Nonlinear dynamics of divide‐by‐two injection‐locked frequency dividers in locked operation mode

A method for analyzing the nonlinear dynamics of the injection‐locked frequency dividers in synchronized operation mode is presented, including the stability analysis of locked states. We use a specific divide‐by‐two circuit, namely a differential LC CMOS divider with a complementary topology, as a guideline for presentation, showing that the sizing of the devices significantly affects the synchronization mechanism of the divider, which exhibits a very rich dynamical behavior. We provide closed‐form expressions to determine the amplitude and the phase in the locked state, as well as the locking range, leading to accurate results, which are validated by numerical simulations. The presented analysis of the frequency divider dynamics enables us to establish that stable locked oscillations occur on the whole locking range predicted by the well‐known Adler's equation and that these are possible also beyond that range. Copyright © 2013 John Wiley & Sons, Ltd.     

A study of superharmonic injection locking in multiband frequency dividers

A superharmonic voltage‐controlled injection‐locked frequency divider, implemented using a modified Colpitts oscillator operating at 2.5, 5 and 10 GHz and a cross‐coupled LC oscillator operating at 1.25, 2.5 and 5 GHz, is demonstrated. The proposed triple‐band operation is achieved by employing a novel technique that uses pin‐diodes and negative power supply. The discrete dividers, built with low noise hetero‐junction FETs and high‐frequency SiGe BJTs, are described theoretically while their functionality is proven experimentally. Additionally, a short phase noise analysis, which is missing in the literature, is given. Phase noise, frequency range of operation, and locking range measurement results are presented. Finally, post‐layout simulation results of a 5 GHz fully differential injection‐locked frequency divider, implemented in a 0.25µm SiGe process are provided. Copyright © 2010 John Wiley & Sons, Ltd.     

一种电容补偿型高压电容分压器的设计

根据高压脉冲实验测量的需要,阐述了外带积分器型、电阻补偿型及电容补偿型等几种电容分压器的工作原理,分析了影响各自响应时间的主要因素即对于测量ns量级快前沿高压脉冲信号,使用外带积分器型电容分压器时不宜采用大尺寸的伞式探针结构;使用电阻补偿型电容分压器时对其高压臂大电阻要求较高。在缺少高性能大阻值电阻的情况下,利用高压电容尝试设计并制作了电容补偿型电容分压器,其分压比约为9348,它在一定范围内可通过改变补偿电容值而方便地改变。实验结果与理论计算及PSpice软件的模拟结果基本一致,方波响应时间约为4.4ns,基本达到了设计目的。定标结果表明该分压器可用于测量高功率脉冲调制系统和强流电子束加速器中的高压脉冲。     

Design and analysis of a millimeter‐wave injection locked frequency divider with transconductance boosting technique

This paper presents a degenerated injector (mixer) with transconductance boosted by biasing the mixer transistor in the knee region of its I‐V curve, without increasing the transistor size and its parasitics. This mixer can enhance the locking range of millimeter‐wave injection‐locked frequency dividers. To compensate the degradation of mixer transconductance (conversion‐gain) due to the degeneration effect, a neutralization technique is employed. Analyses are given for locking‐range and induced phase‐noise of the proposed divider for arbitrary injection strength. It is shown that the locking‐range, as a function of injection strength, is improved by increasing the fundamental component of transconductance. Using 180‐nm CMOS technology, a 1.78‐mW divider‐by‐two is designed with free‐running frequency of 27.92 GHz, locking‐range of 51 to 59.6 GHz, and figure‐of‐merit of 4.83 (GHz/mW). EM simulation results of the proposed and conventional structure are compared, which illustrates 56% improvement in locking‐range.     

