INTRODUCTION This application note describes the circuit architecture and details required to measure the impedance profile of a grounded sensor using the AD5933 impedance-to-digital converter. The AD5933 is a high precision impedance converter system (see Figure 1) that combines an on-board frequency generator with a 12-bit, 1 MSPS, analog-to-digital converter (ADC). The frequency generator al...

An approximate formula for the frequency of oscillations is theoretically derived for skeleton models for electrochemical systems exhibiting negative differential resistance (NDR) under conditions close to supercritical Hopf bifurcation points. The theoretically predicted omega infinity (k/R)1/2 relationship (where R is the series resistance of the cell and k is the rate constant of the charge ...

The frequencies of the highest-frequency kilohertz QPOs recently discovered in some sixteen neutron stars in low-mass X-ray binary systems are most likely orbital frequencies. If so, these QPOs provide tight upper bounds on the masses and radii of these neutron stars and interesting new constraints on the equation of state of neutron star matter. If the frequency of a kilohertz QPO can be estab...

Abstract—Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables...

We have demonstrated experimentally the existence of a giant frequency down-conversion of the translational oscillatory motion of individual submillimeter acoustic bubbles in water in the presence of a high frequency (500 kHz) ultrasonic standing wave. The frequency of the translational oscillations (~170 Hz) is more than three orders of magnitude smaller than that of the driving acoustic wave....

A kinetic theory of linear electrostatic plasma waves with frequencies near the cyclotron frequency Ωcs of a given plasma species s is developed for a multispecies nonneutral plasma column with general radial density and electric field profiles. Terms in the perturbed distribution function up to O(1/Ωcs) are kept, as are the effects of finite cyclotron radius rc up to O(r 2 c ). At this order t...

Dielectric spectroscopy is a powerful tool for investigating the dielectric properties of biological particles in suspension. For low volume fractions, the dielectric properties of the particles are related to the measured properties of the suspension by Maxwell’s mixture equation. A number of different techniques can be used to measure the dielectric spectrum in the frequency domain or the tim...

The multiple scale expansion method is used to derive amplitude equations for a system with thermohaline convection in the neighborhood of Hopf and Taylor bifurcation points and at the double zero point of the dispersion relation. A complex Ginzburg-Landau equation, a Newell-Whitehead-type equation, and an equation of the φ type, respectively, were obtained. Analytic expressions for the coeffic...

We prove the existence of strong solutions to a class of inhomogeneous boundary-value problems for an elliptic-hyperbolic equation. The equation is an arbitrarily small lower-order perturbation of an equation that arises in the linearization of an approximate model for high-frequency waves near a caustic. The domain boundary is allowed to extend into both the elliptic and hyperbolic regions of ...

Starting from the simple point process model of 1/f noise, we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise, in any desirably wide range of frequency. A stochastic differential equation (the general Langevin equation with a multiplicative noise) that gives 1/f noise is derived. The solution of the equation exhibits the power-law distribution. The proces...