We study non-equilibrium behaviors of a particle subjected to a high-frequency cutoff noise in terms of generalized Langevin equation, where the spectrum of internal noise is considered to be of the generalized Debye ...We study non-equilibrium behaviors of a particle subjected to a high-frequency cutoff noise in terms of generalized Langevin equation, where the spectrum of internal noise is considered to be of the generalized Debye form. A closed solution is impossible even if the equation is linear, because the Laplace transform of the memory kernel is a multi-value function. We use a numerical method to calculate the velocity correlation function of a force-free particle and the probability of a particle passing over the top of an inverse harmonic potential. We indicate the nonergodicity of the second type, i.e., the auto-correlation function of the velocity approaches to non-stationary at large times. Applied to the barrier passage problem, we find and analyse a resonant phenomenon that the dependence of the cutoff frequency is nonmonotonic when the initial directional velocity of the particle is less than the critical value, the latter is determined by the passing probability equal to 0.5.展开更多
With the rapid evolution of wireless communication technology, integrating various communication modes in a mobile terminal has become the popular trend. Because of this, multi-standard wireless technology is one of t...With the rapid evolution of wireless communication technology, integrating various communication modes in a mobile terminal has become the popular trend. Because of this, multi-standard wireless technology is one of the hot spots in current research. This paper presents a wideband fractional-N frequency divider of the multi-standard wireless transceiver for many applications. High-speed divider-by-2 with traditional source- coupled-logic is designed for very wide band usage. Phase switching technique and a chain of divider-by-2/3 are applied to the programmable frequency divider with 0.5 step. The phase noise of the whole frequency synthesizer will be decreased by the narrower step of programmable frequency divider. A-E modulator is achieved by an improved MASH 1-1-1 structure. This structure has excellent performance in many ways, such as noise, spur and input dynamic range. Fabricated in TSMC 0.18/tin CMOS process, the fractional-N frequency divider occupies a chip area of 1130 × 510μm^2 and it can correctly divide within the frequency range of 0.8-9 GHz. With 1.8 V supply voltage, its division ratio ranges from 62.5 to 254 and the total current consumption is 29 mA.展开更多
文摘We study non-equilibrium behaviors of a particle subjected to a high-frequency cutoff noise in terms of generalized Langevin equation, where the spectrum of internal noise is considered to be of the generalized Debye form. A closed solution is impossible even if the equation is linear, because the Laplace transform of the memory kernel is a multi-value function. We use a numerical method to calculate the velocity correlation function of a force-free particle and the probability of a particle passing over the top of an inverse harmonic potential. We indicate the nonergodicity of the second type, i.e., the auto-correlation function of the velocity approaches to non-stationary at large times. Applied to the barrier passage problem, we find and analyse a resonant phenomenon that the dependence of the cutoff frequency is nonmonotonic when the initial directional velocity of the particle is less than the critical value, the latter is determined by the passing probability equal to 0.5.
文摘With the rapid evolution of wireless communication technology, integrating various communication modes in a mobile terminal has become the popular trend. Because of this, multi-standard wireless technology is one of the hot spots in current research. This paper presents a wideband fractional-N frequency divider of the multi-standard wireless transceiver for many applications. High-speed divider-by-2 with traditional source- coupled-logic is designed for very wide band usage. Phase switching technique and a chain of divider-by-2/3 are applied to the programmable frequency divider with 0.5 step. The phase noise of the whole frequency synthesizer will be decreased by the narrower step of programmable frequency divider. A-E modulator is achieved by an improved MASH 1-1-1 structure. This structure has excellent performance in many ways, such as noise, spur and input dynamic range. Fabricated in TSMC 0.18/tin CMOS process, the fractional-N frequency divider occupies a chip area of 1130 × 510μm^2 and it can correctly divide within the frequency range of 0.8-9 GHz. With 1.8 V supply voltage, its division ratio ranges from 62.5 to 254 and the total current consumption is 29 mA.
