Loading [MathJax]/extensions/MathZoom.js
Continuous-time Analog Computing Circuits for Solving The Electromagnetic Wave Equation | IEEE Conference Publication | IEEE Xplore

Continuous-time Analog Computing Circuits for Solving The Electromagnetic Wave Equation


Abstract:

Two continuous-time mathematical computing methods are proposed for solving the multidimensional wave equation leading to realizable analog computing circuits. The propos...Show More

Abstract:

Two continuous-time mathematical computing methods are proposed for solving the multidimensional wave equation leading to realizable analog computing circuits. The proposed analog computing processors will potentially be able to solve a certain special classes of computational problems involving partial differential equations, which are defined from continuous-time systems. The new analog computing methods are first derived and physically implemented for the first-time using low-frequency operational amplifier circuits in order to experimentally verify the correctness of the proposed methods. Both algorithms approximate the spatial domain partial derivatives using discrete finite differences. The first method performs a direct Laplace transform (with respect to the time variable) on the resulting expression. The second method applies the finite difference along the time dimension and then replaces the discrete time difference with a continuous-time delay operator, which in turn, can be realized as an analog all-pass filter. Analog circuit architectures are introduced for different boundary conditions relevant to common electromagnetic simulation problems. A low frequency prototype of the analog wave equation solver (based on method 1) has been designed, realized and tested using board-level operational amplifier circuits. Test results and measurements are provided to demonstrate the wave propagation in the space-time domain.
Date of Conference: 27-30 May 2018
Date Added to IEEE Xplore: 04 May 2018
ISBN Information:
Electronic ISSN: 2379-447X
Conference Location: Florence, Italy

I. Introduction

Analog computing can accelerate certain special classes of computational problems involving partial differential equations (PDEs) defined from continuous-time systems [1]–[11]. Most physics based simulations involve either linear or nonlinear PDE systems. Electromagnetics, which is an extremely important branch of physics, is completely described by Maxwell's equations, which are in turn, first order linear PDEs [12]–[14]. Therefore, there has been immense efforts in the computational electromagnetics community to simulate electromagnetic models by first descretizing the Maxwell's equations using a staggered computational grid and then solving by digital computers using software [15]–[19]. However, Maxwell's equations are themselves time-continuous, and therefore allow a natural fit for linear analog computing systems using simulation models based on spatially-discrete-time-continuous update equations. We demonstrate the concept by proposing a simplified analog computer that solves the spatio-temporal wave-equation using an analog array processor that operates in continuous-time mode. We have developed two methods producing mathematical models, one of which has been realized using analog circuits. A low-frequency implementation based on operational amplifiers (op-amps) is used to demonstrate the new analog algorithms, with RF extension part of on-going work not covered in this paper.

Systolic array architecture of the second order continuous-time PDE solver. Block diagram of the internal module (IM) derived from (b) method 1 and (c) method 2.

References

References is not available for this document.