Small-signal Behavior Research Articles

Unified linear response theory of quantum electronic circuits

Modeling the electrical response of multi-level quantum systems at finite frequency has been typically performed in the context of two incomplete paradigms: (i) input-output theory, which is valid at any frequency but neglects dynamic losses, and (ii) semiclassical theory, which captures dynamic dissipation effects well but is only accurate at low frequencies. Here, we develop a unifying theory, valid for arbitrary frequencies, that captures both the small-signal quantum behavior and the non-unitary effects introduced by relaxation and dephasing. The theory allows a multi-level system to be described by a universal small-signal equivalent-circuit model, a resonant RLC circuit, whose topology only depends on the number of energy levels. We apply our model to a double-quantum-dot charge qubit and a Majorana qubit, showing the capability to continuously describe the systems from adiabatic to resonant and from coherent to incoherent, suggesting new and realistic experiments for improved quantum state readout. Our model will facilitate the design of hybrid quantum–classical circuits and the simulation of qubit control and quantum state readout.

Dynamic Patterns in the Small-Signal Behavior of Power Systems with Wind Power Generation

This paper investigates the dynamic patterns in the small-signal behavior of power systems with wind power generation. The interactions between synchronous generators and wind generators are investigated. In addition, the impact of increased wind generation penetration on the damping and frequency of the synchronous generator’s electromechanical oscillations is addressed. Wind generators of three different technologies are considered throughout this study. Very detailed dynamic models of wind generators are used and detailed.

Small signal and noise analysis of T-gate HEMT with polarization doped buffer for LNAs

Small signal behavior and RF noise performance of T-gate InAlN/GaN HEMT with polarization doped buffer (PDB-HEMT) have been examined in this paper and compared to conventional HEMTs at GHz frequency range. Enhancement mode operation is possible in the PDB-HEMT device, which has a recessed T-gate structure with a gate length of 10 nm and delivers the threshold voltage (Vth) of 0.9 V and a high transconductance of 1.55 S/mm. This study examines the auto/cross-correlation factor, minimum noise figure, reflection/transmission coefficients, noise conductance, and optimal noise resistance and reactance. The enhanced transconductance of PDB-HEMT has resulted in a considerable increase in the forward transmission coefficient and a decrease in the input/output reflection coefficient compared to traditional HEMTs. It has also been shown that the PDB- HEMT has a lower noise figure and noise conductance than the GaN buffer HEMT by 57% and 20%, respectively. This research demonstrates that the T-gate polarization doped buffer (PDB-HEMT) structure is an excellent choice for Low Noise Amplifiers (LNA) operating at higher frequencies.

A thermodynamically consistent lumped-element model for magnetic shape memory components

A novel lumped-element modeling approach for magnetic shape memory alloys is presented. Building on concepts borrowed from rate-independent plasticity, the model describes the magnetic and magneto-mechanical behavior of a magnetic shape memory component subjected to a particular load case in a thermodynamically consistent way. The approach remedies the common issues of existing models regarding the representation of inner hysteresis loops and small-signal behavior. The model is parametrized in terms of a small number of parameters, which can be determined from single variant magnetic curves and mechanical first order reversal curves at constant magnetic input. The results indicate that the model predicts the magnetic and magneto-mechanical behavior with sufficient accuracy, which makes it appropriate for system design.

Black-Box Large-Signal Average Modeling of DC-DC Converters Using NARX-ANNs

This paper investigates the use of non-linear autoregressive exogenous (NARX) artificial neural networks (ANNs) to achieve black-box average dynamic models of dc-dc converters capable of capturing the main converter non-linearities. Non-linearities may include, for example, dynamic behavior variations due to changes of operating point or operating mode (e.g., discontinuous conduction mode, continuous conduction mode). This paper presents design guidelines for determining the NARX-ANN architecture and the dataset to be used in the training process. Dataset definition includes the choice of the perturbations for stimulating the aimed system behaviors and optimizations for dataset size reduction. The proposed approach is first derived for a dc-dc boost converter. To verify the generality of the proposed method, the same methodology is also applied to a Ćuk converter. In both cases, the proposed NARX-ANN modeling provided accurate results, with only limited deviations observed in the time-domain responses to step variations of duty-cycle and output current. The proposed model provided accurate small-signal behavior under different operating conditions. The validity of the approach is evaluated experimentally by considering a boost converter prototype.

