Time- and frequency-domain modeling of passive interconnection structures in field and circuit analysis

Die vorliegende Arbeit widmet sich den theoretischen Grundlagen und numerischen Verfahren zur Analyse passiver Verbindungsstrukturen auf der Basis der elektromagnetischen Feld- und Netzwerktheorie. Die Simulation elektromagnetischer Phänomene gewinnt eine immer stärkere Bedeutung sowohl im Entwicklungsprozess elektronischer Komponenten und Systeme als auch bei der EMV-Analyse. Ständig steigende Operationsfrequenzen erfordern die Einbeziehung der passiven Verbindungsstrukturen in die Analyse sowohl im Frequenz- als auch im Zeitbereich. Dabei wächst insbesondere die Bedeutung von Zeitbereichsmethoden bei der Behandlung elektrodynamischer Probleme infolge zunehmender Schaltfrequenzen und immer steilerer Anstiegsflanken. Frequenzbereichsmethoden in Kombination mit der Fourierrücktransformation erfordern bei extrem breiten Frequenzspektren einen hohen Rechenaufwand, um Zeitbereichslösungen mit hinreichender Genauigkeit zu erhalten. Im Falle von Nichtlinearitäten sind Zeitbereichsmethoden sogar die einzige Möglichkeit. Aus diesem Grunde wird in der vorliegenden Arbeit ein besonderer Schwerpunkt auf die Zeitbereichsmodellierung der Verbindungsstrukturen einschließlich der Schaltungsumgebung sowie die Behandlung mittels Netzwerksimulatoren gelegt.  Throughout the first period of electrical-engineering history, passive interconnections, i.e., conductors serving as the connection of electronic devices or system components, were typically not considered in the system modeling, except for some special cases and "electrically long" structures, which were successfully described via the transmission-line theory. This changed dramatically after the wide-spread introduction of digital, radio-frequency, and microwave technologies, which required transmission via the passive interconnection structures of high-frequency (HF) signals. The parasitic effects introduced by passive interconnections at high frequencies have motivated modern digital-system designers to consider such interconnections more precisely. &nbsp

The semiclassical tool in mesoscopic physics

Semiclassical methods are extremely valuable in the study of transport and thermodynamical properties of ballistic microstructures. By expressing the conductance in terms of classical trajectories, we demonstrate that quantum interference phenomena depend on the underlying classical dynamics of non-interacting electrons. In particular, we are able to calculate the characteristic length of the ballistic conductance fluctuations and the weak localization peak in the case of chaotic dynamics. Integrable cavities are not governed by single scales, but their non-generic behavior can also be obtained from semiclassical expansions (over isolated trajectories or families of trajectories, depending on the system). The magnetic response of a microstructure is enhanced with respect to the bulk (Landau) susceptibility, and the semiclassical approach shows that this enhancement is the largest for integrable geometries, due to the existence of families of periodic orbits. We show how the semiclassical tool can be adapted to describe weak residual disorder, as well as the effects of electron-electron interactions. The interaction contribution to the magnetic susceptibility also depends on the nature of the classical dynamics of non-interacting electrons, and is parametrically larger in the case of integrable systems.Comment: Latex, Cimento-varenna style, 82 pages, 21 postscript figures; lectures given in the CXLIII Course "New Directions in Quantum Chaos" on the International School of Physics "Enrico Fermi"; Varenna, Italy, July 1999; to be published in Proceeding

Electrically driven convection in a thin annular film undergoing circular Couette flow

We investigate the linear stability of a thin, suspended, annular film of conducting fluid with a voltage difference applied between its inner and outer edges. For a sufficiently large voltage, such a film is unstable to radially-driven electroconvection due to charges which develop on its free surfaces. The film can also be subjected to a Couette shear by rotating its inner edge. This combination is experimentally realized using films of smectic A liquid crystals. In the absence of shear, the convective flow consists of a stationary, azimuthally one-dimensional pattern of symmetric, counter-rotating vortex pairs. When Couette flow is applied, an azimuthally traveling pattern results. When viewed in a co-rotating frame, the traveling pattern consists of pairs of asymmetric vortices. We calculate the neutral stability boundary for arbitrary radius ratio $\alpha$ and Reynolds number ${{\cal R} e}$ of the shear flow, and obtain the critical control parameter ${\cal R}_c (\alpha, {{\cal R} e})$ and the critical azimuthal mode number ${m_c (\alpha, {{\cal R} e})}$. The Couette flow suppresses the onset of electroconvection, so that ${\cal R}_c (\alpha, {{\cal R} e}) > {\cal R}_c (\alpha,0)$. The calculated suppression is compared with experiments performed at $\alpha = 0.56$ and $0 \leq {{\cal R} e} \leq 0.22$.Comment: 17 pages, 2 column with 9 included eps figures. See also http://mobydick.physics.utoronto.c

Quick Computation of [C] and [L] Matrices of Generalized Multiconductor Coplanar Waveguide Transmission Lines

An enhanced spectral domain quasi-TEM analysis of generalized coplanar waveguide transmission lines (GCPWTL) is presented. The analysis starts from the formulation of a convolution-type integral equation for the electric field at the slots. Chebyshev polynomials including Maxwell singularities are used as basis functions to solve the integral equation by the Galerkin method. Fast and accurate quasi-analytical formulas are used to calculate the Galerkin’s matrix entries, thereby significantly reducing the involved CPU time and increasing reliability and accuracy. These features make this technique useful and competitive as CAD tool for coplanar waveguide designs

Shot Noise in Mesoscopic Conductors

Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and Boltzmann-Langevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.Comment: 99 two-column pages; 38 .eps figures included. Submitted to Physics Reports. Many minor improvements; typos corrected; references added and update

Mesoscopic conductance and its fluctuations at non-zero Hall angle

We consider the bilocal conductivity tensor, the two-probe conductance and its fluctuations for a disordered phase-coherent two-dimensional system of non-interacting electrons in the presence of a magnetic field, including correctly the edge effects. Analytical results are obtained by perturbation theory in the limit $\sigma_{xx} \gg 1$. For mesoscopic systems the conduction process is dominated by diffusion but we show that, due to the lack of time-reversal symmetry, the boundary condition for diffusion is altered at the reflecting edges. Instead of the usual condition, that the derivative along the direction normal to the wall of the diffusing variable vanishes, the derivative at the Hall angle to the normal vanishes. We demonstrate the origin of this boundary condition from different starting points, using (i) a simplified Chalker-Coddington network model, (ii) the standard diagrammatic perturbation expansion, and (iii) the nonlinear sigma-model with the topological term, thus establishing connections between the different approaches. Further boundary effects are found in quantum interference phenomena. We evaluate the mean bilocal conductivity tensor $\sigma_{\mu\nu}(r,r')$, and the mean and variance of the conductance, to leading order in $1/\sigma_{xx}$ and to order $(\sigma_{xy}/\sigma_{xx})^2$, and find that the variance of the conductance increases with the Hall ratio. Thus the conductance fluctuations are no longer simply described by the unitary universality class of the $\sigma_{xy}=0$ case, but instead there is a one-parameter family of probability distributions. In the quasi-one-dimensional limit, the usual universal result for the conductance fluctuations of the unitary ensemble is recovered, in contrast to results of previous authors. Also, a long discussion of current conservation.Comment: Latex, uses RevTex, 58 pages, 5 figures available on request at [email protected]. Submitted to Phys. Rev.