LC振荡器相位噪声的非线性摄动分析技术

相位噪声是振荡器的重要性能指标,通过对振荡器的非线性微分方程的推导,从而引入新的参数来考虑振幅噪声和相位噪声之间的相关性同时把这些参数和振荡器的工作点联系起来。并且这些公式推导也考虑了LC谐振回路中振幅噪声和相位噪声之间的相关性。在此基础上这里研究了如何在时域状态方程下将噪声看成是对振荡输出信号的小扰动,并建立引入噪声后的随机微分方程,实现LC振荡器的相位噪声分析技术。     

不同类型噪声作用下振荡器的相位噪声分析

相位噪声是振荡器最重要的性能指标.文中从描述振荡器的非线性微分方程出发,提出将噪声作为非线性微分方程的一项,通过建立随机非线性微分方程来分析振荡器的相位噪声,为振荡器的相位噪声提出了一种新的分析方法.用这种方法,在相同强度下,针对白噪声分别为加性和乘性的情形,分析其产生的相位噪声,得出了乘性噪声产生的相位噪声远大于加性噪声所产生的相位噪声的结论.     

基于等效小参量法的CMOS LC振荡器特性分析

建立了描述CMOS LC振荡器特性的二阶非线性微分方程.利用等效小参量法原理导出了原系统的等效线性方程组及其特性解析表达式,得到了交叉耦合MOS特性对振荡器性能的影响,包括起振条件、输出幅度与参数间的解析表达式、振荡器输出频率与LC谐振回路和交叉耦合CMOS管非线性特性影响的关系、振荡器输出的谐波特性.这些结论揭示了CMOS LC差分振荡器新的现象,对设计者了解振荡器的工作状态和优化设计有一定的参考意义.     

基于高次谐波体声波谐振器的微波振荡器设计

基于高次谐波体声波谐振器(HBAR)的高品质因数(Q)值和多模谐振特性,设计了Colpitts和Pierce两种形式的微波振荡器。采用HBAR与LC元件组成谐振回路的方法,与放大电路构成反馈环路直接基频输出微波频段信号。Colpitts振荡器输出信号频率为980 MHz,信号输出功率为-4.92dBm,信号相位噪声达-119.64dBc/Hz@10kHz;Pierce振荡电路输出信号频率达到2.962GHz,信号输出功率为-9.77dBm,信号相位噪声达-112.30dBc/Hz@10kHz。     

基于随机非线性微分方程的振荡器相位噪声研究

根据振荡器电路的时变非线性特性 ,运用一种通用的相位噪声理论 ,通过对噪声源随机过程建模 ,求解具有严格数学意义的随机非线性微分方程 ,得到一个常数 c来描述时间抖动和频谱扩散。分别用基于随机非线性微分方程和线性时变的方法求解 ,结果表明线性时变得到的相位噪声频谱在基频附近分布的能量之和超过载波能量 ,在物理意义上有一定不足 ;而文中的相位噪声分析结果表明相位噪声只改变能量的分布并不能使能量显著增加 ,得到的结果为设计电路时减少相位噪声影响提供了思路。     

宽带LC压控振荡器的相位噪声优化设计

采用0.35 μm BiCMOS工艺,设计了一款基于开关电容阵列结构的宽带LC压控振荡器.同时分析了电路中关键参数对相位噪声的影响.基于对VCO中LC谐振回路品质因数的分析,优化了谐振回路,提高了谐振回路的品质因数以降低VCO的相位噪声.采用噪声滤波技术,减小了电流源晶体管噪声对压控振荡器相位噪声的影响.测试结果表明,优化后的压控振荡器能够覆盖1.96～2.70 GHz的带宽,频偏为100 kHz和1 MHz的相位噪声分别为-105和-128 dBc/Hz,满足了集成锁相环对压控振荡器的指标要求.     

