Thermal and flicker phase noise analysis in rotary traveling-wave oscillator

This paper analyzes the thermally induced phase noise and the up-conversion of flicker noise into phase noise of rotary traveling-wave oscillator (RTWO). Based on the analyses, this paper extracts the closed-form formulas for the thermal and flicker phase noise of the RTWO. This paper compares the theoretical results with appropriate simulations to evaluate the accuracy of the derived closed-form formulas. Comparisons confirm the accuracy of the extracted phase noise formulas. By using the presented straightforward approach along with accurate phase noise formulas, the designers can understand the RTWO ' s design tradeoffs. Also, they can design the RTWO for a specific phase noise without needing lengthy simulations.     

A series‐coupled LC quadrature oscillator using phase/amplitude calibration

In this paper, an analytic approach for the estimation of the phase and amplitude error in series coupled LC quadrature oscillator (SC‐QO) is proposed. The analysis results show that imbalances in source voltage of coupling transistor because of mismatches between LC tanks are the main source of the phase and amplitude error in this oscillator. For compensation of the phase and amplitude error, a phase and amplitude‐tunable series coupled quadrature oscillator is designed in this paper. A phase shift generation circuit, designed using an added coupling transistor, can control the coupling transistor source voltage. The phase and amplitude error can simply be controlled and removed by tuning the phase shifter, while this correction does not have undesirable impact on phase noise. In fact, the proposed SC‐QO generates a phase shift in the output current, which reduces the resonator phase shift (RPS) and improves phase noise. The phase and amplitude tunable SC‐QO is able to correct the phase error up to ±12°, while amplitude imbalances are reduced as well. To evaluate the proposed analysis, a 4.5‐GHz CMOS SC‐QO is simulated using the practical 0.18‐μm TSMC CMOS technology with a current consumption of 2 mA at 1.8‐V supply voltage. Copyright © 2016 John Wiley & Sons, Ltd.     

Phase error analysis in CMOS injection‐coupled LC quadrature oscillator (IC‐QO)

This paper presents a novel approach to study the phase error in source injection coupled quadrature oscillators (QOs). Like other LC QOs, the mismatches between LC tanks are the main source of phase error in this oscillator. The QO is analyzed where the phase error and oscillation frequency are derived in terms of circuit parameters. The proposed analysis shows that the output phase error is a function of injection current and the current of source equivalent capacitor. As a result, it is shown that increasing of tail current and LC tank quality factor decreases the phase error. Derived equations show that the phase error can be cancelled and even controlled by adjusting bias currents. To evaluate the proposed analysis and consequent designed QO, a 5.5 GHz CMOS QO is designed and simulated using the practical 0.18 µm TSMC CMOS technology. The experiments show good agreement between analytical equations and simulation results. Copyright © 2013 John Wiley & Sons, Ltd.     

Phase noise characterization of subharmonic injection locked oscillators

In this work we present a detailed study of the phase noise of subharmonic injection locked oscillators (s‐ILOs). A new simple and efficient model has been presented for accurately predicting the phase noise of a microwave s‐ILO. The validity of the analytical technique is verified with measurement results obtained from a 5‐GHz fully differential Colpitts‐based s‐ILO. The results showed that a phase noise improvement of 12 dB at 1 kHz offset frequency compared to the free‐running case can be achieved, whereas the power consumption is 21 mW. Copyright © 2010 John Wiley & Sons, Ltd.     

Phase noise analysis in CMOS differential Armstrong oscillator topology

This paper reports a phase noise analysis in a differential Armstrong oscillator circuit topology in CMOS technology. The analytical expressions of phase noise due to flicker and thermal noise sources are derived and validated by the results obtained through SpectreRF simulations for oscillation frequencies of 1, 10, and 100 GHz. The analysis captures well the phase noise of the oscillator topology and shows the impact of flicker noise contribution as the major effect leading to phase noise degradation in nano‐scale CMOS LC oscillators. Copyright © 2016 John Wiley & Sons, Ltd.     

