模擬有源濾波器設(shè)計(jì)的MATLAB實(shí)現(xiàn)

摘  要

本文闡述了濾波器的基本概念，介紹了模擬有源濾波器的設(shè)計(jì)原理和逼近理論。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、橢圓函數(shù)逼近和貝塞爾逼近。并研究了模擬有源濾波器的設(shè)計(jì)流程及性能測試。
綜合了傳統(tǒng)的硬件設(shè)計(jì)方法與軟件編程技術(shù),由MATLAB仿真出了各種濾波器逼近技術(shù)的幅頻特性曲線并進(jìn)行了實(shí)例分析。對巴特沃思濾波器實(shí)例的研究仿真，由程序快速的得到了最小階數(shù)和截止頻率，取代了傳統(tǒng)繁復(fù)的計(jì)算；方便的實(shí)現(xiàn)了由模擬低通濾波器向高通、低通和帶阻濾波器的轉(zhuǎn)換；對四運(yùn)放復(fù)雜電路進(jìn)行了設(shè)計(jì)仿真，通過求取其不同點(diǎn)的輸出傳遞函數(shù)，模擬了二階低通、高通和帶通濾波器的響應(yīng)曲線。得到了較好的仿真結(jié)果。

關(guān)鍵詞：模擬有源濾波器，逼近理論，最小階數(shù)選擇，MATLAB程序設(shè)計(jì)

 
 
ABSTRACT

This article shows Design of Analog and Active Filter Based on MATLAB.It starts by covering the fundamentals of filters .And then introduces the design principle of analog and active filter, the choice of the minimum order, the performance testing of the analogy filter and the theory of approximation, goes on to introduce the basic types like Butterworth, Chebyshev I, Chebyshev Ⅱ, Ellipse and Bessel filter, and then guides the reader through the design process for analog and active filters.
It synthesizes the conventional method and MATLAB program means, studying how to carry out an analog filter with MATLAB. This text includes numerous examples of the magnitude curve. We can easily carry out a low pass, high pass, band pass, band stop filter and change parameters such as pass band ripple and stop band attenuation as long as changing certain program. It largely simplifies the design of analog filter.

Keywords: Analog and Active Filter，Theory of Approximation, The Choice of the minimum order，MATLAB program design

 
 
目  錄

引言……………………………………………………………………………1
第1章  濾波器的基本概念…………………………………………………3
1.1 濾波原理.................................................3
1.2 濾波器的分類.............................................4
第2章 模擬有源濾波器的設(shè)計(jì)原理…………………………………………6
2.1信號(hào)無失真?zhèn)鬏數(shù)臈l件.......................................6
2.2 理想濾波器的特性..........................................8
2.3 模擬有源濾波器傳遞函數(shù)設(shè)計(jì)原理.............................9
2.3.1 設(shè)計(jì)步驟.............................................11
2.3.2 設(shè)計(jì)函數(shù).............................................11
2.4 濾波器最小階數(shù)選擇.......................................12
2.4.1 最小階數(shù)選擇原理......................................12
2.4.2 最小階數(shù)選擇函數(shù)......................................13
2.5 頻率變換................................................15
2.5.1 低通——低通變換......................................15
2.5.2 低通——高通變換......................................16
2.5.3 低通——帶通變換......................................16
2.5.4 低通——帶阻變換......................................17
2.5.5 頻率變換工具函數(shù)......................................17
2.6 模擬濾波器的性能測試......................................19
第3章 模擬有源濾波器的逼近理論……………………………………… 21
3.1巴特沃思逼近.............................................21
3.1.1巴特沃思濾波器........................................21
3.1.2應(yīng)用實(shí)例.............................................23
3.2 Chebyshev I型逼近.........................................25
3.2.1 Chebyshev I型濾波器....................................26
3.2.2應(yīng)用實(shí)例.............................................28
3.3 Chebyshev II型逼近........................................33
3.3.1 ChebyshevII型濾波器...................................33
3.3.2應(yīng)用實(shí)例.............................................34
3.4橢圓函數(shù)逼近.............................................36
3.4.1橢圓函數(shù)濾波器........................................36
3.4.2應(yīng)用實(shí)例.............................................37
3.5貝塞爾逼近...............................................40
3.5.1貝塞爾濾波器..........................................40
3.5.2應(yīng)用實(shí)例.............................................41
第4章 設(shè)計(jì)舉例…………………………………………………………….43
   4.1有源一階濾波電路.................................... ......43
4.1.1 一階濾波電路...................... ............ .... ..43
4.1.2 應(yīng)用實(shí)例............................................ .44
   4.2雙二階濾波電路.................................... ...... .45
     4.2.1雙二階電路.................................... ...... .45
     4.2.2應(yīng)用實(shí)例.................................. .......... .46
4.3低通和高通濾波器.................................... .... .50
     4.3.1 二階低通濾波器...................... ............ .... 50
     4.3.2 二階高通濾波器...................... .....  ...... ... 51
結(jié)論…………………………………………………………………………53
致謝…………………………………………………………………………54
參考文獻(xiàn)……………………………………………………………………55