Stability Analysis of Injection-Locked Oscillators in Their Fundamental Mode of Operation

Phase-lock stability of fundamental-wave injection-synchronized oscillators is investigated on the basis of a new time-domain approach. Starting from a quite general oscillator modeling and assuming single-frequency quasi-static operation, both exact and first-order approximate stability criteria are derived in a fully analytical form suitable for computer implementation. The examples worked out demonstrate good agreement of this theory with experimental observations available in the literature on multiple-tuned oscillators, whose behavior under large-signal injection was so far predictable only through graphical methods.     

Noise Due to Pulse-to-Pulse Incoherence in Injection-Locked Pulsed Microwave Oscillators

It is demonstrated that partial pulse-to-pulse coherence in a pulsed oscillator system gives rise to no excess noise, which may be significantly reduced by injection Iocking.     

Amplitude Behavior of Injection-Locked Oscillators

Subject to a reasonable constraint on the frequency of the amplitude modulation of the injected signal, the reduced amplitude equation for an injection-locked oscillator, a nonlinear differential equation, is reduced to a nonlinear algebraic equation which is solved numerically. AM limiting, power limiting, and output-power increment are calculated as functions of injected-signal amplitude for several types of negative-conductance nonlinearities. A method of characterizing the conductance nonlinearity from the measured output-power increment is given and is used to characterize avalanche- and tunnel-diode oscillators. Excellent agreement between calculated and measured limiting is shown. In addition to clarifying the amplitude behavior of the locked oscillator, the results show what types of nonlinearities are desirable for limiter applications, that avalanche-diode oscillators have the potential for excellent limiting, and that the output-power increment is indicative of the oscillator impedance match.     

Phase-Noise Analysis of Injection-Locked Oscillators and Analog Frequency Dividers

In-depth investigation of the phase-noise behavior of injection-locked oscillators and analog frequency dividers is presented. An analytical formulation has been obtained, which allows a better understanding of the shape of the output phase-noise spectrum of these circuits. The simplicity of this formulation is also helpful for circuit design. Approximate expressions for the corner frequencies of the spectrum are determined, identifying the most influential magnitudes and deriving design criteria. In particular, a technique has been developed to shift the frequency of the first corner of the phase-noise spectrum, up to which the output phase noise follows the input one. The expressions for the corner frequencies can be introduced in either in-house or commercial harmonic-balance software, thus allowing an agile design, as no separate phase-noise analysis is required. The validity of the analytical techniques is verified with the conversion-matrix approach and with measurements using two field-effect-transistor-based circuits: a 4.9-GHz injection-locked oscillator and a frequency divider by 2 with 9.8-GHz input frequency.     

Injection-Locked Hybrid Optoelectronic Oscillators for Single-Mode Oscillation

We demonstrate single-mode extraction from multiple modes in a 30-GHz optoelectronic oscillator (OEO) by injecting OEO modes into an electrical oscillator. The electrical oscillator is injection-locked by one OEO mode resulting in single-mode oscillation. The single-mode oscillation frequency can be tuned by changing the electrical oscillation frequency.      

CMOS Oscillators for Clock Distribution and Injection-Locked Deskew

The distribution and alignment of high-frequency clocks across a wide bus of links is a significant challenge in modern computing systems. A low power clock source is demonstrated by incorporating a buffer into a cross-coupled oscillator. Because the load is isolated from the tank, the oscillator can directly drive 50-Ohm impedances or large capacitive loads with no additional buffering. Using this topology, a quadrature VCO (QVCO) is implemented in 0.13 $mu hbox{m}$ digital CMOS. The QVCO oscillates at 20 GHz, consumes 20 mW and provides 12% tuning range. The measured phase noise is $-101~hbox{dBc}/hbox{Hz}$ @ 1 MHz frequency offset. A clock alignment technique based upon injection-locked quadrature-LC or ring oscillators is then proposed. Although injection-locked oscillators (ILOs) are known to be capable of deskewing and jitter filtering clocks, a study of both LC and ring ILOs indicates significant variation in their jitter tracking bandwidth when used to provide large phase shifts. By selectively injecting different phases of a quadrature-LC or ring VCO, this problem is obviated resulting in reduced phase noise. The technique is demonstrated using a LC QVCO at 20 GHz while burning only 20 mW of power and providing an 8 dB improvement in phase noise. A ring oscillator deskews a 2 to 7 $~$GHz clock while consuming 14 mW in 90 nm CMOS.      

