Study of intermodulation in RF MEMS variable capacitors

This paper provides a rigorous study of the causes and physical origins of intermodulation distortion (IMD) in RF microelectromechanical systems (MEMS) capacitors, its analytical dependence on the MEMS device design parameters, and its effects in RF systems. It is shown that not only third-order products exist, but also fifth order and higher. The high-order terms are mainly originated by the nonlinear membrane displacement versus applied voltage and, in the case considered in this study, with an additional contribution from the nonlinear dependence of the reflection coefficient phase on the displacement. It is also shown that the displacement nonlinear behavior also contributes to the total mean position of the membrane. In order to study these effects in depth, an analytical frequency-dependent IMD model for RF MEMS based on a mobile membrane is proposed and particularized to the case of a MEMS varactor-a device for which IMD can be significant. The model is validated, up to the fifth order, theoretically (using harmonic balance) and empirically (the IMD of a MEMS varactor is measured). To this end, a two-tone IMD reflection measurement system for MEMS is proposed.     

Analytical performance evaluation of the OFDM systems in the presence of jointly fifth order nonlinearity and phase noise

This paper presents an exact theoretical analysis of the performance degradation in an orthogonal frequency division multiplexing (OFDM) system when the signal including phase noise is passed through a nonlinear circuit such as high power amplifier (HPA). This circuit is modeled as a fifth order memory-less nonlinear polynomial model (5th order MLNPM). The nonlinear model is derived from important electrical parameters such as gain, 1-dB compression and 3rd order intercept point. Theoretical analysis shows that the detected data symbol at the receiver consists of attenuated version of the original transmitted data symbol, common phase error (CPE), inter-sub-carrier interference (ICI), third and fifth order intermodulation (IM) components. The analytical expressions for intermodulation noise term are derived using combinatorial methods. By use of the derived expressions, a closed-form output signal to noise ratio (SNR), degradation factor (DF) and probability of error can be evaluated theoretically. For verifying the accuracy of our analysis, comparisons between the theoretical and simulated results with electrical parameter of an actual and applicable HPA are presented. The comparisons show that bit error rate (BER) of analytical results is closely match with simulation results for OFDM system using M-QAM modulation.     

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     

RF VCO tuning using MEMS piezoelectric actuated variable inductors

This paper presents a study on the use of microsystems technology in the design of radio frequency voltage-controlled oscillators. In particular, the application of a micro-electro-mechanical systems (MEMS) based variable inductor for frequency tuning purposes is presented. Although traditionally a MEMS variable inductor is considered as a means to extend the tuning range, in this work it is shown that with correct inductor design it is also possible to facilitate and improve the voltage-controlled oscillator design in terms of phase noise response and power consumption in comparison to a design based on standard capacitive tuning.     

缓冲器输出端相位噪声模型分析

相位噪声是振荡器的重要性能指标。近年来,研究人员在振荡器相位噪声表征方面已经做了大量的工作,在这些过程中开发出了很多不同类型的振荡器相位噪声模型。但是在这些模型中,都没有分析缓冲器噪声对振荡器相位噪声的影响。而在研究课题中,首先要对缓冲器噪声的功率谱密度函数进行数学建模,并易于将这个模型嵌入到相位噪声的非线性扰动分析模型,这样就得到了含有缓冲器噪声的振荡器相位噪声模型。     

激光陀螺信号检测系统的理论与实验研究

本文研制了一种新型的、低噪声、大动态范围的激光陀螺信号检测系统。通过引入数学机械化的方法,我们采用近些年提出的旨在统一求解一大类非线性问题的理论方法-分解法对系统模型进行了分析,并给予实验验证。理论分析和实验结果表明:该检测系统完全能满足陀螺的应用要求。     