Modelling of impedance‐loaded wire frequency‐selective surfaces with tunable reflection and transmission characteristics

In this paper an efficient means to control the reflection and transmission characteristics of wire‐based frequency‐selective surfaces (FSS) using linear‐lumped impedance loading is presented. We show that by varying the topology of the RLC loading circuits and the component values it is possible to control the resonance frequency of the array as well as its angular characteristics. We discuss several examples, particularly a switchable dual band bandpass filter and enhancement of FSS angle‐of‐arrival properties. The analysis is based on the self‐consistent solution of thin wire Hallen's type integral equation solved by Galerkin's method. The periodic Green's function in the kernel of integral equation has been accelerated using the Ewald transformation, which leads to a highly accurate and efficient numerical procedure. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

常用高压阻容分压器频率特性的研究

由于高压阻容分压器频率特性存在差异,可能会影响测量结果,因此实测了常用的高压阻容分压器在40～300 Hz频率范围内的频率特性,初步确定了几种频率特性良好的阻容分压器。     

A Two‐Stage Inductive Voltage Divider Using a Special Winding Method

Inductive voltage dividers (IVDs) are widely used in the field of ac measurements, such as impedance measurements at audio frequencies. The two‐stage guarded IVD was developed by D.N. Homan and T.L. Zapf about 40 years ago. However, it is not easy to construct a two‐stage guarded IVD. Therefore, we have developed a two‐stage IVD using a special winding method without guarding by magnetic and electrical shields. To reduce the admittances of the winding wires, corrugated polypropylene board is used for the new two‐stage IVD. In addition, the ratio winding and excitation winding are wound toroidally around two FINEMET ring cores using PEW flat cable 0.7 mm in diameter. As a result, the in‐phase ratio errors are within 10^?8 of the input at frequencies of 1 kHz or below. In this report, the winding methods and measurement results of the new two‐stage IVD are described.     

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.     

电力系统强迫功率振荡的基础理论

以单机无穷大系统模型为基础,阐述了电力系统强迫功率振荡的基础理论,分析了影响电力系统强迫功率振荡的主要因素,并对单机无穷大系统的强迫功率振荡进行了仿真验证。电力系统强迫功率振荡理论指出,持续的周期性小扰动会引起电力系统强迫振荡,当扰动频率接近系统固有振荡频率时,会引起系统谐振,导致大幅度的功率振荡。谐振引起的强迫振荡的幅值与扰动的幅值、系统固有的振荡阻尼大小有关:扰动的幅值越大,谐振幅值越大;系统固有的振荡阻尼越强,谐振幅值越小。谐振引起的强迫振荡的表现形式类似于属于自由振荡的电力系统负阻尼低频振荡,但两种振荡的起因不同。     

Mode dynamics in fourth‐order LC oscillators

We present a complete analysis of single and concurrent modes in fourth‐order LC‐voltage‐controlled oscillators ( VCOs), which are increasingly applied in dual‐band communication systems. We give a procedure based on the averaging method that simplifies the derivation of the abridged equations, which are derived without resorting to a change of co‐ordinates. The amplitudes of the oscillatory modes in steady state and in transient are found in explicit form. Conditions for the stability of the single and concurrent modes are derived, which apply to any active one‐port dual‐band LC‐VCO and allow one to predict the nonlinearities ensuring the occurrence of a stable concurrent mode. Numerical and experimental results show a good accuracy of the presented formulas. Copyright © 2016 John Wiley & Sons, Ltd.     

一种应用于无线电能传输的谐振频率跟踪方法

针对锂电池在无线充电过程中特性参数实时变化导致充电系统失谐的缺点,提出了谐振频率跟踪控制方法,并给出实现方案。使用Matlab/Simulink来实现谐振频率跟踪算法,通过改变模拟电池内阻参数来模拟锂电池的充电过程。搭建了实验验证平台,实验结果证明该方法能够使工作频率与谐振频率相一致,工作可靠,并能够有效提高系统的传输效率。     

基于SS型磁耦合谐振无线电能传输频带序列划分

磁耦合谐振无线电能传输(MCR-WPT)具有传递功率较大、距离适中、传递效率高等优点。针对MCR-WPT中频率资源划分尚未统一的问题,基于两线圈串联-串联(SS)模型的WPT系统,用电路模型分析WPT系统的运行特性,提出了WPT谐振频率范围划分的距离原则。使不同传递距离范围对应不同谐振频率序列,并结合改进几何均值原则对划分结果进行修正,得到修正后的谐振频率序列推荐值。同时,为增强WPT对负载变化的适应性,将谐振频率点拓展为工作频段,提出基于负载特性的工作频段确定方法。再将谐振频率序列和工作频段结合,实现了基于SS型MCR-WPT系统的频带序列划分。最后搭建实验平台验证频带序列划分结果的合理性。     

