Full Time-Varying Phase Noise Analysis for MOS Oscillators Based on Floquet and Sylvester Theorems

In this paper a set of full time-varying analyzing methods of phase noise for oscillators based on Floquet and Sylvester theorems are established, it provides a good idea for designing oscillators with perfect phase noise performance. The periodic state solution space of a linear periodic time-varying system is constructed with Floquet and Sylvester theorems, and the phase noise perturbation vectors of an oscillator autonomous system are characterized on this space. The analytical expressions of the phase noise spectrums, both 1/(Δ f)² and Lorentzian forms, are obtained, and the contributions to the phase noise of each noise sources are determined. With a generator approach and some modification, the method could be extended to the flicker noise. For RF front-end oscillators composed of MOS active devices, planar inductors and MOS varactors, the time-varying model parameters of the small signal equivalent circuits are constructed according to the periodic varying working-points. By the means of automatic small-signal equivalent-circuit construction, state-variable selection and periodic time-varying state-matrix generation, the system perturbation vectors and phase noise power spectrums are efficiently calculated. For a 10 GHz MOS oscillator, the 1/(Δ f)² and Lorentzian spectrums are calculated. Comparing with the results of SpectreRF, it indicates the proposed methods are accurate and reliable, especially the Lorentzian spectrum close to the carrier is more reasonable than previous methods. Every noise source contributions to the phase noise are listed and the results are analyzed. At last the applications of the methods to designing low phase noise oscillators and to analyzing the phase noise of composite systems, as well as the difficulty of flicker noise analysis, are addressed.     

Hybrid high temperature superconductor/GaAs 10 GHz microwaveoscillator: temperature and bias effects

Hybrid YBa₂Cu₃O_7-x superconductor/GaAs microwave oscillators have been designed, fabricated and characterized. The planar oscillators were built on a single 10 mm×10 mm LaAlO₃ substrate. The active elements in the hybrid oscillators were GaAs MESFETs. A ring resonator was used to select and stabilize the frequency. A superconducting ring resonator had a loaded Q at 77 Kg which was 8 times larger than the loaded Q of a ring resonator fabricated out of copper. S-parameters of the GaAs FET were measured at cryogenic temperatures and used to design the oscillator which had a reflection mode configuration. The transmission lines, RF chokes and bias lines were all fabricated from YBa₂Cu₃ O_7-x superconducting thin films. The performance of the oscillators was measured as a function of temperature. The rate of change of the frequency as a function of temperature was smaller for an oscillator patterned from a pulsed laser deposited film than for an oscillator patterned from a sputtered film. As a function of bias at 77 K, the best circuit had an output power of 11.5 dBm and a maximum efficiency of 11.7% The power of the second harmonic was 25 dB to 35 dB below that of the fundamental, for every circuit. At 77 K, the best phase noise of the superconducting oscillators was 68 dBc/Hz at an offset frequency of 10 kHz and less than -93 dBc/Hz at an offset frequency of 100 kHz. At an offset frequency of 10 kHz, the superconducting oscillator had 12 dB less phase noise than the copper oscillator at 77 K     

Microstructure Fiber Based Optical Parametric Oscillators

The current status of fiber based optical parametric oscillators is presented with a focus on pulsed systems employing microstructure fibers. It is shown based on standard expressions for parametric processes in optical fibers that systems employing short (less than a few cm) optical fibers lead to superior performance in terms of wavelength tunability and output power. Practical guidelines for realizing a working system are given. These devices are now practical as ultrafast pulsed-light sources and for extending the wavelengths of operation of existing mode-locked fiber lasers.      

