不要忽视信噪比

作者：Bill McGovern，Dataforth 公司项目经理 -- Control Engineering China 2006-07-19 点击:153

　　无论是自动过程控制系统还是太空飞行器，信噪比（SNR）都是信息通信上衡量系统质量的一个度量，也是系统设计中的一个参数。显而易见的是：SNR值越大，系统或器件的性能就越好，但是维持高的信号水平通常是不现实，所以解决方案一般都是抑制电子噪声。
　　提高信噪比绝不是一项简单的任务，因为系统中存在有大量噪声源，常见的包括传感器噪声、信号调节电子噪声、模数转换误差（可建模为噪声）、以及从信号中提取数据的软件算法错误（可建模为噪声）。
　　旅行者二号宇宙飞船是SNR管理的一个极端例子。这艘飞船于27年前发射，已经飞出了我们的太阳系70多亿英里，预计还将继续传送数据直到2020年为止（飞行43年）。它向NASA发送了数万亿比特的数据，其信号发射器功率仅与地球上的广播和电视基站相当，但NASA仍然可以从几十亿英里外接收到这些信息，而它使用的还是1977年制造的古老的宇宙飞船电子设备。由于距离遥远，这些以接近光速（18.6万英里每秒）传播的无线电波信号的延迟有10个小时之多。

图：SNR通常被表示为电压比值，这是从最初的功率比值定义转换而来
的，关系为：功率＝ V2/R。电阻项是多余的可以去掉，因为测量时信号
和噪声电压通过的电阻值通常是相等的，所以有Log10(1)＝ 0。　　旅行者二号还要抵抗其它噪声源的干扰，例如发射器内部产生的噪声、空间电磁波、天线和接收器电子噪声等。从“嘈杂”的通信系统信号中提取信息需要大量的滤波处理和精密复杂的软件算法。
　　数学运算
　　计算总的系统SNR的算法是很复杂的，但是以分贝（dB）表示的基本定义还是非常直观的（请参见所附方程式）。SNR的这个原始定义一般和音频、广播或电视通信信号相关。如今的自动过程控制系统需要现代的SNR定义，以表征使用高速模数转换器（ADC）拓扑结构的数据采集系统。
　　通常，过程控制系统里的ADC决定了采集传感器数据的精度和速度。典型的规格参数，比如分辨率、精度、线性度、转换时间、采样速率、单调响应、元件噪声，等等，对于系统设计者来说仍然非常重要。但是，如今N位分辨率的高速ADC的SNR规格更准确表征了过程控制数据采集模块的动态行为，为比较数据采集系统的行为提供了有效的工具。
　　一个转换误差为±LSB/2（“量化”噪声）的理想N位ADC模块的信噪比可以由SNR的电压形式推导得到，即SNR＝6.02×N＋1.76 dB。现在，通过使用快速傅立叶变换（FFT）算法来计算离散傅立叶变换（DFT），制造商可以测量ADC模块的SINAD——信号（SI）与噪声及失真（NAD）的dB电压比。测量的SINAD（直流除外）值被用来计算有效位数（ENOB），这是更真实表征ADC模块总体性能的规格参数，ENOB＝（SINAD－1.76）/6.02。
　　例如，考虑一个包含前置放大器、多路复用器、采样保持、ADC和输出缓冲的16位ADC模块，其测量的SINAD值为86.3dB。使用上面的公式可以算得ENOB＝14，意味着该16位模块的性能在这种SINAD条件下相当于一个理想的14位ADC。SINAD的FFT测量受信号频率、幅度、以及采样速率的影响，ENOB值因此也当然会受到影响，所以过程控制设计者应该向制造商进行咨询，再决定SINAD和ENOB的测量方法。  http://www.cechinamag.com/Article/html/2006-07/2006718125258.htm  

