Uncorrelated Noise Sources Research Articles

(Invited) In-Depth Understanding of the Key Contributors to the Total Flicker Noise in Advanced Logic Devices

The aim of this work is to perform an in-depth analysis in order to identify the key contributors to the total flicker noise in advanced MOSFET technologies, e.g. UTBOX, FinFET or Gate-all-around (GAA) nanowire or nanosheet FET devices.In this abstract, as an example, we will focus on p-type gate all around silicon vertical nanowire devices fabricated at imec. The transistors have a fixed gate length (LG) of 50 nm and 1200 nanowires in parallel (N), each nanowire (NW) having a diameter (WNW) of 20 nm. The total width (W) of the device is calculated as . The gate stack corresponds to an equivalent oxide thickness (EOT) of 0.9 nm. A full description of the process flow of the devices is presented in [1]. Comparison between the Y-function strategy of [2] and McLarty methodology [3] permits to estimate with accuracy the DC parameters necessary for low frequency noise modelling, which are summarized in Table 1.Typical low frequency noise spectra are shown in Figure 1. The methodology for the estimation of the low frequency noise parameters is described in [4], but it is obvious that the noise spectra are dominated by 1/f noise and only few Lorentzian contributions appear for some gate voltage polarization. As the corresponding flicker noise levels (K f ), plotted in Figure 2 present a plateau and rise with the increase of the applied gate voltage, the responsible 1/f noise mechanism should be related to the carrier number or correlated carrier number fluctuations mechanism, with a possible contribution of the access resistance 1/f noise.Firstly, the model described in [5-9] expressed as in equation (1) is employed. A linear dependence of the square root of the 1/f noise levels on the measured Id/gm is observed in Figure 3, permitting to estimate from the intercept and slope the flat-band noise level (Svfb) and the W coefficient, respectively. Using the methodology of [9] the estimated W parameter is corrected by the access resistance influence. Good agreement with experimental data in strong inversion may be observed in both cases (Figure 4).Secondly, the model which considers the small signal model of the MOSFET is used, assuming that the channel resistance noise and access resistances noise are uncorrelated noise sources [2,10,11]. The model may be expressed by equation (2) ((13) of [11]), in order to make no assumption concerning the gm/gch ratio. Beyond the threshold voltage, the impact of the cannot be neglected, as observed from Figure 5. It may be observed from Figure 6 that the correlated number fluctuation and mobility noise mechanism cannot explain the flicker noise behavior in very strong inversion, and an additional contribution of the access resistances noise may be considered in order to agree with the experimental data.The noise parameters estimated to agree with the experimental data for both models are summarized in Table 2. It is interesting to note that the experimental data may be explained by both models, but the key contributors are not the same: only correlated number fluctuations and mobility noise mechanism for the first model, and correlated number fluctuations and mobility and access resistance noise mechanisms contribution for the second one. Moreover, the estimated flat-band noise levels are not the same, a much lower Svfb is obtained when the first model is employed. Considering the access resistance impact may correct the W coefficient, but leads to even lower flat-band noise levels, as already reported in [9].These results lead to some questioning about which of these two models is most accurate and give good indications on the key contributors and estimated parameters of the total flicker noise.

Finite-time correlations boost large voltage angle fluctuations in electric power grids

Decarbonization in the energy sector has been accompanied by an increased penetration of new renewable energy sources in electric power systems. Such sources differ from traditional productions in that, first, they induce larger, undispatchable fluctuations in power generation and second, they lack inertia. Recent measurements have indeed reported long, non-Gaussian tails in the distribution of local voltage frequency data. Large frequency deviations may induce grid instabilities, leading in worst-case scenarios to cascading failures and large-scale blackouts. In this article, we investigate how correlated noise disturbances, characterized by the cumulants of their distribution, propagate through meshed, high-voltage power grids. For a single source of fluctuations, we show that long noise correlation times boost non-Gaussian voltage angle fluctuations so that they propagate similarly to Gaussian fluctuations over the entire network. However, they vanish faster, over short distances if the noise fluctuates rapidly. We furthermore demonstrate that a Berry–Esseen theorem leads to the vanishing of non-Gaussianities as the number of uncorrelated noise sources increases. Our predictions are corroborated by numerical simulations on realistic models of power grids.

