Saturation Amplitude Research Articles

Weakly nonlinear incompressible Kelvin–Helmholtz instability in plane geometry

A weakly nonlinear (WN) theoretical model for the two-dimensional incompressible Kelvin–Helmholtz instability (KHI) is proposed. Its solution form is the complete expansion in real space. The transition from linear to nonlinear growth is analytically studied via third-order solutions of plane KHI initiated by a single-mode surface perturbation. The difference between the WN growth of the Rayleigh–Taylor instability (RTI) in plane geometry and the WN growth of the KHI in plane geometry is discussed. It is found that there are resonance solutions in the higher harmonics of KHI but not in RTI. The vertex of spikes and bubbles is deflected because of the shearing effect in KHI compared with that in RTI. The spike velocity increases with the Atwood number before a particular time and then inversely after that time. There is no such reversal in RTI. However, the bubble velocity with the Atwood number of KHI has the same evolution rule as that of RTI. In addition to the influence of initial perturbation on the nonlinear saturation amplitude, the influence of Atwood number on the nonlinear saturation amplitude of the fundamental mode is obtained. Finally, compared with the numerical simulations, at the same initial conditions, the analytical solutions up to the third harmonics are well consistent with the simulated datum in the linear and weakly nonlinear stages for a widely varied Atwood number.

Modal Decomposition of the Precessing Vortex Core in a Hydro Turbine Model

We report on the experimental study of a precessing vortex core (PVC) in an air model of a Francis turbine. The focus is placed on the modal decomposition of the PVC that occurs in the draft tube of the model turbine for a range of operation conditions. The turbulent flow fluctuations in the draft tube are assessed using stereo particle image velocimetry (PIV) measurements. Proper orthogonal decomposition (POD) is applied to the antisymmetric and symmetric components of the velocity fields to distinguish the dynamics of the azimuthal instabilities. The pressure pulsations induced by the PVC are measured by four pressure sensors mounted on the wall of the hydro turbine draft tube. Spatial Fourier decomposition is applied to the signals of the pressure sensors to identify the contributions of azimuthal modes, m=1 and m=2, to the total pressure fluctuations. The analysis based on velocity and pressure data shows similar results regarding the identification of the PVC. The contribution of the m=2 mode to the overall turbulent kinetic energy is significant for the part load regimes, where the flow rates are twice as low as at the best efficiency point (BEP). It is also shown that this mode is not the higher harmonic of the PVC, suggesting that it is driven by a different instability. Finally, we show a linear fit of the saturation amplitudes of the m=1 and m=2 oscillations to determine the critical bifurcation points of these modes. This yields critical swirl numbers of Scr=0.47 and 0.61, respectively. The fact that the PVC dynamics in hydro turbines are driven by two individual instabilities is relevant for the development of tailored active flow control of the PVC.

The effect of hydrogen enrichment, flame-flame interaction, confinement, and asymmetry on the acoustic response of a model can combustor

To maximise power density practical gas turbine combustion systems have several injectors which can lead to complex interactions between flames. However, our knowledge about the effect of flame-flame interactions on the flame response, the essential element to predict the stability of a combustor, is still limited. The present study investigates the effect of hydrogen enrichment, flame-flame interaction, confinement, and asymmetries on the linear and non-linear acoustic response of three premixed flames in a simple can combustor. A parametric study of the linear response, characterised by the flame transfer function (FTF), is performed for swirling and non-swirling flames. Flame-flame interactions were achieved by changing the injector spacing and the level of hydrogen enrichment by power from 10 to 50%. It was found that the latter had the most significant effect on the flame response. Asymmetry effects were investigated by changing one of the flames by using a different bluff-body to alter both the flame shape and flow field. The global flame response showed that the asymmetric cases can be reconstructed using a superposition of the two symmetric cases where all three bluff-bodies and flames are the same. Overall, the linear response characterised by the flame transfer function (FTF) showed that the effect of increasing the level of hydrogen enrichment is more pronounced than the effect of the injector spacing. Increasing hydrogen enrichment results in more compact flames which minimises flame-flame interactions. More compact flames increase the cut-off frequency which can lead to self-excited modes at higher frequencies. Finally, the non-linear response was characterised by measuring the flame describing function (FDF) at a frequency close to a self-excited mode of the combustor for different injector spacings and levels of hydrogen enrichment. It is shown that increasing the hydrogen enrichment leads to higher saturation amplitude whereas the effect of injector spacing has a comparably smaller effect.