Phase noise characterization of oscillators through Ito calculus

Recent phase noise analysis techniques of oscillators mainly rely on solving a stochastic differential equation governing the phase noise process. This equation has been solved in the literature using a number of mathematical tools from probability theory like deriving the Fokker–Planck equation governing the phase noise probability density function. Here, a completely different approach for solving this equation in presence of white noise sources is introduced that is based on the Ito calculus for stochastic differential equations. Time‐domain analytical expressions for the correlation of the noisy variables of the oscillator are derived that in asymptotically large times give the steady‐state stochastic correlations as well as the power spectral densities of the variables. The validity of the new approach is verified by comparing its results against extensive Monte‐Carlo simulations. This approach is applied to an oscillator with a dielectric resonator at 4.127 GHz, and a very good agreement between its results with those of the Monte‐Carlo simulations and the previous approaches is observed. Copyright © 2014 John Wiley & Sons, Ltd.     

Survey of integrated‐circuit‐oscillator phase‐noise analysis

This tutorial distills the salient phase‐noise analysis concepts and key equations developed over the last 75 years relevant to integrated circuit oscillators. Oscillator phase and amplitude fluctuations have been studied since at least 1938 when Berstein solved the Fokker–Planck equations for the phase/amplitude distributions of a resonant oscillator. The principal contribution of this work is the organized, unified presentation of eclectic phase‐noise analysis techniques, facilitating their application to integrated circuit oscillator design. Furthermore, we demonstrate that all these methods boil down to obtaining three things: (1) noise modulation function; (2) noise transfer function; and (3) current‐controlled oscillator gain. For each method, this paper provides a short background explanation of the technique, a step‐by‐step procedure of how to apply the method to hand calculation/computer simulation, and a worked example to demonstrate how to analyze a practical oscillator circuit with that method. This survey article chiefly deals with phase‐noise analysis methods, so to restrict its scope, we limit our discussion to the following: (1) analyzing integrated circuit metal–oxide–semiconductor/bipolar junction transistor‐based LC, delay, and ring oscillator topologies; (2) considering a few oscillator harmonics in our analysis; (3) analyzing thermal/flicker intrinsic device‐noise sources rather than environmental/parametric noise/wander; (4) providing mainly qualitative amplitude‐noise discussions; and (5) omitting measurement methods/phase‐noise reduction techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

基于信号源与频谱仪的相位噪声测试软件设计

基于VC＋＋平台设计一款信号源与频谱仪的联控相位噪声测试软件,由于具有前置放大器的先进频谱仪的电平测量准确度高本地噪声小,因此可用此类频谱仪测得信号源的相位噪声。利用Agilent信号源与频谱仪联合测试的方法,推导出频谱仪测量被测系统噪声的修正公式,并在相位测试软件中对所测噪声加以修正,最终利用Agilent VISA编程接口设计出测试软件实现了智能化测试被测系统的相位噪声。     

Increasing power efficiency in the design of a low power and low phase noise CMOS LC oscillator

This study developed a local oscillator (LO) with low phase noise and low power consumption. The proposed oscillator core comprises a pair of cross‐coupled transistors, which are fed by another pair of transistors that injects current at moments close to the peak of output voltage. The position of the current injection transistors, which are inserted in series with the cross‐coupled transistors, affects the waveform of current injected into an inductive–capacitive (LC) tank. Installing a capacitor on the source node of the cross‐coupled transistors increases the current injected into the LC tank and thereby augments the output voltage amplitude and power efficiency of the LO. The resonator phase shift and Q can be corrected by adjusting the source capacitance, which filters noise. These changes reduce the phase noise to ?123.4 dBc/Hz at a frequency offset of 1 MHz and improve oscillator performance with a figure of merit equal to ?193.5 dBc/Hz. To evaluate the LC tank, a 5 GHz LO was simulated at 1.8 V power supply and 2.5 mW power consumption. The simulation was conducted using a practical 0.18 complementary metal–oxide–semiconductor model manufactured by the Taiwan Semiconductor Manufacturing Company. The simulation results confirmed the analytical findings.     