一种高性能CMOS晶体振荡电路的设计

本文对晶体振荡器的线性和非线性理论给出一般性的理论描述。它建立在高Q值的谐振电路基础上。常见的是三点振荡器，包括Pierce振荡器以及单端口振荡器。通过对电路的阻抗进行根轨迹分析，则能更清晰地了解电路的非线性性能。通过无损耗假设，可得到起振的基本条件以及频率牵引度、临界阻抗及启动时间等表达式。作为在RF设计中的一个应用电路，本文给出一种应用在接收器芯片中的高性能CMOS晶体振荡器设计，该芯片用0．25μm CMOS工艺实现，仿真结果与系统要求一致。     

一种改进的CMOS差分LC压控振荡器

介绍了一种改进的LC振荡器设计方法.谐振回路采用非对称电容结构,与常见的振荡器结构相比,经改进后的电路结构可以获得更好的相位噪声.基于0.35μm CMOS工艺,设计了一种采用补偿Colpitts振荡器电路结构实现的差分LC压控振荡器,工作电压为2.5V.经仿真证明,在设计中通过调整非对称电容谐振回路中的电容值,可以获得最优的相位噪声.     

一种改进的CMOS差分LC压控振荡器

介绍了一种改进的LC振荡器设计方法.谐振回路采用非对称电容结构,与常见的振荡器结构相比,经改进后的电路结构可以获得更好的相位噪声.基于0.35μm CMOS工艺,设计了一种采用补偿Colpitts振荡器电路结构实现的差分LC压控振荡器,工作电压为2.5V.经仿真证明,在设计中通过调整非对称电容谐振回路中的电容值,可以获得最优的相位噪声.     

LC振荡器的设计要点

主要介绍了LC振荡器的设计要点.从LC振荡器的模型出发,研究了VCO的电路结构、谐振回路对于输出幅度的影响、VCO的噪声源、VCO的相位噪声以及谐振回路的Q值对于VCO的影响.给出了LC振荡器的设计要点及设计中需要考虑的约束条件.     

A LiÉnard Oscillator Resonant Tunnelling Diode-Laser Diode Hybrid Integrated Circuit: Model and Experiment

We report on a hybrid optoelectronic integrated circuit based on a resonant tunnelling diode driving an optical communications laser diode. This circuit can act as a voltage controlled oscillator with optical and electrical outputs. We show that the oscillator operation can be described by LiÉnard's equation, a second order nonlinear differential equation, which is a generalization of the Van der Pol equation. This treatment gives considerable insight into the potential of a monolithic version of the circuit for optical communication functions including clock recovery and chaotic source applications.      

Perturbation-Based Stochastic Modeling of Nonlinear Circuits

This paper presents a general model for a nonlinear circuit, in which, the circuit parameters (e.g. resistance and capacitance) are subject to random fluctuations due to noise, which vary with time. The fluctuating amplitudes of these parameters are assumed to be Ornstein–Uhlenbeck (O.U.) processes and not the white noise owing to temporal correlations. The nonlinear circuit is represented by a system of nonlinear differential equations depending upon a set of parameters that fluctuate slowly with time. To model these fluctuations, we use the theory of Ito’s stochastic differential equations (SDEs). Then the driving force of the circuit dynamics is in accordance with the general perturbation theory decomposed into the sum of a strong linear component and a weak nonlinear component by the introduction of a small perturbation parameter. The circuit states are expanded in the powers of this small perturbation parameter and recursive solutions to the various approximates obtained. Finally, the approximate expressions for the output states are obtained as stochastic integrals with respect to Brownian motion processes. The proposed method is applied to a half-wave rectifier circuit which is built out of a diode, a resistor and a capacitor. The diode is represented by nonlinear voltage–current equation, and resistance and capacitance are subject to random fluctuations due to noise, which vary slowly with time. The results, obtained using the proposed method, are compared with those obtained via the conventional perturbation-based deterministic differential equations model for a nonlinear circuit. Hence, the noise process component, present at the output, is obtained.     

