dB到底是个啥？这个毫不起眼的单位，撑起了通信大厦的基石

admin 发表于 2019-3-27 10:19:34

<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">01<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">—<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dB到底是个啥？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">在移动通信领域，目前最火的话题是5G。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">关于5G的讨论一片热火，反映了大家对这个新时代的无限憧憬。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">然而，对于一些通信最基本的，习以为常的概念，探究起来仍然饶有趣味。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">这不，问题来了：<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJMG0HVNwuaB" img_width="595" img_height="1056" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dB到底是啥意思？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">关于dB，最直接的解释就是：两个功率的比值取对数之后再乘以10，下面公式中的Log就表示取对数的意思。然而这样解释既拗口又难以理解。<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJMGG7Nrgefn" img_width="239" img_height="122" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dB的计算公式<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">比如，想知道一个100比5大多少，直接说100是5的20倍就行了，为什么还要费这么大劲，非要取个对数呢？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">另外，为什么这个值叫“dB”而不叫其他名字？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">正所谓空穴来风，必有其因，我们先暂且绕远一点，先从对数的本质说起。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">02<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">—<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">对数的本质<blockquote style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 1em 0px; padding: 12px 10px; position: relative; font-size: 16px; line-height: 1.5; color: rgb(153, 153, 153); background-color: rgb(244, 245, 246); border: 1px solid rgb(232, 232, 232); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">给我空间、时间及对数，我就可以创造一个宇宙。</blockquote><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">——伽利略<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">话说在500年前，随着奥斯曼帝国的崛起和拜占庭的灭亡，大量人才带着古希腊罗马典籍来到西欧，文艺复兴时代揭开序幕。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">除了文艺复兴，这还是一个科学大发现的时代。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">哥白尼公布了“日心说”，证明了地球绕着太阳转的事实；伽利略创制了天文望远镜，发现了月球山岭、土星光环以及太阳黑子等现象，还推算出了太阳的自转周期。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">天文学的蓬勃发展，对大规模数学计算的需求非常迫切。数学这样一个基础学科，也在需求的驱动之下迅速发展。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">1544年，德国数学家斯蒂菲尔写了一本叫做《整数的算术》的书，在这本书中他应用“一一对应”的方法几乎造就了一座数学丰碑。<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJMGR8FUliNB" img_width="220" img_height="267" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">斯蒂菲尔（1487-1567）<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">斯蒂菲尔在书中写道：“关于整数的这些奇妙性质，可以写成整本整本的书！”下面就是他书中列出的两列数字：<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJMGdJfD0nm" img_width="200" img_height="444" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">两列数字（X列为“代表数”，Y列为“原数”）<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">可以看出：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">Y列其实就是通项公式为2的n次方的等比数列（n为整数），他称其为“原数”；<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">X列则是一个由整数构成的等差数列，他称其为“代表数”。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">他发现：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">两个“原数”相乘等于“代表数”相加后得到的“代表数”所对应的“原数”；<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">两个“原数”相除等于“代表数”相减后得到的“代表数”所对应的“原数”。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">也就是说，利用这两列数可以把较为复杂的乘除法变成较为简单的加减法，大大提高计算的效率。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">其实，在我们看来，这个结论没有什么神奇之处，因为所谓的“代表数”其实就是“原数”以2为底的对数。但是在当时，这种计算方法思想是开创性的。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">比如说，想要计算128和32768的乘积，我们可以查这个表：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">1、128对应的“代表数”是7，32768对应的“代表数”是15。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">2、计算加法：7+15=22。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">3、再查表可得22对应的“原数”为4194304。大功告成！<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">只需查表之后做加法，然后再查表就搞定了。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">这里最大的问题是：都知道查表快，这个表是从哪里来的？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">时代的使命，召唤重量级人物的出场。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">这位大师就是：英国人约翰·纳皮尔。<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJMGoIfU9DEE" img_width="317" img_height="339" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">约翰·纳皮尔（1550-1617）<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">纳皮尔是一位数学家、物理学家兼天文学家。他在计算各种行星轨道数据时，也被浩瀚的计算量所折磨，因此非常痛恨这些乏味的重复性工作。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">为了解决这一问题，他用了20年的时间，进行了数百万次的计算，发明了对数和对数表。从此之后，天文数字的乘除计算，只需要查表，做加减法，再查表就搞定了。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">1614年，纳皮尔在英国爱丁堡出版了《奇妙的对数定律说明书》中首次提出了对数的概念:<blockquote style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 1em 0px; padding: 12px 10px; position: relative; font-size: 16px; line-height: 1.5; color: rgb(153, 153, 153); background-color: rgb(244, 245, 246); border: 1px solid rgb(232, 232, 232); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">看起来在数学实践中，最麻烦的莫过于大数字的乘法、除法、开平方和开立方，计算起来特别费事又伤脑筋，于是我开始构思有什么巧妙好用的方法可以解决这些问题。</blockquote><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">这个不想做重复工作的人坚持不懈地做了20年重复性工作。他的努力为后人减少了大量的重复性工作，大大减少了数学家、天文学家的计算量。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">这在天文学界算得上是一项伟大的发明，我们来看看名人们对其的评价就能知道对数发明的划时代意义。<blockquote style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 1em 0px; padding: 12px 10px; position: relative; font-size: 16px; line-height: 1.5; color: rgb(153, 153, 153); background-color: rgb(244, 245, 246); border: 1px solid rgb(232, 232, 232); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">对数的发现，因其节省劳力而延长了天文学家的寿命。</blockquote><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">——拉普拉斯<blockquote style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 1em 0px; padding: 12px 10px; position: relative; font-size: 16px; line-height: 1.5; color: rgb(153, 153, 153); background-color: rgb(244, 245, 246); border: 1px solid rgb(232, 232, 232); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">对数的发明、解析几何的创始和微积分的建立是17世纪数学的三大成就。