Non-linear excitation of low-frequency modes by overstable convective modes in rotating stars

ABSTRACT We discuss non-linear excitation and amplitude saturation of g-, r, and overstable convective (OsC) modes in early-type main sequence stars, taking account of the effects of three-mode couplings on amplitude evolutions. OsC modes are rotationally stabilized convective modes in the convective core and they resonantly excite low-frequency g-modes to obtain large amplitudes in the envelope when the rotation rate of the core is larger than critical rates. We use, for a network of three-mode couplings, amplitude equations governing the time evolution of the mode amplitudes where each of three-mode couplings is assumed to occur between two stable modes and one unstable mode. Assuming that the unstable modes in the couplings are OsC modes in the core and the stable modes are g- and r-modes in the envelope, we integrate the amplitude equations to see how the g- and r-modes are non-linearly excited by the OsC modes and whether or not the amplitude evolutions tend toward a state of finite amplitudes. We find that the non-linear three-mode couplings do excite low-frequency g- and r-modes but they are not necessarily effective to achieve amplitude saturation since the three-mode couplings between the OsC modes with large growth rates and g- and r-modes with small-damping rates tend to destabilize amplitude evolutions.

Harnessing rotational geometry to design reconfigurable dispersion and refractive index in nonlinear acoustic metamaterials

We investigate 1D and 2D monatomic lattice structures composed of in-plane rotators coupled by angled elastic linkages and explore their reconfigurable dispersion, negative refraction, amplitude-dependent dynamics, and acoustoelastic effect. At small amplitude, the linear band structure can be configured to be either acoustic or optical in nature by changing the connecting locations on the rotators, which corresponds to positive and negative refractive index. An interface problem between two rotator lattices with opposite dispersion type is modeled, and illustrates negative refraction in numerical simulations—experimental measurements are in progress. Its frequency–transmission relation matches the linear theory. At higher amplitude, the hardening nonlinearity shifts the dispersion and induces amplitude-dependent transmission. A novel nonlinear phenomenon–amplitude saturation (a constant far-field transmission independent of input amplitude) is observed when the transmitted wave falls in the nonlinear stopband and simultaneously the linear passband of the receiving lattice. We analyze the nonlinear effects via perturbation methods and propose a framework for evanescent-specific nonlinear waves to explain the saturation phenomenon. Additionally, we observe a strong acoustoelastic effect in chiral-patterned rotator lattices, where a static stretch can shift the equilibrium positions of the rotators and morph the band structure from acoustic to optical.

Generalized predictive control of the aircraft system with actuator saturation to prevent Pilot-induced Oscillations

Amplitude and rate saturations are one of the problems of flight control systems which puts the closed-loop system stability at risk. These nonlinear elements are mainly responsible for the type II pilot induces oscillations (PIOs). In this paper, a robust unconstrained generalized predictive controller (GPC) with a self-tuning regulator (STR) structure is designed in the frequency domain to prevent the type II PIOs. Furthermore, the sensitivity function is used for tuning the GPC parameters and investigating the stability and robustness of the system against the uncertainties of the controller parameters. To get better results, a constrained GPC is further designed considering the rate, amplitude, and both saturations. Rate and amplitude saturations are considered as input constraints in the design stage. Finally, the performances of the proposed controllers are compared to that of a PID controller.

Ultrafast vibrational excitation transfer on resonant antenna lattices revealed by two-dimensional infrared spectroscopy.

High-quality lattice resonances in arrays of infrared antennas operating in an open-cavity regime form polariton states by means of strong coupling to molecular vibrations. We studied polaritons formed by carbonyl stretching modes of (poly)methyl methacrylate on resonant antenna arrays using femtosecond 2DIR spectroscopy. At a normal incidence of excitation light, doubly degenerate antenna-lattice resonances (ALRs) form two polariton states: a lower polariton and an upper polariton. At an off-normal incidence geometry of 2DIR experiments, the ALR degeneracy is lifted and, consequently, the polariton energies are split. We spectrally resolved and tracked the time-dependent evolution of a cross-peak signal associated with the excitation of reservoir states and the unidirectional transfer of the excess energy to lower polaritons. Bi-exponential decay of the cross-peak suggests that a reversible energy exchange between the bright and dark lower polaritons occurs with a characteristic transfer time of ∼200fs. The cross-peak signal further decays within ∼800fs, which is consistent with the relaxation time of the carbonyl stretching vibration and with the dephasing time of the ALR. An increase in the excitation pulse intensity leads to saturation of the cross-peak amplitude and a modification of the relaxation dynamics. Using quantum-mechanical modeling, we found that the kinetic scheme that captures all the experimental observations implies that only the bright lower polariton accepts the energy from the reservoir, suggesting that transfer occurs via a mechanism involving dipole-dipole interaction. An efficient reservoir-to-polariton transfer can play an important role in developing novel room-temperature quantum optical devices in the mid-infrared wavelength region.