The use of saw oscillators to suppress fm noise in local oscillators for on-board satellite applications

SAW oscillators can provide fundamental frequency operation to above 1·5 GHz, with stability and FM noise performance approaching that offered by bulk crystal oscillator technology. Their high fundamental frequency, small size and rugged construction gives SAW technology a unique capability at UHF and microwave frequencies. The low FM thermal noise floor associated with fundamental frequency operation can be combined with the stability and low close-to-carrier noise of multiplied bulk crystal oscillators by locking a high frequency SAW oscillator to a bulk crystal reference. SAW oscillator stability is compatible with conventional phase-locked-loop techniques and also with injection lock stabilization, and their own low close-to-carrier FM noise ensures that such locked sources exhibit minimum phase noise. Furthermore, locked oscillator phase noise is not significantly degraded when extreme operating conditions, such as those experienced in space applications, demand a reduced SAW device Q for reliable locking using either technique. Use of a PLL avoids any need for reference frequency multiplication, and provides additional design flexibility with respect to reference frequency selection and phase noise optimization. Injection locking offers design simplicity and uses fewer frequency control components, which can contribute additional noise in PLL sources.     

Phase Locking of 2-mm Wave Sources Upon High-Order IMPATT Multipliers

We describe experiments resulting in the phase locking of two electrically tunable 2-mm wave sources based on active high-order IMPATT multipliers. Phase locking modes were tested on a pair of identical multiplying sources (master and slave) with the tuning ranges 138.5+/?1.5 GHz (master) and 140.0+/? GHz (slave). The phase lock loop (PLL) system is used to lock the slave source to the master source. The multipliers of this type can translate the spectra of highly stable centimeter-wave oscillators to any part of the millimeter range with the output power 100÷20 mW over the 30 to 140 GHz range without additional amplification. The phase locked sources operate over a 3% frequency band with low phase noise and rapid frequency tuning. The amplitude-frequency characteristics of the sources are presented with the locking-mode signal spectra.     

基于注频锁相技术的发射波束形成系统

研究了利用注频锁相技术实现低成本、高集成度、高效率的发射波束形成系统。首先介绍了发射波束形成的原理,并研究了注频锁相振荡器相位系统平衡点的稳定性,根据注频锁相振荡器的相位噪声理论给出了注频锁相振荡器阵列的设计原则,然后根据理论分析设计了一种可以产生高稳定度、低相位噪声具有任意相位加权系数的多通道射频相干信号的波束形成系统,利用计算机仿真该系统实现了发射波束扫描,证明了基于注频锁相技术的发射波束形成系统的可实现性。最后搭建了四通道注频锁相振荡器阵列,测量结果表明注频锁相振荡器阵列可以产生具有任意相位加权系统的多通道相干信号,进一步证明了该发射波束形成系统的有效性。     

Mode coupling in superconducting parallel plate resonator in acavity with outer conductive enclosure

We have carefully studied the mode coupling effect from analysis of the measured microwave scattering parameters of superconducting films using a parallel-plate-resonator technique. Due to its high resolution and simplicity, this technique has been widely employed to identify the quality of high-T_c superconducting films by measuring the resonance bandwidth, from which the microwave surface resistance is directly derived. To minimize the radiation loss, the resonator is usually housed in a conductive cavity. Using this method, we observe that a number of strong “cavity” modes due to the test enclosure fall around the lowest TM mode of the superconducting resonator and that a strong interaction between these two types of resonant modes occurs when their eigenfrequencies are close, causing a significant distortion or a strong antiresonance for the resonator mode. To describe this effect, a coupled harmonic-oscillator model is proposed. We suggest that the interaction arises from a phase interference or a linear coupling among the individual oscillators. Our model fits very well the observed Fano-type asymmetric or antiresonant features, and thus can be used to extract the intrinsic Q of the superconducting resonator     

Optical synchronization of millimeter-wave oscillators fordistributed architecture

A review of various methods of phase and frequency synchronization of active MMIC based transmit/receive modules is presented, and particular emphasis is placed on the synchronization of oscillators through the use of an indirect subharmonic optical injection locking technique. In this approach, the nonlinear behavior of large-signal modulated laser diodes and solid-state oscillators is exploited to extend the bandwidth of the synchronizing link to the millimeter-wave frequency range. Experimental results of the phase and frequency coherency of two 21.5 GHz FET oscillators are reported. Optimum performance is achieved at a subharmonic factor of 1/4, with a locking range of 84 MHz and a phase noise degradation of only 14 dB. The phase coherency measurement of two injection-locked oscillators points to a phase shift, which is introduced as a result of the frequency detuning between the slave and master oscillator signals. A scheme to correct for this phase error is presented     

