Nonlinear Analog Research Articles

Fault diagnosis of nonlinear analog circuits using generalized frequency response function and LSSVM.

A fault diagnosis method of nonlinear analog circuits is proposed that combines the generalized frequency response function (GFRF) and the simplified least squares support vector machine (LSSVM). In this study, the harmonic signal is used as an input to estimate the GFRFs. To improve the estimation accuracy, the GFRFs of an analog circuit are solved directly using time-domain data. The Fourier transform of the time-domain data is avoided. After obtaining the fault features, a multi-fault classifier is designed based on the LSSVM. In order to improve the training speed and reduces storage, a simplified LSSVM model is used to construct the classifier, and the conjugate gradient algorithm is used for training. The fault diagnosis simulation experiment is conducted on a biquad filter circuit to verify the proposed method. The experimental results show that the proposed method has high diagnostic accuracy and short training time.

A 28 GHz balun‐first LNA with db‐linear 32 db gain range for 5 G applications

AbstractThis letter presents a 28 GHz balun‐first low noise amplifier (LNA) featuring a wide dB‐linear variable gain range. The architecture of LNA includes three‐stage cascode amplifiers. An integrated balun at the input stage provides RF ESD protection and converts a single‐ended signal to a differential one (S‐to‐D). A transformer‐based dual‐resonant matching network is designed and analyzed to achieve wideband performance. To realize a continuous dB‐linear variable gain range and consistent input/output matching, gain control is implemented in the second stage using a 5‐bit digital‐to‐analog converter (DAC) for a 32 dB gain range. The DAC can generate a nonlinear analog voltage to control the gate of the common‐gate transistor in the second cascode stage, inversely compensating for the nonlinear gain variations of the cascode amplifier. The LNA is fabricated in 65‐nm CMOS process with a core size of 0.154 mm². Measurement results exhibit a maximum gain of 33.5 dB and a minimum noise figure (NF) of 3.65 dB with a 3‐dB bandwidth of 23–29.5 GHz. The measured variable gain range is approximately 32 dB across 32 different gain states, with a linear gain step of ~1 dB per state and an IP1dB ranging from −6.5 dBm to −35.25 dBm. The power consumption is 35.4–48 mW from a 1.2 V supply voltage.

Homogenisation of nonlinear Dirichlet problems in randomly perforated domains under minimal assumptions on the size of perforations

AbstractIn this paper we study the convergence of nonlinear Dirichlet problems for systems of variational elliptic PDEs defined on randomly perforated domains of $$\mathbb {R}^n$$ R n . Under the assumption that the perforations are small balls whose centres and radii are generated by a stationary short-range marked point process, we obtain in the critical-scaling limit an averaged nonlinear analogue of the extra term obtained in the classical work of Cioranescu and Murat (Res Notes Math III, 1982). In analogy to the random setting recently introduced by Giunti, Höfer and Velázquez (Commun Part Differ Equ 43(9):1377–1412, 2018) to study the Poisson equation, we only require that the random radii have finite $$(n-q)$$ ( n - q ) -moment, where $$1<q<n$$ 1 < q < n is the growth-exponent of the associated energy functionals. This assumption on the one hand ensures that the expectation of the nonlinear q-capacity of the spherical holes is finite, and hence that the limit problem is well defined. On the other hand, it does not exclude the presence of balls with large radii, that can cluster up. We show however that the critical rescaling of the perforations is sufficient to ensure that no percolating-like structures appear in the limit.

Machine learning without a processor: Emergent learning in a nonlinear analog network

Standard deep learning algorithms require differentiating large nonlinear networks, a process that is slow and power-hungry. Electronic contrastive local learning networks (CLLNs) offer potentially fast, efficient, and fault-tolerant hardware for analog machine learning, but existing implementations are linear, severely limiting their capabilities. These systems differ significantly from artificial neural networks as well as the brain, so the feasibility and utility of incorporating nonlinear elements have not been explored. Here, we introduce a nonlinear CLLN-an analog electronic network made of self-adjusting nonlinear resistive elements based on transistors. We demonstrate that the system learns tasks unachievable in linear systems, including XOR (exclusive or) and nonlinear regression, without a computer. We find our decentralized system reduces modes of training error in order (mean, slope, curvature), similar to spectral bias in artificial neural networks. The circuitry is robust to damage, retrainable in seconds, and performs learned tasks in microseconds while dissipating only picojoules of energy across each transistor. This suggests enormous potential for fast, low-power computing in edge systems like sensors, robotic controllers, and medical devices, as well as manufacturability at scale for performing and studying emergent learning.

ANISOTROPIC PICONE IDENTITIES FOR HALF LINEAR CONFORMABLE ELLIPTIC EQUATIONS

This study is devoted to investigating the anisotropic picone identities for half-linear Conformable elliptic equations and the Hardy-type inequality. Further, we provide some results for the nonlinear analogue to Picone identity.

