Finite Gain Research Articles

The statistics of electron–hole avalanches

Charge multiplication through avalanche processes is commonly employed in the detection of single photons or charged particles in high-energy physics and beyond. In this report, we provide a detailed discussion of the properties of avalanches driven by two species of charge carriers, e.g. electrons and holes in a semiconductor exposed to an electric field. We derive equations that describe the general case of avalanches developing in position-dependent electric fields and give their analytical solutions for constant fields. We discuss consequences for the time resolution achievable with detectors that operate above the breakdown limit, e.g. single-photon avalanche diodes (SPADs) and silicon photomultipliers (SiPMs). Our results also describe avalanches that achieve finite gain and are important for avalanche photodiodes (APDs) and low-gain avalanche detectors (LGADs).

Post-acceleration of electron bunches from laser-irradiated nanoclusters

In this paper the energy gain of attosecond electron bunches emitted during the interaction of intense, few-cycle linearly polarized lasers with nanoscale spherical clusters is determined. In this case electron bunches are emitted from the rear side of the cluster and are then further accelerated while co-propagating with the laser. A previous study has shown how this two-stage process readily occurs for clusters whose radii lie between the relativistic skin depth, δ r = γ 1/2 c/ω p , and the laser spot size σ L (Di Lucchio & Gibbon, Phys. Rev. STAB 18, 2015). An analytical model for focused light waves interacting with compact, overdense electron bunches in vacuum is derived heuristically from world-line equations of motion of an electron. The functional integral approach is followed under the mathematical point of view of integration with respect to a stochastic variable. The resulting picture of the laser wave crossing the electron’s trajectory leads to a finite energy gain of the electron in light–matter interaction in vacuum. The analytical theory is compared with three-dimensional PIC simulations from which trajectories of the electron bunches can be extracted. The effective increase in bunch energy is determined under realistic conditions both for the peak (mode) and the cutoff energy of the emitted bunch, in order to make quantitative comparisons with theory and the experimental findings of Cardenas et al , Nature Sci. Reports 9 (2019).

Deterministic Digital Calibration Technique for 1.5 bits/stage Pipelined and Algorithmic ADCs with Finite op-amp Gain and Large Capacitance Mismatches

This paper proposes a high-speed deterministic digital technique to calibrate the errors due to capacitance mismatch and finite op-amp gain. Unlike other calibration techniques, this technique requires neither forcing the inputs of the intermediate stages being calibrated to exact voltages, nor reducing the gains of each stage to avoid saturation of output digital codes. A 1.5 bits/stage, 10 stages, 9 bits pipeline ADC with the three most significant stages calibrated is demonstrated in this paper. For a 10% mismatch in capacitances in the 3 MSB stages of the pipelined ADC, the calibration technique improved SNDR by more than 20 dB and SFDR by around 27 dB. The technique can also be slightly modified to calibrate algorithmic ADCs. For a 7% mismatch in capacitances of the algorithmic ADC, the proposed calibration technique improved SNDR by 18 dB and SFDR by around 28 dB.

Feedback–feedforward control for high-speed trajectory tracking of an amplified piezoelectric actuator

Piezoelectric actuators (PAs) are increasingly used in industrial and research applications requiring high speed and accurate positioning at the micro and nano scales such as atomic force microscopy. This is due to their high positioning resolution, compactness, and fast response. There are, however, two main factors that significantly limit their performance, namely hysteresis and the structural resonance. To overcome these limitations, while avoiding using inversion-based feedforward compensators, we propose, a new learning controller for high speed amplified PA (APA) trajectory tracking. To further enhance the robustness of the APA against sensor noise and other disturbances, a simple proportional and integral (PI) controller is added in the feedback loop. The proposed feedback–feedforward controller compensates for the above-mentioned phenomena without requiring access to the ‘complex’ mathematical model of the APA. Using the notions of system passivity and finite gain stability, we show that the closed-loop system is stable, and the tracking error is bounded for continuous reference inputs. These results are experimentally confirmed using a sinusoidal reference input with varying frequencies. The controller is able to track reference signals with frequencies up to 500 Hz (very close to the resonance frequency of the APA) with relatively small tracking errors. To further assess the quality of the proposed controller, we compare its tracking performance against a previously proposed controller. We show that our controller consistently achieves smaller tracking errors and the performance gap between the two controllers increases with an increase in frequency. We finally show the advantage of using the feedforward learning controller by comparing the tracking performance of our feedforward–feedback controller against that of the PI. The results show a clear performance improvement and that this improvement becomes even more evident at higher frequencies.

