A two-step perturbation technique for nonuniform single and differential lines

A novel two-step perturbation technique to analyze nonuniform single and differential transmission lines in the frequency domain is presented. Here, nonuniformities are considered as perturbations with respect to a nominal uniform line, allowing an interconnect designer to easily see what the effect of (unwanted) perturbations might be. Based on the Telegrapher's equations, the proposed approach yields second-order ordinary distributed differential equations with source terms. Solving these equations in conjunction with the pertinent boundary conditions leads to the sought-for currents and voltages along the lines. The accuracy and efficiency of the perturbation technique is demonstrated for a linearly tapered microstrip line and for a pair of coupled lines with random nonuniformities. Moreover, the necessity of adopting a two-step perturbation in order to get a good accuracy is also illustrated

Influence of the line characterization on the transient analysis of nonlinearly loaded lossy transmission lines

The analysis of nonlinearly terminated lossy transmission lines is addressed in this paper with a modified version of a method belonging to the class of mixed techniques, which characterize the line in the frequency domain and solve the nonlinear problem in the time domain via a convolution operation. This formulation is based on voltage wave variables defined in the load sections. The physical meaning of such quantities helps to explain the transient scattering process in the line and allows us to discover the importance (so far often overlooked) of the reference impedance used to define the scattering parameters. The complexity of the transient impulse responses, the efficiency of the algorithms, and the precision of the results are shown to be substantially conditioned by the choice of the reference impedance. The optimum value of the reference impedance depends on the amount of line losses. We show that a low-loss line can be effectively described if its characteristic impedance or the characteristic impedance of the associated LC line is chosen as the reference impedance. Based on the physical interpretation of our formulation, we are able to validate the numerical results, and to demonstrate that, despite claimed differences or improvements, the formulations of several mixed methods are fundamentally equivalen

High Finesse Fiber Fabry-Perot Cavities: Stabilization and Mode Matching Analysis

Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications, where they typically require precise stabilization of their optical resonances. Here, we study two different approaches to construct fiber Fabry-Perot resonators and stabilize their length for experiments in cavity quantum electrodynamics with neutral atoms. A piezo-mechanically actuated cavity with feedback based on the Pound-Drever-Hall locking technique is compared to a novel rigid cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal self-locking and external temperature tuning. Furthermore, we present a general analysis of the mode matching problem in fiber Fabry-Perot cavities, which explains the asymmetry in their reflective line shapes and has important implications for the optimal alignment of the fiber resonators. Finally, we discuss the issue of fiber-generated background photons. We expect that our results contribute towards the integration of high-finesse fiber Fabry-Perot cavities into compact and robust quantum-enabled devices in the future.Comment: The Supplemental Material is included in the source code of the article that can be downloaded from this arXiv page (see "Other formats"). Peer-reviewed version with changes to text and figure

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