模拟有源滤波器

摘要

本文阐述了滤波器的基本概念，介绍了模拟有源滤波器的设计原理和逼近理论。其中包括巴特沃思逼近、切比雪夫I型逼近、切比雪夫Ⅱ型逼近、椭圆函数逼近和贝塞尔逼近。并研究了模拟有源滤波器的设计流程及性能测试。

综合了传统的硬件设计方法与软件编程技术,由MATLAB仿真出了各种滤波器逼近技术的幅频特性曲线并进行了实例分析。对巴特沃思滤波器实例的研究仿真，由程序快速的得到了最小阶数和截止频率，取代了传统繁复的计算；方便的实现了由模拟低通滤波器向高通、低通和带阻滤波器的转换；对四运放复杂电路进行了设计仿真，通过求取其不同点的输出传递函数，模拟了二阶低通、高通、带通和带阻滤波器的幅频特性曲线并得到了较好的仿真结果。

关键词：模拟有源滤波器；逼近理论；幅频特性；MATLAB程序设计

ABSTRACT

This paper describes the basic concepts of filters introduced analog active filter design principles and approximation theory. Including Butterworth approximation, Chebyshev type I approximation, Chebyshev Ⅱ type approximation, elliptic function approximation and Bezier approximation. And studied the analog active filter design process and performance testing.

Combines the traditional hardware design methods and software programming techniques, by the MATLAB simulation of a variety of filter approximation technique of amplitude-frequency characteristic curve and an illustrative example. Butterworth filter instance on simulation studies, by the program to quickly get the minimum order and the cutoff frequency, replacing the traditional complex calculations; conveniently achieved by the analog low-pass filter to the high-pass, low-pass and band-stop filter the conversion; complex on quad op amp circuit design simulation, through its different points strike output transfer function to simulate the second-order low-pass, high pass, band pass and band-stop filter frequency characteristic curve and get better simulation results.

Keywords:Analog and Active Filter;Theory of Approximation,Amplitud-frequency characteristics，MATLAB program design

目录

1 绪论 (1)

2 滤波器的基本概念 (3)

2.1滤波原理 (3)

2.2滤波器分类 (3)

2.2.1 根据滤波器的选频作用分类 (3)

2.2.2 根据“最佳逼近特性”标准分类 (4)

2.2.3 按滤波器元件性质 (5)

3 模拟有源滤波器的设计原理 (6)

3.1信号无失真传输的条件 (6)

3.2理想滤波器的特性 (7)

3.3模拟滤波器传递函数设计原理 (7)

3.3.1 模拟滤波器设计步骤 (8)

3.3.2 模拟滤波器设计函数 (8)

3.4滤波器最小阶数选择 (9)

3.4.1 滤波器最小阶数选择原理 (9)

3.4.2 滤波器最小阶数选择函数 (10)

3.5模拟滤波器的性能测试 (11)

3.6频率变换 (12)

3.6.1 频率变换工具函数 (12)

4 模拟滤波器的逼近理论 (14)

4.1B UTTERWORTH滤波器 (14)

4.1.1 Butterworth滤波器应用 (15)

4.2切比雪夫（CHEBYSHEV）滤波器 (17)

4.2.1 Chebyshev I型 (17)

4.2.2 Chebyshev II型滤波器 (18)

4.2.3 应用举例 (20)

4.3椭圆滤波器 (22)

4.3.1 应用举例 (23)

4.4B ESSEL滤波器 (24)

4.4.1 应用举例 (25)

5 模拟有源滤波器设计举例 (27)

5.1有源一阶滤波电路 (27)

5.1.1 一阶滤波电路 (27)

5.1.2 应用实例 (28)

5.2双二阶滤波电路 (29)

5.2.1 双二阶电路 (29)

5.2.2 应用实例 (30)

5.3二阶有源带阻滤波电路 (33)

5.3.1 带阻滤波电路举例 (34)

结束语 (37)

参考文献 (38)

致谢 (39)