MEMS微波功率传感器的悬臂梁弯曲模型研究北大核心

为了研究电容式MEMS微波功率传感器悬臂梁的非线性运动，建立了MEMS悬臂梁在空间域上的弯曲特性模型，综合考虑静电力、轴向应力以及残余应力对悬臂梁非线性运动的影响，求解得到动力学微分方程。在此基础上研究在不同杨氏模量、驱动电压和残余应力下悬臂梁的弯曲特性，解析得到对应的悬臂梁弯曲特性曲线与轴向应力曲线。使用有限元分析软件ANSYS对不同驱动电压下的悬臂梁下拉位移进行仿真，并对仿真结果与解析结果进行比较。结果表明，在驱动电压从10 V到20 V的变化过程中，仿真结果与模型解析结果具有一致的趋势，两者间的最大误差仅有8.81%。对电容式MEMS微波功率传感器的悬臂梁弯曲特性的研究具有一定的参考价值和指导意义。     

MEMS陀螺仪随机误差的动态辨识

针对经典Allan方差在分析和定量描述微机电系统(MEMS)陀螺仪噪声项时存在的问题,提出将动态Allan方差用于MEMS陀螺仪输出信号分析并加以改进。根据Allan方差的原理,实现误差项系数的动态辨识,得到各类型误差随时间的变化规律。普通最小二乘法求解误差系数时存在个别为负的问题,因此,将非线性最优化的单纯形法用于方差曲线的拟合。实验结果表明,改进后的方法不仅能准确描述数据的噪声量值,还能反映信号的频率稳定性和误差项的变化特征。     

The design and analysis of a DLL-based frequency synthesizer for UWB application

A delay-locked loop (DLL)-based frequency synthesizer is designed for the ultrawideband (UWB) Mode-1 system. This frequency synthesizer with 528-MHz input reference frequency achieves less than 9.5-ns settling time by utilizing wide loop bandwidth and fast-settling architecture. Additionally, a discrete-time model of the DLL and an analytical model of phase noise of the delay line are proposed in this work. Experimental results show great consistency with predicted settling time and phase noise. The circuit has been fabricated in a 0.18-/spl mu/m CMOS technology and consumes only 54 mW from a 1.8-V supply. It exhibits a sideband magnitude of -35.4 dBc and -120-dBc/Hz phase noise at the frequency offset of 1 MHz.     

PLL performance of DS-CDMA systems in the presence of phase noise,multiuser interference, and additive Gaussian noise

The performance of decision-directed phase-locked loops (PLL) for use in direct-sequence code-division multiple-access (DS-CDMA) systems is investigated in the presence of phase noise, multiuser interference, and additive white Gaussian noise (AWGN). A unified and accurate analysis of the effect of these sources of noise on the PLL is carried out based on a nonlinear model (the Fokker-Planck method) since a linear analysis yields a large deviation between analytical results and actual performance at low signal-to-noise ratios (SNR). After describing the implementation of the PLL, the steady-state probability density function (PDF) of the phase estimator error in a first-order loop is derived. It is shown that a tradeoff exists between the effect due to the phase noise, the magnitude of the multiuser interference, and the AWGN as a function of loop bandwidth. The optimal loop bandwidth minimizing the impact of these sources of noise on the PLL and the requirements on the frequency uncertainty of the carrier source for a required accuracy of the phase estimator are detailed. Numerical results of the variance of the phase estimator error are discussed for Gold codes     

A New Low-Noise Dual-Band VCO for WLAN/WIMAX

In this paper, a new dual-band voltage-controlled oscillator (VCO) is proposed. The proposed VCO utilizes a fourth-order LC resonator that oscillates at two different frequencies. Moreover, its oscillation frequency can be chosen by switching the tail current between two different values. The switches are placed in a way that their resistances do not affect the quality factor of LC tanks, and phase noise does not increase. The proposed VCO is thoroughly analyzed by deriving a nonlinear model. The required conditions for oscillation and switching between two oscillation frequency bands are calculated approximately using averaging. Moreover, the VCO transient behavior in switching the oscillation frequency is investigated, and amplitudes of oscillation at two oscillation modes are calculated. The VCO is designed and simulated in \(0.18\,\upmu \hbox {m}\) CMOS technology to verify the design and analytical equations and to evaluate the performance of the proposed VCO. In comparison with the literature, proposed simulations show acceptable phase noise and transient behavior. In addition, the accuracy of the analytical equations is also verified.     