Peak-time sensitivity kernels for noise cross-correlation envelopes.

The envelope of the time-lagged cross-correlation of an underwater noise field between two hydrophones can under certain conditions be used as a proxy for active acoustic receptions between the two locations enabling the study of ocean variability. Previous work looked at the sensitivity of cross-correlation peak amplitudes with respect to the distribution of the noise sources. The present study examines the sensitivity of the cross-correlation envelope peak times with respect to changes in the sound-speed distribution. A wave-theoretic scheme allowing for finite-frequency calculations in two and three dimensions, combined with the Born approximation for perturbations of the Green's function and the peak arrival approach, is used to obtain sensitivity kernels with respect to environmental (sound-speed) changes. These kernels provide a way to infer ocean structure from the cross-correlation peaks, considered as observables on their own and valid even in cases where the cross-correlation function does not approximate the time-domain Green's function between the two receivers. The sensitivity behavior is studied for different propagation conditions and noise-source distributions, ranging from spatially distributed uncorrelated noise sources to point sources, such as individual ships. Deviations from linearity are addressed and discussed.

Peak-time sensitivity kernels for noise cross-correlation patterns

Sensitivity kernels for travel-time observables defined on the noise cross-correlation pattern – the envelope of the cross-correlation function of the underwater noise field between two locations – with respect to changes in the sound-speed field in refractive underwater environments will be addressed. A wave-theoretic scheme allowing for finite-frequency calculations in 2 and 3 dimensions combined with the Born approximation for perturbations of the Green’s function and the peak-arrival approach is used to obtain peak-time sensitivity kernels (PTSKs) with respect to environmental (sound-speed) changes. PTSK results for different propagation conditions and noise-source distributions, ranging from spatial distributions of uncorrelated noise sources to point sources such as individual ships, will be presented. The PTSKs can be a useful tool for obtaining environmental information from noise measurements. [Work supported by the Office of Naval Research.]

Semianalytical Modelling and 2D Numerical Simulation of Low-Frequency Noise in Advanced N-Channel FDSOI MOSFETs

Thorough investigations of the low-frequency noise (LFN) in a fully depleted silicon-on-insulator technology node have been accomplished, pointing out on the contribution of the buried oxide (BOX) and the Si-BOX interface to the total drain current noise level. A new analytical multilayer gate stack flat-band voltage fluctuation-based model has been established, and 2D numerical simulations have been carried out to identify the main noise sources and related parameters on which the LFN depends. The increase of the noise at strong inversion could be explained by the access resistance contribution to the 1/f noise. Therefore, considering uncorrelated noise sources in the channel and in the source/drain regions, the total low-frequency noise can simply be obtained by adding to the channel noise the contribution of the excess noise originating from the access region (Δr). Moreover, only two fit parameters are used in this work: the trap volumetric density in the BOX, and the 1/f access noise level originating from the access series resistance, which is assumed to be the same for the front and the back interfaces.

A spatial correlation model for broadband surface noise.

The spatial correlation function for broadband ocean surface noise is considered in horizontally stratified media. It is expressed as an integral over the correlation function of the sound field radiated by a single noise source in the waveguide, assuming spatially uncorrelated noise sources with the same intensity that are distributed on the sea surface uniformly. An equation for the spatial-temporal correlation coefficient of the surface noise in a certain frequency band can then be derived. Numerical simulations are carried out for band limited white noise and wind noise, which show that the fluctuation of the correlation coefficient decreases with increasing bandwidth.

An adapted eigenvalue-based filter for ocean ambient noise processing

Accurate approximations of Green’s functions retrieved from the correlations of ambient noise require a homogeneous distribution of random and uncorrelated noise sources. In the real world, the existence of highly coherent, strong directional noise generated by ships, earthquakes, and other human activities can result in biases in the ambient-noise crosscorrelations (NCCs). We have developed an adapted eigenvalue-based filter to attenuate the interference of strong directional sources. The filter is based on the statistical model of the sample covariance matrix and can separate different components of the data covariance matrix in the eigenvalue spectrum. To improve the effectiveness and make it adaptable for different data sets, a weight is introduced to the filter. Then, the NCCs can be calculated directly from the filtered data covariance matrix. This approach is applied to a 1.02 h data set of ambient noise recorded by a permanent reservoir monitoring receiver array installed on the seabed. The power spectral density indicates that the noise recordings were contaminated by strong directional noise over nearly half of the whole observation period. Beamforming and crosscorrelation results indicate that the interference still exists even after applying traditional temporal and spectral normalization techniques, whereas the adapted eigenvalue-based filter can significantly attenuate it and help to obtain improved crosscorrelations. The approach makes it possible to retrieve reliable approximations of Green’s functions over a much shorter recording time.