Dual-polarization MZM-based photonic nonlinear analog self-interference cancellation for in-band full-duplex radios

In this paper, we propose a dual-polarization Mach-Zehnder modulator-based photonic nonlinear analog self-interference cancellation (SIC) technique for in-band full duplex (IBFD) systems. By using the proposed technique, an arbitrary 4th order nonlinear transfer function can be generated, meaning the performance limitation caused by the nonlinearity of the analog SIC circuit can be overcome by imitating the nonlinear transfer function of the analog SIC circuit before cancellation. This paper also presents a performance analysis through simulations and the results of a proof-of-concept demonstration. In the experiment, the proposed nonlinear SIC technique could achieve 29 dB cancellation over 500 MHz bandwidth centered at 1.25 GHz frequency along various degree of distortion caused by nonlinearity. In addition, the performance enhancements achieved by the proposed technique are evaluated in terms of error vector magnitudes (EVMs) and constellations of the signal-of-interest (SOI) in the simulation which is based on the experimental SIC results. More than 3 dB of SOI power gain could be obtained in evaluated EVM performances.

Acoustic metamaterials for realizing a scalable multiple phi-bit unitary transformation

The analogy between acoustic modes in nonlinear metamaterials and quantum computing platforms constituted of correlated two-level systems opens new frontiers in information science. We use an inductive procedure to demonstrate scalable initialization of and scalable unitary transformations on superpositions of states of multiple correlated logical phi-bits, classical nonlinear acoustic analog of qubits. A multiple phi-bit state representation as a complex vector in a high-dimensional, exponentially scaling Hilbert space is shown to correspond with the state of logical phi-bits represented in a low-dimensional linearly scaling physical space of an externally driven acoustic metamaterial. Manipulation of the phi-bits in the physical space enables the implementation of a non-trivial multiple phi-bit unitary transformation that scales exponentially. This scalable transformation operates in parallel on the components of the multiple phi-bit complex state vector, requiring only a single physical action on the metamaterial. This work demonstrates that acoustic metamaterials offer a viable path toward achieving massively parallel information processing capabilities that can challenge current quantum computing paradigms.

Distortion Analysis and Fault Detection in Weakly Non-linear Analog Circuits Using Simplified Volterra Series Method

In this paper a new method to find the parametric faults in weakly nonlinear analog circuit is proposed. Frequency domain volterra kernels are derived to calculate the test parameters i.e., nonlinear distortions and the cross spectral density. Volterra kernels are sensitive to device parameter and the components used to build the circuit. Device parameter and each component value are varied within the tolerance limit using Monte Carlo simulation. For the fault free circuit maximum and minimum values of the 3rd order harmonic, intermodulation distortion and the cross spectral density are measured. During testing, single and multiple faults are injected and the test parameters are measured. If any one or more test parameters are outside the predetermined bounds the circuit is declared to be faulty. This proposed method offers high fault coverage capability. To validate this method CMOS differential amplifier circuit is taken under consideration.

Low-Complexity Digital-Assisted Nonlinear Analog Self-Interference Cancellation in the Optical Domain

Low-Complexity Digital-Assisted Nonlinear Analog Self-Interference Cancellation in the Optical Domain

A Simple Family of Non-Linear Analog Codes

A Simple Family of Non-Linear Analog Codes

Stability of oscillator Ising machines: Not all solutions are created equal

Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the global minima of the cost function describing the coupled oscillator system and the ground state of the Ising Hamiltonian. However, the properties of the oscillator Ising machine (OIM) from a nonlinear control viewpoint, such as the stability of the OIM solutions, remain unexplored. Therefore, in this work, using nonlinear control-theoretic analysis, we (i) identify the conditions required to ensure the functionality of the coupled oscillators as an Ising machine, (ii) show that all globally optimal phase configurations may not always be stable, resulting in some configurations being more favored over others and, thus, creating a biased OIM, and (iii) elucidate the impact of the stability of locally optimal phase configurations on the quality of the solution computed by the system. Our work, fostered through the unique convergence between nonlinear control theory and analog systems for computing, provides a new toolbox for the design and implementation of dynamical system-based computing platforms.

Bespoke two-dimensional elasticity and the nonlinear analogue of Cauchy’s relations

Is it possible to design an architectured material or structure whose elastic energy is arbitrarily close to a specified continuous function? This is known to be possible in one dimension, up to an additive constant (Dixon et al., Bespoke extensional elasticity through helical lattice systems, Proc. R. Soc. A. (2019)). Here, we explore the situation in two dimensions. Given (1) a continuous energy function E ( C ) , defined for two-dimensional right Cauchy–Green deformation tensors C contained in some compact set and (2) a tolerance ϵ > 0 , can we construct a spring-node unit cell (of a lattice) whose energy is approximately E , up to an additive constant, with L ∞ -error no more than ϵ ? We show that the answer is yes for affine E s (i.e., for energies E that are quadratic in the deformation gradient), but that the general situation is more subtle and is related to the generalisation of Cauchy’s relations to nonlinear elasticity.

