Abstract
In this paper we establish a simplified model of general spatially periodic linear electronic analog networks. It has a two-scale structure. At the macro level it is an algebro-differential equation and a circuit equation at the micro level. Its construction is based on the concept of two-scale convergence, introduced by the author in the framework of partial differential equations, adapted to vectors and matrices. Simple illustrative examples are detailed by hand calculation and a numerical simulation is reported.
Highlights
It is well known that when the size of an analog electronic network increases too much, the size of the unknown vectors, namely the voltages, the currents and the electric node′s voltage, become very large and the system of equation becomes impossible to solve on existing computers
We are concerned by such large systems of electronic equations arising in the case of spatially periodic architectures of analog electronic circuits
Among the applications that we have in mind, some of them are for purely analog electronic systems or for Micro-Electro-Mechanical Systems (MEMS) arrays which have always a periodic structure and include or will include in a near future an electronic network
Summary
It is well known that when the size of an analog electronic network increases too much, the size of the unknown vectors, namely the voltages, the currents and the electric node′s voltage, become very large and the system of equation becomes impossible to solve on existing computers. The ground nodes in N0Γ correspond to some nodes in N located on the cell boundary They belong to NC which have been separated in many connected components NCk which in turn define a partition of N0Γ = ∪nk=c 1N0Γk. The solution of the simplified model introduced in this paper realizes an approximation of the solution of 5 for small values of ε (ε
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