We consider circuits driven by two or more signals with very different periods and propose a method to determine their steady state solution in the time domain. We present a new version of the shooting method based on the envelope following technique. We show how to use the envelope following method as the new engine to efficiently determine the trajectory of the circuit starting from the new guess of the initial conditions. It substitutes the less efficient time domain analysis used in the conventional implementation of the shooting method. We show that it is well suited to circuits where the ratio between the periods of the slow and fast behaviour is particularly high and characterised by strong non-linearities. The numerical properties at the basis of the proposed method are presented. Its features are shown by simulating different types of slow-fast circuits.

中文翻译：

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包络跟踪技术在拍摄方法中的应用


我们考虑由两个或多个具有不同周期的信号驱动的电路，并提出一种方法来确定它们在时域中的稳态解。我们提出了一种基于包络跟踪技术的新版本拍摄方法。我们展示了如何使用包络跟踪方法作为新引擎，从初始条件的新猜测开始有效地确定电路的轨迹。它取代了传统射击方法实施中使用的效率较低的时域分析。我们表明，它非常适合慢速和快速行为周期之间的比率特别高且具有强非线性特征的电路。给出了基于所提出方法的数值特性。通过模拟不同类型的慢-快电路来展示其特点。