Lock Range Research Articles

An Injection-Current-Boosting Locking-Range Enhancement Technique for Ultra-Wideband mm-Wave Injection-Locked Frequency Triplers

An injection-current-boosting (ICB) locking-range enhancement technique is presented to increase the locking range (LR) of the millimeter-wave (mm-wave) injection-locked frequency triplers (ILFTs). With a transformer-based fourthorder injection-coupling network, the parallel capacitance from the injection devices is resonated out over a wide frequency range and the injection current is boosted greatly. Analytical models of the ICB-ILFT are introduced, based on which the current-boosting phenomenon is analyzed. Meanwhile, the design concepts of the ultra-wideband mm-wave ILFT are presented. With the proposed ICB technique, an ICB-ILFT is designed and fabricated in 65-nm CMOS process. With a 0-dBm RF injection source, the ICB-ILFT can be locked from 22.8 to 43.2 GHz without calibration, achieving a 61.8% LR. The power consumption is only 5.0 mW and a 9.5-dB phase noise difference is observed, which is close to the theoretical value.

Cause investigation of high-mode vortex-induced vibration in a long-span suspension bridge

A significant vortex-induced vibration (VIV) was observed in a suspension bridge under a wind velocity of approximately 6 and 7 m/s, and with a maximum amplitude that exceeded the serviceability limitations. Since the observation of VIV in an operating bridge was an infrequent event, this study investigated the cause of unexpected VIV. A series of wind tunnel tests revealed the main cause of the VIV was temporary screens applied over the guardrails to shield the curing surface during replacement of epoxy-coated pavement. The characteristics of the measured VIV were consistent with those from experimental results in terms of amplitude and lock-in wind speed range. The effect of Scruton numbers on VIV amplitude was examined for several dominant modes with different modal mass and damping ratios. Since the VIV amplitude is sensitive to the inherent damping ratio, the modal damping ratios of the bridge were identified from output-only modal analysis by using the frequency domain decomposition. This approach was efficient in identifying the damping ratios of high modes that were challenging due to weakly excited signals. The damping ratio of the triggered mode for VIV was the lowest among the investigated modes and estimated to be the level of the design-damping ratio.

A $6.5\times7\,\mu$ m2 0.98-to-1.5 mW Nonself-Oscillation-Mode Frequency Divider-by-2 Achieving a Single-Band Untuned Locking Range of 166.6% (4–44 GHz)

The common self-oscillation-mode (SOM) frequency dividers have a high- $Q$ sensitivity curve limiting the locking range (LR). This letter reports a non-SOM (NSOM) frequency divider-by-2. Fabricated in 65-nm CMOS, it occupies a die area of $6.5\,\,\times 7\,\,\mu \text{m}^{2}$ , and measures a single-band untuned LR of 166.6% (4–44 GHz), over a small input range $ . The key technique is a load-modulated dynamic latch aided by a current-reuse cross-coupled pMOS pair. The achieved figure-of-merit of 26.6 GHz/mW compares favorably with the state-of-the-art.

Effect of Higher Harmonics on the Accurate Calculation of Dynamic Phase-Locked-Loop Characteristics Using the Quasi-Harmonic Method

Abstract—The effect of higher harmonics on the accurate calculation of the dynamic characteristics of piecewise-linear phase-locked-loop frequency control using the quasi-harmonic method has been demonstrated at exactly known values of the lock-in range and the frequency of rotational motions.

Numerical study for energy harvesting of the tandem wavy cylinders in cross flow

In order to make the bladeless wind turbine better convert wind energy into electric energy, this paper based on the method of passively controlling vortex-induced vibration, by changing the shape of the cylindrical surface, selecting three different parameters of the wavy cylinder (λ/Dm=6, ɑ/Dm=0.15; λ/Dm=2, ɑ/Dm=0.15, λ/Dm=2, ɑ/Dm=0.3), and performing a numerical simulation at Re=100. The results show that the wavy cylinder of λ/Dm=2, ɑ/Dm=0.15 is more susceptible to induced vibration. Compared to straight cylinders, the wavy cylinder of λ/Dm=2, ɑ/Dm=0.15 have a wider range of lock-in and a larger amplitude.

