TI高精度实验室-噪声 2.pdf.pdfTI高精度实验室-噪声 2.pdfpdf,TI高精度实验室

文件名称: TI高精度实验室-噪声 2.pdf.pdf

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详细说明：TI高精度实验室-噪声 2.pdfpdf,TI高精度实验室-噪声 2.pdf1k Noise Gain) Referred te Output R1 1k U1 OPAI了 1 W±v5 Noise Source 中 TEXAS INSTRUMENTS o a key concept that we must understand before doing a noise analysis is noise gain noise gain is the gain seen by the noise voltage source, which is always on the non-inverting input of the amplifier. It can be different from the signal gain The example above shows a circuit with a noise gain of 2 and a signal gain of-1 In other words the circuit is an inverting amplifier with respect to the signal source but a non-inverting amplifier to the noise voltage source ●在进行噪声计算前,我们需要知道一个很关键的概念,即 noise gaIn(噪声增囧)。噪声增益是指运敚电路对于总的输入端噪声的增益,输入端噪声源模型被放置在运放的同相输入端。噪声増益在某些情况下并不等于信号增益。这里给出的例」中,噪声增益是2,而信号增益则是-1。换句话说,相对于信号源来说,这个电路是反相输入的配置;而相对于噪声电压源来说这是一个同相输入运放。 Convert Spectral Density to Peak-to-Peak INPUT VOLTAGE NOISE DENSITY VS FREQUENCY ≥E8goz 6.E fL 10 rms pp Frequency (Hz) d=E 中 TEXAS INSTRUMENTS o This slide summarizes the general procedure for converting voltage spectral density to RMs noise voltage and for converting rms to peak-to-peak voltage o convert voltage spectral density to RMS, you must square the voltage spectral density, integrate across the desired bandwidth and take the square root of the result. This is effectively integrating the power spectral density and taking the square root to convert back to voltage or current. Remember that P= V2/R and p=2xr. We will discuss this in more detail soon Once the RMS noise voltage is calculated, it can be converted to peak-to-peak by multiplying by 6. As discussed in the first noise video, the factor of 6 is a statistical estimate, representing +3 standard deviations or 6o, and there is a 0. 3% chance that noise will exceed the peak-to-peak estimate at any instant in time ●这里总结了如何将电压频谱密度转换成为RMS噪声屯压,再进·步转换成为峰峰值的一般过程。将电压频谱密度转挨成RMS,需要先将频谱密度函数平方,再对其在想要的带宽范围内进行积分,积分之后开根号即可得到RMS 值。这样的一个过程其实是对功率频谱密度进行积分,然后再开根号转换回电压或者电流的过程。大家可以回忆一下功率的表达式,P=V2/R和P=2 ⅹR。对于这一点我们接下来会深入探讨。 ●得到RMS噪声电压之后,将其乘以6就可以得到峰峰值了。我们在之前视频中提到,这里的系数6只是一个统计意义上的估计系数,它代表的是+/-3 个标准差或者6个σ,其意味着还有0.3%的概率噪声的峰峰值会在这个范围之外。 Calculus reminder 4dx=4. 9=36 Height x Width 4 Height Area Width Integral= Area under the curve 5 TEXAS INSTRUMENTS o In order to gain a deeper understanding of the conversion from spectral density to RMs, we will need to use a little calculus. As a quick reminder, remember that the integral of a function is the area under its curve. the area of a rectangle is simply the width times the height, so the integral of a rectangle is also the width times the height This simple fact will be useful in doing a dimensional analysis for noise 这里我们简单回顾一下积分的方式。积分其实就是求曲线以下所包围的区域的面积。这里所示的是个长方形区域,所以其积分就是简单地宽乘以高。这个简单的原理会对我们之后做噪声维度分析很有帮助。 