</blockquote><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">——恩格斯<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">由此可见，对数最初的意义，就是用较小数值的加减法来代替天文数字的乘除法，达到简化计算的目的。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">03<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">—<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dB和它的朋友们<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">电话这个划时代的发明深刻地改变了我们的生活方式。贝尔，作为电话的发明者，也成为了是一位备受尊敬的百万富翁科学家和企业家。<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJML65QFn655" img_width="480" img_height="624" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">贝尔（1847-1922）<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">上个世纪的通信工程师们通过实验发现，电话线越长信号衰减越厉害、信号越弱，这衰减量也是无比巨大的天文数字，那怎么来比较方便地表示衰减量呢？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">这些聪明的工程师自然而然地想到了对数。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">为了纪念贝尔，他们决定用贝尔的名字来命名信号的衰减或者增强的多少：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">Bel=Log(输入信号的功率/输出信号的功率)<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">在使用中，他们发现这个单位太大，不是很实用，所以就把Bel这个单位缩小了1/10。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">因为1/10的英文是deci，所以新引入了一个单位deciBel，我们一般把它简写为dB，这就是dB的由来。<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJMLO1jVpfP0" img_width="380" img_height="111" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dB的计算公式<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">另外，dB在中文中被翻译为分贝，但大多数人还是习惯读写都用dB。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dB的使用<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">一经创造，dB在射频和无线通信领域得到了及其广泛的使用。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">在实际的使用中，其实直接使用dB即可，大家都已经非常习惯了，不比再进行转换。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">但是，记住下面几个转换方式还是非常有用的：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">+3dB是指增加为2倍大<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">+10dB是指增加为10倍大<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">-3dB是指减小到1/2<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">-10dB是指减小到1/10<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">另外，dB是基于对数的，因此只能加减，不能乘除。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">下面我们做一道题，热个身：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">如果一路信号经过了功率放大器，功率增强为原先的40000倍，那么增益是多少dB？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">首先将40000分解为如下的最小因数：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">40000=10x10x10x10x2x2<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">现在可以因数替换成简单的dB加法：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">40000=10dB+10dB+10dB+10dB+3dB+3dB=46dB<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">可见，通过对数和dB，我们把40000这样的大数，转化成了46dB这样较小的数值，方便计算和描述。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">理解了如何转换之后，下面要做的就是忘记它。因为在通信世界里通常只需要处理dB，只需要简单地加加减减就够了。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">理解了dB表征的是一个值相对于另一个的大小这一含义之后，随着对比参照物的不同，dB的一大帮伙伴也诞生了。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">看着一大家子好不热闹，除了dB外包含：dBm，dBi，dBd，dBc等等。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dBm<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dBm的直接含义就是功率相对1毫瓦的大小。计算方式和dB是完全一样的：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dBm=10*Log(P功率值/1毫瓦)<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">0dBm=1毫瓦<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">10dBm=10毫瓦<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">30dBm=1000毫瓦=1瓦<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">40dBm=10000毫瓦=10瓦<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">下面我们再来做一道题，加深理解：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">如果一路信号的发射功率是20瓦，功率衰减为原先的一亿分之一，那么最后的功率是多少dBm？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">首先将20瓦转换成dBm。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">因为10瓦是40dBm，20瓦是10瓦的2倍，根据+3dB是指增加为2倍大的算法：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">20瓦=43dBm<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">然后再将一亿转换成dB。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">10*Log(100000000)=10*8=80dB<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">因此，可以得出，20瓦，功率衰减为原先的一亿分之一之后：<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">43dBm-80dB=-37dBm<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">现在就可以直接说：发射功率为43dBm，衰减80dB之后，功率为-37dBm。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">是不是比用一亿分之一这样的大数字计算要方便一些？这里的举例还用的都比较是简单的数字，如果是衰减为81234609040分之一呢？<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dBi和dBd<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dBi和dBd均用于表达天线的增益，两者都是一个相对值，只是其参考的基准不一样。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dBi的参考基准为全方向性天线：<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJMLbHwMFcI0" img_width="240" img_height="240" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">全方向性天线<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dBd的参考基准为偶极子，因此两者的值略有不同，同一增益用dBi表示要比用dBd表示大2.15。<img src="https://p1-tt.byteimg.com/origin/pgc-image/RJiJMLuJIWuZlP" img_width="408" img_height="318" alt="这个毫不起眼的单位，撑起了通信大厦的基石" inline="0" style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; border-style: none; max-width: 100%; display: block; margin: 10px auto; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">偶极子<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">dBc<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">一般来说，dBc是相对于载波功率而言的，是一个用来度量与载波功率比干扰大多少的相对值，如度量干扰（同频干扰、互调干扰、交调干扰和带外干扰）、耦合、杂散等相对量值，在采用dBc的地方，原则上都可以使用dB替代。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">好了，关于dB的故事就到这里。<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">来源：无线深海<p style="-webkit-tap-highlight-color: transparent; box-sizing: border-box; margin: 16px 0px; padding: 0px; color: rgb(34, 34, 34); font-family: 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'Helvetica Neue', Arial, sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">编辑：井上菌