A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

An experimental proof of concept of a new semi-passive nonlinear piezoelectric shunt absorber, introduced theoretically in a companion article, is presented in this work. This absorber is obtained by connecting, through a piezoelectric transducer, an elastic structure to a resonant circuit that includes a quadratic nonlinearity. This nonlinearity is obtained by including in the circuit a voltage source proportional to the square of the voltage across the piezoelectric transducer, thanks to an analog multiplier circuit. Then, by tuning the electric resonance of the circuit to half the value of one of the resonances of the elastic structure, a two-to-one internal resonance is at hand. As a result, a strong energy transfer occurs from the mechanical mode to be attenuated to the electrical mode of the shunt, leading to two essential features: a nonlinear antiresonance in place of the mechanical resonance and an amplitude saturation. Namely, the amplitude of the elastic structure oscillations at the antiresonance becomes, above a given threshold, independent of the forcing level, contrary to a classical linear resonant shunt. This paper presents the experimental setup, the designed nonlinear shunt circuit and the main experimental results.

Comprehensive Quantitative and Calibration-Free Evaluation of Hyperpolarized Xenon–Host Interaction by Multiparametric NMR

The probing of microscopic environments by hyperpolarized xenon NMR has spurred investigations in supramolecular chemistry as well as important biosensing and molecular imaging applications. While xenon exchange with host structures at micromolar concentrations and below can be readily detected, a quantitative analysis is limited, requiring complementary experimentation by different methodologies and thus lacking completeness and compromising the validity and comparability of numerical results. Here, a new NMR measurement and data analysis approach is introduced for the comprehensive characterization of the host-xenon binding dynamics. The application of chemical exchange saturation transfer of hyperpolarized 129Xe under parametric modulation of the saturation RF amplitude and xenon gas saturation of the solution enables a delineation of exchange mechanisms and, through modeling, a numerical estimation of the various reaction rate constants (and thus magnetization exchange rate constants), the xenon affinity, and the total host molecule concentration. Only the numerical xenon solubility is additionally required for input, a quantity that has a low impact on the measurement uncertainty and is derivable from metrological data collections. Signal calibration by a reference material may thus be avoided, qualifying the method as calibration-free. For demonstration a xenon exchange with the host cucurbit[6]uril at low concentration is investigated, with the numerical results being validated by standard quantitative NMR data obtained at high concentration. The readiness to evaluate xenon exchange for the one sample at hand and in a single experimental attempt by the proposed method may allow comprehensive quantitative studies in supramolecular chemistry, biomacromolecular structure and dynamics, and sensing.

A nonlinear piezoelectric shunt absorber with a 2:1 internal resonance: Theory

In this paper, a semi-passive nonlinear piezoelectric shunt absorber is presented, aiming at attenuating the vibration of a resonant elastic structure under external excitation. This is done by connecting the elastic structure to a nonlinear shunt circuit via a piezoelectric patch. The nonlinear shunt circuit consists of resonant circuit that includes a quadratic non-linearity. A particular tuning of the natural frequency of the shunt enables to create a two to one internal resonance. This generates a strong coupling between the mechanical mode and the electrical mode, leading to replace the mechanical resonance with a nonlinear antiresonance associated with an amplitude saturation, thus leading to an efficient vibration reduction. In this paper, we first propose a theoretical model that is expanded onto a suitable electromechanical modal basis and reduced to the two modes of interest, nonlinearly coupled by quadratic terms. Then, analytical solutions are obtained by the multiple scale method and compared to a reference numerical solutions stemming from the harmonic balance method. This enables to investigate the performance of the system in term of vibration absorption as well as giving design rules to tune the nonlinear shunt and to choose the free parameters of the system.