SINAD ENOB SNR THD THD+N SFDR的详细比较]

iC921 发表于 2006-7-25 18:21 模拟技术 ←返回版面

MT-003: Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so You Don't Get Lost in the Noise Floor by Walt Kester REV. 0, 10-03-2005 INTRODUCTION Six popular specifications for quantifying ADC dynamic performance are SINAD (signal-to-noise-and-distortion ratio), ENOB (effective number of bits), SNR (signal-to-noise ratio), THD (total harmonic distortion), THD + N (total harmonic distortion plus noise), and SFDR (spurious free dynamic range). Although most ADC manufacturers have adopted the same definitions for these specifications, some exceptions still exist. Because of their importance in comparing ADCs, it is important not only to understand exactly what is being specified, but the relationships between the specifications. There are a number of ways to quantify the distortion and noise of an ADC. All of them are based on an FFT analysis using a generalized test setup such as shown in Figure 1. Figure 1: Generalized Test Setup for FFT Analysis of ADC Output The spectral output of the FFT is a series of M/2 points in the frequency domain (M is the size of the FFT—the number of samples stored in the buffer memory). The spacing between the points is fs/M, and the total frequency range covered is dc to fs/2, where fs is the sampling rate. The width of each frequency "bin" (sometimes called the resolution of the FFT) is fs/M. Figure 2 shows an FFT output for an ideal 12-bit ADC using the Analog Devices' ADIsimADC® program. Note that the theoretical noise floor of the FFT is equal to the theoretical SNR plus the FFT process gain, 10×log(M/2). It is important to remember that the value for noise used in the SNR calculation is the noise that extends over the entire Nyquist bandwidth (dc to fs/2), but the FFT acts as a narrowband spectrum analyzer with a bandwidth of fs/M that sweeps over the spectrum. This has the effect of pushing the noise down by an amount equal to the process gain—the same effect as narrowing the bandwidth of an analog spectrum analyzer. The FFT data shown in Figure 2 represents the average of 5 individual FFTs. Note that averaging a number of FFTs does not affect the average noise floor, it only acts to "smooth" the random variations in the amplitudes contained in each frequency bin. Figure 2: FFT Output for an Ideal 12-Bit ADC, Input = 2.111MHz, fs = 82MSPS, Average of 5 FFTs, M = 8192, Data Generated from ADIsimADC® The FFT output can be used like an analog spectrum analyzer to measure the amplitude of the various harmonics and noise components of a digitized signal. The harmonics of the input signal can be distinguished from other distortion products by their location in the frequency spectrum. Figure 3 shows a 7-MHz input signal sampled at 20 MSPS and the location of the first 9 harmonics. Aliased harmonics of  fa fall at frequencies equal to |±Kfs ± nfa|, where n is the order of the harmonic, and K = 0, 1, 2, 3,.... The second and third harmonics are generally the only ones specified on a data sheet because they tend to be the largest, although some data sheets may specify the value of the worst harmonic. Harmonic distortion is normally specified in dBc (decibels below carrier), although in audio applications it may be specified as a percentage. It is the ratio of the rms signal to the rms value of the harmonic in question. Harmonic distortion is generally specified with an input signal near full-scale (generally 0.5 to 1 dB below full-scale to prevent clipping), but it can be specified at any level. For signals much lower than full-scale, other distortion products due to the differential nonlinearity (DNL) of the converter—not direct harmonics—may limit performance. Figure 3: Location of Distortion Products: Input Signal = 7 MHz, Sampling Rate = 20 MSPS Total harmonic distortion (THD) is the ratio of the rms value of the fundamental signal to the mean value of the root-sum-square of its harmonics (generally, only the first 5 harmonics are significant). THD of an ADC is also generally specified with the input signal close to full-scale, although it can be specified at any level. Total harmonic distortion plus noise (THD + N) is the ratio of the rms value of the fundamental signal to the mean value of the root-sum-square of its harmonics plus all noise components (excluding dc). The bandwidth over which the noise is measured must be specified. In the case of an FFT, the bandwidth is dc to fs/2. (If the bandwidth of the measurement is dc to fs/2 (the Nyquist bandwidth), THD + N is equal to SINAD—see below). Be warned, however, that in audio applications the measurement bandwidth may not necessarily be the Nyquist bandwidth. Spurious free dynamic range (SFDR) is the ratio of the rms value of the signal to the rms value of the worst spurious signal regardless of where it falls in the frequency spectrum. The worst spur may or may not be a harmonic of the original signal. SFDR is an important specification in communications systems because it represents the smallest value of signal that can be distinguished from a large interfering signal (blocker). SFDR can