电阻越大噪声越大？不一定!

[{"insert":"#行业知识科普#\n大家好，我是工程师看海，原创文章欢迎"},{"attributes":{"bold":true},"insert":"点赞分享！"},{"insert":"\n以前写过一篇文章《电阻噪声哪里来？》"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"（https://www.dianyuan.com/eestar/article-4761.html）里面有个观点："},{"attributes":{"bold":true},"insert":"电阻越大噪声越大"},{"insert":"。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"很多同学便把这个结论应用于所有场景，这是不对的，今日特撰新文，补充、拓宽下电阻噪声的问题，以及使用采样电阻的注意事项（ir drop+0 Ωpdn），环环相扣，欢迎点赞、收藏、转发。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"正所谓阴在阳之内，不在阳之对。凡事有坏的一面，也往往有好的一面。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"attributes":{"align":"justify"},"insert":"\n"},{"attributes":{"bold":true},"insert":"1 先看坏的一面，回顾下电阻噪声问题"},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"电阻的噪声通常指的热噪声，哪怕电阻没有连接到电路中，没有电流流过电阻，电阻两端也会有电压变化，这就是电阻热噪声，在系统工作频率范围内，电阻的热噪声可以认为是白噪声。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"电阻两端开路时，它的热噪声有效值的计算公式是："},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/7dd1383c97cd209f.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"k是玻尔兹曼常数，k=1.38*10-23 J/K，T是开尔文热力学温度，R是电阻值，B是系统等效噪声带宽。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"举例："},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"当温度是27℃（300开尔文）时，10KΩ的电阻，在100KHz放大电路中，电阻两端的开路热噪声电压有效值是4uV。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"相同环境下，如果电阻是20KΩ，则热噪声电压有效值是5.8uV。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/7f8e85c38ecfcac2.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"根据公式我们可以看出来，电阻越大，噪声也越大，噪声随着电阻阻值的增加而增加（这句话就是本文的起源）。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"同样的，噪声也与温度有关，只是这个噪声对温度并不敏感，因为公式中是热力学温度，当温度变化为十几或几十摄氏度时，对噪声的影响并不是很大。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"比如上面例子中，17℃和27℃下，电阻两端的噪声基本差别不大。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"attributes":{"align":"justify"},"insert":"\n"},{"attributes":{"bold":true},"insert":"2 再看好的一面，电阻增加反而增加信噪比"},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"不知道有没有同学听说过“电阻加一倍，信噪比加3dB”这个说法。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"这个是使用电阻来测量电流时成立的结论，在用电阻测量电流的例子中，更大的电阻反而可以优化噪声性能，一般而言，我们测量电流的方法是让电流流过一个采样电阻R，通过检测电路两端的电压V，间接得到电流I=U/R，根据这个公式，在目标电流大小不变的情况下，电阻越大，电阻两端的电压就越大，见下图。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/9d3e3839278ac126.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":" "},{"attributes":{"align":"center"},"insert":"\n"},{"attributes":{"bold":true},"insert":"3 为什么电阻加一倍，信噪比加3dB？"},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"信噪比的计算公式："},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/8e791b5c53d4ce10.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"比如一个正弦电流I为：2*sin(t)"},{"attributes":{"align":"justify"},"insert":"\n"},{"attributes":{"bold":true},"insert":"采样电阻的阻值为R，"},{"insert":"那么电阻两端的电压就是I*R=2R*sin(t)，这个电压的有效值Vrms_sig1："},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/dc8ea4fda2fb0720.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"根据公式1，电阻两端噪声电压的有效值Vrms_noise1:"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/9de21bd67997c6a1.png"}},{"insert":" "},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"那么把Vrms_sig1和Vrms_noise1带入公式2，得到SNR1："},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/0b7e1761ac21e4ea.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"attributes":{"bold":true},"insert":"现在采样电阻阻值增加一倍，变为2R，"},{"insert":"那么电阻两端的电压就是I*R=4R*sin(t)，这个电压的有效值Vrms_sig2："},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/ba91f7c4806fcdc3.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"根据公式1，电阻两端电压的有效值Vrms_noise2:"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/96c3007b4cab9a8e.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"那么把Vrms_sig2和Vrms_noise2带入公式2，得到SNR2："},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/74a773ee0e36f855.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":" "},{"attributes":{"align":"center"},"insert":"\n"},{"attributes":{"bold":true},"insert":"4 SNR2比SNR1大了多少呢？"},{"attributes":{"align":"center"},"insert":"\n"},{"attributes":{"bold":true},"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/fb17d3ebea4b994d.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"所以电阻加一倍，电流采样的信噪比加3dB。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":"备注：高中log对数计算公式"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/578a3b57e542c4b0.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":" "},{"attributes":{"align":"justify"},"insert":"\n"},{"attributes":{"bold":true},"insert":"5 电流采样电阻有什么注意事项呢？"},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"咱们看图说话，下图中电源电压是U0，电流是I，电阻是R，那么电阻两端的压降就是IR，负载上的电压就是U0-IR，因此，如果为了提高采样电流信噪比而过度的用大电阻，那么导致负载上的电压U0-IR就会很小，无法满足负载要求，而且这个电阻越大，消耗的功耗也就越大。"},{"attributes":{"align":"justify"},"insert":"\n"},{"insert":" "},{"insert":{"image":"https://community-1252773949.cos.ap-guangzhou.myqcloud.com/article/2033/793aa97c7c595580.png"}},{"attributes":{"align":"center"},"insert":"\n"},{"insert":"有的同学会在调试时，用一个稍微大一点的采样电阻来采集电流，调试后用0欧姆代替这个电阻，这种做法无可厚非，但是不能用于电源性能敏感的负载，比如在PDN链路上，哪怕放一个0Ω的电阻，也可能会有几个或几十个mΩ电阻存在，这可能会严重减低PDN性能，需要慎重考虑。"},{"attributes":{"align":"justify"},"insert":"\n"},{"attributes":{"bold":true},"insert":"如果看到这里，请点赞、收藏、分享三连！"},{"attributes":{"align":"right"},"insert":"\n"},{"insert":"\n"}]