Fundamental Oscillation Research Articles

A 165-GHz Transmitter With 10.6% Peak DC-to-RF Efficiency and 0.68-pJ/b Energy Efficiency in 65-nm Bulk CMOS

This paper presents a high-efficiency 165-GHz ON–OFF keying transmitter in a 65-nm CMOS technology with the record efficiency to the best of our knowledge. This is due to the proposed holistic design and optimization procedure, which links all the performance and figure-of-merits to the device sizes, including both actives and passives. This transmitter includes a high-efficiency transformer-based fundamental frequency cross-coupled oscillator and a high-speed and high ON–OFF ratio single-pole single-throw switch-based modulator. The transmitter demonstrates the highest dc-to-RF efficiency (10.6%) beyond 140 GHz in silicon processes, with a high output power (0.66 dBm), a high ON–OFF ratio (>32 dB), and a low phase noise (−104.8 dBc/Hz at 1-MHz offset). The transmitter achieves 9.4-Gbps data rate of less than $1 \times 10^{-12}$ bit error rate with 0.68-pJ/b energy efficiency. The standalone oscillator also demonstrates the record dc-to-RF efficiency of 25.9% beyond 140 GHz in silicon processes. The transmitter consumes core area of 240 $\mu \text {m} \times 130~\mu \text{m}$ .

Dynamical tides in general relativity: Effective action and effective-one-body Hamiltonian

Tidal effects have an important impact on the late inspiral of compact binary systems containing neutron stars. Most current models of tidal deformations of neutron stars assume that the tidal bulge is directly related to the tidal field generated by the companion, with a constant response coefficient. However, if the orbital motion approaches a resonance with one of the internal modes of the neutron star, this adiabatic description of tidal effects starts to break down, and the tides become dynamical. In this paper, we consider dynamical tides in general relativity due to the quadrupolar fundamental oscillation mode of a neutron star. We devise a description of the effects of the neutron star's finite size on the orbital dynamics based on an effective point-particle action augmented by dynamical quadrupolar degrees of freedom. We analyze the post-Newtonian and test-particle approximations of this model and incorporate the results into an effective-one-body Hamiltonian. This enables us to extend the description of dynamical tides over the entire inspiral. We demonstrate that dynamical tides give a significant enhancement of matter effects compared to adiabatic tides, at least for neutron stars with large radii and for low mass-ratio systems, and should therefore be included in accurate models for gravitational-wave data analysis.

The Sun–Earth connect 2: Modelling patterns of a fractal Sun in time and space using the fine structure constant

Abstract Self-similar matrices of the fine structure constant of solar electromagnetic force and its inverse, multiplied by the Carrington synodic rotation, have been previously shown to account for at least 98% of the top one hundred significant frequencies and periodicities observed in the ACRIM composite irradiance satellite measurement and the terrestrial 10.7cm Penticton Adjusted Daily Flux data sets. This self-similarity allows for the development of a time–space differential equation (DE) where the solutions define a solar model for transmissions through the core, radiative, tachocline, convective and coronal zones with some encouraging empirical and theoretical results. The DE assumes a fundamental complex oscillation in the solar core and that time at the tachocline is smeared with real and imaginary constructs. The resulting solutions simulate for tachocline transmission, the solar cycle where time-line trajectories either ‘loop’ as Hermite polynomials for an active Sun or ‘tail’ as complementary error functions for a passive Sun. Further, a mechanism that allows for the stable energy transmission through the tachocline is explored and the model predicts the initial exponential coronal heating from nanoflare supercharging. The twisting of the field at the tachocline is then described as a quaternion within which neutrinos can oscillate. The resulting fractal bubbles are simulated as a Julia Set which can then aggregate from nanoflares into solar flares and prominences. Empirical examples demonstrate that time and space fractals are important constructs in understanding the behaviour of the Sun, from the impact on climate and biological histories on Earth, to the fractal influence on the spatial distributions of the solar system. The research suggests that there is a fractal clock underpinning solar frequencies in packages defined by the fine structure constant, where magnetic flipping and irradiance fluctuations at phase changes, have periodically impacted on the Earth and the rest of the solar system since time immemorial.