Vortex-Induced Vibration of symmetric airfoils used in Vertical-Axis Wind Turbines

We present an experimental study on a flexibly-mounted NACA 0021 airfoil, allowed to oscillate in the crossflow direction to investigate its Vortex-Induced Vibration (VIV) response at varying angles of attack, α, in the range of 0°≤α≤180°. This airfoil is considered since it is one of the airfoils used in Vertical-Axis Wind Turbine (VAWT) designs. Based on the experimental results of the current work, oscillations are observed for angles of attack in the range of 60°≤α≤130°. The peak amplitude, A∗=1.93, and the largest lock-in range, 1.7<U∗<12, are observed at α=90∘. For angles of attack for which oscillations are observed, the frequency ratio remains close to unity, implying that lock-in has occurred. The wake and crossflow force magnitudes and frequency contents for the airfoil at angles of attack symmetric about α=90∘ are compared and differences in terms of the airfoil displacement, width of the wake, force coefficient magnitudes and frequencies are shown when the leading edge of the airfoil is facing the incoming flow (0°≤α≤85°) or the trailing edge is facing the incoming flow (95°≤α≤180°). It is also shown that the observed VIV occurs within the range of reduced velocities that are expected for the full-scale VAWTs.

Flow-induced vibration of a circular cylinder with rigid splitter plate

Flow-induced vibration (FIV) of a circular cylinder with an attached rigid splitter plate is studied. A stabilized finite element formulation is utilized to solve the incompressible flow equations in two-dimensions. Three regimes of FIV are identified for the range of reduced speed (1≤U∗≤70) studied: vortex-induced vibration (VIV), steady flow and galloping. The effect of mass ratio, 2≤m∗≤1000, is studied for the Re=150 flow (Reynolds number is based on diameter of the cylinder, D) and splitter plate of length, Lp=3.5D. In contrast to an isolated cylinder, the peak response of the cylinder with splitter plate is associated with a significantly smaller amplitude and the lock-in occurs over a wider range of U∗. The U∗ for the onset of lock-in increases with increase in m∗. The end of lock-in, however, is independent of m∗. In addition, unlike the isolated cylinder, the transition from desynchronization to lock-in is gradual, except for very large m∗. Although galloping occurs for all m∗, its onset is strongly dependent on m∗. The end of lock-in regime of VIV is immediately followed by onset of galloping for small m∗. For this range of m∗, the galloping is strongly influenced by vortex shedding. A steady regime, wherein the vibration is completely suppressed for a certain range of U∗, occurs beyond the lock-in regime for moderate m∗. However, galloping eventually ensues and revives the unsteadiness at large U∗. For very large m∗, the steady flow regime is replaced by a desynchronization region. In general, the onset of galloping is delayed to larger U∗ with increase in m∗. The effect of the length of the splitter plate (Lp∕D=1.5, 2.5 and 3.5) on FIV is studied for m∗=10. The steady flow regime is observed only for Lp=3.5D. Increase in Lp leads to a small increase in the peak amplitude and range of lock-in during VIV. The effect on galloping is more significant; the amplitude of vibration, at a given U∗, decreases with increase in Lp. The frequency of vibration decreases, during both VIV and galloping, with increase in Lp. The effect of Re, within the laminar regime, is studied. Its effect on the amplitude of vibration is found to be similar to that of Lp.

Injection signaling in relaxation oscillators

This paper investigates relation between injection signaling and the lock range of relaxation oscillators. We show that lock range is determined by the effective injection signals of Volterra circuits contributed by both external injection signals and the nonlinearity of oscillators. The larger the harmonic tones of injection signals and the higher the degree of the nonlinearity of oscillators, the larger the effective injection signals subsequently the larger the lock range. We further show in order to maximize the contribution of external injection signals, injection phase needs to be $$\pi /2$$ , valid for oscillators with either single or multi-tone injections. Moreover, we show to maximize lock range, the duty cycle of injection signals needs to be 50%. Finally, we show the phase noise of relaxation oscillators has a similar profile as that of harmonic oscillators. The quality factor of relaxation oscillators is smaller as compared with that of harmonic oscillators. The higher the degree of the nonlinearity of the relaxation oscillator, the smaller the quality factor of the relaxation oscillator subsequently the higher the phase noise. The theoretical findings on the lock range of relaxation oscillators are validated using the simulation results of a dual-comparator relaxation oscillator designed in TSMC 180 nm 1.8 V CMOS technology.

