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研究与设计 电 子 测 量 技 术ELECTRONIC MEA SUREM ENT T ECH NOLOGY 第31卷第2期2008年2月Butterworth有源抗混叠滤波器设计林祥金 张志利 朱 智(西安二炮工程学院 西安 710025)摘 要:信号混叠是视频采样系统中的一种失真。
为了防止这种失真,本文设计了一个4阶的视频有源低通抗混叠滤波器。
通过对二阶Bessel、Butter wo rth和Chebyshev等多种滤波器的性能分析比较,本文采用Butterw or th滤波器来设计该抗混叠滤波器,电路的拓扑结构采用Sallen K ey结构,并采用高速双运算放大器(SN10502),以构造一个可放入狭小印刷电路板中的4阶But terw or th滤波器。
测量结果表明,该滤波器在视频频段内几乎不出现峰值、平坦度好,并且阻带抑制效果好。
微分增益和相位同样也很不错。
最后,还讨论了在设计视频有源滤波过程中应该如何根据实际应用选择运算放大器,如何选择电容、电阻值,如何布局布线以及如何消除振荡。
关键词:Butter wo rth滤波器;有源抗混叠滤波器;Sallen key中图分类号:T P273 文献标识码:ADesign of butterworth active anti aliasing filterL in Xiangjin Zhang Zhili Zhu Z hi(Second Artillery Engin eering In stitu te,Xi an710025)Abstract:Sig nal aliasing is an obvious distor tio n in high speed video sampling system.T o avo id that,this paper presents a design of a four o rder active anti aliasing filter using hig h speed dual o perat ional amplifier SN10502,which can be placed in a tiny P CB(P rinted Circuit Boa rd).A n o ptimum design of this filter is intr oduced.Results show that the designed filter o ffers g oo d flatness of f requency r esponse,g oo d effects of sto pband rejectio n,hig h differential g ain and hig h differ ent ial phase,and almost no peaking occurs w it hin video fr equency r ang e.Finally this paper ends w ith discussions on ho w to cho ose o per ational amplifiers based o n practical application,how to choo se capacit ance and resistance,how to eliminate oscillation and on how to layout.Keywords:Butt erw ort h filter;act ive anti aliasing filter;Sallen key0 引 言信号混叠是采样视频系统中的一个明显失真。
一种抗混叠滤波器的设计郭红玉【摘要】针对信号采集时，频率混叠现象的发生，为了能够有效地提取有用信号，本文介绍了滤波器的设计原理。
通过分析混叠现象产生的原因，探讨了几种常见滤波器的特点并进行了比较；最后设计了一种基于二阶巴特沃斯带通抗混叠滤波器。
通过仿真结果可以得出，该滤波器具有通带衰减特性平坦，能够有效避免混叠现象发生，为工程实践提供了可靠的理论指导。
%Aim at signal acquisition, the frequency alias happened regularly, in order to getting available signals,the paper introduced the principle of filters. By analyzed the appearance of the signal aliasing phenomenon;discussed and compared the characteristic of several common filters; at last designed a kind of anti-alias filter which based on 2nd order band pass Butterworth filter. The filter had a smooth band pass damping, voiding alias happened, supplied reliable theory guide for engineering practice.【期刊名称】《电子设计工程》【年(卷),期】2015(000)003【总页数】3页(P110-112)【关键词】滤波器;抗混混叠;巴特沃斯滤波器;归一化【作者】郭红玉【作者单位】朔州职业技术学院山西朔州 036002【正文语种】中文【中图分类】TN99滤波是指从混杂的信号中提取有用信息的过程。
基于光端机的Butterworth有源滤波器的改进型设计章小兵;金鑫;方挺【摘要】An improved five-order active Butterworth filter is designed according to characteristics of input video signal. Sampling frequency is increased to reduce filter order, the group delay and the frequency characteristic of the filter are also adjusted, and quality of input video signal is improved. The reconstruction filter is built with specialized chipfor filtering and driving of the output video signal. The fiber transmitting and processing terminal including improved filter and programmable controller is implemented.Simulation and experimental results show that the designed filter has the characteristics of flatter passband, bigger stop-band attenuation, and better group delay in the passband.