Localized electrons and phonons in branched polyacetylene molecules

The electronic and vibrational characteristics of a Y splitter based on trans-polyacetylene molecular chains are studied using the density functional method. It is shown that the localized electronic states are formed at the branching point. Their energy is determined by the mutual orientation and length of the branches. The Raman-active localized vibrational modes are present in a phonon spectrum of a splitter. The intensity of the fundamental oscillation is determined by the maximum length of the linear conjugated fragment of a splitter.

Room-Temperature Oscillation of Resonant Tunneling Diodes close to 2 THz and Their Functions for Various Applications

Compact and coherent source is a key component for various applications of the terahertz (THz) wave. We report on our recent results of THz oscillators using resonant tunneling diodes (RTDs). To achieve high-frequency oscillation, the electron delay time of RTD was reduced with a narrow quantum well and an optimized collector spacer thickness. Conduction loss at the air bridge connecting RTD and slot antenna, which works as a resonator and a radiator, was also reduced. By these structures, a fundamental oscillation up to 1.92 THz was obtained at room temperature. Theoretical calculation shows that an oscillation over 2 THz is further expected by improved structures of RTD and antenna. Using the offset slot antenna and two-element array configuration, high output power of 0.61 mW was obtained at 620 GHz. A direct intensity modulation of RTD oscillators up to 30 GHz, which is useful for high-speed wireless data transmission, was demonstrated. By the integration of a varactor diode, wide frequency sweep of 580–700 GHz in a single device and 580–900 GHz in a four-element array were also demonstrated. This result expands possible applications of RTD oscillators.

Interaction of ULF waves with different ion species: Pitch angle and phase space density implications

AbstractULF waves can accelerate/decelerate the charged particles including the ring current ions via drift‐bounce resonance, which play an important role in the dynamics of ring current during storm times. This study compares the different behaviors of oxygen ions (10.5–35.1 keV) and protons (0.3–12.3 keV) which simultaneously interact with Pc5 ULF waves observed by Cluster on 3 June 2003. The ULF waves are identified as the fundamental mode oscillations. Both oxygen ions and protons show periodic energy dispersion and pitch angle dispersion signatures, which satisfy the drift‐bounce resonance condition of N=2. The different behaviors of oxygen ions and protons include (1) the resonant energy of oxygen ions is higher than that of protons due to mass difference; (2) the phase space density (PSD) of oxygen ions show relative variations (3.6–6.3) that are much larger than that of protons (<0.4), which indicates a more efficient energy exchange between oxygen ions and ULF waves; (3) the PSD spectra show that oxygen ions are accelerated, while protons are decelerated, which depend on the radial gradient of their PSD; (4) the pitch angle distributions (PADs) of the oxygen ions and protons show negative slope and bidirectional field‐aligned features, respectively, which is related to the preexisting state of ion PADs before the interaction with the ULF waves. In addition, the resonant ions with peak fluxes tracing back to the magnetic equator are always collocated with the accelerating (westward) electric field, which indicate that the ions are mainly accelerated near the magnetic equator and the electric field intensity of ULF waves peaks there.

Energetic particle-driven compressional Alfvén eigenmodes and prospects for ion cyclotron emission studies in fusion plasmas**This manuscript has been authored by Princeton University under Contract Number DE-AC02-09CH11466 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to

As a fundamental plasma oscillation the compressional Alfvén waves (CAWs) are interesting for plasma scientists both academically and in applications for fusion plasmas. They are believed to be responsible for the ion cyclotron emission (ICE) observed in many tokamaks. The theory of CAW and ICE was significantly advanced at the end of 20th century in particular motivated by first DT experiments on TFTR and subsequent JET DT experimental studies. More recently, ICE theory was advanced by ST (or spherical torus) experiments with the detailed theoretical and experimental studies of the properties of each instability signal. There the instability responsible for ICE signals previously indistinguishable in high aspect ratio tokamaks became the subjects of experimental studies. We discuss further the prospects of ICE theory and its applications for future burning plasma experiments such as the ITER tokamak-reactor prototype being build in France where neutrons and gamma rays escaping the plasma create extremely challenging conditions for fusion alpha particle diagnostics.