Nonlinear error analysis and calibration model for cyclic ADCs in large array CMOS image sensors

A mathematical model is established to study the impact of nonlinear errors on the performance of cyclic analog-to-digital converters (ADCs) and imaging quality of CMOS image sensors (CIS). And a radix-based foreground digital calibration method for cyclic ADCs in large array CIS is proposed and modeled. The nonlinear errors caused by capacitor mismatch and finite operational amplifier (OPAMP) gain are mainly studied. Simulation results show that the proposed calibration method based on the statistical characteristics of large array CIS can effectively reduce the influence of nonlinear errors, greatly improve ADC linearity under large capacitor mismatch and finite OPAMP gain. In a CIS with 1500 columns of parallel ADCs, when the capacitor mismatch and OPAMP gain are 1% and 40 dB respectively, the effective number of bits (ENOB) of the calibrated ADC can be increased from about 6bit to 13bit. These results provide a new guideline for the calibration of cyclic ADCs in large array CMOS image sensors.

Exponential quasi-dissipativity and boundedness property for switched nonlinear systems

This paper is concerned with exponential quasi-dissipativity for switched nonlinear systems using multiple storage functions and multiple supply rates. First, a new concept of exponential quasi-dissipativity for a switched nonlinear system is proposed. In contrast with dissipative system which does not produce energy in some abstract sense, the supply rate of quasi-dissipativity is the sum of the conventional dissipativity supply rate and the constant supply rate. This means quasi-dissipative system can produce energy by itself. Each active subsystem is only required to be exponentially quasi-dissipative, while the energy changing of each inactive subsystem characterized by cross-supply rates is considered as the transformation of “energy” from the active subsystem. By weakening the conventional dissipation inequality, a broader class of open-loop systems and controllers are admissible, leading to broader application. Second, the ultimate boundedness property is obtained under some constraints on the energy changing of inactive subsystems. Third, the exponential quasi-dissipativity conditions for switched nonlinear systems are obtained by the design of a state-dependent switching law. In particular, the sufficient conditions of exponential quasi-passivity and exponential finite power gain for switched nonlinear systems are given thereby providing generalizations of KYP conditions and HJI inequality. Finally, the effectiveness of the obtained results is verified by two examples.

On the use of low-pass filters in high-gain observers

To address the well-known noise sensitivity problems associated with high-gain observers, we insert a low-pass filter on the measurement channel. Considering nonlinear plants in observability canonical form, we first motivate an architecture where the output error is filtered by a linear system parametrized by its arbitrary order and a scalar positive gain. Our main result establishes an exponential finite gain bound for the estimation error, from the measurement noise, this gain being dependent on the high-gain and filter parameters. We also prove bounds depending on the filter parameters characterizing improved high-frequency gains from the measurement noise to the estimation error. The proposed construction is shown to behave desirably in numerical simulations.

Stability analysis of interconnected nonlinear mixed passive and negative-imaginary systems

This paper presents an analytical framework to establish finite gain stability for nonlinear interconnected mixed passive and negative imaginary systems. The stability analysis is presented using the notation of dissipitivity. The proposed stability framework enables us to extend the number of existing results from the linear mixed systems to the wide range of nonlinear mixed systems. Accordingly, the stability analysis of this paper extends the work of Das et al. (in: 2013 Australian control conference. IEEE, pp 445–449, 2013) to nonlinear cases. A numerical example is presented in the paper to test the results of the proposed analytical framework.

GENERAL STRUCTURE OF INTEGRATOR-BASED CONTINUOUS-TIME ACTIVE-RC FILTER AND APPLICATIONS

In the paper, a general structure of integrator-based continuous-time Active-RC filter is presented. More specifically, filter structures containing inverting amplifiers and passive feedback network are considered. The structure is analyzed using matrix description. The extensions of the model that take into account finite DC gain and finite bandwidth of operational amplifiers as well as other non-ideal effects are presented. The matrix-based approach is formulated especially for efficient use in computer analysis and design of Active-RC filters. An application example of the proposed approach to obtain OPAMP specifications for 3rd order low-pass Chebyshev filter for Analog Front End for VDSL is given. In this paper, we consider a general Active-RC filter topology suitable for computer-aided analysis, design and optimization of Active-RC filters. The structure is not the most general one, since it is restricted to filter topologies containing only inverting amplifiers (especially integrators) and RC feedback network.