Convert Noise Spectrum to Noise Voltage 10 VHZ V spec dens df-5-—10·Hz-50 Hz (H Freq(h Incorrect You must integrate the Power spectral density curve to get noise 10 NoisePower =(V- spec_ dens )df= 25-10Hz=250. Noise Voltage=√ NoisePower=√20y2=158RMs correct 6 TEXAS INSTRUMENTS o In this slide we will reiterate the method for converting from voltage spectral density to RMs voltage. a common misunderstanding with noise analysis is that total noise can be computed by integrating the voltage or current spectral density when in fact you must integrate the power spectral density o The example at the top of the slide shows what happens when integrating voltage spectral density Remember from the previous slide that the integral of a rectangle is the width times the height, so in this case the result is 5 V/vhz X 10Hz. Notice that the units for this example are very unusual, v*Hz /VHz. In fact the units should be volts the point is that through dimensional analysis you can see that integrating voltage spectral density directly is not the correct way to convert spectral density to rms o The example at the bottom, on the other hand, integrates power spectral density Again, remember that that power is equal to v2/R for voltage and 12*R for current When integrating power spectral density and taking the square root of the result, you get the correct units of volts. Thus, when computing total noise make sure to integrate the power spectrum o Now that we understand how to properly integrate a spectral density curve, let's consider the difterent regions ●在这一页中我们会重中将电压频谱密度转换成RMS电压的方法。在噪声分析中,一个常见的误解是对电压或者电流频谱密度进行直接积分就可以得到总噪声。但事实上正确的做法是对功率频谱密度进行积分。 ●上面所示的这个例子就是对电压频谱密度直接进行积分的结果。回顾一下之前我们讲过,对长方形的积分是宽乘以高,所以使用这个原理,这里就是5 V/VHX10Hz。注意到最后我们得到的单位很奇怪,是V*Hz/VHz。但正确的单位应该是V(伏特)。根据维度分析或者说计算结果的单位我们可以得知直接对电压频谱密度进行积分是无法正确地将频谱密度转换成RMS的。 ●下面所示的例子则是对功率频谱密度进行积分。回忆一下功率的表达式,用电压计算是V2/R,用电流计算是12*R。对功率频谱密度进行积分再开根号, 就可以得到单位为伏特的结果。因此,计算总噪声的时候要记住对功率频谱积分。 ●以上我们已经理解如何正确地对一个频谱密度曲线进行积分,接下来考虑不同的区域。 1/f and Broadband region INPUT VOLTAGE NOISE DENSITY VS FREQUENCY 100 1/f region Slope 10 ■■ Broadband region slope= 0 0.1 10 100 1k 10k100k Frequency(Hz) TEXAS INSTRUMENTS The spectral density curve has two regions: the 1f region and the broadband region In the previous presentation we looked at 1f and broad band noise in the time domain 1f noise occurs at low frequency and has a slope of one divided by the square root of frequency for both voltage and current spectral density. Remember that power spectral density is voltage spectral density squared so for power spectral density the slope of 1f noise is equal to one divided by frequency this is where it gets the name 1 f. Broadband, or white noise, has a flat spectral density. o Let's take a closer look at 1f noise ●频谱密度曲线有两个区域:1f区域和宽带区域。此前我们曾在时域里探讨过这两个区域。1/噪声发生在低频区域,对于其电压和电流频谱密度来说其斜率都是根号频率分之一,即⑩Ⅵ。出于功率频旾密度是电压频谱密度的平方,所以功率频谱密度的斜率即为1/。这也是我们把这个区域叫做1/区域的原因。宽带噪声,或者白噪声则有一个平坦的频谱密度。 ●接下来我们深入学习一下这个1噪声 Different Regions: 1/f or Flicker INPUT VOLTAGE NOISE DENSITY VS FREQUENCY 100 ef norm =eat f En ficker ef norm 0 100 8 8 TEXAS INSTRUMENTS o To get the total rms noise associated for the 1f region we have to integrate the power spectral density and take the square root of the result. Using this method gives the formulas shown on the right. Later on, we will discuss these equations in detail and work through a real-world example ●为∫计算1/f区域相关的RMS噪声,我们需对其功率频谱密度积分冉开根号。右手边给出了这个计算方程。之后我们会详细介绍这些方程并在实际的例子中进行练习。

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