Synchronous and asynchronous operation in dual‐band VCOs

We present a comprehensive analysis of the asynchronous and synchronous operations of fourth‐order oscillators underlying dual‐band voltage‐controlled oscillators. We analyze the occurrence of the self‐synchronization phenomenon (internal resonance) if the ratio of normal frequencies is nearly a ratio of integers, which is 1:3 in the cubic approximation of the nonlinear oscillator characteristic. In this case, we have the simultaneous presence of 2 oscillations with a frequency ratio 1:3, which was demonstrated to be very effective in generating high‐frequency signals in mm‐wave range. The analysis is carried out by developing an analytical approach relying on the averaging principle, as it follows the van der Pol method. The averaging equations, derived simply by a quadrature, allow us to analyze easily the stationary and transient oscillations, and their stability, both in asynchronous and synchronous operations. Expressions for the amplitudes and phases were derived for a cubic nonlinearity and verified by Spice simulations.     

发电机组汽水管道振动特征及其治理

通过分析发电机组汽水管道振动案例,对汽水管道振动的相关频谱特征进行总结,研究表明,汽水管道同一测点频谱图相似度高,频谱图中主要振动成分的重现性及稳定性良好,主振动具有周期振动特征;共振型振动频谱图较为简单,主振动频率谱线突出,其它频率成分谱线强度微弱;受迫振动通常无明显的主振动频率,当其全频率下的振动速度超标,管道振动剧烈时,其几个主要频率的振动速度并不高。建议结合管道振型分析进行振动治理可获得良好的减振效果。     

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.     

The frequency tuning characteristics of transistor voltage‐controlled oscillators with distributed parameters

The frequency varactor tuning characteristics of voltage‐controlled oscillators (VCO) on elements with distributed parameters are analysed and presented in a generalized form. The recommendations on the choice of transmission line type, circuit and varactor parameters for the purposes of widening and linearization of the voltage frequency tuning characteristics are given. Large amounts of numerical and experimental results are performed to illustrate the theoretical assumptions. Copyright © 1999 John Wiley & Sons, Ltd.     

A method for analysing the transient and the steady‐state oscillations in third‐order oscillators with shifting bias

We provide an asymptotic method for systematically analysing the transient and the steady‐state oscillations in third‐order oscillators with shifting bias. The method allows us to construct the general solution of the weakly non‐linear differential equation describing these oscillators through an iteration procedure of successive approximations typical of perturbation methods. The approximation to first order is obtained solving a system of two first‐order non‐linear differential equations in the leading terms of solution (dc component and fundamental harmonic), whereby the dominant dynamics, the stationary states and their stability can be easily analysed. Unlike existing approaches, our method also enables us to determine the higher harmonics as well as the frequency shift from the system's natural frequency in the exact solution through analytical formulae. In addition, formulae for higher‐order approximations of the above quantities are determined. The proposed method is applied to a practical circuit to show its usefulness in both analysis and design problems. Copyright © 2001 John Wiley & Sons, Ltd.     

由汽轮机压力脉动引发电力系统共振机理的低频振荡研究

强制型共振机理是引起电力系统低频振荡的原因之一,该文针对此原因,根据其共振机理,探讨了汽轮机功率变化的可能性,并综合考虑了汽轮机热力系统和电力系统的相互影响,从热力系统中寻找出电力系统发生共振机理的低频振荡扰动源。在仿真中采用详细的汽轮机压力功率模型,着重研究了汽轮机蒸汽压力脉动与电力系统发生共振振荡的关系。仿真分析表明,汽轮机主蒸汽压力和再热蒸汽压力脉动,当其脉动频率与电力系统自然振荡频率一致或相近时,均有可能引起电力系统发生共振机理的低频振荡。该研究结果对探讨电力系统低频振荡的原因具有一定的参考价值。     

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.