滤波器

滤波器&= #30340;分类

§ 按其频率特性可分= 0026;低๩= 0;（LPF）= 2289;高通（HPF）= 2289;带๩= 0;（BPF）= 1644;带阻（BEF）= 8388;波器。

<= span lang=3DZH-CN style=3D'mso-ansi-language:EN-US'> 无源滤= 874;器是由无源器件&= #26500;成。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.63%'>• 电阻、电感和电容= 2452;成的RLC滤波器。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.36%'>• 晶体滤波器是利用= 0707;英晶体薄片构成。

• 声表面波滤波器(SAW)：利用压电效应构= 5104;的。

有଎= 4;滤波器是指在所构成&= #30340;滤波器中，除无源= 120;件外还含<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>有放大器等有&= #28304;电路。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.69%'>• RC有源滤波器（&= #21547;有运算放大器）。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-2.6%'>• 开关电容滤波器(SCF)。

= <= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.48%;font-family:Wingdings'>§ <= /span>按处理的信号&= #24418;式可分为模ৣ= 1;滤波器、数ढ= 3;滤波器和抽੫= 9; = ;

数ৱ= 4;滤波器等。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.75%;font-family:Wingdings'>§ <= /span>按其所用器件&= #30340;特点可分为无源和有源ଖ= 8;波器。

------=_NextPart_01D13E5F.0CC271E0 Content-Location: file:///C:/B2FC02A8/file0200.files/slide0059.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 滤波器

电子线&= #36335;的基本形式及它们之间的&= #32852;系

抽样= 数据电路

模拟= 电路

数字= 电路

抽样= 电路

编码= 器

滤波= 器

解码= 器

模= 拟信号输入

模= 拟信号输出

抽样= ;信号

数字= ;信号

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滤波器

滤波器&= #30340;分类（&= #32493;1）

= 3;

滤波器的= ;理想幅度-频率= 9305;性曲线

按ࠥ= 4;幅度频率特性可分为&= #20302;通、高通、带通和= 102;阻滤波器。

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<= span lang=3DEN-US style=3D'font-family:SimSun;mso-ascii-font-family:SimSun;font= -size: 82%;mso-fareast-language:ZH-CN'>LC 滤波器<= br>

<= span style=3D'font-family:SimSun'>&se= ct;阻抗特性(ल= 8;纳特性)

<= span style=3D'font-family:SimSun;visibility:hidden'>§

<= span style=3D'font-family:SimSun'>&se= ct;谐振特性和= ;回路谐振频率
<= span style=3D'font-family:SimSun;visibility:hidden'>§

<= span style=3D'font-family:SimSun'>&se= ct;频率特性（= ;幅频特性与相频特性&#= 65289;

l=

------=_NextPart_01D13E5F.0CC271E0 Content-Location: file:///C:/B2FC02A8/file0200.files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 滤波器

电= 路特点

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.55%;font-family:Wingdings'>§ <= /span>回路电感元件&= #30340;固有损耗电阻       。

包括电感线圈&= #23548;线的欧姆电阻、由$= 235;肤效应引起的高频损= ;耗电阻。

=3D        可以得出：
(当= Q>>1 <= /span>时 )

§ 固有损耗也可等效= 4920;示为并联谐振电阻       。

§ <= /span>回路&= #31354;载（固有）品质 =

   因数 Q 。（易૭= 9;量）

由：
返回

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2. 回路= ;阻抗特性（导纳特性&#= 65289;

并联回路端༅= 9;抗的模和相角随频率&= #21464;化的关系为：

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回= 路阻抗特性（&= #32493;）

并联回路的阻抗特性
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= = =
并联回路的电抗特性

电感

电容

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3.&= #35856;振特性和回路谐振'= 057;率

§ 谐振特性：= 并联回路谐振时，流过&= #20854;电抗支路的电流      、

比= 8608;励电流      大 = Q 倍，故并联谐&= #25391;又称电૬= 9;谐振。

=

式中，

为回路无阻尼&= #25391;荡频率。

&se= ct; 当 Q= >>1 时：

串= 2852;回路谐振时，电容ࢤ= 0;上电压是激励电压的<= /span> Q 倍，故串联<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>谐振又称电࡚= 7;谐振。所以品质因&= #25968; Q 易测量。（ Q表原理= ）

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-5.12%;font-family:Wingdings'>§ 回路谐振频率：

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LC 串、并联= 谐振回路比较

谐振频率

谐振条件

恒流源

恒压源

激励源

电路形式

并联谐振回ั= 5;

串联谐振回ั= 5;

电路名称

例1

例2

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LC 串、并联= 谐振回路比较（续1）=

谐振参数

= 品质因数= = Q

端阻抗

（导纳）

= ;

并联谐振回ั= 5;

串联谐振回ั= 5;

电路名称

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LC 串、并联= 谐振回路比较（续2）=

谐振特性=

= 相对幅频特性

= 相频特性

电流谐振

电压谐振

谐振性质

并联谐振回ั= 5;

串联谐振回ั= 5;