Considering noise orbital deviations on the evaluation of power density spectrum of oscillators

This brief presents a new application of the theory of noise in free running oscillators based on the Floquet eigenvector decomposition. In oscillators, all orbital deviations contribute to the power density spectrum (PDS) as much as the "phase" term, usually considered. Each orbital deviation component shows a time evolution depending on the related Floquet eigenvalue, which thus characterizes statistical properties related to that component. Orbital deviations are partially correlated, due to their common origin from noise sources, thus also correlation terms are considered in the evaluation of the PDS. In this brief, we introduce a simplified method of calculation of PDS and apply it to an example of RLC negative resistance oscillator. Results show the relevance of orbital deviations in PDS in presence of stationary noise, these contributions becomes particularly relevant when noise is cyclostationary.     

Balanced monolithic oscillators at K- and Ka-band

A technique for generating accurate antiphase signals is presented in this paper. Monolithic oscillators at 20 and 40 GHz are realized using this technique. These oscillators have dual outputs that are mutually locked in antiphase. The inherent amplitude and phase balances between the output signals are verified. This is achieved by direct measurement using injection-locking polar diagrams, as well as low-frequency measurements of the down-converted oscillator outputs. The operation of the balanced oscillator as a multidevice power-combining oscillator is also investigated. Improvements of phase noise reduction and frequency stabilization are demonstrated at the combined oscillator output. This new oscillator topology shows significant potential in balanced circuits like mixers, multipliers, and modulators where circuit performance relies on the precise generation of the balanced signals     

Outils de CAO pour I’étude des circuits autonomes non linéaires: Détermination de I’état établi et du spectre du bruit résultant

This paper presents two new algorithms for non linear autonomous circuitscad. The first software is an extension of harmonic-balance method to oscillators analysis, this one allows to determine the frequency oscillation and the steady state of all non linear oscillators. The second algorithm is based on the conversion matrix method, which allows to simulate the field effect transistor non linear oscillators phase and amplitude noise spectra. These oscillators can be realised with distributed or lumped elements.     

On the dynamics of two-dimensional array beam scanning viaperimeter detuning of coupled oscillator arrays

Arrays of voltage-controlled oscillators coupled to nearest neighbors have been proposed as a means of controlling the aperture phase of one-dimensional (1-D) and two-dimensional (2-D) array antennas. It has been demonstrated, both theoretically and experimentally, that one may achieve linear distributions of phase across a linear array aperture by tuning the end oscillators of the array away from the ensemble frequency of a mutually injection-locked array of oscillators. These linear distributions result in steering of the radiated beam. It is demonstrated theoretically that one may achieve similar beamsteering in two dimensions by appropriately tuning the perimeter oscillators of a 2-D array. The analysis is based on a continuum representation of the phase in which a continuous function satisfying a partial differential equation of diffusion type passes through the phase of each oscillator as its independent variables pass through integer values indexing the oscillators. Solutions of the partial differential equation for the phase function exhibit the dynamic behavior of the array during the beamsteering transient     

A general theory of phase noise in electrical oscillators

A general model is introduced which is capable of making accurate, quantitative predictions about the phase noise of different types of electrical oscillators by acknowledging the true periodically time-varying nature of all oscillators. This new approach also elucidates several previously unknown design criteria for reducing close-in phase noise by identifying the mechanisms by which intrinsic device noise and external noise sources contribute to the total phase noise. In particular, it explains the details of how 1/f noise in a device upconverts into close-in phase noise and identifies methods to suppress this upconversion. The theory also naturally accommodates cyclostationary noise sources, leading to additional important design insights. The model reduces to previously available phase noise models as special cases. Excellent agreement among theory, simulations, and measurements is observed     

