Sideband Amplitude Research Articles

Micromagnetic Analysis of Nonlinear Dynamics in Spintronic Analog Modulators

The simultaneous action of dc and ac spin-polarized current traversing a magnetic nanocontact device results in a combined amplitude-frequency nonlinear modulation process, a promising application of spin-transfer oscillators. A micromagnetic analysis of the nonlinear magnetization dynamics occurring in such devices is carried out in both spatial and frequency domain. Numerical results show that the proposed combined modulation scheme affects the amplitude of the sidebands as well as their phase, and remark a substantial difference with respect to the properties exhibited by a classical linear modulator. Further investigations performed as function of the frequency of the modulating signal allow to establish that, when the modulating frequency approaches the carrier one, no modulation occurs and a frequency pulling, typical of injection locking phenomena, takes place instead.

Impact damage detection in composite laminates using nonlinear acoustics

The paper demonstrates the application of nonlinear acoustics for impact damage detection in composite laminates. A composite plate is monitored for damage resulting from a low-velocity impact. The plate is instrumented with bonded low-profile piezoceramic transducers. A high-frequency acoustic wave is introduced to one transducer and picked up by a different transducer. A low-frequency flexural modal excitation is introduced to the plate at the same time using an electromagnetic shaker. The damage induced by impact is exhibited in a power spectrum of the acoustic response by a pattern of sidebands around the main acoustic harmonic. The results show that the amplitude of sidebands is related to the severity of damage. The study investigates also the effect of boundary conditions on the results.

A modulation model for mode splitting of magnetic perturbations in the Mega Ampere Spherical Tokamak

Recent observations of magnetic fluctuation activity in the Mega Ampere Spherical Tokamak (MAST) reveal the presence of plasmas with bands of both low and high frequency magnetic fluctuations. Such plasmas exhibit a spectrum of low frequency modes with adjacent toroidal mode numbers, for which the measured frequency is near the Doppler shifted rotation frequency of the plasma. These are thought to be tearing modes. Also present are a spectrum of high frequency modes (e.g. Alfvén, fishbone and/or ICE). The frequency and mode number of the tearing mode and its harmonics is identical to the frequency and mode number splitting of the high frequency MHD activity, strongly suggesting that the high frequency splitting is produced by modulation of the high and low frequency modes. We describe a strong modulation model, in which the nonlinear terms are fitted to produce the amplitude envelope profile of the tearing mode. A bispectral analysis proves that the low frequency modes are indeed in phase with the fundamental, while Fourier-SVD mode analysis confirms the mode numbers are toroidal harmonics. Employing this model, the sideband amplitude profile of the high frequency modes is predicted, and found to be in good agreement with experimental observations. Also, toroidal mode number splitting of the high frequency activity matches the mode number of the tearing mode. Weak evidence is found to indicate the Alfvénic sidebands are in phase with the Alfvén eigenmode fundamental. The findings support predictions of a strong modulation model, and suggest a need to further develop nonlinear MHD theory to predict the amplitude of coupled sidebands, and so corroborate the observed nonlinear plasma response.

Unitary and singular value decompositions of parametric processes in fibers

Parametric (four-wave mixing) processes in fibers, driven by one or two strong pumps, couple the evolution of two weak sidebands. These processes are governed by the (spatial) evolution equations dzX=AX+BX†t and their associated input–output relations X(z)=M(z)X(0)+N(z)X†t(0), where X is the (sideband) amplitude vector, A and B are coefficient matrices, and M and N are transfer matrices. In principle, one can use unitary decompositions (UDs) to facilitate the mathematical analyses of evolution equations, or singular value decompositions (SVDs) to facilitate the physical interpretations of input–output relations (by diagonalizing them). In these notes, the SVD method is reviewed, and applied to studies of modulation interaction (MI), phase conjugation (PC) and Bragg scattering (BS). The UD method is also reviewed. It works for BS driven by continuous-wave (CW) or pulsed pumps. Although it works for MI and PC driven by CW pumps, it does not work for MI and PC driven by pulsed pumps (because the coefficient matrices are not simultaneously diagonalizable). Another decomposition method, based on eigenvectors of an extended coefficient matrix, and their adjoints, works for CW and pulsed pumps. Further work is required, to clarify the relation between the SVD and adjoint methods, and apply the latter method to processes of current interest.

Effects of low-frequency biasing on spontaneous otoacoustic emissions: amplitude modulation.