Experimental comparison of phase‐noise in cross‐coupled RC‐ and LC‐oscillators

Relaxation RC‐oscillators are notorious for their poor phase‐noise performance. However, there are reasons to expect a phase‐noise reduction in quadrature oscillators obtained by cross‐coupling two relaxation oscillators. We present measurements on 5 GHz oscillators, which show that in RC‐oscillators the coupling reduces both the phase‐noise and quadrature error, whereas in LC‐oscillators the coupling reduces the quadrature error, but increases the phase‐noise. A comparison using standard figures of merit indicates that quadrature RC‐oscillators may be a viable alternative to LC‐oscillators when area and cost are to be minimized. Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis of flicker noise conversion to phase noise in CMOS differential LC oscillators

An analysis of the flicker noise conversion to close‐in phase noise in complementary metal‐oxide semiconductor (CMOS) differential inductance‐capacitance (LC)‐voltage controlled oscillator is presented. The contribution of different mechanisms responsible for flicker noise to phase noise conversion is investigated from a theoretical point of view. Impulse sensitivity function theory is exploited to quantify flicker noise to phase noise conversion process from both tail and core transistors. The impact of different parasitic capacitances inside the active core on flicker noise to phase noise conversion is investigated. Also, it is shown how different flicker noise models for core metal‐oxide semiconductor (MOS) transistors may result in different close‐in phase noise behaviors. Based on the developed analysis, design guidelines for reducing the close‐in phase noise are introduced. Copyright © 2015 John Wiley & Sons, Ltd.     

Time‐domain analysis of phase‐noise and jitter in oscillators due to white and colored noise sources

This paper presents an original time‐domain analysis of the phase‐diffusion process, which occurs in oscillators due to the presence of white and colored noise sources. It is shown that the method supplies realistic quantitative predictions of phase‐noise and jitter and provides useful design‐oriented closed‐form expressions of such phenomena. Analytical expressions and numerical simulations are verified through measurements performed on a relaxation oscillator whose behavior is perturbed by externally controlled noise sources. Copyright © 2011 John Wiley & Sons, Ltd.     

Channel noise enhancement in small geometry MOSFET and its influence on phase noise calculation of integrated voltage‐controlled oscillator

Channel noise enhancement due to MOSFET scaling and its influence on phase noise estimation of fully integrated VCO have been studied. The channel noise of MOSFET increases due to the hot electron effect of small geometry MOSFET is obvious. The channel noise coefficient, γ, of NMOS is 3.5 for 40‐nm gate length, 2.0 for 90‐nm gate length in spite of being ⅔ for long channels MOSFET. Simultaneously, calculation of phase noise of fully integrated VCO shows large difference using γ=⅔ because the part of noise performance of VCO gain‐cell depends on channel noise of MOSFET. Calculated phase noise showed good agreement with measured data when the optimum value of channel noise of MOSFET was adopted. Copyright © 2005 John Wiley & Sons, Ltd.     

低相噪低杂散短波频率源的原理与设计

采用宽带锁相环芯片HMC830设计实现了应用于短波接收机的小型化、低成本、低相噪低杂散频率源。通过优化寄存器配置及工作模式实现了低相噪的频率源,并且在输出增加差分巴特沃兹滤波器降低杂散幅度,抑制共模干扰及偶次谐波,避免单端输出的寄生参数。短波频率源输出频率范围为30~120MHz,步进1kHz,相位噪声≤-120dBc(10kHz),杂散抑制度优于90dB,体积仅为5cm×4cm。     

Electronically controlled oscillator with linear frequency adjusting for four‐phase or differential quadrature output signal generation