An empirical noise model for III-V compound semiconductor based HBT

This paper presents a novel approach for the modeling of noise behavior of III-V compound semiconductor based HBT’s over a wide frequency range. The main advantage is that the proposed model is based on two individual un-correlated noise sources, and easy to be incorporated with commercial circuit simulation software. The model is verified by measurements of the four noise parameters of an InP HBT up to 20 GHz and a GaAs HBT up to 26 GHz. The good agreements have been obtained.

Cross-correlation of shipping noise: Refraction and receiver-motion effects.

The spatial correlation of a diffuse isotropic noise field generated from a uniform distribution of uncorrelated noise sources contains information about the time-domain Green's function (TDGF) corresponding to propagation between the correlated locations. The distribution of noise in the ocean due to shipping-the prevailing origin of continuous low-frequency noise-is far from uniform. Besides the location of noise sources, the propagation conditions and the hydrophone locations have a significant influence on whether the TDGF can be reliably reconstructed through the cross-correlation procedure. A wave-theoretic scheme is implemented to simulate the cross-correlation function of a noise field in the time domain for arbitrary distributions of deterministic or random noise sources in refractive environments, and it is used to study the influence of propagation conditions and receiver motion on the efficiency of the cross-correlation procedure to obtain the TDGF from shipping noise.

Synchronous multi-color laser network with daily sub-femtosecond timing drift

Filming atoms in motion with sub-atomic spatiotemporal resolution is one of the distinguished scientific endeavors of our time. Newly emerging X-ray laser facilities are the most likely candidates to enable such a detailed gazing of atoms due to their angstrom-level radiation wavelength. To provide the necessary temporal resolution, numerous mode-locked lasers must be synchronized with ultra-high precision across kilometer-distances. Here, we demonstrate a metronome synchronizing a network of pulsed-lasers operating at different center wavelengths and different repetition rates over 4.7-km distance. The network achieves a record-low timing drift of 0.6 fs RMS measured with 2-Hz sampling over 40 h. Short-term stability measurements show an out-of-loop timing jitter of only 1.3 fs RMS integrated from 1 Hz to 1 MHz. To validate the network performance, we present a comprehensive noise analysis based on the feedback flow between the setup elements. Our analysis identifies nine uncorrelated noise sources, out of which the slave laser’s inherent jitter dominates with 1.26 fs RMS. This suggests that the timing precision of the network is not limited by the synchronization technique, and so could be much further improved by developing lasers with lower inherent noise.

Jitter analysis of timing-distribution and remote-laser synchronization systems.

We present a powerful jitter analysis method for timing-distribution and remote-laser synchronization systems based on feedback flow between setup elements. We synchronize two different mode-locked lasers in a master-slave configuration locally and remotely over a timing-stabilized fiber link network. Local synchronization reveals the inherent jitter of the slave laser as 2.1 fs RMS (>20 kHz), whereas remote synchronization exhibits an out-of-loop jitter of 8.55 fs RMS integrated for 1 Hz - 1 MHz. Our comprehensive feedback model yields excellent agreement with the experimental results and identifies seven uncorrelated noise sources, out of which the slave laser's jitter dominates with 8.19 fs RMS.