The dynamic effects of low-frequency biasing on spontaneous otoacoustic emissions (SOAEs) were studied in human subjects under various signal conditions. Results showed a combined suppression and modulation of the SOAE amplitudes at high bias tone levels. Ear-canal acoustic spectra demonstrated a reduction in SOAE amplitude and growths of sidebands while increasing the bias tone level. These effects varied depending on the relative strength of the bias tone to a particular SOAE. The SOAE magnitudes were suppressed when the cochlear partition was biased in both directions. This quasi-static modulation pattern showed a shape consistent with the first derivative of a sigmoid-shaped nonlinear function. In the time domain, the SOAE amplitudes were modulated with the instantaneous phase of the bias tone. For each biasing cycle, the SOAE envelope showed two peaks each corresponded to a zero crossing of the bias tone. The temporal modulation patterns varied systematically with the level and frequency of the bias tone. These dynamic behaviors of the SOAEs are consistent with the shifting of the operating point along the nonlinear transducer function of the cochlea. The results suggest that the nonlinearity in cochlear hair cell transduction may be involved in the generation of SOAEs.

Characterization of electromagnetically-induced-transparency-based continuous-variable quantum memories

We present a quantum multimodal treatment describing electromagnetically induced transparency (EIT) as a mechanism for storing continuous-variable quantum information in light fields. Taking into account the atomic noise and decoherences of realistic experiments, we numerically model the propagation, storage, and readout of signals contained in the sideband amplitude and phase quadratures of a light pulse using phase space methods. An analytical treatment of the effects predicted by this model is then presented. Finally, we use quantum information benchmarks to examine the properties of the EIT-based memory and show the parameters needed to operate beyond the quantum limit.

Application of nonlinear dynamics to monitoring progressive fatigue damage in human cortical bone

In this work, the results of applying nonlinear dynamics to study progressive material fatigue in human bone are described. Material nonlinear dynamical response has been shown to be associated with mechanical damage. The progressive mechanical damage experiments were conducted in cortical bone extracted from a human femur. After each damage step, the material dynamical nonlinear response was measured by applying wave modulation and extracting a nonlinear parameter proportional to the sideband amplitude. The nonlinear parameter increases rapidly with damage step, indicating increased damage after the initial cycling procedure, while the quasistatic stiffness taken from the cycling experiments shows little change.

Optical phase-based beamformer using MZM SSB modulation combined with crystal polarization optics and a spatial light modulator

The performance of a widely tunable phase-based beamformer for phased array antennas using a new technique to cross-polarized the carrier and the sideband, in order to allow the phase control by means of a spatial light modulator, is experimentally demonstrated. The technique relies on the combination of single sideband amplitude modulation (SSB) using a Mach–Zehnder modulator (MZM) and birefringence (to cross-polarized the carrier and the sideband). The architecture has the potential of controlling multiple independent beams simultaneously. The beamformer feeds an eight elements array showing an insertion loss and a reset speed of around 12dB and 70ms, respectively. Far-field antenna patterns between 7.5GHz and 8.5GHz for nine elevation angles within a range of ±20° have been measured showing beam steering capability, amplitude distribution weighting as well as multibeam operation.

Damage detection in an aircraft foam sandwich panel using nonlinear elastic wave spectroscopy

A novel damage detection technique, based on nonlinear elastic wave spectroscopy (NEWS) approach, is presented in this paper. This technique detects the presence of structural changes by monitoring the presence of harmonics and sidebands generated by the interaction between a low frequency and a high frequency harmonic excitation signal, due to the nonlinear material behaviour caused by the presence of damage. The proposed methodology was tested on a sandwich plate after being impacted by a foreign object under low velocity impact conditions. The high frequency signal was modulated in amplitude and the changes of the structural response, in terms of harmonic and sidebands amplitude, were recorded. The spectra and time frequency representation (TFR) were evaluated using wavelet transformations (WT). The experimental harmonic and sidebands amplitude resulted in close agreement with the theoretical behaviour of nonlinear behaviour of damaged materials. More specifically, the 3rd harmonics of the low frequency signal component showed a quadratic dependence with the low frequency response amplitude, as predicted by the theory for a hysteretic nonlinear material. Differently, the experimental second sidebands of the high frequency signal resulted bounded by curves representing the second sideband behaviour for pure hysteretic material (lower bound) and classical nonlinear material (upper bound). In particular, for small low frequency response amplitudes, the experimental second sidebands tended to be closer to the classical nonlinear material curve, while for the largest amplitudes investigated the response resembled a hysteretic material behaviour. The results showed that the proposed methodology was capable of detecting successfully the presence of impact damage and can be used as a first assessment of the presence of damage in aircraft structures where the presence of damage should be quickly estimated.

Sideband control of optical bistability and multistability

We present sideband control of optical bistability and multistability based on trichromatic electromagnetic-field induced transparency and quantum interference. Appearance or disappearance of the bistability and multistability, manipulation of the hysteresis loop widths, and switching between bistability and tristability are achieved simply by varying the sideband amplitudes or the relative phases of the sidebands to the central component.