Deep reservoir computing based on self-rectifying memristor synapse for time series prediction

Herein, a self-rectifying resistive switching memristor synapse with a Ta/NbOx/Pt structure was demonstrated for deep reservoir computing (RC). The memristor demonstrated stable nonlinear analog switching characteristics, with a rectification ratio of up to 1.6 × 105, good endurance, and high uniformity. Additionally, the memristor exhibited typical short-term plasticity and dynamic synaptic characteristics. Based on these characteristics, a deep memristor RC system was proposed for time series prediction. The system achieved a low normalized root mean square error (NRMSE) of 0.04 in the time series prediction of the Henon map. Even at 90 °C, deep RC retains good predictive power with an NRMSE of only 0.07. This work provides guidance for efficient deep memristive RC networks to handle more complex future temporal tasks.

Analysis of pattern generation in non-periodic clock-driven unidirectionally coupled phase oscillators in a ring

Unidirectionally coupled phase oscillators in a ring are simple structures but unsuitable for application in central pattern generators (CPGs) for six-legged walking due to coexisting stable synchronization patterns. This paper shows that the coupled oscillators can be applied to a CPG by utilizing a non-periodic signal generator as a clock. The non-periodic clock-driven coupled oscillators are implemented by a sequential logic circuit using a field programmable gate array (FPGA) and a nonlinear analog circuit. A laboratory experiment confirms that a hexapod robot mounting the implemented circuits can realize six-legged walking.

INFORM: Inverse Design Methodology for Constrained Multiobjective Optimization

Many system design methods use population-based optimization or a surrogate model for solving constrained multi-objective optimization. When designing a system with multiple objectives and constraints, the designer may first be interested in understanding the trade-offs among different objectives from a small number of simulations. In the next step, the designer may focus on specific regions of interest in the design space near a set of non-dominated solutions to further improve performance on the targeted objectives. This may help make the search process sample-efficient. We propose INFORM: a two-step approach for sample-efficient constrained multi-objective optimization of real-world nonlinear systems. In the first step, we modify a genetic algorithm (GA) to make the design process sample-efficient. We inject candidate solutions into the GA population using inverse design methods instead of determining the candidate solutions for the next generation using only crossover and mutation, as is done in standard GA. We present three types of inverse design techniques based on a (i) neural network verifier, (ii) neural network, and (iii) Gaussian mixture model. The candidate solutions for the next generation are thus a mix of those generated using crossover/mutation and solutions generated using inverse design. At the end of the first step, we obtain a set of non-dominated solutions. In the second step, we choose the regions of interest around the non-dominated solutions to further improve the objective function values using inverse design methods. We demonstrate the efficacy of INFORM through synthesis of nonlinear systems and analog circuits. The experimental results show that INFORM reduces synthesis time by up to 29× and improves the value of the objective function by up to 33% compared to a state-of-the-art baseline design methodology.

A supersymmetric nonlinear sigma model analogue of the ModMax theory

A decade ago, it was shown that associated with any model for U(1) duality-invariant nonlinear electrodynamics there is a unique U(1) duality-invariant supersymmetric nonlinear sigma model formulated in terms of chiral and complex linear superfields. Here we study the mathcal{N} = 1 superconformal σ-model analogue of the conformal duality-invariant electrodynamics known as the ModMax theory. We derive its dual formulation in terms of chiral superfields and show that the target space is a Kähler cone with U(1) × U(1) being the connected component of the isometry group.

The p-widths of a surface

The p-widths of a closed Riemannian manifold are a nonlinear analogue of the spectrum of its Laplace–Beltrami operator, which corresponds to areas of a certain min-max sequence of possibly singular minimal submanifolds. We show that the p-widths of any closed Riemannian two-manifold correspond to a union of closed immersed geodesics, rather than simply geodesic nets.We then prove optimality of the sweepouts of the round two-sphere constructed from the zero set of homogeneous polynomials, showing that the p-widths of the round sphere are attained by lfloor sqrt{p}rfloor great circles. As a result, we find the universal constant in the Liokumovich–Marques–Neves–Weyl law for surfaces to be sqrt{pi }.En route to calculating the p-widths of the round two-sphere, we prove two additional new results: a bumpy metrics theorem for stationary geodesic nets with fixed edge lengths, and that, generically, stationary geodesic nets with bounded mass and bounded singular set have Lusternik–Schnirelmann category zero.

A study of nonlinear multiview varieties

We study the nonlinear generalization of the classical multiview variety, which is a fundamental concept in computer vision. In this paper, we take the first comprehensive step to develop the nonlinear analogue of multiview varieties. To this end, we introduce a multigraded version of the saturated special fiber ring. By applying this tool, we are able to compute the multidegrees of several families of nonlinear multiview varieties.

Nonlinear analog of the complexity-stability transition in random dynamical systems: a replica calculation

We consider large-dimensional dynamical systems involving a linear force and a random force comprising both potential and non-conservative contributions. Such systems are known to exhibit a topological trivialization phase transition as the strength of the random force is increased. This is reflected in the number of stationary points of the dynamical systems that transitions from one to an exponential in the number of degrees of freedom. We analyze this transition by means of a replica calculation.

Toughening polylactide with nonlinear, degradable analogues of PEG and its copolymers

P(VL-Teg), a non-linear analogue of PEG, and its block copolymers are effective additives for PLA toughening without a significant loss of elastic modulus due to their branched molecular architecture.