在伯德图上求截止频率的一种解析方法

An Analytical Method of Seeking Cutoff Frequency in Bode Diagram

伯德图由对数幅频特性和对数相频特性两条曲线构成。在实际的教学过程中发现,通过绘制伯德曲线得到准确的截止频率是不容易的。本文讨论了开环对数幅频渐近特性的解析表达式用于计算开环系统的截止频率。通过举例介绍了它的求解方法及其应用。虽然这种表达式有助于学生用频率特性法分析和综合系统,但在教学过程中仍应强调绘制伯德图的重要性。

Bode diagram is composed of two curves, logarithm amplitude frequency characteristic and logarithm phase frequency characteristic. During the practical teaching process, we find that it is not easy to get exact cutoff frequency by drawing bode curve. In this paper, the analytical expression of open loop logarithm amplitude frequency asymptotic characteristic is discussed, which is usually used to calculate cutoff frequency of open loop systems. The solving method and application are introduced through exampies. Though the presented expression is helpful for students to analyze and synthesize control systems by frequency characteristic method, the importance of drawing bode diagram should still be emphasized during the teaching process.