Design issues in CMOS differential LC oscillators

An analysis of phase noise in differential cross-coupled inductance-capacitance (LC) oscillators is presented. The effect of tail current and tank power dissipation on the voltage amplitude is shown. Various noise sources in the complementary cross-coupled pair are identified, and their effect on phase noise is analyzed. The predictions are in good agreement with measurements over a large range of tail currents and supply voltages. A 1.8 GHz LC oscillator with a phase noise of -121 dBc/Hz at 600 kHz is demonstrated, dissipating 6 mW of power using on-chip spiral inductors     

Optically controlled oscillators for millimeter-wave phased-arrayantennas

An approach for the design of optically synchronized millimeter-wave local oscillators based on a subharmonically injection-locked phase-lock-loop technique is introduced. The experimental results support the desired goal of frequency and phase coherency, phase shift control of millimeter-wave oscillators, and self-oscillating mixing to downconvert a millimeter-wave RF signal. Experimental results and theoretical analysis show the advantages of the proposed approach: large locking range of two subharmonically locked oscillators, lower FM noise degradation, and smaller phase error caused by frequency detuning     

Phase-noise measurement using two inter-injection-locked microwave oscillators

Phase noise in two mutually coupled oscillators is analyzed by the describing function method, and the after-lock phase noise of the oscillators is calculated in terms of their free-running phase noise. A new phase-noise measurement technique based on inter-injection locking of two similar oscillators is proposed. Experimental results are presented, which confirm the theory. It is shown that in the case of zero phase of coupling coefficient, the system is in the optimum state where the only required parameter for the measurement is the locking bandwidth. In this optimum state, as far as the locking bandwidth is measured correctly, imperfections such as the frequency drift, parameters discrepancy, and nonlinear susceptance of the oscillators have no serious effect on the measurement accuracy. The proposed method is compared to the conventional ones.     

Non linear dynamics of memristor based 3rd order oscillatory system

In this paper, we report for the first time the nonlinear dynamics of three memristor based phase shift oscillators, and consider them as a plausible solution for the realization of parametric oscillation as an autonomous linear time variant system. Sustained oscillation is reported through oscillating resistance while time dependent poles are present. The memristor based phase shift oscillator is explored further by varying the parameters so as to present the resistance of the memristor as a time varying parameter, thus potentially eliminating the need of external periodic forces in order for it to oscillate. Multi memristors, used simultaneously with similar and different parameters, are investigated in this paper. Mathematical formulas for analyzing such oscillators are verified with simulation results and are found to be in good agreement.     

Two-dimensional array beam scanning via externally and mutuallyinjection-locked coupled oscillators

The use of arrays of injection-locked voltage-controlled oscillators coupled to nearest neighbors has been proposed as a means of controlling the aperture phase of one and two-dimensional (2-D) phased-array antennas. It has been demonstrated both theoretically and experimentally that one may achieve linear distributions of phase across a linear array aperture by injection locking to an external oscillator the end oscillators of an array of a mutually injection-locked oscillators. These linear distributions cause steering of the radiated beam. It is demonstrated theoretically here that one may achieve beamsteering in a similar manner in two dimensions by injecting appropriately phased signals into the perimeter oscillators of a 2-D array. The analysis is based on a continuum representation of the phase previously developed in the context of beamsteering via tuning of the perimeter oscillators     

Terahertz BWO-Spectrosopy

Modern Terahertz-subTerahertz (THz-subTHz) spectrometers, based on continuously frequency-tunable coherent sources of radiation, the backward-wave oscillators (BWOs), are described which cover the frequencies v = 1 cm^?1 ? 50 cm^?1 (0.03 ? 1.5 THz) and allow for measurements at temperatures 2 ? 1000 K, also in magnetic fields. They allow for direct determination of spectra of any optical parameter of a material at millimeter-submillimeter wavelengths, the domain where infrared or microwave spectrometers encounter serious methodological difficulties. We report on new technical abilities of the quasioptical BWO-spectrometers and discuss their main components. We demonstrate abilities of the THz-subTHz BWO-spectroscopy by presenting some latest results on measurements of dielectric, conducting, superconducting and magnetic materials.