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单极点、单级放大器
在现实的世界中,
无论是音频、射频,还是微波,
所有的放大器都有频宽的限制,
无限频宽的放大器并不存在!
也就是说,
所有的放大器都可以视为一个滤波器!
而一般音频放大器则相当于低通滤波器,
要深入了解放大器必须先了解滤波器。
基本的滤波器是由电阻R、电感L、电容C所组成。
电阻是消耗能量的组件,
电感和电容则是不会消耗能量,
而把能量储存起来的储能组件。
下图为基本的一阶RC低通滤波器的电路图,
-3db频宽设定在100Hz。
<img src="attachments/dvbbs/2004-11/2004111072913810.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111072913810.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
其频率─振幅响应和频率─相位响应如下图所示:
<img src="attachments/dvbbs/2004-11/20041110729493.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/20041110729493.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
一阶低通滤波器是单极点的频率响应,
上图中,振幅在100Hz处下降了3db,
相位延迟了45度。
100Hz以上的频率以频率每增加一倍、振幅衰减6db的斜率下降,
相位延迟则渐渐趋近90度。
下图为一阶RC低通滤波器的步阶(方波)瞬时响应:
<img src="attachments/dvbbs/2004-11/2004111072920211.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111072920211.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111072928409.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111072928409.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
其输出方波的前后缘呈指数函数的方式上升和下降。
下面这几张图为基本的一阶RL低通滤波器的电路图和频率响应、方波响应,
<img src="attachments/dvbbs/2004-11/2004111072956991.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111072956991.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111072951131.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111072951131.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/200411107302707.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/200411107302707.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/200411107307494.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/200411107307494.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
它的表现都跟一阶RC低通滤波器一样。
如果把两个一阶低通滤波器串接起来会如何?
下图为两个一阶低通滤波器串接的电路及其频率响应:
<img src="attachments/dvbbs/2004-11/2004111072945415.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111072945415.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111072938519.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111072938519.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
由于两个一阶低通滤波器的-3db频宽都设定在100Hz,
因此在100Hz处的振幅下降了6db,
相位延迟了90度。
100Hz以上的频率以频率每增加一倍、振幅衰减12db的斜率下降,
相位延迟则渐渐趋近180度。
其步阶(方波)瞬时响应如下:
<img src="attachments/dvbbs/2004-11/2004111081539439.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111081539439.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111081640625.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111081640625.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
其输出方波的前后缘呈现出二重积分的现象。
如果把电容和电感一起做成滤波器又如何?
这样就形成二阶LC滤波器。
下图为二阶LC低通滤波器的电路图和频率响应:
<img src="attachments/dvbbs/2004-11/2004111081933385.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111081933385.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111082019786.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111082019786.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
上图中,振幅在100Hz处下降了3db,
相位延迟了90度。
100Hz以上的频率以频率每增加一倍、振幅衰减12db的斜率下降,
相位延迟则渐渐趋近180度。
跟前面两个一阶低通滤波器串接的电路相比,
差别在振幅响应一个在100Hz处的振幅下降了6db,
另一个在100Hz处的振幅下降了3db。
为什么?
因为LC滤波器中的储能源件─电容和电感,
在释放其储存的能量时,
其释放的能量并不完全被电阻吸收,
有一部分被另一个储能组件所吸收储存起来,
释放的能量没有全部被消耗掉所致。
这种现象就是「谐振」!
如果电阻消耗的能量越少,
其谐振尖锐度(Q值)越高,
谐振的现象就越明显。
像下图中,
把电阻的阻值增加三倍,
其频率响应在100Hz处振幅不但没有下降,
反而上升了一些。
<img src="attachments/dvbbs/2004-11/200411108229743.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/200411108229743.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111082225130.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111082225130.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
下面这几张图为二阶LC低通滤波器的步阶(方波)瞬时响应:
<img src="attachments/dvbbs/2004-11/2004111082335469.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111082335469.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111082348901.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111082348901.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/200411108244186.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/200411108244186.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111082454443.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111082454443.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
从二阶LC低通滤波器的方波瞬时响应可以发现波形的突起甚至铃振的现象,
这是因为谐振时产生的「自然谐振频率」所造成!
即便是谐振Q值小到让方波波形没有突起,(如下图所示)
<img src="attachments/dvbbs/2004-11/200411108385395.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/200411108385395.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/200411108391654.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/200411108391654.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
这也只是谐振时产生的「自然谐振频率」很小,
肉眼难以观察而已,
并不表示完全没有产生「自然谐振频率」出来。
如果把两个一阶低通滤波器串接的电路,
后端输出的讯号回授到前面起来会如何?
电路及其频率响应、方波响应如下:
<img src="attachments/dvbbs/2004-11/2004111083955990.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111083955990.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/200411108405525.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/200411108405525.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111084016354.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111084016354.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
<img src="attachments/dvbbs/2004-11/2004111084039596.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor=\'hand\'; this.alt=\'Click here to open new window\nCTRL+Mouse wheel to zoom in/out\';}" onclick="if(!this.resized) {return true;} else {window.open(\'attachments/dvbbs/2004-11/2004111084039596.jpg\');}" onmousewheel="return imgzoom(this);" alt="" />
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