Combined Finite Element and Electronic Circuit Model of a Wire-Mesh Sensor

A new wire-mesh sensor model based on electric field and circuit simulations is presented. In our approach, the excitation and amplification stages of the capacitance WMS are created as macromodels and coupled to the electrodes of a 3D geometry of the sensor. Thus, the effects caused by nonideal characteristics of the amplifiers are considered (e.g. finite open-loop gain and bandwidth). In order to evaluate the performance of the model, a static validation based on phantom measurement was performed. The phantoms were created with paraffin to emulate typical flow regimes, i.e. annular, slug and bubble flow. A mapping containing the position and the electrical properties of the patterns was obtained by image processing and incorporated to the field simulation. Hence the numerical simulations could be directly compared to the experimental data. The results show that coupling the external circuits to the capacitance WMS model is crucial to provide reliable synthetic data.

Optimal design of a fractional order immittance in the second quadrant with wide CPZ

This paper presents a design technique to realize fractional order (FO) immittance in the second quadrant of the impedance plane, using Bruton’s generalized immittance converter (GIC). Design guidelines are developed based on a sub-optimal analysis of phase error resulted by non-ideal op amps. The analysis takes into account finite open-loop dc gain and finite unity-gain frequency of practical op amps and aim to maximize the constant phase zone for a given phase band specification. The fractance of the realized fractor can also be tuned to a desired value by varying one of the GIC resistances. Several simulations and experimental validations are demonstrated. Also, high Q, FO bandpass filter with wide tuning range is presented as an application of the designed obtuse angle fractor.

A Square Wave-Based Digital Foreground Calibration Algorithm of a Pipeline ADC Using Approximate Harmonic Sampling

This brief proposes a digital foreground calibration algorithm of a pipeline ADC, using the Square wave signal as the input. The principle of equivalent radix extraction technique using approximate harmonic sampling is used to remove the ADC non-linearities. Linearity errors caused due to finite op amp gain, capacitor mismatches and effect of parasitic capacitance are eliminated by the proposed calibration technique. Two front-end stages of a 12-bit pipeline ADC are incorporated with low amplifier gain of 40 dB, capacitor mismatch of ±5 % ≤ γ ≤ ±10 %. Non-linearities arising due to these factors are calibrated and results are verified using behavioural simulation.

Saturated Lipschitz Continuous Sliding Mode Controller for Perturbed Systems With Uncertain Control Coefficient

In this article, a Lipschitz continuous sliding mode controller (LCSMC) is proposed to stabilize an integrator chain with a saturated control input, Lipschitz continuous perturbations, and an unknown control coefficient. The proposed controller ensures global finite-time convergence to the sliding surface by means of a control signal that is Lipschitz continuous (i.e., has finite gain) and is bounded by a given actuator limit. Stability conditions for the controller's tuning parameters are derived and the effectiveness of the approach is demonstrated in the course of a numerical simulation.

Event-triggered dynamic anti-windup augmentation for saturated systems

This paper considers the dynamic output-based event-triggered strategy design for linear systems subject to input saturation. The dynamic event-triggered control reduces the communication burden, and a minimum inter-event time is explicitly provided to exclude Zeno behaviour. A dynamic linear anti-windup augmentation is presented to deal with the input saturation. For the given anti-windup compensator, a criterion is formulated to achieve practical stability with finite gain. Moreover, an algorithm with projection lemma is proposed to design the anti-windup augmentation when it is unknown. For two special cases, i.e. the anti-windup compensator is static or of the plant-order, the feasibility conditions become convex. Simulations are given to illustrate the theoretical results.

A Type-3 PLL for Single-Phase Applications

This article proposes an effective solution by means of gain and phase-lead compensations to overcome the challenges of instability and slow dynamic performance exhibited by single-phase type-3 phase-locked loops (PLLs). By considering a single-phase second-order generalized integrator based type-3 PLL, a detailed design guideline is provided in choosing the PLL's parameters. Stability analysis of the designed PLL reveals that its finite gain margin causes PLL instability under severe voltage dip, while its limited phase margin results in poor dynamics. Therefore, gain compensation is carried out within a limited region such that the PLL's stability limit is not exceeded, while phase-lead compensation is employed to enhance the PLL's damping. When both modifications are incorporated within the PLL loop, the PLL's speed of estimation is improved significantly when compared with those of existing solutions applied to type-3 PLLs and the response obtained is comparable to that of a type-2 PLL. The performance evaluation of the proposed solution is carried out by experimental comparison with a standard single-phase type-3 PLL, a type-3 PLL with the amplitude normalization system, a phase feed-forward type-3 PLL, a dual-loop type-3 PLL, and a type-2 PLL.

