2.1
频率的测量2.1.1
频率的模拟测量
一、直读法
1．平衡电桥法
图2-1-1
电桥平衡条件：file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image002.gif
实部相等
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image004.gif，
虚部相等
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image006.gif
，即file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image008.gif
取file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image010.gif
则须file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image012.gif，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image014.gif
在file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image012.gif条件下，R调节旋纽按频率刻度，可从刻度上直接读得被测信号频率fx。
2．谐振法
图2-1-2
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image017.gif
变电感——改变频段（频率粗调）
调电容——频率细调（电容旋纽按频率刻度）
3．频率电压转换法
图2-1-3
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image019.gif
电压表接频率刻度
二、比较法
1、
拍频法
2、
差频法
三、示波法
1、测被测信号周期——被测信号加Y通道，扫描信号加X通道
2、观察李沙育图形：被测信号加Y通道、标准信号加X通道2.1.2
频率（周期）的数字测量
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image021.gif一、计数法测量的基本原理
图2-1-4，图2-1-5
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image023.giffile:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image025.giffile:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image027.giffile:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image029.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image031.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image033.gif当file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image035.gif时，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image037.gif当file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image039.gif，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image041.gif时，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image043.gif当file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image045.gif，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image047.gif时，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image049.gif脉冲计数最大绝对误差（量化误差）file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image043.gif脉冲计数最大相对误差
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image052.gif二、通用计数器的基本组成及工作方式1、基本组成
图2-1-6
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image054.gif
所以
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image056.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image058.gif——分频系数2、工作方式工作方式A端输入B端输入计数结果测频率比file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image060.giffile:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image062.giffile:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image064.gif测频file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image066.gif（待测）file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image068.gif（已知）file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image070.gif测周file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image068.gif（已知）file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image072.gif（待测）file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image074.gif三、频率（周期）的测量误差与测量范围1．“测频”方式
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image076.gif
所以file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image078.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image080.gif——标准频率准确度①最大相对误差：file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image082.gif
②测量范围file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image084.gif
1°上限file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image086.gif受计数器容量和速度限制
（a）
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image088.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image090.gif
计数器最大数字file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image092.gif
K—十进制计数器位数
（b）file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image094.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image096.gif——计数脉冲频率最大允许值
故取file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image086.gif＝file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image096.gif或file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image098.gif（较小者）
2°下限file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image100.gif受测量精度要求限制
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image102.gif
即
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image104.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image106.gif
2．“测周”方式
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image108.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image110.gif①最大相对误差
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image112.gif②测量范围1°受计数器容量和速度限制
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image114.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image116.gif，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image118.gif2°受测量精度要求限制
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image120.gif所以
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image122.gif测周范围
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image124.gif
或
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image126.gif3、“测频”还是“测周”——file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image066.gif与file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image068.gif在图2-3-1中输入方式中界频率file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image128.gif——“测频”与“测周”误差相同的频率
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image130.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image066.gif越高，误差越小，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image132.gif—测频时标准频率
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image134.gif
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image066.gif越低，误差越小，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image136.gif—测周时标准频率令file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image138.gif得，中界频率file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image140.gif若file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image142.gif，则采用测频方式；
若file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image144.gif则采用测周方式。若file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image146.gif，则：file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image148.gif应采用测频方式file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image150.gif，故必有N>m
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image152.gif应采用测周方式file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image154.gif，故必有N 3°file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image158.gif（K为十进制数显示位数）
测频
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image160.gif
测周
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image162.gif
N——显示数字
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image164.gif——显示数的单位（N=1的file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image066.gif或file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image072.gif）
n——决定小数点位置
例
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image166.gif（即file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image168.gif），K=5，
file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image170.gif，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image172.gif
若选file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image174.gif，则N=100，file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image066.gif显示001.00（MHz），file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image072.gif显示001.00（μs）
若选file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image178.gif
则N=1000,file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image066.gif显示01.000（MHz），file:///C:/DOCUME%7E1/BLUEWA%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image072.gif显示01.000（μs）