This paper introduces novel four‐phase oscillator employing two Dual‐Output Controlled Gain Current Follower Buffered Amplifiers (DO‐CG‐CFBAs), single Current Amplifier, three resistors, and two grounded capacitors suitable for differential quadrature signal production (floating outputs). To control the frequency of oscillation (FO) and condition of oscillation (CO), only the current gain adjustment of active elements is used. The circuit was designed by well‐known state variable approach. The oscillator employs three active elements for linear control of FO and to adjust CO and provides low‐impedance voltage outputs. Furthermore, two straightforward ways of automatic amplitude gain control were used and compared. Active elements with very good performance are implemented to fulfill required features. Suitable CMOS implementation of introduced DO‐CG‐CFBA was shown. Important characteristics of the designed oscillator were verified experimentally and by PSpice simulations to confirm theoretical and expected presumptions. Copyright © 2013 John Wiley & Sons, Ltd.     

A 4.8–6.8 GHz low phase noise LC VCO in 0.13‐µm CMOS technology

This letter presents a novel LC voltage controlled oscillator (VCO) supporting the high‐speed serial transmission standard of RapidIO in 0.13‐µm complementary metal‐oxide semiconductor technology. The low phase noise is achieved through several techniques including current source switching, parallel coupled negative transconductance cell, and varactor bias combination scheme. Measured results of proposed circuit show a low phase noise of ?120 dBc/Hz at 1 MHz offset from 6.25 GHz carrier and tuning range of 4.8 ~ 6.8 GHz (34.48%) while consuming 7.4 mW under the supply voltage of 1.2 V. Copyright © 2015 John Wiley & Sons, Ltd.     

Analysis and design of LC oscillators associated with frequency multipliers: a phase noise perspective

When a local oscillator signal generation system is based on an LC oscillator and a frequency multiplier, the question of determining the optimal multiplication factor is a key issue. In this paper, the problem is addressed in order to minimize the 1/f ² phase noise within a tuning range constraint. The analysis, with a practical graphical representation, reveals the oscillator phase noise dependence on the oscillating frequency in the transition from two different regimes, named the inductor‐limited quality factor and the capacitor‐limited quality factor. The results obtained enable the evaluation of the phase noise performance of systems based on a sub‐harmonic and super‐harmonic oscillators and how they compare with an oscillator in the fundamental mode. Crucial questions like the phase noise improvement that these systems can achieve are analytically answered. A design methodology is thus proposed and verified through measurements on a frequency source at 31 GHz, composed by a sub‐harmonic voltage‐controlled oscillator followed by an injection‐locked frequency tripler, dedicated to backhauling applications, designed on a BiCMOS process technology. The tuning range is 10%, and the phase noise at a 1‐MHz offset is −112 dBc/Hz. Copyright © 2017 John Wiley & Sons, Ltd.     

Quadrature VCOs based on direct second harmonic locking: Theoretical analysis and experimental validation

We propose a theoretical analysis of the class of quadrature VCOs (QVCOs) based on two LC‐oscillators directly coupled by means of the second harmonic. The analysis provides the conditions for the existence and stability of steady‐state quadrature oscillations and a simplified model for the phase noise (PN) transfer function with respect to a noise source in parallel to the tank. We show that the figure of merit defined as the product between PN and current equals that of the single VCO, confirming that quadrature generation is achieved by this class of QVCO without degrading that figure of merit. An analytical model for the phase quadrature error due to tank mismatches is also proposed. The validity of all analytical models is discussed against numerical simulations. A practical implementation at 3.26 GHz with ±20% tuning range in a 0.13µm CMOS technology is also presented, confirming the main theoretical findings. Copyright © 2009 John Wiley & Sons, Ltd.     

弱电网下电压源型变换器静态稳定性分析

电压源型变换器(Voltage Source Converter,VSC)作为新能源发电的并网接口广泛地应用于电力系统.以单台VSC经线路阻抗并入无穷大电网为例,推导弱电网下VSC功率输出特性.基于VSC系统阻尼转矩模型得出阻尼系数直接决定系统静态稳定,同步系数通过影响阻尼功率相位间接影响系统稳定.根据阻尼功率与同步功...