Observations on the evolution of wave modulation

A series of laboratory experiments on the long-time evolution of nonlinear wave trains in deep water was carried out in a super wave flume (300×5.0×5.2 m) at Tainan Hydraulics Laboratory of National Cheng Kung University. Two typical wave trains, namely uniform wave and imposed sideband wave, were generated by a piston-type wavemaker. Detailed discussions on the evolution of modulated wave trains, such as transient wavefront, fastest growth mode and initial wave steepness effect, are given and the results are compared with existing experimental data and theoretical predictions. Present results on the evolution of initial uniform wave trains cover a wide range of initial wave steepness ( ) and thus, greatly extend earlier studies that are confined only to the larger initial wave steepness region ( ). The amplitudes of the fastest growth sidebands exhibit a symmetric exponential growth until the onset of wave breaking. At a further stage, the amplitude of lower sideband becomes larger than the carrier wave and upper sideband after wave breaking, which is known as the frequency downshift. The investigations on the evolution of initial imposed sideband wave trains for fixed initial wave steepness but different sideband space indicate that the most unstable mode of initial wave train will manifest itself during evolution through a multiple downshift of wave spectrum for the wave train with the smaller sideband space. It reveals that the spectrum energy tends to shift to a lower frequency as the wave train propagates downstream due to the sideband instability. Experiments on initial imposed sideband wave trains with varied initial wave steepness illustrate that the evolution of the wave train is a periodic modulation and demodulation at post-breaking stages, in which most of the energy of the wave train is transferred cyclically between the carrier wave and two imposed sidebands. Meanwhile, the wave spectra show both temporal and permanent frequency downshift for different initial wave steepness, suggesting that the permanent frequency downshift induced by wave breaking observed by earlier researchers is not permanent. Additionally, the local wave steepness and the ratio of horizontal particle velocity to linear phase velocity at wave breaking in modulated wave group are very different from those of Stokes theory.

Accurate velocity measurements of AFM-cantilever vibrations by Doppler interferometry

Doppler velocimetry is widely used in the measurement of nanometre resonance vibrations of micro-electromechanical systems (MEMS). It has excellent sensitivity and precision, but typical engineering applications do not require traceability of these velocity measurements to the SI system. While Doppler velocimetry is, in principle, easy to make traceable to the velocity of light, in practice a frequency-to-voltage conversion in common commercial instruments breaks this traceability unless calibrated. Typically, though, calibration is performed at a much lower frequency than those typical of MEMS devices, without the guarantee that the calibration is applicable in this higher frequency regime. We present a method of traceable measurement of velocity in terms of the velocity of light, valid for the range of frequency and nanometre amplitudes typical of MEMS devices driven to resonance vibration. This is achieved by analysis of sideband amplitudes in the interference spectrum before demodulation of the Doppler signal. These sideband amplitudes can conveniently be measured using a benchtop spectrum analyser, a piece of widely available electrical test equipment. We illustrate the method with measurements on individual AFM cantilevers. In combination with cantilever calibration methods based on MEMS devices this method enables traceable calibration of those cantilevers employed for the measurement of pico- and nanonewton forces between individual biomolecules.

A generalized nonlinear Schrödinger equation and optical soliton in a gradient index cylindrical media

A generalized form of nonlinear Schrodinger equation is deduced for the propagation of an optical pulse in a fiber with a cylindrical geometry having a gradient in refractive index in the radial direction. The configuration gives a simple model for a fiber with a cladding or multicore fiber. To begin with we have analyzed in detail the modulational instability in terms of Stokes and anti-Stokes side band amplitudes which shows a significant change with respect to the depth parameter L and dispersion constant. Next we have deduced the equations governing the modulation of parameters of a Gaussian pulse as it propagates through it. The moment method is used for the derivation. The gradient of the refractive index leads to the trapping of the pulse, whereas the balance between nonlinearity (Kerr type) and dispersion in the longitudinal direction guides the propagation. Instead of a constant dispersion profile we have considered the standard dispersion map which helps in shaping of the pulse. The numerical simulation of these derived equations shows how the chirp, width, amplitude of the pulse change with type of gradient and the distance travelled.

Vibration Monitoring for Local Tooth Damage in Multistage Gearboxes

An adaptive approach was applied for local tooth damage diagnostics in gearboxes. The expediency of adaptation was proved experimentally for the new diagnostic feature, the sum of normalized sideband amplitudes. The positive correlation between mesh amplitudes and their sideband amplitudes was found experimentally for the first time. Novel adaptive vibration condition monitoring technology for local tooth damage in gearboxes was developed and experimentally validated. The experimental results showed an increase in effectiveness of the diagnostics when the adaptive technology was used.

Adaptive vibration condition monitoring technology for local tooth damage in gearboxes

An adaptive approach was applied for local tooth damage diagnostics in gearboxes. The expediency of adaptation was proved experimentally for the new diagnostic feature, the sum of normalised sideband amplitudes. The positive correlation between mesh amplitudes and their sideband amplitudes was found experimentally for the first time. Novel adaptive vibration condition monitoring technology for local tooth damage in gearboxes was developed and experimentally validated. The experimental results showed an increase in effectiveness of the diagnostics when the adaptive technology was used.