Ground Effects on the Vortex-induced Vibration of Bridge Decks

The present study investigated the ground effects on the VIV of a closed box girder based on wind tunnel tests and numerical methods. First, we presented a vibration measurement system for wind-tunnel test to simulate ground effects on the bridge girder. Second, we investigated the Strouhal number (St), the VIV lock-in phenomena over a range of wind velocities, and the maximum VIV amplitudes and their change laws in correlation with the height from the ground in two different ground conditions. The outcomes showed the following: that a low height from the ground can lead to high St numbers; that ground effects did not change the width of VIV lock-in range, but did impel VIVs to occur earlier in the uniform flow field; and that the maximum VIV amplitudes was reduced and the VIV lock-in range narrowed in the turbulent flow field. Finally, we conducted the numerical simulation method to study the ground effect mechanism on VIVs. The numerical results showed that the periodic vortex shedding will generate periodic forces on the structure, which leads to the occurrence of VIVs. Ground effects can speed up vortex shifting, whereas aerodynamic forces on the deck are weakened.

Hold-in, Pull-in and Lock-in Ranges for Phase-locked Loop with Tangential Characteristic of the Phase Detector

In the present paper the phase-locked loop (PLL), an electric circuit widely used in telecommunications and computer architectures is considered. A new modification of the PLL with tangential phase detector characteristic and active proportionally-integrating (PI) filter is introduced. Hold-in, pull-in and lock-in ranges for given circuit are studied rigorously. It is shown that lock-in range of the new PLL model is infinite, compared to the finite lock-in range of the classical PLL.

A Phasor-Based Analysis of Sinusoidal Injection Locking in LC and Ring Oscillators

A new perspective into the locking behavior of LC and ring oscillators is presented. By decomposing a sinusoidal injection current into in-phase and quadrature-phase components, exact expressions for the amplitude and phase of an injection-locked LC oscillator which hold for any injection strength and frequency are derived and confirmed by simulation. The analysis, which can be naturally extended to an arbitrary LC resonator topology, leads to a rigorous understanding of the fundamental physics underlying the locking phenomenon. Furthermore, an investigation of the different necessary and sufficient conditions for injection locking to occur is carried out, leading to a more precise notion of the lock range. The ring oscillator is also analyzed in an analogous fashion, resulting in simple yet accurate closed-form expressions for the fractional lock range in the small-injection and long-ring regimes; the expressions are validated by simulations of single-ended inverter-based ring oscillators in 65-nm CMOS. The mathematics behind how the injection modifies the phase delay contributed by each stage in the ring is discussed. A corollary that generalizes the small-injection lock range to any feedback-based oscillator topology is established. Conceptual and analytical connections to the existing literature are reviewed.

Non-linear analysis of a modified QPSK Costas loop

A Costas loop is one of the classical phase-locked loop based circuits, which demodulates data and recovers carrier from the input signal. The Costas loop is essentially a nonlinear control system and its nonlinear analysis is a challenging task. In this article for a modified QPSK Costas loop we analyze the hold-in, pull-in and lock-in ranges. New procedure for estimation of the lock-in range is considered and compared with previously known approach.

Control of jet using burst modulation by coaxial type DBD plasma actuator (Changes in jet diffusion process by applied voltage and burst frequency)

This study demonstrated jet control through the generation of an intermittently induced flow via burst-modulation from a coaxial type, axisymmetric nozzle shape DBD plasma actuator (DBD-PA). Here, a lock-in phenomenon occurred and was characterized by synchronization of the burst-frequency (frequency of burst-modulation) and the jet-generated vortex within a specific burst-frequency range, which aimed to clarify the change in the development process of the jet by the driving condition of the DBD-PA where the applied voltage and burst-frequency were varied. In the main text of this study the Reynolds number that is based on mean velocity and nozzle diameter of the jet was set at 5000. The applied voltages for DBD-PA were Vp-p = 16 kV, 14 kV, and 12 kV, while the burst-frequency was fburst = 0.2–2.0fn ( fn: frequency of occurrence of the initial vortex of free jet is 716 Hz). Results of the control demonstration showed that the lock-in phenomenon occurred at 0.9–1.4fn for all applied voltages. In the downstream, when the driving condition was Vp-p = 14 kV and fburst = 0.7fn, diffusion was dominant in all driving conditions due to fast collapse of the developed vortex ring. Moreover, such collapse was gradual with higher applied voltage. At the end of the burst-frequency of the lock-in phenomenon range, where the driving conditions was Vp-p = 16 kV and fburst = 1.4fn, diffusion became more suppressed as compared to the free jet, as the vortex ring near the nozzle collapsed due to vortices pairing, and did not develop. This work emphasizes that changing the applied voltage and the burst-frequency of DBD-PA potentially promotes and suppresses the diffusion of the jet.