U-Model-Based Finite-Time Control for Nonlinear Valve-Controlled Hydraulic Servosystem

Valve-controlled servosystems are widely used in dynamic tracking, but, not properly studied, nonlinearity, perturbation of internal parameters, and external disturbance have significant impacts on the control performance and challenge in the controller design. This study, with consideration of the finite pressure gain of actual servovalves, proposes a new unified nonlinear model of the valve-controlled servosystem. Based on a U-control platform, this study makes the control strategy design independent from the nonlinear plant, and a virtual nominal plant is presented to eliminate the unmodeled high-frequency characteristics, acquire the desired control performance, and enable the control variable to be explicitly expressed. Then, there follows, designing the U-model-based finite-time control in the valve-controlled systems. Simulation demonstrations show the consistency with theoretical development that the valve-controlled system can smoothly track the command signal within the specified time, and the phase lag is eliminated. Moreover, U-model’s application effectively copes with the system chattering, and with the maximum of 1 m/s the dynamic position error caused by discretization of the controller is reduced to less than 0.15%, which can satisfy the demand of general valve-controlled servosystems.

On the Converse Passivity Theorems for LTI Systems

Converse passivity theorems are established for finite-dimensional (FD) linear time-invariant (LTI) systems. Consider an FD LTI system G1 interconnected in positive feedback with another FD LTI system G2. It is demonstrated that when the closed-loop system is (robustly) stable (in the sense of finite L2 gain) for arbitrary strictly passive G2, then -G1 must necessarily be passive. It is also demonstrated that when the closed-loop system is uniformly stable across the set of arbitrary passive G2, then -G1 must necessarily be strictly passive. The proofs are constructive; i.e., we show how to find a de-stabilizing FD LTI G2 when G1 violates the necessity condition of stability.

Stability analysis for nonlinear closed loop system structure

In this paper, stability analysis is studied for the nonlinear closed loop system with a nonlinear plant and a nonlinear controller. Without the linearizing process for the nonlinear plant and the nonlinear controller, a Lipschitz continuous assumption of nonlinear plant is added and the notion of finite gain stability is defined. Then some inequalities about Lipschitz constants are derived to guarantee that the nonlinear system outputs are finite gain stability. To avoid the construction of the Lyapunov function, the convergence properties about the geometric series are applied to obtain two inequality conditions on the defined finite gain stability. Furthermore, one more complicated system, coming from engineering practice, is used to extend the nonlinear closed loop system, where the inner loop is applied to help another two controllers in achieving the desired tracking accuracy. Then the controller design for one flight simulation platform with six degrees of freedom confirms the theoretical results.

Impact on Gain and Noise : ECG Amplifier & Comb Filter Design using OTA

The research paper ventures a novel modelling strategy of finite gain and noise of an electrocardiogram (ECG) amplifier at 0.18, 0.5 and 0.9 micron standard CMOS technologies respectively. An active comb filter is used to design the amplifier for removing the selected frequencies of numerous signals. The presented filter is configured with only Operational Transconductance Amplifiers (OTAs) and capacitors that makes it apt for implementation of monolithic integrated circuits (ICs). The relevance of this analog circuit is verified for a suitable test signal of 60 Hz as in the ECG signal. Using Cadence Virtuoso analog design environment, the effect of transistor channel length and width is examined for analysis of noise and bandwidth. It is observed that the performance in terms of noise and gain considerably increases for advanced technology node. However, for a suitable supply of bias current, a portable ECG system can also provide an improved bandwidth performance of advanced CMOS technology.

A 0.4-V 13-bit 270-kS/s SAR-ISDM ADC With Opamp-Less Time-Domain Integrator

This paper presents a 13-bit high-resolution two-step analog-to-digital converter (ADC). Successive approximation register (SAR)-ADCs and an incremental sigma-delta modulator (ISDM) act as the coarse and fine ADCs, respectively. By using the proposed time-domain ISDM, the integrator is relaxed from the finite gain error and static current consumption. For the matching of the capacitive digital-to-analog converter(CDAC), the integral non-linearity (INL) splitting (INLS) switching procedure is developed to reduce the INL and switching energy to 25% and 9% of the reference common-mode voltage (VCM)-based scheme, respectively. With a reduced capacitance of the capacitor array, the requirements of the input driver and reference buffer are effectively relaxed. A prototype was fabricated in Taiwan Semiconductor Manufacturing Company (TSMC) 90-nm CMOS technology, which occupies an area of 0.059 mm2. The achieved spurious-free dynamic range (SFDR) and signal-to-noise and distortion ratio (SNDR) at Nyquist rate are 90.38 and 73.57 dB, respectively. The maximum differential non-linearity (DNL) and INL are 0.45 and 0.75 LSB, respectively. The prototype consumes 638 nW at 0.4-V supply and 270-kHz sampling rate. The resultant Schreier figure of merit (FoM) is 186.8 dB, and the Walden FoM is 0.61 fJ/conversion step.