Let Students Discover an Important Physical Property of a Slinky

This paper describes a simple experiment that lets first-year physics and engineering students discover an important physical property of a Slinky. The restoring force for the fundamental oscillation frequency is provided only by those coils between the support and the Slinky center of mass.

Acoustic omni meta-atom for decoupled access to all octants of a wave parameter space.

The common behaviour of a wave is determined by wave parameters of its medium, which are generally associated with the characteristic oscillations of its corresponding elementary particles. In the context of metamaterials, the decoupled excitation of these fundamental oscillations would provide an ideal platform for top–down and reconfigurable access to the entire constitutive parameter space; however, this has remained as a conceivable problem that must be accomplished, after being pointed out by Pendry. Here by focusing on acoustic metamaterials, we achieve the decoupling of density ρ, modulus B−1 and bianisotropy ξ, by separating the paths of particle momentum to conform to the characteristic oscillations of each macroscopic wave parameter. Independent access to all octants of wave parameter space (ρ, B−1, ξ)=(+/−,+/−,+/−) is thus realized using a single platform that we call an omni meta-atom; as a building block that achieves top–down access to the target properties of metamaterials.

Experimental Study of the Global and Local Flame Responses to Acoustic Perturbation

In this study, the global and local flame responses to the acoustic perturbation were investigated to understand the thermoacoustic features of a low swirl flame. The effects of the Strouhal number and the acoustic perturbation level were examined. The global flame response was investigated with flame chemiluminescence. With the images captured with the planar laser-induced fluorescence of hydroxyl radicals method, the phase-averaged flame surface density was calculated to examine the flame dynamics and the local mean heat release oscillation. The results showed that the Strouhal number was useful in characterizing the flame responses: especially the oscillation amplitude. The flame showed a significant shape deformation when intense flame rollup happened; otherwise, the flame shape deformed weakly. The local analysis showed that large flame deformations caused strong local fundamental oscillations. However, the contribution of the local fundamental oscillation to the global fundamental fluctuation was affected by the local phase distribution, which was associated with the shape deformation characterized by the Strouhal number. The global first harmonic oscillation was generally much weaker than the global fundamental oscillation. The global first harmonic and fundamental oscillations only had comparable amplitudes when the intense local fundamental oscillations tended to cancel each other out.

Effect of pressure variation on acoustically perturbed swirling flames

The current study aims to experimentally examine the effect of pressure variation on lean premixed low swirl flames, which were perturbed acoustically with three frequencies (61Hz, 86Hz, and 115Hz). In the experiment, the hydroxyl (OH) chemiluminescence captured with a photomultiplier (PMT) indicated the global heat release. Furthermore, the phase-averaged flame surface density (FSD), which was calculated from the images of planar laser-induced fluorescence of the OH radical (OH-PLIF), was used to examine the local flame behavior. Global, local, and flame dynamics analyses were then used to investigate the flame oscillation. Results showed that when the perturbation level was sufficiently high, the fundamental oscillation tended to be amplified by the elevated pressure in the cases with perturbation frequencies of 61Hz and 115Hz. In contrast, in the cases with a frequency of 86Hz, the fundamental oscillation was inhibited when the chamber pressure was elevated to 0.3MPa. Analysis of flame dynamics and local flame response then showed that the effect of the pressure was affected by the phase delay between the pressure and the heat release oscillations. This was in turn dictated by the flame rollup process. Based on these analyses, it can be found that the general flame responses at different pressures showed similar trends when the perturbation frequency was the same. When the perturbation level and the pressure were sufficiently high, the fundamental mode oscillation was intensified by the elevated pressure when the heat release oscillation was in phase with the pressure fluctuation; otherwise, the fundamental oscillation tended to be inhibited. Moreover, both the strength and the distribution of the local heat release oscillations were affected by the elevated pressure.