A 0.0043-mm2 0.3–1.2-V Frequency-Scalable Synthesized Fractional-N Digital PLL With a Speculative Dual-Referenced Interpolating TDC

This paper presents a synthesized fractional-N digital phase-locked loop (PLL) with a speculative dual-referenced interpolating time-to-digital converter (DI-TDC). The DI-TDC measures a fractional phase by referencing two adjacent quadrant boundaries which are given by a four-phase digitally controlled oscillator (DCO). It achieves a robust gain matching to the first order without need of any calibration. By predicting a time region of interest for the next TDC conversion, the power and area overheads for DI-TDC is minimized. Except for DCO and a reference delay chain, the PLL is implemented with register-transfer level (RTL) behavioral descriptions followed by an automated synthesis. It is fabricated in 28-nm CMOS with an active area of 0.0043 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The PLL shows a wide frequency lock range operating at a supply voltage from 0.3 to 1.2 V, achieving a stable figure-of-merit of better than -220 dB for a supply voltage above 0.6 V.

Improvement of Scanlan’s Nonlinear Model based on Residual Analysis

Scanlan’s semi-empirical nonlinear model has been widely applied in bridge engineering because of its simplicity. However, it is based on the oscillation displacement, and thus it fails to describe the Vortex-induce Vertical Force (VIVF) on a flat closed-box bridge deck. In the study, in order to better depict VIVFs, a new improved model was proposed. First, the residual of the Vortexinduced Vertical Force (VIVF) is regular and maintains the significant quadratic relation with the VIVF reconstructed by Scanlan’s model, which means Scanlan’s model needs to be improved by adding quadratic terms. Second, an appropriate quadratic term was a dot product of dimensionless displacement and velocity, because this term has a significant linear relation with the reconstructed VIVF in the residual plot, and is independent of the other terms in Scanlan’s model. Furthermore, in lock-in range, the maximum oscillation displacement of a blunt body at different wind speeds was predicted by the proposed model. Simulation results showed that the proposed model is suitable for describing the nonlinearity of the VIVF and well fit the measured data. Due to simplicity, validity, and parameters to be easily identified, the proposed model has potential application in engineering.

A 3.1–10.6-GHz 57-Bands CMOS Frequency Synthesizer for UWB-Based Cognitive Radios

An ultra-wideband (UWB)-based cognitive radio (CR) is a promising technique to utilize 3.1–10.6-GHz band efficiently for high data-rate short-range wireless connectivity even in overcrowdedness of the frequency spectrum. Frequency synthesizers tailored to the UWB-based CR should provide wide lock range, multiple frequency bands, and low in-band spurs while consuming low power. This paper investigates a low power, wide lock range, integer-N frequency synthesizer approach with 132-MHz frequency step and 57 subbands in the UWB band. Two-stage supply regulated differential ring oscillator provides linear and wide tuning range with voltage controlled oscillator gain of 22.5 GHz/V and low supply-noise sensitivity. A modular true-single-phase-clock programmable divider achieves wide operating frequency range of 0.1–6.5 GHz and power efficiency of 6.25 GHz/mW by compensating leakage current at the dynamic nodes with conditional latches. Replica-based digital calibration reduces the current mismatch of the charge pump to <1% for low in-band reference spurs of <−60 dBc. A frequency synthesizer test chip was fabricated in 65-nm complementary metal–oxide–semiconductor technology. The active area of the frequency synthesizer is 0.12 mm2. It achieves <−30-dBc integrated phase noise and enables the UWB-based CR to get bit error rate of <10−3 while consuming <−10.1 mW.