Detecting head and neck lymph node metastases with white light reflectance spectroscopy; a pilot study

IntroductionA challenge in the treatment of patients with head and neck cancer is the management of occult cervical lymph node (LN) metastases. Single-fiber reflectance (SFR) spectroscopy has the potential to detect physiological tissue changes that occur in a positive LN. This pilot study aimed to investigate whether SFR spectroscopy could serve as an alternative or additional technique to detect cervical lymph node metastases. Materials and MethodsWe performed intraoperative SFR spectroscopy measurements of LNs with and without malignancies. We analyzed if physiological and scattering parameters were significantly altered in positive LNs. ResultsNine patients with a total of nineteen LNs were included. Three parameters, blood volume fraction (BVF), microvascular saturation (StO2), and Rayleigh amplitude, were significantly lower in positive LNs. They were combined into one optical parameter ‘delta’, using discriminant analysis. Delta was significantly decreased in positive LNs, p = 0,0006. It had a high diagnostic accuracy where the sensitivity, specificity, PPV, and NPV were 90,0%, 88.9%, 90,0%, and 88.9%, respectively. The area under the ROC curve was 96.7% (95% confidence interval 89.7–100.0%). ConclusionThis proof of principle study is a first step in the development of an SFR spectroscopy technique to detect LN metastases in real time. A next step towards this goal is replicating these results in LNs with smaller metastases and in a larger cohort of patients. This future study will combine SFR spectroscopy with fine-needle aspiration, using the same needle, to perform preoperative in vivo measurements.

Nonlinear intensity dependence of edge photocurrents in graphene induced by terahertz radiation

We report on the observation of terahertz radiation induced edge photogalvanic currents in graphene, which are nonlinear in intensity. The increase of the radiation intensities up to MW/cm$^2$ results in a complex nonlinear intensity dependence of the photocurrent. The nonlinearity is controlled by the back gate voltage, temperature and radiation frequency. A microscopic theory of the nonlinear edge photocurrent is developed. Comparison of the experimental data and theory demonstrates that the nonlinearity of the photocurrent is caused by the interplay of two mechanisms, i.e. by direct inter-band optical transitions and Drude-like absorption. Both photocurrents saturate at high intensities, but have different intensity dependencies and saturation intensities. The total photocurrent shows a complex sign-alternating intensity dependence. The functional behaviour of the saturation intensities and amplitudes of both kinds of photogalvanic currents depending on gate voltages, temperature, radiation frequency and polarization is in a good agreement with the developed theory.

Evolution of Switchbacks in the Inner Heliosphere

Abstract We analyze magnetic field data from the first six encounters of Parker Solar Probe, three Helios fast streams and two Ulysses south polar passes covering heliocentric distances 0.1 ≲ R ≲ 3 au. We use this data set to statistically determine the evolution of switchbacks of different periods and amplitudes with distance from the Sun. We compare the radial evolution of magnetic field variances with that of the mean square amplitudes of switchbacks, and quantify the radial evolution of the cumulative counts of switchbacks per kilometer. We find that the amplitudes of switchbacks decrease faster than the overall turbulent fluctuations, in a way consistent with the radial decrease of the mean magnetic field. This could be the result of a saturation of amplitudes and may be a signature of decay processes of large amplitude Alfvénic fluctuations in the solar wind. We find that the evolution of switchback occurrence in the solar wind is scale dependent: the fraction of longer-duration switchbacks increases with radial distance, whereas it decreases for shorter switchbacks. This implies that switchback dynamics is a complex process involving both decay and in situ generation in the inner heliosphere. We confirm that switchbacks can be generated by the expansion, although other types of switchbacks generated closer to the Sun cannot be ruled out.

Simulation of equilibrium and transport in advanced FRCS

The advanced beam-driven FRC is a field reversed configuration (FRC) with the addition of neutral beam (NB) injection, electrode biasing, and magnetic expander divertors. The resulting configuration has novel features that make it necessary to revisit many key results in FRC theory. Three of these features include (i) a large energetic ion population, (ii) in-principle capability to adjust the electric field and rotation profiles, and (iii) a combination of magnetic and electrostatic confinement of electrons in the SOL. In some fueling scenarios the electron density profile may exhibit a significant peak outside of the separatrix. To explore these features a hybrid fluid/kinetic equilibrium model has been used to reconstruct typical experimental profiles of the C-2W experiment. Results indicate that the energetic ions provide at least 50% of the total plasma pressure. These equilibrium profiles have been used as initial conditions for global, cross-separatrix, turbulent transport simulations using the 3D electrostatic particle-in-cell code ANC. Electrostatic fluctuations were found to nonlinearly saturate at an amplitude which is an order magnitude lower than that observed previously. The tokamak turbulence code GTC code has also been extended to handle FRC physics in the new GTC-X version, which has been used to perform simulations of turbulent transport in the SOL relevant to electrode biasing. It is found that equilibrium E × B flow shear significantly decreases ion temperature gradient saturation amplitude and ion heat transport. Also in the SOL, a 1D2V continuum code has been developed and applied to parallel electron heat transport. Results show the formation of pre-sheath potential and reduction of parallel electron heat loss close to the ideal ambipolar limit, a result which has been validated by experimental diagnostics. These transport modifications caused by the three novel configuration features help to explain the remarkable plasma performance of the C-2W experiment.