Analysis of noise up-conversion in microwave field-effecttransistor oscillators

The conversion process of the low frequency noise into phase noise in field-effect transistors (FET) oscillators is investigated. First, an evaluation of the baseband noise contribution to the oscillator phase noise is provided from the analysis of the baseband noise and the frequency noise spectra. A distinction is made within the different components of the low frequency noise contributions to close-in carrier phase noise. Next, the frequency noise of the oscillator circuit is analyzed in terms of the FET's low frequency noise multiplied by the oscillator's pushing factor. Though this product usually provides a good evaluation of the phase noise, experimental results presented here show the inaccuracy of this method at particular gate bias voltages where the pushing factor decreases to zero. To account for these observations, a new nonlinear FET model involving at least two noise sources distributed along the channel is proposed     

Analytical Equations for Nonlinear Phase Errors and Jitter in Ring Oscillators

In this paper, we present a simple analytical equation for capturing phase errors in 3-stage ring oscillators. The model, based on a simple but useful idealization of the ring oscillator, is provably exact for small noise perturbations. Despite its simplicity and purely analytical form, our model correctly captures the time- dependent sensitivity of oscillator phase to external perturbations. It is thus well suited for estimating both qualitative and quantitative features of ring oscillator phase response to internal noises, as well as to power, ground and substrate interference. The nonlinear nature of the model makes it suitable for predicting injection locking as well. Comparisons of the new model with existing phase models are provided, and its application for correct prediction of thermal jitter demonstrated. Requiring knowledge only of the amplitude and frequency of the oscillator, the model is ideally suited for early design exploration at the system and circuit levels.     

The nonlinear dynamic response of microbeam of MEMS capacitive switch under mechanical shock

The microelectromechanical system (MEMS) capacitive switch based on clamped?Cclamped microbeam has garnered significant attention due to their geometric simplicity and broad applicability, and the accurate model which describes the multiphysical effects of MEMS capacitive switch should be developed to predict the nonlinear dynamic response of clamped?Cclamped microbeam. A improved macromodel of the clamped?Cclamped microbeam-based MEMS capacitive switch is presented to investigate the nonlinear dynamic response of clamped?Cclamped microbeam of MEMS capacitive switch under different mechanical shock in this article, the macromodel provides an effective and accurate design tool for this class of MEMS devices because of taking account into some effects simultaneously including midplane stretching effect, residual stress and different mechanical shock loads. A numerical analytical method based on multimode Galerkin discretization is presented to investigate the nonlinear response of clamped?Cclamped microbeam of MEMS capacitive switch under the different mechanical shock loads. The results show that using five or more modes can be sufficient to capture the nonlinear dynamic response of clamped?Cclamped microbeam, and the microbeam experiences a mechanical shock load as a quasi-static load or a dynamic load depending on the ration between the natural periods of the structure and the period or frequency of mechanical shock load. The proposed method gives the identical results to other numerical methods in the literature. Moreover, this method is straightforward to implement and could save computation efforts while not losing accuracy.     

Influence of the nonlinear phase and ASE noise on DPSK balanced optical receiver in optical fiber communication system

The analytical expression of bit error probability in a balanced differential phase-shift keying(DPSK) optical receiver considering nonlinear phase noise and EDFA ASE noise is given,which is very useful to estimate the performance of DPSK balanced and unbalanced receiver in optical communication system.Through analysis,if only nonlinear phase noise is considered,both the balance and unbalanced receivers have the same performances.But if adding the ASE noise of EDFA,the balanced receiver is better.     