Analysis of the symmetry of the ambient noise and study of the noise reduction

Acoustic environment has a low signal-to-noise ratio (SNR); hence, array signal processing is widely used for noise reduction and signal enhancement. The actual ambient noise includes uncorrelated noise and correlated noise. The received noises of the two arbitrary array elements are correlated. Consequently, the performance of array signal processing method decreases obviously. Aiming at this problem, the real-part elimination of covariance matrix method is proposed. Firstly, from a physical point of view, the noise signals can be generated by using a number of uncorrelated noise sources: the more the noise sources, the less the error between the noise from the model and the actual noise will be. Theoretically, the noise field is decomposed into the symmetrical noise field and the asymmetrical noise field. A number of noise sources generate the symmetrical noise fields; the directions of these noise sources are symmetric, and the powers of two arbitrary symmetric sources are the same. Secondly, the symmetry of the ambient noise is analyzed, as a result, the symmetrical noise can only affect the real part of the covariance matrix. Thirdly, the real part of covariance matrix is eliminated in order to reduce the noise, and then the delay-and-sum beamforming is achieved by using only the imaginary part. The advantages are that the output signal-to-noise ratio is increased and the noise output power is reduced obviously; the disadvantage is that it produces a false target. The azimuth of the actual target differs from that of the false target by 180, and the false target cannot be distinguished. Finally, to eliminate the false target, the real part of the signal covariance matrix is reconstructed by establishing a constrained optimization problem, which is solved by using the particle swarm algorithm. Then, the reconstructed covariance matrix composed of the imaginary part and the reconstruction of real part is applied to delay-and-sum beamforming, as a result, the false target is eliminated. The simulation results show that the real-part elimination of covariance matrix method reduces the symmetrical ambient noise, the noise output power is reduced, the output signal-to-noise ratio is increased, and this method improves the performance of array signal processing. The experimental results show that the output SNRs of two targets with using the imaginary part of covariance matrix are increased by 3.57 dB and 3.149 dB, respectively, and the output SNRs of two targets with using the reconstructed covariance matrix are increased by 7.027 dB and 6.985 dB, respectively. The real-part elimination of covariance matrix method is easy to implemente, and has a definite value for engineering application.

Analysis of jet–airfoil interaction noise sources by using a microphone array technique

The paper is concerned with the characterization of jet noise sources and jet–airfoil interaction sources by using microphone array data. The measurements were carried-out in the anechoic open test section wind tunnel of Onera, Cepra19. The microphone array technique relies on the convected, Lighthill׳s and Ffowcs-Williams and Hawkings׳ acoustic analogy equation. The cross-spectrum of the source term of the analogy equation is sought. It is defined as the optimal solution to a minimal error equation using the measured microphone cross-spectra as reference. This inverse problem is ill-posed yet. A penalty term based on a localization operator is therefore added to improve the recovery of jet noise sources. The analysis of isolated jet noise data in subsonic regime shows the contribution of the conventional mixing noise source in the low frequency range, as expected, and of uniformly distributed, uncorrelated noise sources in the jet flow at higher frequencies. In underexpanded supersonic regime, a shock-associated noise source is clearly identified, too. An additional source is detected in the vicinity of the nozzle exit both in supersonic and subsonic regimes. In the presence of the airfoil, the distribution of the noise sources is deeply modified. In particular, a strong noise source is localized on the flap. For high Strouhal numbers, higher than about 2 (based on the jet mixing velocity and diameter), a significant contribution from the shear-layer near the flap is observed, too. Indications of acoustic reflections on the airfoil are also discerned.

Simultaneous localization of multiple broadband non-impulsive acoustic sources in an ocean waveguide using the array invariant.

The array invariant method, previously derived for instantaneous range and bearing estimation of a single broadband impulsive source in a horizontally stratified ocean waveguide, can be generalized to simultaneously localize multiple uncorrelated broadband noise sources that are not necessarily impulsive in the time domain by introducing temporal pulse compression and an image processing technique similar to the Radon transform. This can be done by estimating the range and bearing of broadband non-impulsive sources from measured beam-time migration lines of modal arrivals along a horizontal array arising from differences in modal group velocity and modal polar angle for each propagating mode. The generalized array invariant approach is used to estimate the range of a vertical source array and vocalizing humpback whales over wide areas from measurements made by a towed horizontal receiver array during the Gulf of Maine 2006 Experiment. The localization results are shown to have roughly 12% root-mean-squared errors from Global Positioning System measured ground truth positions for controlled source transmissions and less than 10% discrepancy from those obtained independently via moving array triangulation for vocalizing humpbacks, respectively.

Speech Intelligibility in Various Noise Conditions with the Nucleus® 5 CP810 Sound Processor.