Frequency-Sextupling Optoelectronic Oscillator Using a Mach–Zehnder Interferometer and an FBG

A frequency-sextupling dual-loop optoelectronic oscillator (OEO) without any electronic microwave filters is proposed and demonstrated. In the proposed OEO, a modulated signal that consists of an optical carrier and odd-order sidebands is generated using a Mach–Zehnder interferometer (MZI). The modulated signal is then divided into reflection components and transmission components by a fiber Bragg grating (FBG). The reflection components, including the optical carrier and the ±1st-order sidebands, are sent to a photodetector (PD1) and then fed back to the MZI to form the OEO loop. The transmission components, including the ±3rd-order sidebands, are sent to another PD (PD2) to generate a frequency-sextupled microwave signal. Meanwhile, a microwave photonic filter is formed by the joint operation of the MZI, the FBG, and an optical domain dual-loop composite cavity that performs the selection of the oscillation mode. As a result, a fundamental oscillation signal at 4.03 GHz and its frequency-sextupled microwave signal at 24.18 GHz are generated with their performance being evaluated.

Effects of Neutron-Star Dynamic Tides on Gravitational Waveforms within the Effective-One-Body Approach.

Extracting the unique information on ultradense nuclear matter from the gravitational waves emitted by merging neutron-star binaries requires robust theoretical models of the signal. We develop a novel effective-one-body waveform model that includes, for the first time, dynamic (instead of only adiabatic) tides of the neutron star as well as the merger signal for neutron-star-black-hole binaries. We demonstrate the importance of the dynamic tides by comparing our model against new numerical-relativity simulations of nonspinning neutron-star-black-hole binaries spanning more than 24 gravitational-wave cycles, and to other existing numerical simulations for double neutron-star systems. Furthermore, we derive an effective description that makes explicit the dependence of matter effects on two key parameters: tidal deformability and fundamental oscillation frequency.

Four-point function in the IOP matrix model

The IOP model is a quantum mechanical system of a large-N matrix oscillator and a fundamental oscillator, coupled through a quartic interaction. It was introduced previously as a toy model of the gauge dual of an AdS black hole, and captures a key property that at infinite N the two-point function decays to zero on long time scales. Motivated by recent work on quantum chaos, we sum all planar Feynman diagrams contributing to the four-point function. We find that the IOP model does not satisfy the more refined criteria of exponential growth of the out-of-time-order four-point function.

Analysis and Design of an E-Band Transformer-Coupled Low-Noise Quadrature VCO in 28-nm CMOS

This paper presents an E-band quadrature voltage-controlled oscillator implemented in 28-nm CMOS. Two fundamental oscillators are coupled by means of gate-to-drain transformers to realize accurate quadrature phases and switched coupled inductors are added for tuning extension. Closed-form expressions of the oscillation frequency and the tuning extension design parameters are derived. The time-variant nature of the circuit noise to phase noise (PN) of the presented topology is investigated, resulting in simple design guidelines for optimal design. Based on the proposed techniques, the realized prototype is tunable over two bands of almost 5 GHz each separated in frequency, while occupying only 0.031 $ {\hbox{mm}}^{2}$ . The peak measured PN at 10-MHz offset is $-{\hbox{117.7 dBc/Hz}}$ from a 72.7-GHz carrier and $-{\hbox{110 dBc/Hz}}$ from a 88.2-GHz carrier and varies less than 3.5 dB within each band.

Empirical formula of crustal torsional oscillations

Crustal torsional oscillations depend on not only crust properties but also the stellar mass and radius. Thus, one could extract stellar information by identifying the observed frequencies of stellar oscillations with the crustal torsional oscillations. Owing to the confinement of torsional oscillations inside the crust region of neutron stars, we successfully derive an empirical formula for the fundamental crustal torsional oscillations as a function of the stellar mass, radius, the so-called slope parameter of the nuclear symmetry energy, and the angular index of oscillations, with which one can estimate the frequencies with high accuracy. This empirical formula could be valuable in both the astrophysics and nuclear physics communities.

