Delay dynamics occur in a wide variety of natural and man-made systems. Even simple delay systems can generate complex dynamics whose exploration is rewarding. To allow such exploration as part of advanced undergraduate laboratory courses and be able to utilize systems that operate at convenient timescales, it is necessary to delay analog signals by several milliseconds. In this paper, we describe an implementation of a programmable digital circuit capable of delaying DC-coupled analog signals up to 262 ms at a 1 MHz sampling rate. The initial history of the system may also be arbitrarily programmed, enabling the study of transient behavior. As an application, we discuss the use of this programmable delay in a feedback circuit that produces period-four triangular solutions, in complete agreement with theoretical predictions.

中文翻译：

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使用可编程电子延迟电路探索延迟动态

延迟动力学发生在各种各样的自然和人造系统中。即使是简单的延迟系统也可以产生复杂的动态，其探索是有益的。为了将这种探索作为高级本科实验室课程的一部分并能够利用在方便的时间尺度上运行的系统，有必要将模拟信号延迟几毫秒。在本文中，我们描述了可编程数字电路的实现，该电路能够以 1 MHz 采样率将直流耦合模拟信号延迟高达 262 毫秒。系统的初始历史也可以任意编程，从而能够研究瞬态行为。作为一个应用，我们讨论了在反馈电路中使用这种可编程延迟，该电路产生四周期三角解，与理论预测完全一致。