Sidebands to the lower kilohertz quasi-periodic oscillation in 4U 1636-53

In this paper we report on further observations of the third and fourth kilohertz quasi-periodic oscillations (QPOs) in the power spectrum of the low-mass X-ray binary (LMXB) 4U 1636-53. These kilohertz QPOs are sidebands to the lower kilohertz QPO. The upper sideband has a frequency 55.5 +/- 1.7Hz larger than that of the contemporaneously measured lower kilohertz QPO. Such a sideband has now been measured at a significance >6sigma in the power spectra of three neutron-star LMXBs (4U 1636-53, 1728-34 and 1608-52). We also confirm the presence of a sideband at a frequency ~55Hz less than the frequency of the lower kilohertz QPO. The lower sideband is detected at a 3.5sigma level only when the lower kilohertz QPO frequency is between 800 and 850Hz. In that frequency interval, the sidebands are consistent with being symmetric around the lower kilohertz QPO frequency. The upper limit to the rms amplitude of the lower sideband is significantly lower than that of the upper sideband for lower kilohertz QPO frequencies >850Hz. Symmetric sidebands are unique to 4U 1636-53. This might be explained by the fact that lower kilohertz QPO frequencies as high as 800-850Hz are rare for 4U 1728-34 and 1608-52. Finally, we also measured a low-frequency QPO at a frequency of ~43Hz when the lower kilohertz QPO frequency is between 700 and 850Hz. A similar low-frequency QPO is present in the power spectra of the other two systems for which a sideband has been observed. We briefly discuss the possibility that the sideband is caused by Lense-Thirring precession.

The influence of transistor nonlinearities on noise properties

A nonlinear field-effect transistor equivalent-circuit model is examined to identify the fundamental mechanisms that up-convert baseband 1/f noise to near-carrier sideband noise when the device is operated in the large-signal regime. This model captures all physical noise sources and nonlinearities in the transistor, and thereby allows a general cause-and-effect treatment. The noise sources in the equivalent-circuit model are determined using low-frequency spectrum analyzer and microwave noise-figure meter data. Using the example of an AlGaN/GaN high electron-mobility transistor, the developed model correctly describes both the measured near-carrier sideband amplitude and phase noise simultaneously.

Frequency modulation of spin-transfer oscillators

Spin-polarized dc electric current flowing into a magnetic layer can induce precession of the magnetization at a frequency that depends on current. We show that addition of an ac current to this dc bias current results in a frequency modulated (FM) spectral output, generating sidebands spaced at the modulation frequency. The sideband amplitudes and shift of the center frequency with drive amplitude are in good agreement with a nonlinear FM model that takes into account the nonlinear frequency-current relation generally induced by spin transfer. Single-domain simulations show that ac current modulates the cone angle of the magnetization precession, in turn modulating the frequency via the demagnetizing field. These results are promising for communications and signal processing applications of spin-transfer oscillators.

Improving the Signal Data Acquisition in Condition Monitoring of Electrical Machines

The occurrence of a broken bar in induction machines causes an internal magnetic imbalance, which is reflected in the stator current. This effect may be detected by estimating the spectral signature of the stator current, particularly the sidebands around the fundamental frequency. However, the fundamental 60-Hz amplitude is considerably greater than the sideband amplitude, which usually requires an analog 60-Hz notch filter in the data acquisition system. Analog filters are sensitive to temperature variations, which, in this case, may shift the filter resonance frequency and degrade the desired response. It is proposed in this paper that the analog notch filter may be replaced by a digital/analog cancelling technique based on the recursive discrete-time Fourier transform. The technique is shown to attenuate the fundamental 60-Hz amplitude considerably before A/D conversion, leaving only the sidebands in the current signal.

Single sideband modulator, a key component of Tore-Supra heterodyne reflectometers

Although single sideband modulation offers a simple solution to active heterodyne devices and is common in devices working over 150 GHz, it has been scarcely used for reflectometers. For a few years, large bandwidth (12–20 GHz), high performance single sideband modulators (SSBM) have been available. For higher frequency application, a sideband rejection around −25 dBc seems necessary to ensure that the image sideband amplitude remains low after a frequency multiplier. A SSBM provided by Miteq Company presents high enough rejection levels to be assembled with frequency multipliers. Based on this SSBM, we developed a simple microwave scheme suitable for all Tore-Supra reflectometers—from 50 to 155 GHz, dedicated either to density profile reconstruction or to density fluctuation measurements. Compared to the double sideband modulator previously used, SSBM offers higher signal to noise ratio and enables fixed frequency measurements, paving the way for new measurement techniques.