1、Noise 1噪声 1TIPL 1311TI Precision Labs Op AmpsPresented by Ying ZhouPrepared by Art Kay and Ian Williams Hello, and welcome to the TI Precision Labs discussing intrinsic op amp noise, part 1.Overall, this video series will show how to predict op amp noise with calculation and simulation, as well how
2、to accurately measure noise. In part 1 we will define intrinsic noise, introduce the different types of noise, and discuss noise spectral density. 大家好，欢迎来到TI Precision Labs（德州仪器高精度实验室）。本节视频将介绍op-amp intrinsic noise（运放的固有噪声）的第一部分。 在整个噪声系列中，我们会探讨如何通过计算和仿真得到运放的噪声，并学习如何准确地测量噪声。在这第一部分中，我们会给出噪声的定义，介绍不同的噪声
3、，以及探讨噪声频谱密度。 2Vout with Noise vs Time-4-3-2-10123450 2 4 6 8 10 12T ime (mS)Vout (mV)Vout Ideal vs Time-4-3-2-1012340 2 4 6 8 10 12T ime (mS)Vout (mV)Vin vs Time-1.5-1-0.500.511.50 2 4 6 8 10 12T ime (mS)Vin(mV)+VG1R1 1k R2 2k+-+U1 OPA335V1 2.5V2 2.5VF1 Ideal OutputReal Output2 Noise can be defined
4、as an unwanted signal that combines with a desired signal to result in an error. In audio, for example, noise can be noticed as a hiss or popping sound. In a sensor system, noise can be an error in the measured sensor output, such as pressure or temperature. Noise can be categorized into two basic g
5、roups: extrinsic and intrinsic. Extrinsic noise is noise produced from some external circuit or natural phenomena. For example, 60Hz power line noise and interference from mobile phones are common examples of extrinsic noise. Cosmic radiation is another example of a natural phenomenon that causes ex
6、trinsic noise. Intrinsic noise is caused by components within a circuit. Resistors and semiconductor devices generate noise, for example. Intrinsic noise is very predictable, where as extrinsic noise is typically difficult to predict. In this noise video series, we will focus on intrinsic noise. As
7、we mentioned before, our discussion will focus on how to calculate, simulate, and measure noise. We will also discuss techniques for reducing noise. 噪声可以定义为一个不希望出现的信号，它掺杂在想要的信号中，从而引起误差。举个例子，在音频中，噪声可以表现为嘶嘶声或者爆破声。在一个传感器系统中，噪声可以表现为测量到的压力或者温度信号的误差。 噪声可以归为两种类别：extrinsic noise（外部噪声）和intrinsic noise（固有噪声）。
8、外部 噪声是指由于外部电路或者自然因素导致的噪声。例如，手机60Hz（美国电力频率）的电力线噪声和干扰就是常见的外部噪声。宇宙辐射则是一个由于自然因素引起外部 噪声的例子。固有噪声是由电路的元器件引起的。例如电阻和半导体器件都可以产生噪声。 固有噪声是可估计的，而外部噪声通常很难估计。在这个噪声的视频系列中，我们主要介绍如何计算、仿真和测量固有噪声，及降低噪声的方法。 33Intrinsic noise 固有噪声 This slide illustrates how an amplifier circuit can be translated into a noise equivalent c
9、ircuit. Each resistor has a noise voltage source associated with it. The noise voltage source is denoted by a circle with an asterisk inside. The amplifier also has a noise voltage source and a noise current source. The noise current source is denoted by a diamond with an asterisk inside. The magnit
10、ude of the noise sources inside the amplifier is given in the amplifiers data sheet. The magnitude of the noise associated with the resistor is dependent on the resistance value and can be calculated. We will soon learn how to combine the effects of all the noise sources to determine the total outpu
11、t noise. But first, lets look at some general categories of noise. 左图是用于噪声分析的示例电路，右图显示的是运放的噪声模型。 每个电阻对应一个noise voltage source（电压噪声源）。这里用一个内带星号的圆圈表示一个电压噪声源。这个运放本身还包含了一个电压噪声源和一个noise current source（电流噪声源）。我们用一个内带星号的菱形表示电流噪声源。在运放的数据手册中已给出噪声源的幅值。电阻所对应的噪声可以根据电阻的大小计算得到。 我们很快就会学习如何综合这些噪声源来计算得到总输出噪声。不过，首先让我
12、们来看看噪声的一些常见的分类。 4White Noise (Broadband Noise)白噪声（宽带噪声） This slide shows the time domain waveform for white noise, also known as broadband noise. The time domain waveform is what you would see if you measured noise with an oscilloscope. Notice that the horizontal axis is 1ms, full scale. Taking the
13、reciprocal of the full-scale time gives a frequency of 1kHz. In general, broadband noise is considered to be in the middle to high frequency range; that is, frequencies greater than 1kHz. In the next slide well consider lower frequency noise sources. Also notice the statistical distribution to the r