%针对输入视频信号特点,设计改进型的五阶Butterworth有源滤波器.通过提高采样频率降低滤波器阶数,同时改善滤波器的频率与群延时特性,从而提高输入视频信号的质量；采用专用芯片搭建重建滤波器以对输出视频信号进行滤波及驱动,实现包含改进滤波器的视频信号光纤传输处理终端.仿真与实验结果表明该滤波器通带平坦、阻带衰减大、群延时特性好.【期刊名称】《安徽工业大学学报（自然科学版）》【年(卷),期】2012(029)003【总页数】5页(P242-246)【关键词】Butterworth滤波;群延时;视频;光纤传输【作者】章小兵;金鑫;方挺【作者单位】安徽工业大学电气信息学院,安徽马鞍山243002;安徽工业大学电气信息学院,安徽马鞍山243002;安徽工业大学电气信息学院,安徽马鞍山243002【正文语种】中文【中图分类】TP39光纤通讯以其频带宽、容量大、衰减小等优势给通信领域带来了革新,基于光纤的视频信号传输应用越来越广泛。
BUTTERWORTH FILTER DESIGN ObjectiveThe main purpose of this project is to learn the procedures for designing Butterworth filters.BackgroundThe Butterworth and Chebyshev filters are high order filter designs which have significantly different characteristics, but both can be realized by using simple first order or biquad stages cascaded together to achieve the desired order, passband response, and cut-off frequency. The Butterworth filter has a maximally flat response, i.e., no passband ripple and a roll-off of -20dB per pole. In the Butterworth scheme the designer is usually optimizing the flatness of the passband response at the expense of roll-off. The Chebyshev filter displays a much steeper roll-off, but the gain in the passband is not constant. The Chebyshev filter is characterized by a significant passband ripple that often can be ignored. The designer in this case is optimizing roll-off at the expense of passband ripple.Both filter types can be implemented using the simple Sallen-Key configuration. The Sallen-Key design (shown in Figure A-1) is a biquadratic or biquad type filter, meaning there are two poles defined by the circuit transfer function(1)where H 0 is the DC gain of the biquad circuit and is a function only of the ratio of the two resistors connected to the negative input of the opamp. The quantity Q is called the quality factor and is a direct measure of the flatness of the passband (in particular, a large value of Q indicates peaking at the edge of the passband.) When C 1 = C 2 = C and R 1 = R 2 =R for the Sallen-Key design, the value of Q depends exclusively on the gain of the op-amp stage and the cut-off frequency depends on R and C, or(2)(3) Notice that the quality factor Q and the DC gain H 0 cannot be independently set in the)(/)()12(/1s H o H s s o o Q ωω=++12f c RC π=13O Q H =−Sallen-Key circuit. Choice of the value of Q depends on the desired characteristics of the filter. In particular the designer must consider both the quality and the stability of the circuit. Calculations with different values of Q demonstrate that for the second order case the flattest response occurs when Q = 0.707, hence the maximally flat response of the Butterworth filter will also be realized when Q = 0.707. In