Antidisturbance Controllability Analysis and Enhanced Antidisturbance Controller Design With Application to Flexible Spacecraft

For a practical engineering system, disturbances usually have a negative impact on system performance. Especially, when the system physical constraints (e.g., actuator amplitude saturation and input channel constraint) are present, the study for antidisturbance controllability (ADC) is of paramount importance. This article presents the concepts of disturbance estimability, disturbance compensability, and an enhanced antidisturbance control (EADC). From the viewpoint of control system design, an example of spacecraft attitude control is given. The control constraints and multiple disturbances are explicitly analyzed for the sake of attitude control system design of flexible spacecraft. Subsequently, an EADC approach with integration of the disturbance observer-based control (DOBC) and active disturbance rejection control (ADRC) is proposed, based on the characteristics of disturbances exposed. Moreover, prescribed performance approach is incorporated into the spacecraft attitude tracking control. In consequence, the presented control can not only achieve superior antidisturbance capability than DOBC or ADRC, but also quantify the control performances. Numerical simulations and hardware-in-the-loop tests exemplify the applicability of the proposed scheme.

The semiannual oscillation (SAO) in the tropical middle atmosphere and its gravity wave driving in reanalyses and satellite observations

Abstract. Gravity waves play a significant role in driving the semiannual oscillation (SAO) of the zonal wind in the tropics. However, detailed knowledge of this forcing is missing, and direct estimates from global observations of gravity waves are sparse. For the period 2002–2018, we investigate the SAO in four different reanalyses: ERA-Interim, JRA-55, ERA-5, and MERRA-2. Comparison with the SPARC zonal wind climatology and quasi-geostrophic winds derived from Microwave Limb Sounder (MLS) and Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) satellite observations show that the reanalyses reproduce some basic features of the SAO. However, there are also large differences, depending on the model setup. Particularly, MERRA-2 seems to benefit from dedicated tuning of the gravity wave drag parameterization and assimilation of MLS observations. To study the interaction of gravity waves with the background wind, absolute values of gravity wave momentum fluxes and a proxy for absolute gravity wave drag derived from SABER satellite observations are compared with different wind data sets: the SPARC wind climatology; data sets combining ERA-Interim at low altitudes and MLS or SABER quasi-geostrophic winds at high altitudes; and data sets that combine ERA-Interim, SABER quasi-geostrophic winds, and direct wind observations by the TIMED Doppler Interferometer (TIDI). In the lower and middle mesosphere the SABER absolute gravity wave drag proxy correlates well with positive vertical gradients of the background wind, indicating that gravity waves contribute mainly to the driving of the SAO eastward wind phases and their downward propagation with time. At altitudes 75–85 km, the SABER absolute gravity wave drag proxy correlates better with absolute values of the background wind, suggesting a more direct forcing of the SAO winds by gravity wave amplitude saturation. Above about 80 km SABER gravity wave drag is mainly governed by tides rather than by the SAO. The reanalyses reproduce some basic features of the SAO gravity wave driving: all reanalyses show stronger gravity wave driving of the SAO eastward phase in the stratopause region. For the higher-top models ERA-5 and MERRA-2, this is also the case in the lower mesosphere. However, all reanalyses are limited by model-inherent damping in the upper model levels, leading to unrealistic features near the model top. Our analysis of the SABER and reanalysis gravity wave drag suggests that the magnitude of SAO gravity wave forcing is often too weak in the free-running general circulation models; therefore, a more realistic representation is needed.

Coarse-to-Fine(r) Automatic Familiar Face Recognition in the Human Brain.