基于CMOS反相器石英晶体振荡电路的PSPICE仿真

石英晶体振荡器是很常用的电子器件,在电路设计和教学工作中经常需要对石英晶体振荡电路进行仿真分析。通过实例介绍使用PSpice仿真软件对石英晶体振荡电路进行模拟仿真的方法。针对石英晶体振荡器的等效电路,分析了石英晶体的串联和并联谐振频率。讨论了石英晶振的仿真模型,并在仿真器中观察其起振波形和稳幅波形,测试其振荡频率。通过对元件的参数扫描,分析不同参数对振荡器的影响。     

A CMOS Readout Circuit for SOI Resonant Accelerometer With 4-$mu rm g$ Bias Stability and 20-$ murm g/sqrt{{hbox{Hz}}}$ Resolution

A fully differential CMOS readout circuit for SOI resonant accelerometer is reported. The readout circuit is essentially an oscillator, consisting of an oscillator and a low noise automatic amplitude control (AAC) loop. A differential sense resonator is proposed to facilitate fully differential circuit topology and improves the SNR under a 3.3-V supply. A second-order AAC loop filter and a novel chopper stabilized rectifier are employed in the AAC loop to remove the noises, in particular, the 1/f noise, and to minimize the phase noise caused by the amplitude stiffening effect. The strong driving feedthrough is avoided by separating the drive and sense operation in the time domain, while using the same electrodes. The complete resonant accelerometer operates under a 3.3-V supply and achieves 140-Hz/g scaling factor, 20 mug/radicHz resolution and 4 mug bias stability. The readout circuit draws 7 mA under 3.3-V supply.     

Phase noise in LC oscillators

Analytical methods for the phase-noise analysis of LC-tuned oscillators are presented. The fundamental assumption used in the theoretical model is that an oscillator acts as a large-signal LC-tuned amplifier for purposes of noise analysis. This approach allows us to derive closed-form expressions for the close-to-carrier spectral density of the output noise, and to estimate the phase-noise performance of an oscillator from circuit parameters using hand analysis. The emphasis is on an engineering approach intended to facilitate rapid estimation of oscillator phase noise. Theoretical predictions are compared with results of circuit simulations using a nonlinear phase-noise simulator. The analytical results are in good agreement with simulations for weakly nonlinear oscillators. Complete nonlinear simulations are necessary to accurately predict phase noise in oscillators operating in a strongly nonlinear regime. To confirm the validity of the nonlinear phase-noise models implemented in the simulator, simulation results are compared with measurements of phase noise in a practical Colpitts oscillator, where we find good agreement between simulations and measurements     

Using Stochastic Differential Equation for Verification of Noise in Analog/RF Circuits

Today’s analog/RF design and verification face significant challenges due to circuit complexity, process variations and short market windows. In particular, the influence of technology parameters on circuits, and the issues related to noise modeling and verification still remain a priority for many applications. Noise could be due to unwanted interaction between the circuit elements or it could be inherited from the circuit elements. In addition, manufacturing disparity influence the characteristic behavior of the manufactured circuits. In this paper, we propose a methodology for modeling and verification of analog/RF designs in the presence of noise and process variations. Our approach is based on modeling the designs using stochastic differential equations (SDE) that will allow us to incorporate the statistical nature of noise. We also integrate the device variation due to 0.18μ m fabrication process in an SDE based simulation framework for monitoring properties of interest in order to quickly detect errors. Our approach is illustrated on nonlinear Tunnel-Diode and a Colpitts oscillator circuits.     

Synchronization of oscillators coupled through narrow-band networks

The ability of two coupled oscillators to synchronize depends critically on the coupling network. Previous analyses have accurately predicted the performance of quasi-optical microwave oscillator arrays for both weak and strong coupling, but have been limited to coupling networks with bandwidths considerably larger than the locking bandwidths of the oscillators. In this paper, the authors develop a method for deriving a suitable system of nonlinear differential equations describing the oscillator amplitude and phase dynamics using a generalization of Kurokawa's method. The method is applied to the case of two Van der Pol oscillators coupled through a resonant network for a wide range of coupling strengths and bandwidths. Simple approximate formulas are developed for the size of the frequency locking region as functions of the basic circuit parameters     

Determination of the correlation spectrum of oscillators with lownoise

A general expression for the correlation spectrum of an oscillator, described by a set of nonlinear ordinary differential equations with intrinsic noise sources, is derived by a first-order perturbation theory. The analytical derivations are well suited to the numerical determination of the correlation spectrum by Poincare mapping methods. The theory is applied to a lumped circuit model of Colpitts oscillator. It is concluded that the noise behavior of complex oscillator circuits used in microwave engineering can be simulated by the derived method