be specified with respect to full-scale (dBFS) or with respect to the actual signal amplitude (dBc). The definition of SFDR is shown graphically in Figure 4. Figure 4: Spurious Free Dynamic Range (SFDR) The Analog Devices' ADIsimADC® ADC modeling program allows various high performance ADCs to be evaluated at various operating frequencies, levels, and sampling rates. The models yield an accurate representation of actual performance, and a typical FFT output for the AD9444 14-bit, 80-MSPS ADC is shown in Figure 5. Note that the input frequency is 95.111 MHz and is aliased back to 15.111 MHz by the sampling process. The output also displays the locations of the first five harmonics. In this case, all the harmonics are aliases. The program also calculates and tabulates the important performance parameters as shown in the left-hand data column. Figure 5: AD9444 14-Bit, 80MSPS ADC fin = 95.111MHz, fs = 80MSPS, Average of 5 FFTs, M = 8192, Data Generated from ADIsimADC® SIGNAL-TO-NOISE-AND-DISTORTION RATIO (SINAD), SIGNAL-TO-NOISE RATIO (SNR), AND EFFECTIVE NUMBER OF BITS (ENOB) SINAD and SNR deserve careful attention, because there is still some variation between ADC manufacturers as to their precise meaning. Signal-to-Noise-and-Distortion (SINAD, or S/(N + D) is the ratio of the rms signal amplitude to the mean value of the root-sum-square (rss) of all other spectral components, including harmonics, but excluding dc. SINAD is a good indication of the overall dynamic performance of an ADC because it includes all components which make up noise and distortion. SINAD is often plotted for various input amplitudes and frequencies. For a given input frequency and amplitude, SINAD is equal to THD + N, provided the bandwidth for the noise measurement is the same for both (the Nyquist bandwidth). A typical plot for the AD9226 12-bit, 65-MSPS ADC is shown in Figure 6. Figure 6: AD9226 12-bit, 65-MSPS ADC SINAD and ENOB for Various Input Full-Scale Spans (Range) The SINAD plot shows that the ac performance of the ADC degrades due to high-frequency distortion and is usually plotted for frequencies well above the Nyquist frequency so that performance in undersampling applications can be evaluated. SINAD plots such as these are very useful in evaluating the dynamic performance of ADCs. SINAD is often converted to effective-number-of-bits (ENOB) using the relationship for the theoretical SNR of an ideal N-bit ADC: SNR = 6.02N + 1.76 dB. The equation is solved for N, and the value of SINAD is substituted for SNR: Note that Equation 1 assumes a full-scale input signal. If the signal level is reduced, the value of SINAD decreases, and the ENOB decreases. It is necessary to add a correction factor for calculating ENOB at reduced signal amplitudes as shown in Equation 2: The correction factor essentially "normalizes" the ENOB value to full-scale regardless of the actual signal amplitude. Signal-to-noise ratio (SNR, or sometimes called SNR-without-harmonics) is calculated from the FFT data the same as SINAD, except that the signal harmonics are excluded from the calculation, leaving only the noise terms. In practice, it is only necessary to exclude the first 5 harmonics, since they dominate. The SNR plot will degrade at high input frequencies, but generally not as rapidly as SINAD because of the exclusion of the harmonic terms. A few ADC data sheets somewhat loosely refer to SINAD as SNR, so you must be careful when interpreting these specifications and understand exactly what the manufacturer means. THE MATHEMATICAL RELATIONSHIPS BETWEEN SINAD, SNR, AND THD There is a mathematical relationship between SINAD, SNR, and THD (assuming all are measured with the same input signal amplitude and frequency. In the following equations, SNR, THD, and SINAD are expressed in dB, and are derived from the actual numerical ratios S/N, S/D, and S/(N+D) as shown below: Eq. 3, Eq. 4, and Eq. 5 can be solved for the numerical ratios N/S, D/S, and (N+D)/S as follows: Because the denominators of Eq. 6, Eq. 7, and Eq. 8 are all equal to S, the root sum square of N/S and D/S is equal to (N+D)/S as follows: Therefore, S/(N+D) must equal: and hence, Eq. 12 gives us SINAD as a function of SNR and THD. Similarly, if we know SINAD and THD, we can solve for SNR as follows: Similarly, if we know SINAD and SNR, we can solve for THD as follows: Equations 12, 13, and 14 are implemented in an easy to use design tool on the Analog Devices' website. It is important to emphasize again that these relationships hold true only if the input frequency and amplitude are equal for all three measurements. SUMMARY Because SINAD, SNR, ENOB, THD, THD + N, and SFDR are common measures of ADC dynamic performance, a complete understanding of them in the context of the manufacturers' data sheet is critical. This tutorial has defined the quantities and derived the mathematical relationship between SINAD, SNR, and THD. REFERENCES 1. Walt Kester, Analog-Digital Conversion, Analog Devices, 2004, ISBN 0-916550-27-3, Chapter 2. Also Available as The Data Conversion Handbook Elsevier/Newnes, 2005, ISBN 0-7506-7841-0, Chapter 2.