The Nucleus® 5 System Sound Processor (CP810, Cochlear™, Macquarie University, NSW, Australia) contains two omnidirectional microphones. They can be configured as a fixed directional microphone combination (called Zoom) or as an adaptive beamformer (called Beam), which adjusts the directivity continuously to maximally reduce the interfering noise. Initial evaluation studies with the CP810 had compared performance and usability of the new processor in comparison with the Freedom™ Sound Processor (Cochlear™) for speech in quiet and noise for a subset of the processing options. This study compares the two processing options suggested to be used in noisy environments, Zoom and Beam, for various sound field conditions using a standardized speech in noise matrix test (Oldenburg sentences test). Nine German-speaking subjects who previously had been using the Freedom speech processor and subsequently were upgraded to the CP810 device participated in this series of additional evaluation tests. The speech reception threshold (SRT for 50% speech intelligibility in noise) was determined using sentences presented via loudspeaker at 65 dB SPL in front of the listener and noise presented either via the same loudspeaker (S0N0) or at 90 degrees at either the ear with the sound processor (S0NCI+) or the opposite unaided ear (S0NCI-). The fourth noise condition consisted of three uncorrelated noise sources placed at 90, 180 and 270 degrees. The noise level was adjusted through an adaptive procedure to yield a signal to noise ratio where 50% of the words in the sentences were correctly understood.In spatially separated speech and noise conditions both Zoom and Beam could improve the SRT significantly. For single noise sources, either ipsilateral or contralateral to the cochlear implant sound processor, average improvements with Beam of 12.9 and 7.9 dB in SRT were found. The average SRT of –8 dB for Beam in the diffuse noise condition (uncorrelated noise from both sides and back) is truly remarkable and comparable to the performance of normal hearing listeners in the same test environment. The static directivity (Zoom) option in the diffuse noise condition still provides a significant benefit of 5.9 dB in comparison with the standard omnidirectional microphone setting. These results indicate that CI recipients may improve their speech recognition in noisy environments significantly using these directional microphone-processing options.

Experimental study of passive defect localization in plates using ambient noise.

Passive listening methodology has been shown to be a practical and effective method for passive structural health monitoring. In this work, this approach is applied experimentally to monitor the occurrence of defects in thin aluminum plates. A correlation matrix is estimated from noise vibrations recorded on a transducer array. A defect is localized by applying a beamforming algorithm to the difference between the correlation matrices obtained with and without the defect. We successfully detect defects for different kinds of noise sources. Moreover, we show that this technique is robust to detect massive inclusions, holes, and cracks. With a vibrometer, we observe that the fidelity of the estimated transient responses strongly depends on the number of uncorrelated noise sources. Finally, we show that the defect is successfully localized even if the noise source distribution is not uniform, provided that it remains spatially stationary between the states with and without defect. A simple theoretical framework is proposed to interpret these results.

Novel Noise-Source-Identification Technique Combining Acoustic Modal Analysis and a Coherence-Based Noise-Source-Identification Method

A novel technique is presented, which combines the fields of coherence-based noise-source identification with acoustic modal analysis. Coherence-based noise-source-identification techniques apply the coherence function, estimated between pairs of dynamic pressure sensors, to identify the relative contributions of one or several noise sources to the total noise measured at a location of interest. Acoustic-modal-analysis techniques use arrays of microphones to decompose the pressure field at an axial location of a duct into constituent modal amplitudes. Conditional Spectral Analysis: Modal is the primary novel technique presented herein, and uses conditional spectral analysis to allow the beneficial capabilities of each of these well-regarded fields to be combined into one method. The technique allows the total modal pressure field measured in a duct to be decomposed into parts associated with contributing uncorrelated noise sources. The techniques’ efficacy is validated with a two noise-source-region experimental rig. A second novel technique is also presented: Signal Enhancement: Modal, which is in essence a modal version and enhancement of the now classic signal-enhancement technique, which allows the influence of extraneous noise to be removed from acoustic modal measurements. The modal signal enhancement was developed as part of the modal conditional spectral analysis, but can in fact be used independently in conditions in which only one correlated noise source is measured by the sensors in the duct. The modal-conditional-spectral-analysis technique represents a significant advancement in noise-source identification, and may be applied to a full-scale aeroengine to identify the specific contributions of core-noise sources within the engine to the amplitudes of the acoustic modes propagating through the engine exhaust. This added acoustic modal information can be used to predict the relative contribution of these noise sources to the total noise radiated from the engine and into the far field. Knowledge of the contributions of each core-noise-source contribution to the modal content propagating through the engine exhaust also allows for better mitigation through optimized liner designs and location.