addition the circuit is only stable when H 0 < 3. Higher values will result in poles in the right half-plane and an unstable circuit.The Butterworth filter is an optimal filter with maximally flat response in the passband. The magnitude of the frequency response of this family of filters can be written as(4)where n is the order of the filter and f c is the cutoff frequency . For a single biquad section, i.e., n = 2, the gain for which Q will equal 0.707, and hence yield a Butterworth type response, is found to be 1.586 from equation (2).In the case of a fourth order Butterworth filter (n = 4), the correct response can be achieved by cascading two biquad stages. Each stage must be characterized by a specific value of gain (or Q ) that achieves both a flat response and stability. For a fourth order Butterworth filter, the Q factors of the two stages must be Q = 0.541 and Q = 1.307. From (2) it follows that one stage must have a gain of 1.152 and the other stage a gain of 2.235. As a result the overall DC gain of the fourth-order Butterworth realized with two biquad stages will be equal to the product of the DC gain of the two stages, i.e., 2.575. The gain values required to cascade biquad sections to achieve even-order filters are given in Table A-I. Note that the number of biquad stages needed to realize a filter of order n is n /2.Other types of filters such as high pass, and bandpass filters can be designed the same way, i.e., by cascading the appropriate filter sections to achieve the desired bandpass and roll-off. The high-pass dual to the Sallen-Key low pass filter can be realized by simply exchanging the positions of R and C in the circuit of Figure A-1. Project1. Design a Butterworth lowpass filter with the following specification:Pass Frequency = 10KHzStop Frequency = 20KHzMinimum Attenuation in the stop band = 45 dB2. Design a Butterworth highpass filter with the following specification:Pass Frequency = 10KHzStop Frequency = 2KHzMinimum Attenuation in the stop band = 45 dB3. What is the minimum order for each filter?4.What is the passband gain of the filters?()H f5.Simulate the filters using Spice. Produce Bode plots for magnitude and phase for the two filters. Apply to the lowpass filter a 1V square wave and simulate the response of the lowpass filter. Do this for three cases: square wave frequency equal to 0.1 f c, 0.5 f c, and f c, where f c is the cutoff frequency of the lowpass filter. Apply to the highpass filter a 1V square wave and simulate the response of the highpass filter. Do this for three cases: square wave frequency equal to 10 f c, 2 f c, and f c, where f c is the cutoff frequency of the highpass filterDATA ANALYSISWrite a discussion of the results comparing the predicted values from your calculations with PSpice's predicted values. Make sure that your conclusions are supported by the data. Place all PSpice hard copies in the Report.AppendixFigure A-1 The Sallen-Key low pass filterPoles Butterworth(Gain) Chebyshev (0.5dB) λnGainChebyshev (2.0dB) λnGain2 1.586 1.231 1.842 0.907 2.114 4 1.152 0.597 1.582 0.471 1.9242.235 1.031 2.660 0.964 2.7821.068 0.396 1.537 0.316 1.891 6 1.586 0.7682.448 0.730 2.6482.483 1.011 2.846 0.983 2.9041.038 0.297 1.522 0.238 1.8791.337 0.5992.379 0.572 2.6051.889 0.8612.711 0.842 2.821 82.610 1.006 2.913 0.990 2.946。