admin 发表于 2019-3-27 13:06:36

dB(分贝：10分之1贝尔之意)是以功率比值取10为底的对数值(贝尔)的10分之1。是一个在信息传送中常用的信号强度的单位。
因为它是一个比值取对数而产生的单位，所以在不同的地方分贝值代表的值是不同的。
在信号系统中，用信号大小与1毫瓦的比值作为基数作为信号强度的大小单位，也就是说0分贝就是1毫瓦。每增加一倍大约就增加3分贝。因为在阻抗相同的条件下，电压之比的平方等于功率比，所以对于电压之比，则每增加一倍就增强6分贝。

在电话通信中，通常采用比值取自然对数值作信号强度单位，叫奈贝。

在通信中使用分贝或奈贝作信号强度的单位并不是因为计算简单。因为表面上的计算简单是只说了最后一步的讲得，其实是多了最后一步，前面的计算并没有省去。
比如输出功率/输入功率取对数乘10是分贝数，是在有了比值的下再求一次对数，并没有省去求比值。

取对数作为单位的原因是自然界中的自然强度与感觉强度之间是对数关系。比如我们听声音的大小，每当声音的强度的对数值增大一倍时我们才感觉声音增加了一倍。
再比如音调，声音的频率增加一倍，我们听上去就是增加了一个“8度”(其实是6度，因为所谓的8度中有两个音阶只相差半度，还有一个是重复)。所经每个音阶就是1/7个10为底的对数值。
用分贝值表达信号强度就能与感觉强度直接对应。
比如对于音阶来说，以某一频率作为基数后，其他的音阶之间的关系就符合加减的运算关系了。直接说增加一度、高8度大家都知道是什么意思。

admin 发表于 2019-3-27 13:06:49

通信中常用的频率的单位有：MHz=1000kHz=1000000Hz
注意在物理学的单位中字母的大小写不能乱用。

M=1000000000m，k是千的意思，不能用K。

admin 发表于 2019-3-27 13:07:13

【管理员】泰戈尔 2019/3/27 星期三 13:03:59
g是克或重力加速度，不能用G

【管理员】泰戈尔 2019/3/27 星期三 13:05:45
G是引力常数

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无量觉社区's Archiver

dB到底是个啥？这个毫不起眼的单位，撑起了通信大厦的基石