Analysis and Design of Ultra-Wideband mm-Wave Injection-Locked Frequency Dividers Using Transformer-Based High-Order Resonators

A transformer-based high-order resonator is proposed to improve the locking range (LR) of the millimeter-wave injection-locked frequency dividers (ILFDs). The LR limitations on ILFDs are discussed, and the operating principles of the proposed high-order resonator are analyzed based on their flattened phase response. The inductive gain peaking technique and the tail current source requirement are further analyzed for low power considerations. Two chips are fabricated in a 65-nm CMOS process to implement the proposed techniques: the first one measures an LR of 62.9% from 27.9 to 53.5 GHz while consuming 5.8 mW from a 1-V power supply and the second chip achieves an LR of 62.7% from 32.4 to 61.9 GHz while consuming only 1.2 mW from a 0.42-V power supply. The best figure of merit can achieve up to 24.7 GHz/mW.

A Wide-Range Low-Power PLL-Based PI Multiphase Generator Using an Adaptive Frequency Tracking Technique

A phase-locked loop (PLL) along with a linear phase interpolator that generates 64 phases with low jitter in a continuous lock range of 400 MHz–2.2 GHz for mobile memory interfaces is presented. To provide adaptive and precise phase interpolation (PI), a novel frequency tracking PI bias along with a wide-frequency range PLL and lock-detection control are employed. The PLL-based PI is fabricated in 65-nm CMOS and achieves a peak-to-peak and an RMS jitter of 14.8 ps and 2.16 ps, respectively. The measured DNL and INL of the proposed PI are 0.21 LSB and 0.43 LSB, respectively. The PLL-based PI consumes 8.1 mW at a 1.0-V supply.

Hydrodynamic force investigation of a rigid cylinder under the coupling CF and IL motion

Extensive researches have been conducted to simulate the two-degree-of-freedom (2DOF) vortex induced vibration (VIV) of a cylinder during the past few decades. However, there are still very few publications in terms of the hydrodynamic force of a cylinder with 2DOF motion in cross-flow (CF) and in-line (IL) directions. This study employs the Reynolds-Average-Navier–Stokes (RANS) equations and shear stress transport (SST) k-ω turbulence model to investigate the hydrodynamic force characteristics. The numerical model is firstly validated based on the 2DOF VIV experiment of an elastically supported cylinder in the literature. The results indicate that the predicted displacement and hydrodynamic force are approximately harmonic, and are in reasonable agreement with the experimental data. By imposing harmonic motion on the cylinder in CF and IL directions with period ratio of 2, parametric analyses are carried out to simply broaden the understanding of the sensitivity of the hydrodynamic coefficients including force coefficient, excitation coefficient and added mass coefficient, to the motion-related parameters, such as the motion phase angle, non-dimensional amplitude and frequency. There would be a sudden change for the excitation coefficient and added mass coefficient at a certain motion phase angle approximately corresponding to the peak of the force coefficient. The varying trend of the hydrodynamic coefficient with non-dimensional amplitude is different from that obtained from one-degree-of-freedom (1DOF) forced vibration test in literatures, and is significantly related with the motion phase angle and non-dimensional frequency. The non-dimensional frequency seems to mainly affect the excitation coefficient, added mass coefficient and mean drag coefficient in the lock-in range.

More Discussions on Intrinsic Frequency Detection Capability of Full-Rate Linear Phase Detector in Clock and Data Recovery

The full-rate linear phase detector (PD) has not only phase detection capability but also single-sided frequency detection capability intrinsically. Previously, this fact has been discovered by researching the phase and frequency characteristics of the combined full-rate linear PD and charge pump (CP) under the condition that the ratio of the received data frequency (fDATA) and the recovered clock frequency (fCLK) is set as an integer number. In this paper, for completeness of the theory, the phase and frequency characteristics of the combined full-rate linear PD and CP are studied again while the ratio of fDATA and fCLK is set as a general rational number. Additionally, theoretical analyses of the lock-in range and the lock time of the referenceless single-loop clock and data recovery (CDR) including the full-rate linear PD are newly developed and verified. The calculated lock times by the analysis results agree well with the measured lock times from the MATLAB Simulink simulations.