基於連續弦方法之多重電路模擬

Abstract

本篇論文提出一個多重電路模擬器來加速多重電路模擬(multi-circuit simulation)。在多重電路模擬之中，每個電路的架構都是相同的，但是電路參數和原始電路不同。此模擬器是基於連續弦方法(successive chord method)，它是一個使用固定的逆雅可比矩陣(inverse of Jacobian matrix)的非線性迭代方法。透過連續弦方法，此模擬器重複使用逆雅可比矩陣來模擬很多具有相似偏壓的電路。此模擬器也在連續的時間區間內重複使用逆雅可比矩陣，以加速單一電路模擬。本篇論文使用8微米a-Si有機發光二極體驅動電路及90奈米CMOS漣波進位加法器當作實驗電路，並且將此模擬器和一個使用牛頓法(Newton-Raphson method)及逆向尤拉法(backward Euler method)的傳統模擬器做比較。實驗結果顯示此模擬器達到2.3倍的單一電路模擬加速及3.6倍的多重電路模擬加速，並且維持一樣的準確率。

This thesis proposes MUSIC to speed up multi-circuit simulation, where each circuit under simulation is identical in schematic, but different from the original circuit in some parameters. MUSIC is based on the successive chord method, which is a nonlinear iterative method uses fixed inverse of Jacobian matrix (J-1). With the successive chord method, the J-1 is reused to simulate many circuits whose solutions are very close. Besides multi-circuit simulation, MUSIC also speeds up single-circuit simulation, which simulates a circuit with fixed parameters, by reusing the J-1 between consecutive time steps. We demonstrate MUSIC on two different circuits, OLED Organic Light-Emitting Diode (OLED) pixel driver and ripple-carry adder, designed in 8μm flexible amorphous-Silicon (a-Si) Thin-Film Transistor (TFT) and 90nm bulk silicon CMOS technologies, respectively. We compare MUSIC with a traditional circuit simulator that uses Newton-Raphson method and backward Euler method. Experimental results show that, without any loss of accuracy, MUSIC achieves 2.3X and 3.6X runtime speedup in single-circuit and multi-circuit simulation, respectively.