GaAs FET Applications for Injection-Locked Oscillators and Self-Oscillating Mixers

Injection-locked oscillators (ILO's) using GaAs FET's are described experimentally and theoretically, showing that a wider locking range can be obtained with transmission-type ILO's than with reffection-type, assuming Q/sub ext/, to the load to be the same in each case. Frequency-stabilized FET oscillators are discused in terms of the advantages gained by terminating the gate port by a 50-Omega load. Functioning as a self-oscillating mixer, the circuit showed a 9.5-dB (DSB) noise figure.     

基于注频锁相和非线性振荡器的接收波束形成

本文提出以注频锁相技术为基础接收窄带信号的非线性振荡器波束形成器,给出了注频锁相现象的Adler方程及非线性振荡器的动力微分方程.并提出了零陷多波束形成算法,推导权矢量,并通过仿真分析该算法的信号波达图效果.     

Analysis and Design of Wideband Injection-Locked Ring Oscillators With Multiple-Input Injection

In this paper, the locking range of the injection-locked ring oscillators is investigated. To improve the injection efficiency and the locking range for superharmonic frequency division, a multiple-injection technique is proposed. Using a 0.18-mum CMOS process, a wideband frequency divider based on a three-stage ring oscillator is implemented for demonstration. With a tunable free-running frequency, the fabricated circuit provides 2:1 and 4:1 frequency division with a single-ended input signal ranging from 13 to 25 and 30 to 45 GHz, respectively. Compared with the case of the single-ended injection, the locking range of the frequency divider almost doubles when multiple-input injection with optimum phases is utilized. The experimental results exhibit good agreement with the theoretical derivation and the circuit simulation.     

A Spectral Model for RF Oscillators With Power-Law Phase Noise

In this paper, we apply correlation theory methods to obtain a model for the near-carrier oscillator power-spectral density (PSD). Based on the measurement-driven representation of phase noise as a sum of power-law processes, we evaluate closed form expressions for the relevant oscillator autocorrelation functions. These expressions form the basis of an enhanced oscillator spectral model that has a Gaussian PSD at near-carrier frequencies followed by a sequence of power-law regions. New results for the effect of white phase noise, flicker phase noise and random walk frequency modulated phase noise on the near-carrier oscillator PSD are derived. In particular, in the case of$1/f$phase noise, we show that despite its lack of stationarity it is possible to derive a closed form expression for its effect on an oscillator PSD and show that the oscillator output can be considered to be wide-sense stationary.     

Noise Due to Pulse-to-Pulse Incoherence in Injection-Locked Pulsed-Microwave Oscillators. Part II-Effects of Phase-Locking Dynamics

The problem of noise due to partial pulse-to-pulse coherence in phase-locked pulsed oscillators is investigated. In particular, the analysis includes the dynamic time variation of the phase-locking process. The signal-to-noise ratio of such a system is found to increase as (gamma tau)/sup 2/, where gamma is the frequency locking bandwidth and tau is the pulse length. This result corrects a previous conjecture of an exponential dependence on gamma tau.     

Noise of Negative Resistance Oscillators at High Modulation Frequencies

The theory of AM and FM noise in oscillators of the negative resistance type is extended to higher modulation frequencies, i.e., to modulation frequencies beyond the bandwidth of the stabilizing cavity. The results are expressed in terms of the input impedance of the stabilizing cavity and are found to agree well with measurements.     