A Unified Modeling Approach to Tapped Inductor Converters Accounting for the Leakage Inductance Effects

This article suggests a unified modeling approach to the analysis of tapped-inductor converters. The leakage inductance, inherent to coupled magnetic structures, and the associated snubber circuit effects were considered and incorporated into the suggested model. The proposed nonideal tapped inductor switcher model is formulated as an equivalent subgraph that can help to model most, if not all, converter topologies that comprise a two-winding tapped inductor. Both the continuous current mode and the discontinuous current mode were modeled. To validate the proposed approach, analysis of a Flyback converter with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> snubber is presented. Theoretical prediction of the steady-state and small-signal behavior of the converters were confirmed by simulation and experimental results.

Stability Assessment of Modular Multilevel Converters Based on Linear Time-Periodic Theory: Time-Domain vs. Frequency-Domain

The periodic characteristic of modular multilevel converter (MMC), which originates from the multi-harmonic couplings among internal dynamics, results in challenges to develop the linear time-invariant (LTI) model of MMC. The linearization of MMC is inherently around time-periodic equilibrium trajectory. In this paper, two different methods to assess small-signal stability of MMC are compared. Both are based on the linear time-periodic (LTP) systems theory, but one is in the time domain (TD) and the other is in the frequency domain (FD). The LTP model of MMC is derived from the linearized arm averaged model. Then, an LTI model for the LTP system is constructed in the FD through the harmonic state-space method. Small-signal stability analysis based on Floquet theory and generalized Nyquist criterion, that accompany TD and FD, are introduced and compared. It is demonstrated that models developed in both domains can effectively capture the small-signal behavior of MMC. Third and higher-order harmonic components of the states have significant effect on the impedance-based stability analysis of MMC around mid-frequency range. Analytical results are validated by electromagnetic transient simulations based on the MMC aggregated model.

Behavioral-level modeling of GaN HEMT small-signal intrinsic noise based on DE-SVR algorithm

The Differential Evolution-Support Vector Regression (DE-SVR) algorithm is designed to model the small-signal intrinsic noise behavior of GaN HEMT. It not only overcomes the local minimization shortcoming of the Back Propagation (BP) algorithm, but also uses the DE (Differential Evolution) algorithm to obtain the best parameter c (punishment factor) and parameter g (variance of kernel function) of the Support Vector Regression (SVR) algorithm. In order to validate the superiority of the DE-SVR algorithm, the experiment compares the modeling effects of BP algorithm, SVR algorithm, and DE-SVR algorithm in modeling the small-signal intrinsic noise model of GaN HEMT. The experimental results show that there are obvious advantages for the DE-SVR algorithm in modeling the small-signal intrinsic noise characteristics of GaN HEMT.

A push-pull FVF based LDO voltage regulator with slew rate enhancement at the gate of power transistor

A low-dropout (LDO) voltage regulator based on a push-pull flipped voltage follower cell with slew rate improvement at the gate of power transistor is presented. The proposed three-stage regulator exploits two separate signal paths by cross-coupled common-gate cells to improve the transient response and loop stability with low power consumption. Moreover, a slew rate enhancement technique is employed at the gate of power transistor by adding a new current signal path which also improves the small-signal behavior. It is simulated in Cadence with a 90 nm CMOS process, 2.1 μW minimum power dissipation, and 150 mV dropout voltage for 0.9–1.2 V input voltage. It is stable over a range of 40 μA–100 mA load currents and 100 pF load capacitor. The achieved settling time is about 1.2 μs when the load current changes from 40 μA to 100 mA with 200 ns rise time. The obtained line and load regulations are 0.4 mV/V and 6 μV/mA, respectively.