电路名称

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例= 1：串联回路å= 14;下图所示。

=

        = ;            &n= bsp;            = ;            &n= bsp;            信号源频率     F =3D1MHz。=

电= 1387;振幅        = ; V=3D0.1V。

将1-1端短接，电容C 调= 1040;

100PF时谐振。此&#= 26102;，电容

C 两= 1471;的电压为10V。

如= 1-1端开路再串接= 9968;阻抗 Z （= 电阻和电容串联），则回路

失= 5856;，电容 C = 调到200PF时= 7325;新谐振。此时，电ब= 1; C = 两端

的= 0005;压为2.5V。

试= 7714;：线圈的电感 L，回路&#= 21697;质因数 Q 以及未知阻抗 Z 。=

返回 1

返回 2

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R0lGODlhkQAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACP AB8AgQAAAAD//////wECAwLoVI6py+0sgJy02nvN27wroXni+GHmiYXk6oHs20XojKrw/dn4LtO+ pdvdXMJi74cEBIssIhN3TPqWz5Gz+opKZ1RsrOvdaLcncNhxPYvG5JR6lX5z2G2g3Gq+I+h1Sl4f EAcI0cc1OPenx1eodCiWeLdYCCkn6LjHWHaJRvkm2depZrn5WRd6NnpZ2nYaluq4Stbq9XoYuzWL VTt4K5VbtQvYm/T7FKyYaVLMdByZ7LYJsWz0nBEtfb0wjDQt1FxZbZed8O0ZXtHNkw517jdOvj7U PhEPA3KPn6+/z9/vv/3jn8CBBPEVAAA7 ------=_NextPart_01D13E5F.0CC271E0 Content-Location: file:///C:/B2FC02A8/file0200.files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 滤波器

例= 2：并联回路å= 14;下图= 所示。

        = ;            &n= bsp;            = ;            &n= bsp;      已知：     =3D       =3D= 5UH，Q=3D100。

        = ; =3D     &= nbsp; =3D8PF，    =3D40K。

        = ; =3D10K。

试= 7714;：无阻尼谐振频率ᦂ= 7;

        = ;    等效谐振电&#= 38459; R ；

        = ;    不接       ，BW如何变？

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=
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 滤波器

1. 网络综合方= ;法完成滤波器的设计&#= 30340;要点：

= <= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.6%;font-family:Wingdings'>§ 描述问'= 064;：首先要给出滤&= #27874;器的技术指标，描$= 848;滤波

器的衰减特性&= #26354;线。与理想特性之&= 388;主要的区别在于：=

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.48%;font-family:Wingdings'>§ 逼近问'= 064;：寻找逼近衰减&= #29305;性曲线的可实现的= 256;输函数。

常用的逼近方&= #27861;有巴特沃斯逼近、切比雪夫逼近、椭圆

逼近和贝塞尔&= #36924;近。

§ 实现问'= 064;：在设计中，一&= #33324;只给出了低通滤波= 120;的数据。<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>高通、带通&#= 21644;带阻滤波器的设计ʌ= 92;可以通过对低通滤波= 器= 的变换得到，<= /span>因此通常称߮= 2;通滤波器为原型滤波&= #22120;。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.53%'>• 通带衰耗不为零；= 8459;带衰耗不为无穷大Ӎ= 0;

• 通带和阻带之间有= 6807;渡带。

• 通带和阻带内不一= 3450;平坦，可有起伏。

下图

一ഄ= 4;LC滤波器

------=_NextPart_01D13E5F.0CC271E0 Content-Location: file:///C:/B2FC02A8/file0200.files/slide0035_image207.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSQAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABI ABsAgQAAAAD//////wECAwJZlI+py+2/gpy02ouz3tTwD4aiJ5amSZ7qiqXsy7rwXMr0zdn4fun8 L/EBecIhrmikIZOwJTMmeA6d0hO1Wotid9ctqOvNacMzMDljPvfG6lW63YHI5/S6oQAAOw== ------=_NextPart_01D13E5F.0CC271E0 Content-Location: file:///C:/B2FC02A8/file0200.files/slide0036.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 滤波器

描= 述问题（十个参数）

0

0

Ar表= 1034;通带内最大波纹衰࠮= 3;；wr<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>表示称波纹带&= #23485;；

As表= 1034;阻带最小衰减；ws<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>表示阻带边缘&= #35282;频率；

dp<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>表示通带内幅&= #24230;起伏；ds<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>表示阻带内幅&= #24230;起伏；

wc<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>称为截止频率&= #65288;衰减3分贝处角频率）；= 6824;有特征阻抗。

其中：Ap表= 1034;最大通带衰减；wp<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>表示通带角频&= #29575;；

返回

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quoted-printable Content-Type: text/html; charset="us-ascii" 滤波器

逼= 近问题：

        = ;            &n= bsp;

（1）四మ= 1;逼近衰减特性曲线的&= #26041;法

一ӌ= 9; 巴特沃= 031;逼近（Butterworth）= 5288;幅度最大平坦型）

0

式= 0013; n为滤波器的阶数&= #65292;

        wc = 为截止频率。<= /span>

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.6%;font-family:Wingdings'>§ <= /span>幅频特性和相&= #39057;特性是平坦的。适用于一般性= 8388;波。