Retrieving virtual reflection responses at drill-bit positions using seismic interferometry with drill-bit noise

In the field of seismic interferometry, researchers have retrieved surface waves and body waves by cross-correlating recordings of uncorrelated noise sources to extract useful subsurface information. The retrieved wavefields in most applications are between receivers. When the positions of the noise sources are known, inter-source interferometry can be applied to retrieve the wavefields between sources, thus turning sources into virtual receivers. Previous applications of this form of interferometry assume impulsive point sources or transient sources with similar signatures. We investigate the requirements of applying inter-source seismic interferometry using non-transient noise sources with known positions to retrieve reflection responses at those positions and show the results using synthetic drilling noise as source. We show that, if pilot signals (estimates of the drill-bit signals) are not available, it is required that the drill-bit signals are the same and that the phases of the virtual reflections at drill-bit positions can be retrieved by deconvolution interferometry or by cross-coherence interferometry. Further, for this case, classic interferometry by cross-correlation can be used if the source power spectrum can be estimated. If pilot signals are available, virtual reflection responses can be obtained by first using standard seismic-while-drilling processing techniques such as pilot cross-correlation and pilot deconvolution to remove the drill-bit signatures in the data and then applying cross-correlation interferometry. Therefore, provided that pilot signals are reliable, drill-bit data can be redatumed from surface to borehole depths using this inter-source interferometry approach without any velocity information of the medium, and we show that a well-positioned image below the borehole can be obtained using interferometrically redatumed reflection responses with just a simple velocity model. We discuss some of the practical hurdles that restrict the application of the proposed method offshore.

A Fully Nonlinear Compact Modeling Approach for High-Frequency Noise in Large-Signal Operated Microwave Electron Devices

A technology-independent, inherently nonlinear approach is proposed for the compact modelling of high-frequency noise in microwave transistors under large-signal operating conditions. For the compact nonlinear noise model formulation we assume that noise generation can be described by a suitable set of distributed stochastic processes perturbing a very general, non-quasi-static deterministic description of the electron device, in accordance with the strategies adopted in physics-based methods for the choice and exploitation of microscopic diffusion noise sources. The propagation of the internal distributed noise sources up to the intrinsic device terminals leads to a set of non-stationary, correlated equivalent noise generators, nonlinearly controlled by the instantaneous large-signal working point of the device. Starting from a first formulation for the generators, formally derived from a physics-based description of the noise generation mechanisms widely adopted in distributed numerical modeling, mild approximations provide a fully behavioral representation that can be empirically extracted on the basis of measurement data only, and can be easily implemented into commercial computer-aided design tools by means of conventional, uncorrelated noise sources. As far as small-signal (i.e., linear) bias-dependent operation is concerned, it is shown how well-known, widely applied compact models for high-frequency noise can be considered as linearized special cases of the proposed approach. For a full validation, experimental examples are provided, both in small- and large-signal operation, for a GaAs-pHEMT, by considering the case study of a broad-band low-noise amplifier progressively driven into nonlinear regime by an increasing power interferer.

Simultaneous localization of multiple vocalizing humpback whale calls in an ocean waveguide with a single horizontal array using the array invariant

The array invariant method, previously derived for instantaneous range and bearing estimation of a broadband impulsive source in a horizontally stratified ocean waveguide [Lee and Makris, J. Acoust. Soc. Am. 119, 336–351 (2006)], is generalized to instantaneously and simultaneously localize multiple uncorrelated broadband noise sources that not necessarily impulsive in the time domain. In an ideal Pekeris waveguide, we theoretically show that source range and bearing can be instantaneously obtained from beam-time migration lines measured with a horizontal array through range and bearing dependent differences that arise between modal group speeds along the array. We also show that this theory is approximately valid in a horizontally stratified ocean waveguide. A transform, similar to the Radon transform, is employed to enable simultaneous localization of multiple uncorrelated broadband noise sources without ambiguity using the array invariant method. The method is now applied to humpback whale vocalization data from the Gulf of Maine 2006 Experiment for humpback whale ranges up to tens of kilometers, where it is shown that accurate bearing and range estimation of multiple vocalizing humpback whales can be simultaneously made with little computational effort.