Plenary Lecture

Towards 2D Electronic Circuits in the Spatial Domain

Associate Professor Nicolas Ratier
Graduate engineering school in Mechanics and Microtechnics (ENSMM)
FEMTO-ST laboratory
Besancon, France
E-mail: nicolas.ratier@femto-st.fr

Abstract: Electronic circuits are, by nature, functions of one independent variable in the time domain. They operate (in the sense of differential operators) from an input signal e(t) to an output signal s(t). In this sense, we can speak of the electronic circuits of an ODE (ordinary differential equation) with its associated initial condition.
We show, in this talk, that periodic circuits can be used to define a kind of 2D circuits in the spatial domain. These circuits operate as a PDE (partial differential equations) from an input signal f(x,y) to an output signal g(x,y). The two independent variables are now the coordinate axes x and y. As to the initial conditions, they are replaced by boundary conditions.
We first present how to construct an electronic circuit of a linear PDE and how the boundary conditions are transposed to electronic elements. The discrete solution at each voltage node of this circuit converges towards the solution of the PDE g(x,y) for a given input signal f(x,y) when the number of periodic cells increases.
Next, we consider the reverse problem, i.e. to build the PDE of an electronic linear circuit. Electric conditions imposed at the boundary are converted into Dirichlet or Neumann conditions. The solution of this problem is based on an extension of an homogenization modelling method initially developed by theoretical mechanicians to study composite materials.

Brief Biography of the Speaker:
Nicolas Ratier was born in Paris in 1965. He is graduated in electronics at Paris XI University, Orsay. In 1993, he received the Ph. D. degree in microelectronics from Toulouse III University for his work on the simulation of micromechanical capacitive pressure sensors. He is associated professor at ENSMM (graduate engineering school in Mechanics and Microtechnics) and at FEMTO-ST laboratory, both at Besancon, France. From 1994 to 2006, his primary research activities were the simulation of ultrastable quartz crystal oscillators. Most of these researches have been completed in the framework of contracts executed for the french space agency (CNES). Since 2007, his current research concerns the study of spatially distributed periodic electronic circuits to control array of MEMS.