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如何选择高速A/D转换器 (图)

作者：National semiconductor公司Nicholas Gray 　日期：2000-1-1 　来源：本网

无论是摄像机和有线电视机顶盒还是扫描仪和复印机，A/D转换器（ADC）都是这些现代电子设备中的关键元件。因为它们是模拟信号和数字处理之间的接口，所以常常决定着系统的性能。 分辨率和速度 ---- 高速A/D转换器首先可以用两个参数来描述：分辨率和速度。分辨率以位（bit）来表示，n位A/D转换器将模拟信号分为2n个级，产生2n个单独的数字输出编码。A/D转换器所需要的分辨率取决于系统的信噪比（SNR）和/或动态范围要求。 ---- 高速A/D转换器的速度通常以每秒几百万次采样（Msamples/s）来表示。这就是采样速率，或模拟信号可以在什么样的速率下连续转换为数字形式。对大多数应用来说，采样速率应是A/D转换器输入信号最高频率的3～4倍。 ---- 例如，如果系统的SNR要求是45dB，那么最小A/D转换器分辨率是8位，如表1所示。如果系统内有一两个放大器（或其他电路），那么8位A/D转换器也许不够，这取决于其他器件的噪音特性。 ---- SNR是以分贝表示的比率，它是输入信号的有效值与所有频率小于采样频率一半的其他频谱成份（不包括谐波或直流信号）的总有效值之比。 ---- A/D转换器可获得的理论上最佳SNR是A/D转换器分辨率的函数，定义为 SNR（dB）=6.02n+1.76 ---- 这里n是A/D转换器的位数（分辨率）。 ---- 请注意这是具有理想线性度和无外部噪音的“完美”A/D转换器可得到的理论上的最佳SNR值。实际的A/D转换器的SNR值可能会比这个公式的结果低2到10分贝，或者更多，这是由实际设计方案的非线性度和转换过程当中电路开关期间产生的片上噪音造成的。 ---- 由于选择的电路结构包括pc板布局等问题，最终电路中的实际A/D转换器性能往往比这更低。在真实的A/D转换器中，SNR随着信号频率的升高而降低，因为转换器内部的某些误差机理与频率有关。 ---- 每个器件的SNR象并联的电阻一样，系统的总体SNR要低于具有最低SNR的器件的SNR。例如，假设以每秒20M次的采样速率对4.43MHz的信号进行采样时最小系统SNR应当是45dB，一个4.43MHz时具有52dB SNR的放大器在A/D转换器之前，那么所需的A/D转换器就得有46dB或更好的SNR才能获得45dB的总体SNR。系统SNR可以通过下列公式确定：系统SNR= ---- 因为8位转换器的理论上最佳SNR接近50dB，所以乍一看似乎一个8位的、采样速率每秒20M次的转换器就可以胜任。但是，大致看一下一些8位、每秒20M次的转换器就会发现，大多转换器都不够好。那么许多设计者就会推测，可能需要高精度的A/D转换器。然而，某些A/D转换器（如国家半导体公司生产品ADC1175）就可以提供所需的SNR，并没有必要去寻找更昂贵的转换器就可以获得所需的系统SNR。 误差参数 ---- 然而速度、分辨率和SNR并非一切。分辨率确实表示了A/D转换器可以产生的数字输出编码的数量，但它并未示出这些编码是否真的对应正确的输入电压。诸如微分非线性度（Differential Nonlinearity-DNL）、积分非线性度（Integral Nonlinearity-INL）、偏差和满标度误差等误差参数描述了输出编码响应输入电压的精确程度（见表2）。 ---- DNL相当于转换过程中某一步骤的最大误差。当模拟输入电压升高时，每当模拟输入升高VFS/2n，输出编码应升高1LSB，这里VFS是满标度输入电压范围，它通常等于所加的基准电压。