14、ight hand side of the slide. The distribution is Gaussian, with a mean value of 0V and the skirts of the distribution at approximately 40mV. The distribution indicates that the probability of measuring noise near 0V is high, where as the probability of measuring noise near the skirts of the distribu
15、tion is relatively low. Later we will see how the distribution can be used to estimate the peak-to-peak value of the noise signal. 这里显示的是white noise（白噪声）的时域波形，即人们所知的broadband noise（宽带噪声）。时域波形是你在使用示波器时观察到的波形。注意到横坐标的满量程是1ms。满量程1ms的倒数则就是1kHz的频率。一般来说，宽带噪声是指从中频到高频的范围，即大于1kHz的频率。之后我们会涉及低频噪声源。 在这里，右图显示的是一个
16、统计分布图。这是一个高斯分布，平均值为0V，最大最小值约为40mV。这个分布表示测量的噪声接近0V的概率很高，而接近两边极值的概率相对而言比较低。之后我们会学习如何用这个分布估计peak-to-peak noise（峰峰值噪声）。 51/f, Flicker, or Low Frequency Noise1/f, 闪烁，或低频噪声Distribution of Noise1/f Noise Measured in Time DomainCounts Recorded During Measurement PeriodTime (sec.)5 Flicker noise, also known
17、as 1/f or low frequency noise, is another category of noise. This slide shows the time domain waveform, as well as the statistical distribution for 1/f noise. The time domain waveform is what you would see if you measured noise with an oscilloscope. Notice that the horizontal axis is 10s full scale.
18、 Taking the reciprocal of the full scale time gives a frequency of 0.1Hz. In general, 1/f noise is considered to be in the low frequency range; that is, frequencies less than 1kHz. 另一种噪声类别是Flicker noise（闪烁噪声），也叫1/f或者低频噪声。这里显示的是时域波形及1/f 噪声的统计分布图。这个时域波形是你在使用示波器时观察到的波形。注意到横坐标的满量程是10s，其倒数则就是0.1Hz的频率。一般来
19、说，1/f 噪声是指处于低频范围，即频率小于1kHz的噪声。 6Burst Noise (Popcorn Noise)突发噪声（爆米花噪声） Another category of noise is called burst, or popcorn noise. Popcorn noise is a sudden change (or step) in voltage or current. It does not follow a Gaussian distribution - instead it has a bimodal or multi-modal distribution. The
20、 example above jumps between three discrete modes of operation. Popcorn noise is low frequency, from 0.1 to 1kHz. Popcorn noise sounds like popping popcorn when played on a speaker or headphones. Popcorn noise is caused by defects in a device, and unfortunately it cannot be mathematically predicted.
21、 This presentation does not give further details on popcorn noise. 还有一类噪声是burst noise（突发噪声），或者叫popcorn noise（爆米花噪声）。爆米花噪声表现为电压或电流的跳变。显然，它不是高斯分布。事实上，它是两个或者多个分布的叠加。示例中的分布是3个高斯曲线互相叠加。 爆米花噪声出现在低频（通常频率在0.1到1kHz范围内）。之所以叫这个名字，是因为当用扬声器播放它时，听起来就像是爆米花在跳动。爆米花噪声是由于半导体材料中的细微缺陷导致的，但是我们无法用数学方法估计得到这个噪声。这个视频里，对爆米花噪声
22、的介绍就到此为止。 7 Broadband Noise White Noise, Johnson Noise, Thermal Noise, Resistor Noise宽带噪声白噪声，约翰逊噪声，热噪声，电阻噪声 1/f Noise Pink Noise, Flicker Noise, Low Frequency Noise, Excess Noise Burst Noise Popcorn Noise, Red Noise random telegraph signals (RTS).7Strictly speaking, these terms are not 100% synonymo
23、us!Synonyms 同义词 As we have already seen, the various categories of noise have many synonyms. For example, broadband noise is also called white noise, Johnson noise, thermal noise, and resistor noise. It can become very confusing to engineers that are new to this subject when literature and presentat
24、ions switch between these different terms. 正如我们所见，一类噪声可以有很多同义词。例如，宽带噪声也叫白噪声，Johnson noise（约翰逊噪声），thermal noise（热噪声）或者resistor noise（电阻噪声）。当这些不同的名词出现在不同的文献中时，很多刚入门的工程师可能会不清楚它们分别指的是什么。 A brief background in statistics is helpful with noise analysis, because most noise has a Gaussian distribution. The
25、probability density function creates the outline of the Gaussian curve. The probability distribution is derived by integrating the probability density function. The probability distribution function gives the probability that an event will occur in a certain interval. So, for example, if the probabi
26、lity distribution function is equal to 0.3 for x in the range of -1 to 1, then there is a 30% chance that x will be between 1 and +1 at any instant in time. In the case of noise, we will use the probability distribution function to estimate peak-to-peak noise. 8Statistics Review PDF For example, if
