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在这篇论文中,我们提出一个基于符号化的,计算在参数变化情况下模拟电路的性能变化范围的算法。我们对于模拟电路的参数使用实际测试获得的参数的变化区间数值进行建模。新的算法采用基于图的行列式二分决定树算法(DDD),并且可以导出系数用区间表示的传输函数。然后通过使用Kharitonov定理,可以快速获得传输函数频率响应的振幅和相位的最大值和最小值。在论文中,我们也同时证明在符号化表达式展开求值的过程中,相同项的抵消对于最后的精度有很大影响。并且由于使用了Kharitonov定理,计算获得的振幅和相位的变化范围是对于实际变化范围的保守估计。实验结果证明论文提出的算法与传统的蒙特卡罗算法相比速度上有很大提高。
In this paper, we propose an algorithm based on symbolization that calculates the range of performance variations of an analog circuit under parametric changes. We model the parameters of the analog circuit using the values of the varying intervals of the parameters obtained from the actual test. The new algorithm uses a graph-based deterministic binary deterministic algorithm (DDD) and can derive the transfer function of coefficients in intervals. Then by using Kharitonov’s theorem, the maximum and minimum amplitude and phase of the frequency response of the transfer function can be quickly obtained. In the paper, we also prove that the offset of the same item has a great influence on the final precision during the evaluation of symbolic expressions. And because of the use of Kharitonov’s theorem, the range of variation of the calculated amplitude and phase is a conservative estimate of the actual range of variation. The experimental results show that the proposed algorithm is greatly improved in speed compared with the traditional Monte Carlo algorithm.