamic range the two Σ-Δ schemes can achieve and the wideband spurs-free output of the polar one. Detailed analysis and implementation aspects of the techniques are outside the scope of the paper.