27、P(-1x+1) = 0.3, then there is a 30% chance that x is between -1 and 1.Probability De nsity function for Normal (Gaussian) distributionf x( )1 2ex ( )222Probability Distribution function for Normal (Gaussian) distributionWhereP(a x b) - the probability that x will be in the interval (a, b x- the rand
28、om variable. In this case noise voltage. - the mean value - the standard deviationP a x b( )abxf x( )dabx1 2ex ( )222d8 由于大部分噪声服从高斯分布，在进行噪声分析之前，我们先简单复习一下统计知识。右上图的高斯曲线表示的是概率密度函数。对概率密度函数进行积分便得到了概率分布。 根据概率分布，我们可以得知一个事件在已知区间内的发生概率。例如，如果x落到- 1至1区间内的概率分布函数等于0.3，那么我们可以知道在任何时候测量，x出现在- 11之间的概率为30%。如果是测量噪声，我们
29、可以用概率分布函数计算峰峰值噪声。 9The Probability Distribution Function P(axb) gives thprobability that an event happens between a and b. P a x b( )abxf x( )df x( )1 2ex ( )222Le t 0 because noise has no mean value (dc compoP x ( )abxf x( )dP x ( )x1 2ex( )222dx1 2ex( )222d 0.683=-3368% chance in time that the mea
30、surement will be between 9 The probability distribution function indicates that there is a 68% chance that a peak will occur between 1 standard deviation, or 2. For 3 standard deviations, (or 6) the probability increases to 99.7%. This is often used as an estimate of peak-to-peak noise. Keep in mind
31、, however, that the tails of the Gaussian curve are infinite, so there is always a finite probability that noise can be measured outside of the interval of 3. 根据概率分布函数我们可以知道，一个峰值出现在- 到+ 之间（即- 1个标准差到1个标准差之间）的概率为68%。而在- 3 到+3 之间，即6区间内，这个概率增加到99.7%。这个通常被用来估计峰峰值噪声。需要注意的是，高斯分布的两端是无限延伸的，这说明还是有一定的概率，噪声会处在6
32、之外。 10STDEV Relationship to Peak-to-Peak标准差与峰峰值的关系Number of Standard DeviationsPercent chance of measuring voltage 2 (same as 1) 68.3%3 (same as 1.5) 86.6%4 (same as 2) 95.4%5 (same as 2.5) 98.8%6 (same as 3) 99.7%6.6 (same as 3.3) 99.9%Is standard deviation the same as RMS?10 The table shown here r
33、elates the number of standard deviations to the probability that a measurement is bounded by this range. For example, there is a 68% chance that any instantaneous noise measurement will be in the range of 2, or 1 standard deviation. 6 and 6.6 are common ways of estimating the peak-to-peak noise. In
34、the case of 6, for example, there is a 99.7% chance that any instantaneous measurement will occur within that range. Thus, the chance that a noise reading is outside this limit at any instant in time is only 0.3%. The 0.3% probability is considered to be negligible, so 6 is often used as an approxim
35、ation for peak-to-peak noise. If you are familiar with noise analysis, you may have heard the terms standard deviation and RMS used interchangeably. This leads one to wonder, is RMS equivalent to standard deviation? 这个表格总结了测量数据和标准差之间的关系。例如，测量到的噪声出现在1之间，或2范围内的概率为68%。我们通常用6 或者 6.6 来估算峰峰值噪声。例如测量到的噪声出现在
36、6 范围内的概率为99.7%。所以，测量到的噪声会出现在6 范围之外的概率只有0.3%。这0.3%的概率几乎可以忽略不计，因此，3 （即6 ）经常被用来估算峰峰值噪声。 如果你对噪声分析比较熟悉，可能会见到有些地方将标准差和RMS值交替使用。那么这两个值真的是相等的吗？ 11RMS vs. Standard DeviationRMS1n1nixi2= 2 1n1nixi( )2=DC component). Note that the two = 0 (zero average).Standard deviationWherexi data samples average of all sam
37、plesn number of samples11 So, the question is does RMS = standard deviation? The answer is both yes and no! If the signal has no DC offset, the answer is yes. This is the case for most noise signals. Notice that the equation for RMS and standard deviation are the same, except that the standard devia
38、tion equation subtracts out the average, or dc offset. In the case where a signal has a DC offset, RMS will not be equal to the standard deviation. Fortunately, op-amp and resistor noise do not have a DC offset, so we can consider RMS to be equivalent to the standard deviation in these cases. Some e
39、xtrinsic noise, such as digital switching noise, may not be symmetrical and thus will have a DC offset. It is important to note, however, that some instruments or simulation tools will report RMS noise including the offset term (AC + DC) and others will report RMS without the offset term (AC only).