编码转换间距应该正好是1LSB（VFS/2n）。 ---- 如果编码转换发生时输入模拟电压不是比上一次转换正好大1LSB，那么就产生了DNL误差。高速A/D转换器的DNL数据表限幅一般为±0.2LSB到-1LSB和+2LSB。 ---- 因为人眼对亮度变化十分敏感，所以DNL对显示设备或成像应用中所使用的A/D转换器非常重要。例如，如果文档扫描器中使用的A/D转换器的DNL值太大，那么带有渐变灰色阴影的图片就会出现一些明显的灰色条带。在成像应用中DNL是高速A/D转换器最重要的参数之一。 ---- INL表明转换器的转换功能会偏离零标度和满标度值之间的理想直线有多远。INL是贯穿整个转换功能的DNL误差的总和。具有高INL的A/D转换器的转换功能总曲率更高。高速A/D转换器的INL实际值范围大约是±0.2到±4LSB。 ---- 诸如SNR、THD（Total Harmonic Distortion，总谐波失真）、SINAD或S/（N+D）（信号与噪音加失真比）和ENOB（Effective Number of Bits，有效位数）等动态参数表示当A/D转换器的输入是由正弦波驱动时所产生的频域误差。THD是以分贝表示的输出信号的头几个谐波成份的有效值之和与输出端出现的输入信号的幅度之比。所选的谐波的数量由生产厂家而定，典型的是6个。 ---- 在比较不同厂家生产的A/D转换器（见表3）时，要注意他们计算THD时所取的谐波个数。如果取的谐波数太少（少于5或6个），那么A/D转换器数据表中就会表现出人为的THD乐观值。通信应用中过大的THD会导致可能干扰其他通信通道的多余信号。 ---- SINAD是以分贝表示的输出端出现的输入信号有效值与输出信号当中频率小于采样频率一半（包括谐波但不包括直流）的所有其他频谱成份的有效值之比。SIND可以SNR和THD值计算出来： ---- 这里的SNR和THD在前面讲过。 ---- ENOB是从SINAD推导出来的。理想A/D转换器的SINAD可以从该A/D转换器的分辨率计算出来，ENOB也可以从真实A/D转换器的SINAD测量值计算出来。 ---- ENOB表示，如果一个理想转换器具有候选的真实转换器的SINAD，那么它所应有的分辨率。换句话说，ENOB为7.0的A/D转换器具有与完美7.0位分辨率A/D转换器相同的SINAD。ENOB可以用分数位表示： ---- 这里SINAD以分贝表示，ENOB以位来表示。 ---- 除量化噪音外绝对无失真和噪音的理想8位A/D转换器的ENOB是8。然而，真实的A/D转换器会有些误差，使其SINAD测量值小于理想值。比如，SINAD为45.4dB的A/D转换器的ENOB为7.25位，与完美的7.25位A/D转换器具有相同的SINAD。 ---- 数据表中A/D转换器的ENOB数值应当由SINAD而非SNR得出，许多厂商都这样做。只有当THD优于SNR 12到15dB时ENOB才应当从SNR计算得到。还有，要注意确定ENOB的输入信号频率。频率升高时ENOB会下降。 ---- 请注意，来自不同厂家的具有类似器件号（其管脚配置也很可能相似）的A/D转换器的性能却不一定相同。仅通过阅读不同厂商的数据表来选择A/D转换器不一定合适。应当在实验室对它们进行测试。 ---- 一些厂商（如美国国家半导体公司等）提供A/D转换器评估板，允许设计工程师评估转换器的动态性能。国家半导体公司的评估板带有软件，使设计者可利用计算机或不用计算机更容易地评估A/D转换器的动态性能。 ---- 如果选择了错误的A/D转换器，那么往往很难或不可能满足系统要求。选择符合系统需要性能的A/D转换器十分重要。

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