Systematic analysis of the offset-PLL output spur spectrum

This paper presents a mechanism that explains exactly the cause of spurs at the output of offset-PLL (OPLL) transmitters. By a rigorous analysis of the relationship between the signals and disturbances in OPLL, accurate formulas are obtained which elucidate systematically the intermodulation nature of the output spur spectrum. From the analysis, it is shown that in practical situations the OPLL spurs are due to the disturbances from the voltage-controlled oscillator leakage, the local oscillator leakage, and the image signal, rather than other spurious products of the offset mixer in the loop as previously explained. The formulas give insight into OPLL circuit design and frequencies accommodation and clearly depict the output spur distribution in the more realistic situation when the input is modulated. Finally, the formulas are verified by some elaborate experiments with extensive numerical results.