Modeling and Analysis of Harmonic Spurs in DLL-Based Frequency Synthesizers

Periodic jitter raises the harmonic spurs at frequency synthesizer output spectrum, down-converting the out-of-band interferers into the desired band and corrupting the wanted signal. This paper proposes a comprehensive behavioral model for spur characterization of edge-combining delay-locked loop (DLL)-based synthesizers, which includes the effects of delay mismatch, static phase error (SPE), and duty cycle distortion (DCD). Based on the proposed model and utilizing Fourier series representation of DLL output phases, an analytical model which formulates the synthesizer spur-to-carrier ratio (SCR) is developed. Moreover, from statistical analysis of the analytical derivations, a closed-form expression for SCR is obtained, from which a spur-aware synthesizer design flow is proposed. Employing this flow and without Monte Carlo (MC) method, one can determine the required stage-delay standard deviation (SD) of a DLL-based synthesizer, at which a certain spurious performance demanded by a target wireless standard is satisfied. A design example is presented which utilizes the proposed design flow to fulfill the SCR requirement of -45 dBc for WiMedia-UWB standard. Transistor-level MC simulation of the synthesizer SCR for a standard 65-nm CMOS implementation exhibits good compliance with analytical models and predictions.