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In this brief, a systematic design procedure for a second-order all-digital phase-locked loop (PLL) is proposed. The design procedure is based on the analogy between a type-II second-order analog PLL and an all-digital PLL. The all-digital PLL design inherits the frequency response and stability characteristics of the analog prototype PLL. Index Terms--All-digital phase-locked loop (PLL), bilinear transform, digital loop filter, digitally controlled oscillator.

This paper presents an approach to reduce substrate cross-talk noise between noisy and sensitive circuitry in mixed-signal integrated circuits at different stages of design and layout development. Silencer! a new, fully automated, schematic-driven substrate noise coupling analysis tool is introduced to accomplish this task. The tool seamlessly enables substrate noise coupling analysis in a standard mixed-signal design flow. Two different methods, fast scalable macro-models and a boundary element solver are integrated into Silencer!. These methods allow extractions of a substrate network from geometric layout information. Simulation results obtained with Silencer! are accurate to within 10% of measured integrated circuits. Index Terms--Coupling noise, integrated circuit noise, mixed-signal noise, noise analysis tool, noise minimization, pre-/post-layout analysis, substrate noise, substrate noise analysis, supply noise.

An n-contact to p-contact model is proposed for analyzing substrate noise coupling in mixed-signal integrated circuits. The self-coupling parameters for n-p structures are similar to those for p-p structures and the cross-coupling parameters of the n-p structures are similar to those of the p-p structures at large separations.

A new coupled circuit and electrostatic/mechanical simulator (COSMO) is presented for the design of low phase noise radio frequency (RF) microelectromechanical systems (MEMS) voltage-controlled oscillators (VCOs). The numerical solution of device level equations is used to accurately compute the capacitance of a MEMS capacitor. This coupled with a circuit simulator facilitates the simulation of circuits incorporating MEMS capacitors. In addition, the noise from the MEMS capacitor is combined with a nonlinear circuit-level noise analysis to determine the phase noise of RF MEMS VCO. Simulations of two different MEMS VCO architectures show good agreement with experimentally observed behavior. Index Terms--Circuit simulation, coupled circuit and device simulation, electrostatic/mechanical simulator, microelectromechanical systems (MEMS) capacitor, microelectromechanical systems voltage-controlled oscillator (MEMS VCO), noise simulation, phase noise, radio frequency voltage-controlled oscillator (RF VCO).

In this paper, we present an exact analysis for third-order charge-pump phase-locked loops using state equations. Both the large-signal lock acquisition process and the small-signal linear tracking behavior are described using this analysis. The nonlinear state equations are linearized for the small-signal condition and the z-domain noise transfer functions are derived. A comparison to some of the existing analysis methods such as the impulse-invariant transformation and s-domain analysis is provided. The effect of the loop parameters and the reference frequency on the loop phase margin and stability is analyzed. The analysis is verified using behavioral simulations in MATLAB and SPECTRE. Index Terms--Impulse invariance, jitter, loop delay., phase-locked loop (PLL), phase noise, state space, z-domain.

In this paper, a new formulation for the extraction of substrate parasitics is derived that can account for the nonuniform current distribution on contacts without contact subdivision. This method is orders of magnitude faster than the original Green's function method. The speedup is achieved by a significantly reduced matrix size combined with the application of the discrete sine transform. The method is accurate, and is well suited for large problems. Index Terms--Green's function, noise modeling, substrate coupling, substrate noise, substrate parasitic extraction.

In this paper, a new nonlinear finite element model is presented for the analysis of piezoelectric laminates at large deflections. The element is an eight-node element with 5 mechanical degrees of freedom at each node, and the potential difference across the piezoelectric layer is introduced as an additional electrical degree of freedom on an element level. Application of this model to a clamped square piezoelectric laminate shows the strong nonlinear relationship between the terminal voltage and deflection observed experimentally. Further more, the numerical results also show that the electrode size is an important design parameter in maximizing the power output when the piezoelectric laminates are used as power generators. [970] Index Terms--MEMS devices, micropower generation, non-linear FEM, piezoelectric devices, piezoelectric laminate analysis.

A comparison of various simulation and estimation methods available to predict the phase noise in oscillators is presented in this paper. The phase noise of two ring oscillators and one radio frequency CMOS oscillator was determined using the Hajimiri and Lee phase noise analysis method, and the commercial simulators SpectreRF and EldoRF. Good agreement was obtained between the estimated and simulated phase noise performances. These oscillators were fabricated in a 0.35-[micro]m CMOS process. The measured data also shows reasonable agreement with the analysis and simulations. Index Terms--Noise simulation, oscillators, oscillator noise, phase noise analysis, phase noise simulation.