Small-Signal Model of an Inductive Power Transfer System Using LCC–LCC Compensation

The LCC–LCC compensation is widely used in the inductive power transfer systems. However, there is no simple and accurate small-signal equivalent circuit model for this resonant converter. Based on the extended describing function method, this article proposed a full-order (17th-order) equivalent circuit model to accurately predict the small-signal behaviors. For simplification, the full-order model is gradually simplified to a ninth-order model and finally to a fifth-order model. The input to output transfer function are analytically derived for the first time. Both simulation and experimental results are presented to justify the effectiveness of the model, and the model is accurate up to one-fifth of the switching frequency.

Low-Cutoff Frequency Reduction in Neural Amplifiers: Analysis and Implementation in CMOS 65 nm.

Scaling down technology demotes the parameters of AC-coupled neural amplifiers, such as increasing the low-cutoff frequency due to the short-channel effects. To improve the low-cutoff frequency, one solution is to increase the feedback capacitors' value. This solution is not desirable, as the input capacitors have to be increased to maintain the same gain, which increases the area and decreases the input impedance of the neural amplifier. We analytically analyze the small-signal behavior of the neural amplifier and prove that the main reason for the increase of the low-cutoff frequency in advanced CMOS technologies is the reduction of the input resistance of the operational transconductance amplifier (OTA). We also show that the reduction of the input resistance of the OTA is due to the increase in the gate oxide leakage in the input transistors. In this paper, we explore this fact and propose two solutions to reduce the low-cutoff frequency without increasing the value of the feedback capacitor. The first solution is performed by only simulation and is called cross-coupled positive feedback that uses pseudoresistors to provide a negative resistance to increase the input resistance of the OTA. As an advantage, only standard CMOS transistors are used in this method. Simulation results show that a low-cutoff frequency of 1.5 Hz is achieved while the midband gain is 30.4 dB at 1 V. In addition, the power consumption is 0.6 μW. In the second method, we utilize thick-oxide MOS transistors in the input differential pair of the OTA. We designed and fabricated the second method in the 65 nm TSMC CMOS process. Measured results are obtained by in vitro recordings on slices of mouse brainstem. The measurement results show that the bandwidth is between 2 Hz and 5.6 kHz. The neural amplifier has 34.3 dB voltage gain in midband and consumes 3.63 μW at 1 V power supply. The measurement results show an input-referred noise of 6.1 μVrms and occupy 0.04 mm2 silicon area.

Direct observation of domain wall motion and lattice strain dynamics in ferroelectrics under high-power resonance

Domain wall motion and lattice strain dynamics of ferroelectrics at resonance were simultaneously measured by combining high-power burst excitation and in situ high-energy x-ray diffraction. The increased loss at high vibration velocity was directly related to the increased domain wall motion, driven by dynamic mechanical stress. A general relationship between the microstructural strain contributions and macroscopic electromechanical behavior was established, allowing the prediction of high-power stability of ferroelectric materials. The results indicate that the materials' stability during high-power drive is predominantly related to the basic chemical composition, while the piezoelectric hardening mechanisms mainly influence the small-signal behavior.

Large-Signal Equivalent Circuit for Datacom VCSELs

Increasing the baud rate in optical interconnects (OIs) will require the use of more sophisticated driver and receiver electronics. This will help overcome the stagnated bandwidth of the Vertical-Cavity Surface-Emitting Laser (VCSEL) and the pin-photodetector. Next generation OIs operating at single lane rates of 50+ Gbaud will therefore require careful co-optimization of the electronics and the optoelectronics. To facilitate this work there is a need of an accurate equivalent circuit for the optoelectronic components, functioning over a broad drive current and ambient temperature range. The VCSEL is the most important and complex to model due to its non-linear behavior and strongly varying characteristics with drive current and ambient temperature. For this purpose, a large-signal equivalent circuit dedicated for high-speed datacom VCSELs has been developed and is presented here. The distributed electrical parasitics in the device layout are carefully considered, the intrinsic speed limitation from carrier transport effects in the Separate-Confinement-Heterostructure (SCH) and the carrier-photon interaction in the Quantum Wells (QWs) are included, and self-heating effects in the device are monitored. The circuit is purposely based on physical instead of empirical models so that it can provide usable feedback to VCSEL designers. For circuit demonstration, it is implemented in Keysight's Advanced Design System (ADS) software and thereafter applied to replicate the performance of a state-of-the-art 28-GHz-bandwidth VCSEL at different temperatures and drive currents. Comparison is made between simulated and measured steady-state characteristics, small-signal behavior, and large-signal response under 28 Gbaud On-Off-Keying (OOK) and Pulse-Amplitude-Modulation 4 (PAM4) modulation, showing good agreement.