At what level of spatial resolution can the human brain recognize a familiar face in a crowd of strangers? Does it depend on whether one approaches or rather moves back from the crowd? To answer these questions, 16 observers viewed different unsegmented images of unfamiliar faces alternating at 6Hz, with spatial frequency (SF) content progressively increasing (i.e., coarse-to-fine) or decreasing (fine-to-coarse) in different sequences. Variable natural images of celebrity faces every sixth stimulus generated an objective neural index of single-glanced automatic familiar face recognition (FFR) at 1Hz in participants' electroencephalogram (EEG). For blurry images increasing in spatial resolution, the neural FFR response over occipitotemporal regions emerged abruptly with additional cues at about 6.3-8.7cycles/head width, immediately reaching amplitude saturation. When the same images progressively decreased in resolution, the FFR response disappeared already below 12cycles/head width, thus providing no support for a predictive coding hypothesis. Overall, these observations indicate that rapid automatic recognition of heterogenous natural views of familiar faces is achieved from coarser visual inputs than generally thought, and support a coarse-to-fine FFR dynamics in the human brain.

Gravity Wave Packets in the Venusian Atmosphere Observed by Radio Occultation Experiments: Comparison With Saturation Theory

AbstractThe characteristics of gravity wave packets in the Venusian atmosphere were studied using high‐vertical‐resolution temperature profiles obtained by ESA's Venus Express and JAXA's Akatsuki radio occultation experiments with radio holographic methods. Localized disturbances were detected by applying a wavelet transform to the temperature profiles. The packet lengths were found to be distributed over 0.6–10 km, in which typically 1.5–4.0 oscillations are included. The number of oscillations per wave packet was found to have only a slight dependence on the wavelength, which is consistent with the −3 power law dependence of the spectral density on the wavenumber in the saturation model. The spectral densities of the wave packets are roughly aligned with the power law of the saturation model, while the saturation ratio for each quasi‐monochromatic wave is low. This suggests that the saturated spectrum is produced by the superposition of individually unsaturated quasi‐monochromatic waves. Waves with short vertical wavelengths (<1.5 km) were found to be more prevalent at lower altitudes than at higher altitudes, implying an effect of radiative damping during upward propagation. The amplitude was found to be larger at higher latitudes, which might be attributed to an increase in background static stability at high latitudes, which allows larger saturation amplitudes.

Fault‐tolerant control design for a class of nonlinear systems with actuator malfunctions

AbstractThis article presents a single‐hidden‐layer feedforward network (SLFN) aided fault‐tolerant control (FTC) scheme for a class of nonlinear systems subject to actuator faults. First, the upper bounds of the norms of the unknown functions, which cover information of actuator faults and amplitude saturation degrees, are deployed. The upper bounds are approximated by SLFNs with adaptive techniques. Subsequently, a sliding mode control approach is presented to allow for prompt corrective reactions, with explicit consideration of multivariable conditions and control input constraints. Finally, simulation results based on a nonlinear Boeing 747 aircraft model are presented to demonstrate the effectiveness of the proposed FTC scheme.

A 10-Gb/s Driver/Receiver ASIC and Optical Modules for Particle Physics Experiments

We present the design and test results of a Drivers and Limiting AmplifierS ASIC operating at 10 Gb/s (DLAS10) and three miniature optical transmitter/ receiver/transceiver modules (MTx+, MRx+, and MTRx+) based on DLAS10. DLAS10 can drive two transmitter optical subassemblies (TOSAs) of vertical cavity surface emitting lasers (VCSELs), receive the signals from two receiver optical subassemblies (ROSAs) that have no embedded limiting amplifiers (LAs), or drive a VCSEL TOSA and receive the signal from a ROSA, respectively. Each channel of DLAS10 consists of an input continuous time linear equalizer (CTLE), a four-stage LA, and an output driver. The LA amplifies the signals of variable levels to a saturation amplitude of 800 mV (peak-peak). The output driver drives VCSELs or impedance-controlled traces. DLAS10 is fabricated in a 65-nm CMOS technology. The die is 1 mm ×1 mm. DLAS10 is packaged in a 4 mm ×4 mm 24-pin quad-flat no-leads (QFNs) package. DLAS10 has been tested in MTx+, MRx+, and MTRx+ modules. Both measured optical and electrical eye diagrams pass the 10-Gb/s eye mask test. The input electrical sensitivity is 40 mVp-p, while the input optical sensitivity is -12 dBm. The total jitter of MRx+ is 29 ps (P-P) with a random jitter of 1.6 ps (rms) and a deterministic jitter of 9.9 ps. Each MTx+/MRx+ module consumes 82.6 and 174.4 mW/ch, respectively.