A First-Order Markov Model for Understanding Delta Modulation Noise Spectra

A first-order Markov process is used to model the sequence of quantization noise samples in delta modulation. An autocorrelation parameterCin the Markov model controls the shape of the noise spectrum, and asCdecreases from 1 to 0 and then to -1, the spectrum changes from a low-pass to a flat, and then to a high-pass characteristic. One can also use the Markov model to predict the so-called out-of-band noise rejection that is obtained when delta modulation is performed with an oversampled input, and the resulting quantization noise is lowpass filtered to the input band. The noise rejectionGis a function ofCas well as an oversampling factorFand an interesting asymptotic result is thatG=frac{1-C}{1+C} dot FifF gg frac{1+C}{1-C} dot frac{pi}{2}. Delta modulation literature has noted the importance of the specialGvalues,Fand2F. These correspond to autocorrelation values of 0 and -1/3.     

Analysis of Noise Upconversion in Microwave FET Oscillators

The upconversion of Iow-frequency noise in microwave FET oscillators is investigated. The theoretical analysis is presented in two forms, a general and a simplified one. The latter version yields closed-form expressions for amplitude and phase noise, which are discussed wfth regard to the physics of the upconversion process. Application of the method is demonstrated with an example.     

Stability Criteria for Phase-Locked Oscillators

Stability criteria for negative conductance oscillators or amplifiers are derived in terms of the total circuit admittance. A figure of merit for phase locking at small injected powers is derived. The influence of large injected signals is studied. The conclusions drawn from the calculations are in good qualitative agreement with experimental observations on phase-locked IMPATT-diode oscillators.     

CMOS环形振荡器的噪声分析

在CMOS射频集成电路的设计中，分析振荡器的相位噪声是非常重要的。文章以射频段的一种环形振荡器为例，在时间域，用小信号模型深入分析，得出了设计射频段环形振荡器时进行李产分析的一般方法和分析模型。由此方法得到的结果和仿真结果相符合。     

A New Amplifier Model for Resonance Enhancement of Optically Injection-Locked Lasers

A new Fabry-Perot amplifier model is established based on parameters extracted from the injection-locking rate equations to explain the resonance frequency enhancement and the small-signal frequency response behavior of injection-locked vertical-cavity surface-emitting lasers. Simulations using this amplifier model in conjunction with injection-locking rate equations show excellent agreement with the experimental results.     

Noise in Single-Frequlency Oscillators and Amplifiers

A generalization of previous oscillator noise analyses has been developed to permit reliable noise characterization of active nonlinear devices. Effects due to sideband correlation in the equivalent noise source are included. A rotating wave approximation (RWA) developed by Lax is used in obtaining the amplitude and phase noise spectra. Conditions are given for phase stabilization of free-running oscillators and for minimum phase noise in phase-Iocked oscillators and amplifiers. Stability criteria, discussion of spurious sidetones, and effects of a noisy synchronizing signal are given. The noise measure is used to obtain alternative expressions for the noise spectra and the carrier-to-noise ratios of locked oscillators and amplifiers. It is shown that the noise power gain of AM fluctuations is usually much lower than the corresponding gain for FM noise. The theory should be useful in optimizing the noise performance of nonlinear RF generators, such as IMPATT, BARITT, and Gunn diode oscillators.     

AM and FM Noise of BARITT Oscillators

AM, FM, and baseband noise of a BARITT diode oscillator in the range 100 Hz-50 kHz off the carrier has been measured under various operating conditions. A simple calculation has been made, relating the baseband noise to the oscillator AM and FM noise via measured amplitude and frequency modulation sensitivities and the results have been compared with the noise measured. It is shown that, depending on the bias current applied, both AM and FM noise performance can be degraded by up-conversion. Complete removal of up-converted noise requires a high-impedance low-noise bias supply since both the diode noise and bias supply noise at baseband frequencies may be significant when up-converted. Even with all modulation suppressed, the AM and FM noise has a flicker component almost completely correlated with the diode flicker noise at baseband frequencies. The RF power dependence of the AM and FM noise has also been investigated. It is shown that the BARITT oscillator noise compares very favorably with that of IMPATT's and TEO's. Values of -142 dB/100 Hz (AM noise) and 3.5 Hz/(100 Hz)/sup 1/2/ for Q/sub ext/ = 200 (FM noise) have been measured at 30 kHz off the carrier.