Coherent electron emission beyond Young-type interference from diatomic molecules

It has been known for more than 15 years that the differential cross section of electrons emitted from diatomic molecules during interaction with energetic charged particles oscillates as a function of electron momentum. The origin of the phenomenon is two-center interference, which naturally relates it back to the Young double-slit experiment. In addition to a characteristic frequency which can be described by lowest-order perturbation theories, the observation and origin of higher-order harmonics of the basic oscillation frequency has been much discussed. Here, we show that high harmonics of the fundamental Young-type oscillation frequency observed in electron spectra in fast ion-molecule collisions can be clearly exposed in numerical solutions of the time-dependent Schr\odinger equation within a one-dimensional model. Momentum distribution of the ejected electron is analyzed and shows that the phenomenon emerges when the charged particle beam collides with diatomic molecules with substantial large internuclear distance. Frequency spectra from nonperturbative calculations for electron emission from ${\text{Rb}}_{2}{}^{+}$ and ${\text{Cs}}_{2}{}^{+}$ exhibit a pronounced high-order oscillation in contrast to similar close-coupling calculations performed on ${\text{H}}_{2}$ targets. The electron emission from these heavy molecules contains second- and third-order harmonics which are fully reproduced in an analytic model based on the Born series. Extending to triatomic molecular targets displays an increased range of harmonics. This suggests that electron emission spectra from new experiments on heavy diatomic and linear polyatomic molecular targets may provide a unique insight into competing coherent emission mechanisms and their relative strength.

Numerical Simulations of Thermocapillary Flow of a Binary Mixture with the Soret Effect in a Shallow Annular Pool

In order to understand the characteristics of thermocapillary flow of a toluene/n-hexane mixture with the Soret effect in a shallow annular pool, a series of three-dimensional numerical simulations were carried out. The shallow annular pool was heated from the outer cylinder and cooled at the inner cylinder. The initial toluene concentration in the toluene/n-hexane mixture varied from 0 to 0.4467. Results indicate that the flow undergoes two transitions from the axisymmetric steady flow to the hydrothermal waves, and then to chaos with the increase of the thermocapillary Reynolds number. The critical thermocapillary Reynolds number for the incipience of the oscillatory flow decreases with the increase of the initial solute concentration. When the thermocapillary flow transits to a three-dimensional oscillatory flow, a concentration fluctuation is observed on the free surface, which is similar to the hydrothermal waves. However, compared with that of the temperature, the dimensionless fluctuation amplitude of the concentration is relatively weak. Furthermore, the fundamental oscillation frequency increases linearly with the initial solute concentration, but the wave number of the hydrothermal waves is almost unchangeable.

Five Approaches to Deal With Problem of DC Offset in Phase-Locked Loop Algorithms: Design Considerations and Performance Evaluations

The presence of the dc component in the phase-locked loop (PLL) input results in fundamental frequency oscillations in the phase and frequency estimated by the PLL. The removal of these oscillations is a challenging task because of their low frequency. The aim of this paper is to provide a detailed analysis of several approaches that little work has been conducted on their application for addressing the problem of dc offset in the PLL algorithms. These approaches include using the dq -frame delayed signal cancellation (DSC) operator and the notch filter (NF) as the PLL in-loop filtering stages, and using the $\alpha \beta$ -frame DSC operator, the complex coefficient filter, and a cross-feedback network for blocking the dc offset before the PLL input. Design aspects of these methods are presented, some methods to enhance their performances are proposed, and their advantages and disadvantages are evaluated.

A SiGe Terahertz Heterodyne Imaging Transmitter With 3.3 mW Radiated Power and Fully-Integrated Phase-Locked Loop

A high-power 320 GHz transmitter using 130 nm SiGe BiCMOS technology ( $f_{T}/f_{\max} =$ 220/280 GHz) is reported. This transmitter consists of a 4 × 4 array of radiators based on coupled harmonic oscillators. By incorporating a signal filter structure called return-path gap coupler into a differential self-feeding oscillator, the proposed 320 GHz radiator simultaneously maximizes the fundamental oscillation power, harmonic generation, as well as on-chip radiation. To facilitate the TX-RX synchronization of a future terahertz (THz) heterodyne imaging chipset, a fully-integrated phase-locked loop (PLL) is also implemented in the transmitter. Such on-chip phase-locking capability is the first demonstration for all THz radiators in silicon. In the far-field measurement, the total radiated power and EIRP of the chip is 3.3 mW and 22.5 dBm, respectively. The transmitter consumes 610 mW DC power, which leads to a DC-to-THz radiation efficiency of 0.54%. To the authors' best knowledge, this work presents the highest radiated power and DC-to-THz radiation efficiency in silicon-based THz radiating sources.