40、答案是，这两个值并不一定总是相等。实际上，只有在没有DC成分的情况下才是相等的。对于大部分的噪声而言，这两个值是相等的。注意到RMS的方程式和标准差的方程式是基本一样的，除了标准差方程式里减去了一个平均值，或者说是DC成分。 所以，如果一个信号包含DC成分，RMS和标准差就不相等了。幸运的是，运放噪声和电阻噪声都不含DC成分，所以这种情况下，我们认为RMS和标准差是相等的。一些外部噪声，例如数字转换噪声可能不是对称的，即会包含一个DC成分。值得注意的是，一些仪器或者测试设备显示RMS 噪声时会包含DC 成分，而另一些设备显示的RMS则不包含DC成分，即只有AC成分。 12Vn1Vn2VnTVn
41、12Vn22+Vn1Vn2VnTExampleVn13mVrmsVn25mVrmsVnT3mVrms( )25 mVrms( )2+ 5.83mVrms12 An important concept in nose analysis is adding noise values. Noise cannot be added algebraically, for example, 3+5=8. Noise must be added as a vector as shown here, where we take the square root of 3mVrms squared plus 5m
42、Vrms squared for a result of 5.83mVrms. It is important to note that this relationship applies only to uncorrelated ,random noise. If the noise source is correlated, a different formula applies. 另一个很重要的概念是噪声信号的叠加。噪声的叠加不是数学上的简单相加，例如，3+5=8。它是向量的叠加，例如这里的，3m Vrms的平方加上5mVrms的平方再开根号，继而得到5.83mVrms。值得注意的是，这
43、种计算方式只适用于不相关的随机噪声信号。如果噪声源是相关的，要使用另一种计算方式。 13What is Spectral Density? 频谱密度Noise_Density BWn RMS_NoisenVHzHz nV13 Do you remember that white light is the combination of all colors? Well, white noise is the combination of all frequencies. This figure shows that when you add several signals of differen
44、t frequencies together in the time domain, the result is a random looking signal. In the frequency domain, each one of these signals looks like an impulse. Combining an infinite number of these signals across all frequencies creates what is called a noise spectral density curve. Voltage Noise Spectr
45、al Density is often a confusing parameter to engineers who are not familiar with noise analysis. Spectral density has units of nV per square root Hertz. Multiplying spectral density by the square root of the noise bandwidth gives the RMS noise as shown in the equation on the top right. Looking at th
46、e units in the equation, you can see how the square root Hertz cancels out. The spectral density curve is the main amplifier specification used to describe an amplifiers noise characteristics. In this video series we will use the spectral density curve extensively in noise calculations. 正如白光是由各种颜色的光
47、混合得到的一样，白噪声也是由各种频率的噪声组成的。图中表示，如果你将几个不同频率的信号在时域上叠加在一起，可以得到一个“随机”信号。在频域中，每一个信号看起来就像是一个impulse signal（脉冲信号）。将无数个这样不同频率的信号叠加在一起就可以得到noise spectral density curve（噪声频谱密度曲线）。 对于不太熟悉噪声分析的工程师来说，Voltage Noise Spectral Density（电压噪声频谱密度）常常是一个比较令人困惑的参数。频谱密度的单位是 nV per square root Hertz，即 nV 每平方根赫兹。如右上角的方程式所示，将频谱
48、密度和每平方根噪声宽带相乘便可以得到RMS 噪声。注意观察方程中的单位，你可以看到平方根赫兹是如何相消的。 对于放大器的噪声来说，频谱密度曲线是一个主要的参数。在之后的视频中，我们会讲解如何使用频谱密度曲线计算噪声。 14Resistor Thermal Noise 电阻热噪声The mean- square open-circuit voltage (en) across a resistor (R) is: en= (4kTKRf) where:TK Temperature (K)R Resistance ()f frequency (Hz)k Boltzmanns constant (1.381E-23 joule/K)en volts (VRMS) TK = TC+ 273.15 14 At this point we have introduced many of the fundamentals needed to understand noise. This slide shows how to calculate the noise produced by a resistor. This noise is generated by the random m