基于Butterworth型三阶有源LPF的设计郭俊锋【期刊名称】《电子测试》【年(卷),期】2016(000)006【摘要】给出了一种利用运算仿真法实现三阶有源LPF的方法.利用Butterworth 函数逼近滤波器,对组成滤波器的元件进行了优化设计,使得滤波器的动态范围达到最大,频率特性符合Butterworth函数特点.利用EWB5.0C软件进行了仿真验证,符合设计要求,可应用于任意高阶的低通滤波器设计中.%A methodof implementation three active LPF with calculate & simulation is presented. Butterworth is approximated to filter, optimization design of filters' elements RC, so the dynamic range of the filter is the biggest.The feasibility is verified by simulating in EWB5.0C.【总页数】2页(P25-26)【作者】郭俊锋【作者单位】运城职业技术学院,山西运城,044000【正文语种】中文【中图分类】TN713【相关文献】1.基于光端机的Butterworth有源滤波器的改进型设计 [J], 章小兵;金鑫;方挺2.基于改进的Butterworth传递函数的高阶低通有源滤波器的设计 [J], 吕丹;陈文灵;张文夫;邓发升3.适用于放电信号的ButterWorth有源滤波器快速设计 [J], 曹珂杰;王聪;陈善璐4.基于改进型Butterworth传递函数的高阶低通滤波器的有源设计 [J], 李钟慎;洪健5.三阶Butterworth型极点配置方法的改进 [J], 孟吉红;徐军;邓海波;任克伟因版权原因，仅展示原文概要，查看原文内容请购买。
巴特沃斯低通滤波器简介巴特沃斯低通滤波器（Butterworth low-pass filter）是一种常用的模拟滤波器，被广泛应用于信号处理和电子系统中。
它的设计原则是在通带中具有平坦的幅频特性，而在截止频率处具有最大衰减。
这种滤波器的设计目的是能够尽可能滤除高频噪声，而保留低频信号。
巴特沃斯滤波器的特性巴特沃斯低通滤波器具有以下特性：•通带幅度为1：在通带中，滤波器的增益保持不变，也就是幅度为1。
•幅度频率响应的过渡带是由通带到停带的渐变区域，没有任何波纹。
•幅度频率响应在通带之外都有指数衰减。
•巴特沃斯滤波器是最平滑的滤波器之一，没有任何截止角陡峭度。
巴特沃斯滤波器的传递函数巴特沃斯低通滤波器的传递函数由下式给出：H(s) = 1 / (1 + (s / ωc)^2n)^0.5其中，H(s)为滤波器的传递函数，s为复变量，ωc为截止频率，n为滤波器的阶数。
阶数决定了滤波器的过渡带宽度和滤波特性。
巴特沃斯滤波器设计步骤巴特沃斯滤波器的设计步骤如下：1.确定所需滤波器的阶数和截止频率。
2.根据阶数和截止频率选择巴特沃斯滤波器的标准传递函数，可以从经验图表或计算公式中得到。
3.将标准传递函数的复频域变量进行频率缩放，以得到实际的传递函数。
4.将传递函数进行因式分解，得到一系列一阶巴特沃斯滤波器的传递函数。
5.根据一阶传递函数设计电路原型。
6.将一阶电路原型按照阶数进行级联或并联，构成所需的滤波器电路。
巴特沃斯滤波器的优点和缺点巴特沃斯低通滤波器具有以下优点：•平坦的传递特性：在通带中，滤波器的增益保持不变，不会引入频率响应的波纹或衰减。
•平滑的过渡带：巴特沃斯滤波器的过渡带具有指数衰减特性，没有任何波纹或突变。
•简单的设计：巴特沃斯滤波器的设计步骤相对简单，可以通过标准传递函数和电路原型进行设计。
然而，巴特沃斯滤波器也具有一些缺点：•较大的阶数：为了达到较陡的阻带衰减，巴特沃斯滤波器需要较高的阶数，导致电路复杂度增加。
抗混叠滤波器的设计与运用摘要：在信号采集系统设计中，数据采集的精度及对数据采集的抗混叠滤波是很重要的考虑因素。
本文介绍了如何设计品质优良的抗混叠滤波器。
首先阐述了如何用分离元件设计滤波器，并以巴特沃斯滤波器为例进行分析。
然后讨论了使用集成芯片来设计抗混叠滤波电路，并总结了它们的优缺点。
关键词：信号采集；滤波器；抗混叠1.引言在信号采集系统中，如果信号的最高频率fh超过1／2采样频率（fs），即fh＞fs／2 时，则各周期延拓分量产生频谱的交叠，称为频谱的混叠现象。
我们将采样频率之半（／2）称为折叠频率，它如同一面镜子，当信号频谱超过它时，就会被折叠回来，造成频谱的混叠。
若原始信号是频带宽度有限的，要想采样后能够不失真地还原出原始信号，则采样频率必须大于或等于两倍信号谱的最高频率，即奈奎斯特采样定理。
若原始信号不是频带宽度有限的，为了避免混叠，一般在抽样器前加入一个保护性的前置低通滤波器，称为抗混叠滤波器。
抗混叠滤波器可选用模拟滤波器电路，也可选用集成的芯片。
模拟滤波器电路可由运放、电阻和电容搭建，由于受分离元件的精度和环境温度影响，很难提高滤波精度，但是电路参数可以根据滤波器的指标自由设计；集成芯片由于集成度的提高，电路的可靠性和精度有了相应的提高，但是滤波器的指标受到了一定的限制。
本文就从这两方面进行滤波器的分析与设计。
2.模拟抗混叠滤波器电路设计抗混叠滤波器需要首先确定所希望的滤波特性（截止频率、过渡带衰减等），然后选择能够满足应用需求的最佳滤波方案。
一般情况下，低通滤波器的阶数越高，幅频特性衰减的速度越快，就越接近理想幅频特性，但实现起来电路越复杂，成本也较高。
下面以4阶巴特沃斯低通滤波器为例来分析滤波器电路中电阻电容参数。
表1所示为4阶Butterworth低通滤波器参数，它可由两个二阶低通滤波网络级联而成。
表1 4阶Butterworth低通滤波器参数由式（2）和表1可确定满足条件的一组电容元件参数：C1A=0.46 ，C1B=0.07 ，C2C=0.19 ，C2B=0.16 。
