巴特沃斯滤波器电路模型分析

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巴特沃斯滤波器电路模型分析 [复制链接]

#巴特沃斯滤波器电路模型分析 ##设计分析 根据[ 单通道声呐接收机——有源巴特沃斯滤波器 ](https://bbs.eeworld.com.cn/thread-1169545-1-1.html " 单通道声呐接收机——有源巴特沃斯滤波器 ")一文可知巴特沃斯滤波器的传递函数为： <ignore_js_op> <img style="cursor:pointer;" id="aimg_545558" aid="545558" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/162829zuhr9p4jw424jr91.png" file="data/attachment/forum/202106/22/162829zuhr9p4jw424jr91.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545558_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>1.png</strong> <em class="xg1">(2.18 KB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545558" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545558&handlekey=savephoto_545558">保存到相册</a> </p> <p class="xg1 y">2021-6-22 16:28 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op>  所以用 <ignore_js_op> <img style="cursor:pointer;" id="aimg_545562" aid="545562" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/163129eln1t55s2e4j74g8.png" file="data/attachment/forum/202106/22/163129eln1t55s2e4j74g8.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545562_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>2.png</strong> <em class="xg1">(992 Bytes, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545562" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545562&handlekey=savephoto_545562">保存到相册</a> </p> <p class="xg1 y">2021-6-22 16:31 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> 代替传递函数中的s得到去归一化后的滤波器传递函数为： <ignore_js_op> <img style="cursor:pointer;" id="aimg_545563" aid="545563" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/163849w942gzx45j9524he.jpg" file="data/attachment/forum/202106/22/163849w942gzx45j9524he.jpg.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545563_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>3.jpg</strong> <em class="xg1">(1.04 MB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545563" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545563&handlekey=savephoto_545563">保存到相册</a> </p> <p class="xg1 y">2021-6-22 16:38 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> ##巴特沃斯滤波器电路模型 按照参考文献：王龙,贾瑞皋. 基于Multisim 8的RC有源模拟滤波器的设计和仿真分析[J]. 聊城大学学报（自然科学版）,2005,18(4):24-27,73. 可知： <ignore_js_op> <img style="cursor:pointer;" id="aimg_545564" aid="545564" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/170556nxrwnnns8n2k6lxw.png" file="data/attachment/forum/202106/22/170556nxrwnnns8n2k6lxw.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545564_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>4.png</strong> <em class="xg1">(245.62 KB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545564" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545564&handlekey=savephoto_545564">保存到相册</a> </p> <p class="xg1 y">2021-6-22 17:05 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> 根据文献，可以知道，常用的二阶有源滤波器有两种结构，一种是压控电压源型（VCVS），一种是无限增益多路负反馈型（MFB）。下面分别列举一下这两种电路模型。 ###压控电压源型（VCVS） 电路结构如下图： <ignore_js_op> <img style="cursor:pointer;" id="aimg_545571" aid="545571" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/171345e0wid0zwrii8rlz8.png" file="data/attachment/forum/202106/22/171345e0wid0zwrii8rlz8.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545571_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>5.png</strong> <em class="xg1">(55.04 KB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545571" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545571&handlekey=savephoto_545571">保存到相册</a> </p> <p class="xg1 y">2021-6-22 17:13 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> 其中，Y均为导纳。根据理想运放的性质：U+=U-，I+=I-=0("虚短"“续断”)可知 <ignore_js_op> <img style="cursor:pointer;" id="aimg_545575" aid="545575" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/171937m4eyicmm8tniorw8.png" file="data/attachment/forum/202106/22/171937m4eyicmm8tniorw8.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545575_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>6.png</strong> <em class="xg1">(290.04 KB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545575" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545575&handlekey=savephoto_545575">保存到相册</a> </p> <p class="xg1 y">2021-6-22 17:19 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> <ignore_js_op> <img style="cursor:pointer;" id="aimg_545621" aid="545621" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/213312j6e1egkzro91uuol.png" file="data/attachment/forum/202106/22/213312j6e1egkzro91uuol.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545621_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>7.png</strong> <em class="xg1">(116.73 KB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545621" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545621&handlekey=savephoto_545621">保存到相册</a> </p> <p class="xg1 y">2021-6-22 21:33 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> ###无限增益多路负反馈型（MFB） 电路结构模型如下图所示： <ignore_js_op> <img style="cursor:pointer;" id="aimg_545622" aid="545622" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/213527szzx7jf99w9vj8wx.png" file="data/attachment/forum/202106/22/213527szzx7jf99w9vj8wx.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545622_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>8.png</strong> <em class="xg1">(19.72 KB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545622" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545622&handlekey=savephoto_545622">保存到相册</a> </p> <p class="xg1 y">2021-6-22 21:35 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> 通过此电路可以得到传递函数如下： <ignore_js_op> <img style="cursor:pointer;" id="aimg_545623" aid="545623" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/213836mq0sws8zgrdspdms.png" file="data/attachment/forum/202106/22/213836mq0sws8zgrdspdms.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545623_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>9.png</strong> <em class="xg1">(75.46 KB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545623" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545623&handlekey=savephoto_545623">保存到相册</a> </p> <p class="xg1 y">2021-6-22 21:38 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> <ignore_js_op> <img style="cursor:pointer;" id="aimg_545624" aid="545624" src="static/image/common/none.gif" onclick="zoom(this, this.getAttribute('zoomfile'), 0, 0, '0')" zoomfile="data/attachment/forum/202106/22/214129jyzvx2yi3c1siyyz.png" file="data/attachment/forum/202106/22/214129jyzvx2yi3c1siyyz.png.thumb.jpg" inpost="1" onmouseover="showMenu({'ctrlid':this.id,'pos':'12'})" /> <div class="tip tip_4 aimg_tip" id="aimg_545624_menu" style="position: absolute; display: none" disautofocus="true"> <div class="xs0"> <p><strong>10.png</strong> <em class="xg1">(146.74 KB, 下载次数: 0)</em></p> <p> <a href="javascript:;" class="loginf" >下载附件</a> <a href="javascript:;" onclick="showWindow(this.id, this.getAttribute('url'), 'get', 0);" id="savephoto_545624" url="home.php?mod=spacecp&ac=album&op=saveforumphoto&aid=545624&handlekey=savephoto_545624">保存到相册</a> </p> <p class="xg1 y">2021-6-22 21:41 上传</p> </div> <div class="tip_horn"></div> </div> </ignore_js_op> ##参考文献 王龙,贾瑞皋. 基于Multisim 8的RC有源模拟滤波器的设计和仿真分析[J]. 聊城大学学报（自然科学版）,2005,18(4):24-27,73.

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关于H1（s）的表达式是如何来的，下面只对压控电压源型（VCVS）的低通滤波器的传递函数进行推导，推导过程如下：

Jacktang

低通滤波器的传递函数推导公式很多，比较麻烦

楼主讲的比较清楚