Underdamped Behavior Research Articles

Interconnect Energy Dissipation in High-Speed ULSI Circuits

This paper presents a detailed empirical study and analytical derivation of voltage waveform and energy dissipation of global lines driven by CMOS drivers. It is shown that at high clock frequencies where the output voltage at the termination point of the transmission line may not reach its steady-state value during the clock period, it is possible to reduce energy dissipation while meeting a dc noise margin by driver sizing. This is in sharp contrast with the steady-state analysis, which states that driver size has no impact on the energy dissipation per output change. In addition, we propose a new design metric which is the product of energy, delay and some measure of ringing in lossy transmission lines. In particular, this paper provides closed-form expressions for the energy dissipation, 50% propagation delay, and the percentage of maximum undershoot when the circuit exhibits an underdamped behavior. This metric is used during the driver sizing problem formulation for minimum energy-delay-ringing product. The experimental results carried out by HSPICE simulation verify the accuracy of our models.

Analysis and compensation of two-pole amplifiers with a pole-zero doublet

A simple representation of a two-pole amplifier with a pole-zero doublet is proposed which can be used in the compensation of transconductance amplifiers. The model is based on the consideration that a pole-zero doublet does not greatly modify the behavior of the closed-loop amplifier. Indeed, assuming an underdamped behavior we have found that the pole-zero doublet only affects the phase margin and, hence, it can accurately be accounted for by properly modifying the second pole of the original two-pole amplifier. Simulations on a two-stage transconductance amplifier show that such a model closely agrees with the time response of the real amplifier.

Josephson properties of basal-plane-faced tilt boundaries in YBa2Cu3O7−δ thin films

The Josephson properties of 90° basal-plane-faced tilt boundaries formed between c-axis and a-axis normal grains in YBa2Cu3O7−δ thin films are reported. These boundaries have a low conductance which results in underdamped junction behavior. The junction capacitance and kinetic inductance both scale directly with junction critical current and conductance. The results emphasize the inhomogeneous and filamentary nature of the superconducting properties of cuprate grain boundaries.

Factors affecting dynamic electrical manipulation of menisci

The dynamics of a conductive meniscus subjected to an external field are examined with a view toward drop-on-demand applications. A low-order model suitable for exploring parametric effects is developed. Equilibrium and stability criteria are derived for the purpose of estimating electric field requirements. The criteria are expressed in terms of dimensionless pressures due to electric stress, gravity, and hydrostatic head, normalized to surface tension pressure. Eigenvalues of the linearized model yield a formula for characteristic frequency analogous to Rayleigh's formula for a free drop and, in addition, indicate that most liquids will show underdamped behavior. Requirements for critical damping are derived and illustrated with root locus plots.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Damping and Resonance Characteristics of Thermal Waves

Amplification of thermal waves in response to high-frequency excitations is studied in this work. The resonance behavior is explored along with the underdamped behavior in thermal wave oscillations. In transition from an overdamped to an underdamped wave behavior, the relaxation distance is found to dominate the process. A relationship between the resonance frequency and the thermal wave speed is derived. The emphasis is placed on the frequency approach determining the thermal wave speed in engineering materials.

Potential pitfalls in ratio control schemes

We study the behavior of various ratio control schemes implemented on distillation columns with many trays. The results show that controller structures using ratios plus direct material balance manipulation (e.g., RR-B, D-BR) can produce underdamped open-loop systems (level loops closed, composition loops open). This underdamped behavior is due to the hydraulic lags in these large columns. Because of this very unusual behavior, it is difficult to derive the transfer function matrix of such ratio control structures by using standard identification techniques. A method is presented for finding the transfer function matrix by appropriately transforming the open-loop transfer function matrices of other conventional control structures (e.g., D-V). Once the necessary transfer function matrix is found, controller tuning is feasible, and the performance of the closed-loop system is very good when the two product composition control scheme is in effect

Quantum fluctuations in a current-biased Josephson junction of small capacitance.

Quantum fluctuations of the charge at a current-biased Josephson junction and of the Josephson current couple to the quasiparticle tunneling when the system is at equilibrium in the zero-voltage state. The effect of reducing the capacitance of the junction is studied by means of a model Hamiltonian. When this becomes smaller, charge fluctuations are reduced, but the effective dissipation is also lowered so that the junction displays an underdamped behavior. The Josephson branch is shifted at the voltage e/2C because of charging due to the quasiparticles. A path-integral formulation of the model leads to a high dynamical subgap resistance at I\ensuremath{\rightarrow}0, as recently found experimentally.

Angular region: a measure of underdamped behavior

The natural modes of an underdamped dynamical system are given by the characteristic numbers of the quadratic operator pencil P(s)=s 2I+sB+A, where the operator A depends on the dissipative and reactive elements of the system, while B depends solely on the reactive elements. The operator P(s) for every applied stimulus vector signal x must satisfy: (Bx,x) 2<4(Ax,x). A measure of underdamped behaviour is suggested by predetermining an angular region |φ| containing all natural modes of the system, | tanφ|⪕ [4(Ax,x)−(Bx,x) 2] 1 2 (Bx,x) . When a comparison between positive operators A and B is available, say B 2= KA, then | tan φ|⪕ √(4−K 2) K . The paper is motivated by Duffin-Krein-Gohberg's earlier mathematical contributions.

Phototransduction in the fly compound eye exhibits temporal resonances and a pure time delay.

Photoreceptor cells in both vertebrates and invertebrates respond to a flash of light with a slow graded change in membrane potential, which is generally depolarising in invertebrates and hyperpolarising in vertebrates. Although some of the early photochemical and biochemical stages of the transduction process have been elucidated in both cases, these reactions are fast compared with the time course of the electrical response, which is typically hundreds of milliseconds long. To explain this slow response in the eye of Limulus, Fuortes and Hodgkin proposed a mechanism in which the light signal passes through a cascade of simple low pass filters. The model was later defined more specifically in terms of a chain of chemical reactions linked together through products and reactants, and has been used with small modifications and different numbers of stages to account for the behaviour of various vertebrate and invertebrate photoreceptors including the fly compound eye. I have now obtained evidence that phototransduction in the fly in small signal conditions involves underdamped resonance behaviour and a significant pure time delay, neither of which can be accounted for by the conventional cascade model.

Magnetization switching in a garnet thin film

An improved technique for observing subnanosecond magnetization changes in thin films has been used to study the underdamped oscillatory behavior in a (Y <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</inf> Gd <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</inf> ) (Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> )O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> sample. The measurement setup uses a version of the alternate sampling technique in which the sensitivity has been upgraded by the use of a lock-in amplifier. By using a shorted stripline of appropriate length to apply to the film two properly timed magnetic field steps, the precession of the magnetization can be quelled, and the magnetization can be switched between initial and final directions in a half-cycle of the resonant frequency.