Comprehensive small-signal stability analysis of islanded synchronous generator-based microgrids

This paper presents a comprehensive small-signal stability analysis for synchronous generator (SG)-based microgrids (MGs) considering the control type of SGs and wide range of loading condition. The original aim is to evaluate the effect of loading conditions on the small-signal stability of droop-controlled and PQ-controlled SGs which has not been adequately addressed in the literature. To this purpose, complete state–space small-signal model of a typical medium voltage AC MG involving both droop-controlled and PQ-controlled SGs is developed. This facilitates stability studies by means of eigenvalue analysis. Results show that the small-signal stability behavior of droop-controlled SGs is different from that of PQ-controlled SGs. It is found that droop-controlled SGs show weaker stability or even instability in light loading condition. It is found that operation of PQ-controlled SGs in the presence of droop-controlled SGs can result in better stability of SG-based MG at light loading conditions. Effect of reference powers of PQ-controlled SGs on small-signal stability is also investigated. Moreover, the effect of Power System Stabilizer (PSS) on the damping of the weak stability or instability observed in low loading conditions of droop-controlled SG-based MGs is investigated. Time-domain simulations are used in order to verify the proposed theoretical analysis. • Droop and PQ-controlled synchronous generators (SGs) are modeled in state-space. • Stability of droop and PQ-controlled SGs is investigated in wide range of loadings. • Droop-controlled SGs show weaker stability or even instability in light loadings. • Operation of some SGs in PQ mode instead of droop results in better stability.

Linear Characterization and Modeling of GaN-on-Si HEMT Technologies with 100 nm and 60 nm Gate Lengths

Motivated by the growing interest towards low-cost, restriction-free MMIC processes suitable for multi-function, possibly space-qualified applications, this contribution reports the extraction of reliable linear models for two advanced GaN-on-Si HEMT technologies, namely OMMIC’s D01GH (100 nm gate length) and D006GH (60 nm gate length). This objective is pursued by means of both classical and more novel approaches. In particular, the latter include a nondestructive method for determining the extrinsic resistances and an optimizaion-based approach to extracting the remaining parasitic elements: these support standard DC and RF measurements in order to obtain a scalable, bias-dependent equivalent-circuit model capturing the small-signal behavior of the two processes. As to the noise model, this is extracted by applying the well known noise-temperature approach to noise figure measurements performed in two different frequency ranges: a lower band, where a standard Y-factor test bench is used, and an upper band, where a custom cold-source test bench is set up and described in great detail. At 5 V drain-source voltage, minimum noise figures as low as 1.5 dB and 1.1 dB at 40 GHz have been extracted for the considered 100 nm and 60 nm HEMTs, respectively: this testifies the maturity of both processes and the effectiveness of the gate length reduction. The characterization and modeling campaign, here presented for the first time, has been repeatedly validated by published designs, a couple of which are reviewed for the Reader’s convenience.

Dynamic Modeling and Eigen Analysis of Adjustable-Speed Pumped Storage Unit in Pumping Mode Under Power Regulation

