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This paper aims to present some “natural philosophy” that may be associated with multivibrator. The motivation is given by the exposition work (Mathis, 2019) of Wolfgang Mathis.

Considering the multivibrator’s states as a realization of Boolean Logic, the author discusses the logical basics in the scope of physical realization, and Brouwer’s concern regarding the “tertium non datur” principle.

A mechanical multivibrator with Coulomb friction is treated to enrich the standard set of the traditional examples. The associated energy analysis lies on the border of Newton’s and Lagrangian’s mechanics.

It is the author’s own work. The author is limited by his modest abilities, given to him by the Great Lord.

Teaching and improving engineering understanding of the oscillatory systems.

Together with Mathis (2019), the present paper outlines the topic of multivibrator as a field having significant heuristic and pedagogical value.

The purpose of this paper is to present a procedure for approximating DC operating points of nonlinear circuits. The presented approach can also be applied in case of multiple DC operating points.

A generalized Carleman linearization is used, which transforms an algebraic nonlinear equation into an equivalent infinite-dimensional linear system. In general, no close-form solution can be given for the infinite-dimensional linear system. Hence, the infinite-dimensional linear system is approximated by a finite one over a predefined interval using a self-consistent technique. The presented procedure allows to approximate all possible DC operating points within a predefined interval. To isolate all DC operating points, the initial interval is gradually divided into subintervals.

It is shown that the presented approach is not restricted to the polynomial case and allows to approximate all DC operating points. The presented approach can be applied in case of multiple DC operating points and does not depend on the domain of attraction of the DC operating points.

A new procedure for the approximation of DC operating points of nonlinear circuits based on a generalized Carleman linearization is presented. This approach can be applied in case of multiple DC operating points and is independent of the domain of attraction. Further, this generalized approach is not restricted to the polynomial case and can be applied to a variety of circuits.

This work is intended to historically commemorate the one hundredth anniversary of the invention of a new type of electronic circuit, referred to in 1919 by Abraham and Bloch as a multivibrator and by Eccles and Jordan as a trigger relay (later known as a flip-flop).

The author also considers the circuit-technical side of this new type of circuit, considering the technological change as well as the mathematical concepts developed in the context of the analysis of the circuit.

The multivibrator resulted in a “circuit shape” which became one of the most applied nonlinear circuits in electronics. It is shown that at the beginning the multivibrator as well as the flip-flop circuits were used because their interesting properties in the frequency domain.

Therefore, it is a very interesting subject to consider the history of the multivibrator as electronic circuits in different technologies including tube, transistors and integrated circuits as well as the mathematical theory based on the concept from electrical circuit theory.

The purpose of this paper is to present the embedding of linear and nonlinear order reduction methods in a theoretical framework for handling hierarchically interconnected dynamical systems.

Based on the component connection modeling (CCM), a modified framework called mCCM for describing interconnected dynamic systems especially with hierarchical structures is introduced and used for order reduction purposes. The balanced truncation method for linear systems and the trajectory piecewise linear reduction scheme are used for the order reduction of systems described within the mCCM framework.

It is shown that order reduction methods can be embedded into the context of interconnected dynamical systems with the benefit of having a further degree of freedom in form of the hierarchical level, on which the order reduction is performed.

The aspect of hierarchy within system descriptions is exploited for order reduction purposes. This distinguishes the presented approach from common methods, which already start with single large-scale systems without explicitly considering hierarchical structures.

The conventional treatment of thermal noise is based on Nyquist’s theorem. This theorem has only been derived for linear, reciprocal (we define “reciprocal networks” as networks that are built of reciprocal network elements) networks. In this paper a description of thermal noise in reciprocal non‐linear RLC networks is presented. This description is derived from first principles, i.e. from a direct application of non‐equilibrium thermodynamics (irreversible thermodynamics) to electrical networks. As an example, the class of “complete” non‐linear networks is considered. Using the idea of equivalent n‐ports, the theory’s extension to certain classes of transistor circuits should be possible.

This paper aims to present a method for the efficient reduction of networks modelling parasitic couplings in very‐large‐scale integration (VLSI) circuits.

The parasitic effects are modelled by large RLC networks and current sources for the digital switching currents. Based on the determined behaviour of the digital modules, an efficient description of these networks is proposed, which allows for a more efficient model reduction than standard methods.

The proposed method enables a fast and efficient simulation of the parasitic effects. Additionally, an extension of the reduction method to elements, which incorporate some supply voltage dependence to model the internal currents more precisely than independent current sources is presented.

The presented method can be applied to large electrical networks, used in the modelling of parasitic effects, for reducing their size. A reduced model is created which can be used in investigations with circuit simulators requiring a lowered computational effort.

Contrary to existing methods, the presented method includes the knowledge of the behaviour of the sources in the model to enhance the model reduction process.

The purpose of this paper is to investigate the accuracy of different force calculation methods and their impact on mechanical deformations. For this purpose, a micrometer scaled actuator is considered, which consists of a micro‐coil and of a permanent magnet (PM) embedded in a deformable elastomeric layer.

For the magnetic field evaluation a hybrid numerical approach (finite element method/boundary element method (FEM/BEM) coupling and a FEM/BEM/Biot‐Savart approach) is used, whereas FEM is implemented for the mechanical deformation analysis. Furthermore, for the magneto‐mechanical coupling several force calculation methods, namely the Maxwell stress tensor, the virtual work approach and the equivalent magnetic sources methods, are considered and compared to each other and to laboratory measurements.

The numerically evaluated magnetic forces and the measured ones are in good accordance with each other with respect to the normal force acting on the PM. Nevertheless, depending on the used method the tangential force components differ from each other, which leads to slightly different mechanical deformations.

Since the force calculations are compared to measurement data, it is possible to give a suggestion about their applicability. The mechanical behavior of the actuator due to the acting forces is solely calculated and therefore only an assumption concerning the deformation can be given.

A new kind of micrometer scaled actuator is numerically investigated by using two different hybrid approaches for the magnetic field evaluation. Based on those, the results of several force calculation methods are compared to measurement data. Furthermore, a subsequent structural analysis is performed, which shows slightly different mechanical deformations depending on the used force calculation method.

This paper seeks to give an outline about the geometric concept of electronic circuits, where the jump behavior of nonlinear circuits is emphasized.

A sketch of circuit theory in a differential geometric setting is given.

It is shown that the structure of circuit theory can be given in a much better way than by means of a description of circuits using concrete coordinates. Furthermore, the formulation of a concrete jump condition is given.

In this paper, an outline is given about the state of the art of nonlinear circuits from a differential geometric point of view. Moreover, differential geometric methods were applied to two example circuits (flip flop and multivibrator) and numerical results were achieved.