四= 种逼近衰减特性曲线= 0340;方法和

滤= 波器的归一 化设计

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逼= 近问题&= #65288;&= #32493;1）

二ӌ= 9;切比雪夫逼近（Chebyshev）= 5288;等波纹型）

0

式中 e为小于1的实常数，&#= 23427;决定通带波纹d，它们之间&#= 30340;关系为

为切比雪夫多&= #39033;式。

三ӌ= 9;贝塞尔逼近（Beseel）= 5288;相位平坦）：在整个通带内，相位-频= 9575;特性的起伏最小或ੌ= 8;平的逼近称为贝塞尔&= #36924;近。

四、椭= 278;逼近：使幅度-频率特性具&#= 26377;陡峭的边缘或狭窄į= 40;过渡频带的逼&= #36817;称为椭圆逼近。

§ 幅频和相频特性在= 6890;带内有小的起伏。๦= 6;用于调制与解调电路&= #12290;

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charset="us-ascii" 滤波器

逼= 近问题&= #65288;续2）

（2）滤波器的归一化设= 5745;

一= 3324;网络结构为梯形网ಯ= 6;,共有2n阶次。

§ 网络综= 512;：在使用上述四&= #31181;滤波器时，可根据= 152;需频= 率特性利用查&= #34920;的方法得到相应的= 256;输函数和电路。<= /div>

§ 滤波器= 340;归一 化= ;设计：为了这些数据&= #34920;格的通用<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>性，将滤波器的阻抗用= 负载阻抗进行了归一= 1270;，频率= 用截止频率๢= 7;行了归一化。

§ 工程设#= 745;数据表格：滤波器计算曲&= #32447;，滤波器衰减<= span lang=3DZH-CN style=3D'font-family:SimSun;mso-fareast-font-family:SimSun; mso-ansi-language:EN-US'>特性曲线，滤&= #27874;器群延时特性曲线= 644;数据表和低通滤<= span style=3D'position:absolute;top:71.42%;left:0%;width:83.94%;height:30.15%'>= 波器归一化元&= #20214;值表等。

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text/html; charset="us-ascii" 滤波器

逼近问&= #39064;（续3） &#= 13;

（2）滤波器的归一化设= 5745;

一ӌ= 9;滤波器阻抗归一化

§ 要求：用负载阻抗= 进行了归一化；

<= span lang=3DZH-CN style=3D'mso-ansi-language:EN-US'>        = ;     保持滤波器= ;各元件间的阻抗关系不变Ӎ= 0;

§ 归一化公式：

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------=_NextPart_01D13E5F.0CC271E0 Content-Location: file:///C:/B2FC02A8/file0200.files/slide0040_image321.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhbgAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgBq AAUAgAAAAP///wIjhI+py+0Powuy2ouzCtzwD4biSJbmiaZqp7XuK4HwTNcsUAAAOw== ------=_NextPart_01D13E5F.0CC271E0 Content-Location: file:///C:/B2FC02A8/file0200.files/slide0041.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 滤波器

逼近问&= #39064;（续4）

（2）滤波器的归一化设= 5745;

二ӌ= 9; 滤波器频率归一化

§ 要求：用截止频率= 进行了归一化；

<= span lang=3DZH-CN style=3D'mso-ansi-language:EN-US'>        = ;     保持滤波器= ;各元件间的阻抗关系不变Ӎ= 0;

§ 归一化公式：

(与频率无关)

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逼近问&= #39064;（续5）

（2）滤波器的归一化设= 5745;

三、真= 491;元件值计算

§ 要将工程设计数据= 4920;格中归一化元件值ࡴ= 4;归一化频率标定成

实际截止频率&= #21644;负载阻抗时的元件= 540;，应该按下式计算：= ;

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quoted-printable Content-Type: text/html; charset="us-ascii" 滤波器

实= 现问题：<= /b>低通滤波器的设计= 和频率、 网= 络变换。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.86%;font-family:Wingdings'>§ 利用滤波器计算曲= 线，确定滤波器的阶= 7425; n。

= § 选择电路。满足同= 一要求的低通滤波器= 0005;路都有两种结构， <= /b>

它们互为对ࠋ= 8;，一般选择电感少的&= #30005;路。

= <= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.44%;font-family:Wingdings'>§ 根据给定的技术指= 标和求得的阶次n，从归一化= 0803;件值表中

查得归一化ࠠ= 3;件值。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.68%;font-family:Wingdings'>§ 使用= 上页公式求得各元件௚= 0;实际值并画出电路图<= /b>。

<= span style=3D'mso-special-format:bullet;color:#FF0033;mso-color-index:6;positio= n: absolute;left:-1.68%;font-family:Wingdings'>§ 信号源电阻和负载= 电阻Rs和RL= ，通常取二= 2773;相等。

（幅= ;度最大平坦型、等波&#= 32441;型………)

§ 根据低通滤波器的= 设计技术指标，选择= 0302;通滤波器的形式。