Matteo Biggio

Accurate and Efficient PSD Computation in Mixed-Signal Circuits: A Time-Domain Approach

The aim of this brief is twofold. On one side, the time-domain technique presented by Vasudevan to obtain the average and instantaneous power-spectral density of electrical variables in analog circuits characterized by (non)stationary noise sources is rigorously extended to the wide class of analog mixed-signal circuits modeled as hybrid dynamical systems. On the other side, an efficient numerical implementation is proposed to overcome the computational effort required by the original approach. The reliability of the method is first tested through the analog ring oscillator analyzed by Vasudevan. A fractional delta-sigma phase-locked loop with dithering is then simulated and the obtained results are partially validated through experimental measurements.

Coulomb blockade microscopy of spin-density oscillations and fractional charge in quantum spin Hall dots

We evaluate the spin density oscillations arising in quantum spin Hall quantum dots created via two localized magnetic barriers. The combined presence of magnetic barriers and spin-momentum locking, the hallmark of topological insulators, leads to peculiar phenomena: a half-integer charge is trapped in the dot for antiparallel magnetization of the barriers, and oscillations appear in the in-plane spin density, which are enhanced in the presence of electron interactions. Furthermore, we show that the number of these oscillations is determined by the number of particles inside the dot, so that the presence or the absence of the fractional charge can be deduced from the in-plane spin density. We show that when the dot is coupled with a magnetized tip, the spatial shift induced in the chemical potential allows to probe these peculiar features.

Reliable and efficient phase noise simulation of mixed-mode integer-N Phase-Locked Loops

In this paper the results obtained by performing the Periodic Noise (PNoise) analysis of a Phase-Locked Loop (pll) modeled as a mixed analog/digital circuit are compared with those from experimental measurements. The PNoise analysis of this class of circuits is done by considering them as hybrid dynamical systems. Since the circuit simulators available on the academic and industrial shelves are not able to carry out this kind of simulation, experimental validation is mandatory to support numerical results and enforce the reliability of the proposed approach. A significant improvement of the PNoise analysis efficiency, in terms of reducing its computational burden when simulating noise in PLLs with a large frequency ratio, is also presented, which allows to more easily manage noise folding.

A Circuit Model of Hysteresis and Creep

A circuit architecture that models hysteretic phenomena is proposed. The model is flexible enough to reproduce both rate-independent hysteresis and thermal relaxation effects (creep), commonly observed in many real-world physical systems such as piezoelectric actuators. By suitably tuning the nonlinear characteristics of the resistive elements of the network, the well-known log(t) time dependence of the creep relaxation dynamics can be accurately reproduced. An identification procedure is proposed, and two test cases are discussed.

Spin textures of strongly correlated spin Hall quantum dots

We study the spin ordering of a quantum dot defined via magnetic barriers in an interacting quantum spin Hall edge. The spin-resolved density-density correlation functions are computed. We show that strong electron interactions induce a ground state with a highly correlated spin pattern. The crossover from the liquid-type correlations at weak interactions to the ground state spin texture found at strong interactions parallels the formation of a one-dimensional Wigner molecule in an ordinary strongly interacting quantum dot.

Non-instantaneous synaptic transmission in spiking neuron networks and equivalence with delay distribution

Synapses in neuron networks filter incoming spikes with a wide variety of time constants, affecting the stability of various collective dynamics [1], the selectivity in transmitting information [2] and the reactivity to suddenly appearing exogenous stimuli [3]. Even for extremely simplified models of spiking neurons and network connectivities, theoretical approaches including non-instantaneous transmission rely on approximations valid for relatively small time scales [3,4] or on the assumption of a quasi-adiabatic dynamical regime [5]. Here, we addressed this issue working out a unified framework in which from small to large synaptic time scales the same approximated theoretical description holds for the firing rate dynamics of spiking neuron networks. Starting from single-neuron stochastic dynamics, we derived a set of ordinary differential equations for the population emission rate relying on the spectral expansion of the associated Fokker-Planck equation, eventually extending to the colored noise case a previous derivation obtained under white noise hypothesis [6]. The resulting population dynamics valid under a low-noise approximation, took into account also finite-size effects. This allowed to compare theoretical power spectra of population emission rates with those estimated from extensive network simulations performed with NEST [7]. Match between theory and simulation was investigated for different integrate-and-fire (IF) neuron models with different levels of complexity, e.g., VLSI IF (VIF [6], a generalization of the Perfect IF model), Leaky IF (LIF), and Exponential IF (EIF), confirming the effectiveness of the reduced theoretical description. Effectiveness which in turn could be further improved relying on higher-order perturbative terms in the fluctuation size of the synaptic current for any synaptic time scale. Moreover, such perturbative approach allowed to avoid the analytical difficulties of dealing with multi-dimensional Fokker-Planck equations with discontinuous boundary conditions. A simplification which helped in highlighting as main result that networks of neurons with non-instantaneous synapses can, under fairly broad assumptions, be described by equivalent networks with suitable distributions of transmission delays. A formal analogy valid from simple VIF models to more realistic point-like simplifications like LIF or EIF neurons.

Effects of numerical noise floor on the accuracy of time domain noise analysis in circuit simulators

This paper is concerned with the time-domain simulation of circuits including noise sources. In general, when a circuit admits a steady-state solution, small signal analyses are used to determine noise effects. There is a class of circuits (e.g., fractional PLLs based on ΔΣ modulators and forced oscillators) not admitting a steady-state solution with a period reasonable low multiple of the characteristic time scales of the circuit. In commercial analog simulators, time domain noise analyses have been implemented by “extending” linear multi-step integration methods or by introducing sampled versions of noise generators. Through a set of basic benchmark circuits, we show that these extensions are often affected by a relevant numerical noise floor hiding the effects of noise sources and drastically limiting the applicability of time domain noise analysis.

A low-complexity circuit model of hysteresis

A circuit architecture modelling rate-independent hysteretic phenomena is presented and discussed. The core of the circuit is a ladder structure with longitudinal nonlinear resistors and transverse linear capacitors. In a separate loop, a linear combination of input and capacitor voltages provides the driving voltage for a resistor with monotonic, piecewise-linear driving-point characteristic. The resistor current represents the output variable. The circuit parameters can be found from experimental data through a standard quadratic programming optimization procedure. The model fitting features are tested by using two experimental data sets. One is the B(H) function of a magnetic material; the other is the deformation of a piezoelectric actuator as a function of the applied voltage. In this last case, an accurate comparison with the predictions of the well-known Preisach model evidences that the circuit model achieves the same accuracy with a much smaller number of parameters. All the circuit simulations are performed by using PSPICE.

Transient dynamics of an adiabatic NEMS

This paper is focused on the transient dynamics of an adiabatic nano-electromechanical system (NEMS), consisting of a nano-mechanical oscillator coupled to a quantum dot. By numerically solving the nonlinear stochastic differential equation governing the oscillator, the time evolution of the oscillator position, of the dot occupation number and of the current are studied. Different parameter settings are studied where the system exhibits bi-stable, tri-stable or mono-stable behavior on a finite-time horizon. It is shown that, after a typically long transient, the system under investigation exhibits no hysteretic behavior and that a unique steady state is reached, independently of the initial conditions. The transient dynamics is marked out by one or two well separated characteristic times, depending on the considered case (i.e., mono- or multi-stable). These times are evaluated for a dot on-resonance or off-resonance. It turns out that the characteristic time scales are long in comparison to the period of the uncoupled oscillator, particularly at low bias, suggesting that the predicted transient dynamics may be observed in state-of-the-art experimental setups.