The main merit of grid-connected adjustable-speed pumped storage unit (ASPSU) is the capability to control the pumping power flexibly, which contributes to active power balance in power system operation. Physics-based dynamic modeling of ASPSU in pumping mode under power regulation is the foundation of the quantitative analysis on its transient performance, which has been studied inadequately. This study aims to derive a dynamic model of ASPSU in pumping mode which embodies reversible pump-turbine characteristics, and to conduct eigen analysis on ASPSU in pumping mode which facilitates a better understanding of its intrinsic dynamics. Firstly, the dynamic model of reversible pump-turbine is revealed to depict its regulation properties that the pumping power is adjusted by rotational speed rather than guide vane opening. Then, the state-space representation of ASPSU in pumping mode is established to be utilized with small disturbances (including indicial and ramp tests) and validated by comparing simulated results with actual records of a commissioned ASPSU in Japan. It is also effective for compensating the wind power fluctuations based on a timescale of seconds in simulation. Finally, the eigenvalues, damping ratios, and participation factors of the state variables are investigated based on the small-signal-stability model of ASPSU in pumping mode under power regulation. The results of eigen analysis indicate that the small-signal behavior of the system is characterized by electromechanical mode and electromagnetic mode, and the latter is dominant. Moreover, the damping ratio of electromagnetic mode which is sensitive to system stability needs to be increased.

Design of Three-Stage OTA Based on Settling-Time Requirements Including Large and Small Signal Behavior

In this paper we are going to analyze the settling-time in single-, two- and three-stage amplifiers with the intent of deriving approximate but useful design equations that include the effects of the zeros and of the slew-rate limitations. The analysis is mainly devoted to the definition of an approach for the design of three-stage CMOS operational transconductance amplifiers from settling-time specifications. A design example is carried out to validate the proposed approach.

Error Performance of Information Decoder for SWIPT With Integrated Receiver

Simultaneous wireless information and power transfer can be realized by means of an integrated receiver, where both the energy harvester and the information decoder operate on the rectified received signal. We investigate the effect of the non-linearity of the rectifier on the error performance of the information decoder when transmitting over a Nakagami- m fading channel. Through analysis and simulation, we demonstrate that the low-noise error performance strongly depends on the small-signal behavior of the rectifier, even when the average operating point is outside the small-signal area. Approximating for analysis purposes the rectifier by a quadratic detector yields accurate bit error rate results for the fading channel in the low-noise regime, whereas an over-optimistic error performance is obtained when applying the envelope detector approximation.

Constrained Rigid Body Attitude Stabilization: An Anti-Windup Approach

This letter considers the rigid body attitude stabilization problem with actuator saturation. This problem has been considered in the literature before, but most approaches achieve stability at the expense of strict constraints on the control gains, thereby limiting small-signal performance. The approach proposed here removes the constraints on the gains of the nominal controller and instead deals with the control constraints through an anti-windup mechanism, effectively allowing for more freedom in small signal behavior whilst preserving stability in the large. Although the rigid body stabilization problem is inherently nonlinear, the spirit of the results developed here resemble constrained-control results for linear systems containing imaginary axis poles, despite some subtle differences which need careful consideration.

Origins of Soft-SwitchingCossLosses in SiC Power MOSFETs and Diodes for Resonant Converter Applications

The recent development and commercialization of wide bandgap (WBG) power semiconductors, specifically gallium nitride (GaN) and silicon carbide (SiC), have driven the increase in switching frequency for soft-switching power converters, such as the Class E, Class Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and Class DE resonant inverters and rectifiers. However, prior literature has characterized numerous commercial GaN and SiC devices using the Sawyer-Tower circuit and discovered significant large-signal C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> oss</sub> charge-voltage hysteresis. This C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> oss</sub> hysteresis, equivalent to OFF-state energy loss, is highly dependent on the frequency and voltage across the device, hindering the efficiency and performance of MHz-range soft-switched converters. This article is the first to explain the origin of the C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> oss</sub> loss in SiC power devices as charging and discharging conduction losses at the termination of the device. The loss characteristics relative to the operating voltage, frequency, dV/dt, and temperature are dictated by incomplete ionization. Incomplete ionization also highlights a significant inconsistency between the large-signal C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> oss</sub> behavior and small-signal behaviors, which is often the model used in manufacturers' datasheets and SPICE simulations. The large-signal charge-voltage behavior is transient, where the charge in C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> oss</sub> depends on the rate of the voltage swing across the device. We validate these hypotheses through mixed-mode simulations using the Sentaurus technology computer-aided design (TCAD) and experimentally using commercial and custom SiC devices.