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The purpose of this paper is to propose a physics-aware algorithm to obtain radio frequency (RF)-reduced models of micro-electromechanical systems (MEMS) switches and show how, together with multiphysics macromodels, they can be realized as circuits that include both lumped and distributed parameters.

The macromodels are extracted with a robust procedure from the solution of Maxwell’s equations with electromagnetic circuit element (ECE) boundary conditions. The reduced model is extracted from the simulations of three electromagnetic field problems, in full-wave regime, that correspond to three configurations: signal lines alone, switch in the up and down positions.

The technique is exemplified for shunt switches, but it can be extended for lateral switches. Moreover, the algorithm is able take frequency dependence into account both for the signal lines and for the switch model. For the later, the order of the model is increased until a specified accuracy is achieved.

The use of ECE as boundary conditions for the RF simulation of MEMS switches has the advantage that the definition of ports is unambiguous and robust as the ports are clearly defined. The extraction approach has the advantage that the simplified model keeps the basic phenomena, i.e. the propagation of the signal along the lines. As the macromodel is realized with a netlist that uses transmission lines models, the lines’ extension is natural. The frequency dependence can be included in the model, if needed.

This paper proposes an algorithm for the extraction of reduced order models of MEMS switches, based on using a physics aware simplification technique.

The reduced model is built progressively by increasing the complexity of the physical model. The approach starts with static analyses and continues with dynamic ones. Physical phenomena are introduced sequentially in the reduced model whose order is increased until accuracy, computed by assessing forces that are kept in the reduced model, is acceptable.

The technique is exemplified for RF-MEMS switches, but it can be extended for any device where physical phenomena can be included one by one, in a hierarchy of models. The extraction technique is based on analogies that are carried out for both the multiphysics and the full-wave electromagnetic phenomena and their couplings. In the final model, the multiphysics electromechanical phenomena is reduced to a system with lumped components with nonlinear elastic and damping forces, coupled with a system with distributed and lumped components which represents the reduced model of the RF electromagnetic phenomena.

Contrary to the order reduction by projection methods, this approach has the advantage that the simplified model can be easily understood, the equations and variables have significance for the user and the algorithm starts with a model of minimal order, which is increased until the approximation error is acceptable. The novelty of the proposed method is that, being tailored to a specific application, it is able to keep physical interpretation inside the reduced model. This is the reason why, the obtained model has an extremely low order, much lower than the one achievable with general state-of-the-art procedures.

The main aim of this study is the modelling of the interaction of on‐chip components with their electromagnetic environment.

The integrated circuit is decomposed in passive and active components interconnected by means of terminals and connectors which represent intentional and parasitic couplings of a capacitive and inductive nature. Reduced order models are extracted independently for each component.

The paper shows that one of the main theoretical problems encountered in the modelling of RF components is the difficulty to define a unique terminal voltage, independent of the integration path (this independence being a condition to allow the connection of the component in an electric circuit, where the voltage does not depend of the path shape). The concept of an electromagnetic circuit element that allows the interconnection between IC models is proposed as a solution for this drawback. The system is described either with EM field models, or by electric/magnetic circuits. By using the new concept of hooks, the EM interaction is described effectively with a reduced number of quantities.

Since hooks have a virtual character, their identification is the result of an optimization procedure. By increasing their number the model accuracy is improved as also is the computational effort. The optimal automatic identification of electric and magnetic hooks is the subject of further research. Currently, the hooks are placed manually.

The modelling of IC components with hooks is part of a new methodology that takes a layout description of typical RF functional blocks that will operate at RF frequencies up to 60 GHz and transform them into sufficiently accurate, reliable electrical simulation models, taking EM coupling and variability into account. This will decrease extra design iterations, over‐dimensioning or complete failures in the design cycle of RF‐IC.

For the first time, the concept of magnetic terminals is used to describe interactions in RF integrated circuits. These EM “hooks” are defined in mathematical terms, as proper boundary conditions. The concept of hooks is also new. The proposed modeling methodology for EM coupling is also new. The paper is useful for nEDA designers.

The paper has the purpose of proposing a new open boundary condition to be used in conjunction with the finite integration technique (FIT) for the modelling of passive on‐chip components.

This boundary condition is ensured by using a virtual layer that surrounds the computational domain.

The paper proves which are the optimal material properties of the equivalent layer of open boundary.

When modelling passive on‐chip components with FIT, the method proposed is more efficient than the strategic dual image technique.

The paper shows the advantage of this approach – that the analysis algorithm remains unchanged, while saving the field‐circuit compatibility properties, such as current conservation.

The numerical solution of electromagnetic field nonlinear problems requires successive building and solving of linear systems of equations. This is the most time–consuming part, especially for large problems. Both fast linear solvers and efficient nonlinear iterative algorithms, are critical for the overall efficiency of the nonlinear electromagnetic field solver. This paper presents an analysis of a variety of techniques that can be efficiently used to reduce the solution time of nonlinear magnetic field equations in large finite element method (FEM) problems.