Pulse Energy Probability Density Functions for Long-Haul Optical Fiber Transmission Systems by Using Instantons and Edgeworth Expansion

In this work, we use a new approach to model pulse energy in long-haul optical fiber transmission systems. Existing approaches for obtaining probability density functions (pdfs) rely on numerical simulations or analytical approximations. Numerical simulations make far tails of the pdfs difficult to obtain, while analytical approximations are often inaccurate, as they neglect nonlinear interaction between pulses and noise. Our approach combines the instanton method from statistical mechanics to model far tails of the pdfs, with numerical simulations to refine the middle part of the pdfs. We combine the two methods by using an orthogonal polynomial expansion constructed specifically for this problem. We demonstrate the approach on an example of a specific submarine transmission system.     

基于SHAKF滤波器的MEMS陀螺随机误差建模补偿

MEMS陀螺随机漂移误差是制约惯性导航精度的关键因素。本文针对标准kalman滤波器陀螺漂移处理方法中,随机动态系统的结构参数和噪声统计特性参数不准确的问题,采用自适应SHAKF(Sage-Husa Adaptive Kalman Filter)滤波器进行参数实时估计,提高陀螺漂移精度。基于此思想,建立了ARMA随机误差模型,搭建了MEMS陀螺组件实验系统,通过高精度三轴转台静态测试采集陀螺数据。Aallan方差分析表明,零偏不稳定性经线性KF滤波后提升17.4%,经自适应SHAKF滤波后提升26.2%。     

Influence of noise intensity on the spectrum of an oscillator

This paper investigates the influence of high-intensity noise on the correlation spectrum of a two-dimensional (2-D) nonlinear oscillator. An exact analytical solution for the correlation spectrum of this 2-D oscillator is provided. The analytical derivations are well suited for oscillators with white noise of any intensity, but computational constraints on the solution of the partial differential equation may make it impractical for cases where the number of state variables exceeds three. The spectral results predicted by our analytical method are verified by numerical simulations of the noisy oscillator in the time domain. We find that the peak of the oscillator spectrum shifts toward higher frequencies as the noise intensity is increased, as opposed to the fixed oscillation frequency predicted in the existing literature. This phenomenon does not appear to have been reported previously in the context of phase noise in oscillators.     

Modelling and Experiment of a Silicon Resonant Pressure Sensor

Modelling of a silicon resonator as a pressure sensor is presented. The resonator is electrothermally excited and the resonance frequency shift is detected by a piezoresistive thin film detector. Computer simulation using the commercial MEMS software tool IntelliSuite is compared with analytical model. Various design aspects, such as the pressure sensitivity, electrothermal heating of vibrating beam, influence of detection current and damping effect are investigated. Silicon resonator sensors have been fabricated and measured. The characteristics predicted by computer simulation has been confirmed by experimental results.     

A performance analysis of an all-optical clock extraction circuitbased on Fabry-Perot filter

A performance analysis of an optical clock extraction circuit based on a Fabry-Perot filter (FPF) is presented. Two analytical methods, time-domain and frequency-domain analysis, are developed in this paper. Time-domain analysis shows that there is no phase jitter in the extracted optical clock if the free spectral range (FSR) of the FPF is exactly equal to the signal clock frequency. Based on this, we obtain an analytical expression for root mean square (rms) amplitude jitter of the extracted optical clock in time domain, in which we have taken the impacts of carrier frequency drift and carrier phase noise into account. When the FSR of the FPF deviates from the signal clock frequency, both phase jitter and amplitude jitter will occur in the extracted optical clock. In this situation, a more general frequency-domain method is developed to deal with the timing performance under the assumption that carrier phase noise is negligible. This method allows us to calculate both rms phase jitter and rms amplitude jitter of the extracted optical clock. Using the developed two methods, we present a detailed numerical investigation on the impacts of finesse of the FPF, carrier frequency drift, resonator detuning, carrier phase noise, and optical pulse chirp on the timing performance. Finally, the application of this circuit in multiwavelength clock recovery is discussed