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首页> 外文期刊>Circuits and Systems I: Regular Papers, IEEE Transactions on >Continuous-Time Algorithms for Solving Maxwell’s Equations Using Analog Circuits
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Continuous-Time Algorithms for Solving Maxwell’s Equations Using Analog Circuits

机译：使用模拟电路求解麦克斯韦方程组的连续时间算法

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摘要

Two analog computing methods are proposed to compute the continuous-time solutions of one-dimensional (1-D) Maxwell's equations. In the first method, the spatial domain partial derivatives in the governing partial differential equation (PDE) are approximated using discrete finite differences while applying the Laplace transformation along the time dimension. The resulting spatially discrete time-continuous update equation is utilized to design an analog circuit that can compute the continuous-time solution. The second method replaces the discrete-time difference operators in the standard finite difference time domain (FDTD) cell (Yee cell) using continuous-time delay operators, which can be realized using analog all-pass filters. Both methods have been simulated using ideal analog circuits in Cadence Spectre for the Dirichlet, Neumann, and radiation boundary conditions. The performance of the proposed methods has been quantified using: i) mean squared differences between the results and fully discrete FDTD simulations and ii) the noise to signal energy ratio. Both methods have been extended to design the analog circuits that compute the continuous-time solution of the 1-D and 2-D wave equations. The 1-D wave equation solver is simulated with a dominant-pole model (which better approximates the non-ideal circuit behavior) along with a propagation delay compensation technique. The experimental results from a simplified board-level low-frequency implementation are also presented. The key challenges toward CMOS implementations of the proposed solvers are identified and briefly discussed with possible solutions.
机译：提出了两种模拟计算方法来计算一维（1-D）Maxwell方程的连续时间解。在第一种方法中，控制离散偏微分方程（PDE）中的空间域偏导数是使用离散有限差分近似的，同时沿时间维度应用了Laplace变换。所得的空间离散时间连续更新方程用于设计可计算连续时间解的模拟电路。第二种方法使用连续时间延迟算子代替标准有限时域（FDTD）信元（Yee信元）中的离散时差算子，该算子可以使用模拟全通滤波器实现。两种方法均已使用Cadence Spectre中的理想模拟电路针对Dirichlet，Neumann和辐射边界条件进行了仿真。所提出方法的性能已通过以下方式量化：i）结果与完全离散的FDTD模拟之间的均方差，以及ii）噪声与信号能量之比。两种方法都已扩展到设计模拟电路，以计算一维和二维波动方程的连续时间解。一维波动方程求解器通过一个主极模型（可以更好地近似非理想电路行为）以及传播延迟补偿技术进行仿真。还介绍了简化的板级低频实现的实验结果。提出的求解器对CMOS实施的主要挑战已经确定，并通过可能的解决方案进行了简要讨论。

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