分辨率与准确性与敏感性削减混乱

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当选择一个模拟数字(A / D),n external data acquisition system, or other measurement device, many parameters must be considered. Product characteristics such as price and measurement speed are easily understood.

But when you examine the resolution, accuracy, and sensitivity of a product, be careful. Even experienced engineers confuse these related, yet very different, specifications.

The most common mistake is to assume that more resolution always represents a better measurement. As a result, you assume that an A/D board with 16-bit resolution is better than a 14-bit board, and a 20-bit board is still better. Actually, the 14-bit board may be a better choice if it is more accurate and has better sensitivity than other higher-resolution products.

There is a false implication that the higher the resolution, the better suited the product is to make measurements. The reality is that accuracy and sensitivity are of equal or greater importance than resolution. You should pay equal attention to these parameters when selecting a product.

Keep in mind, too, that it is rare when more resolution comes without penalizing acquisition speed.

Accuracy

精度描述了相关绝对标准中测量中存在的不确定性量。它可以通过几种不同的方式定义，并取决于供应商的规范理念以及产品设计。

Most accuracy specifications include a gain and an offset parameter. Offset parameters, usually expressed as an absolute amount such as volts or ohms, generally are independent of the magnitude of the input. Typically, gain errors depend on the magnitude of the input and usually are expressed as a percentage of the reading. An example of an accuracy specification and what can be expected of the reading is found in Table 1.

Table 1. Readings as a Function of Accuracy

Resolution

In relative amounts, resolution describes the degree to which a change can be detected. It is expressed as a fraction of an amount to which you can easily relate. For example, printer manufacturers often describe resolution as dots per inch, which is easier to relate to than dots per page.

In the data acquisition world, resolution most often is expressed as a number of bits, such as 12, 16, or 20. In the digital multimeter world, resolution usually is described in digits, such as 4, 5, or 6.

To relate bits of resolution to actual measurement parameters such as voltage or temperature, first you must do some math. Suppose that a data acquisition device with ±10 V full scale has 16 bits of resolution. To relate this to volts, first calculate 2¹⁶，是65,536。

As a result, the device can resolve one part out of 65,536; on a ±10-V range having a 20-V peak-to-peak (p-p) range, the device can resolve 20 V/65,536 = 305 µV. This generally means that the smallest change that can be detected by the measurement device is 305 µV.

In reality, not all of the resolution is necessarily useful because other factors enter into the situation-most notably noise. A product specified to 16-bit resolution may have 16 counts (4 bits) p-p noise. Instead of resolving 16 bits, it can only resolve 12. If the noise is random in nature, then simple averaging can improve resolution nearer to the stated specification if you are willing to live with the effective reduction in sampling rate.

让我们看看另一个例子。平均样品数量的平方根降低了噪声。如果测量有3位P-P噪声，则等于2³or 8 counts of noise, then averaging 64 samples would reduce the noise to one count. The net result would be achieving 1 bit out of 16-bit resolution.

With this approach, the measurement rate would be 64 times slower than without averaging, which may or may not be a limitation, depending on the application. Although averaging is very effective, it isn’t perfect. You will never be able to average things such as nonlinearity, so this technique only goes so far.

This approach only works as long as the noise is Gaussian. It is difficult to reduce slowly varying 1/f noise with averaging, and the net result often is worse than the square root of the samples might predict.

Sensitivity

Sensitivity is an absolute quantity; resolution is a relative quantity. Sensitivity describes the smallest absolute amount of change that can be detected by a measurement, often expressed in terms of millivolts, microhms, or tenths of a degree.

Sensitivity should not be confused with accuracy—they are entirely different parameters. For example, a device specified with 1-mV sensitivity may only be accurate to 10 mV with an applied input of 10 V. Yet if the 10-V input signal changed by 1 mV, the device still could observe the difference. Sensitivity sometimes can be improved by averaging.

The actual sensitivity is as much a function of the measurement device as it is the environment in which the measurement is being made. A device may be perfectly capable of making measurements with 1-µV sensitivity. But if the cabling is not adequately shielded and void of thermally generated voltages, then achieving 1-µV sensitivity will be impossible.

确定设备敏感性的最简单方法是在其最低范围内查看其性能。该范围的噪声规范在很大程度上将决定设备的灵敏度。其他微妙的因素，例如短期输入偏移电压漂移以及输入连接器的质量也会影响它。除非采取适当的注意，否则测试设置（互连，屏蔽）通常会限制最终灵敏度。

现在，让我们将这三条线应用于真实的应用程序中。对于此插图，让我们使用Iotech个人DAQ/基于USB的数据采集系统。表2包括该产品的测量规范的摘录。假设我们有一个传感器或换能器，其输出的范围从几微伏到3V。

表2.个人DAQ/56规格

假设在一定条件下,output of our sensor is 200 mV, and under another condition, the output is 3 V. Let’s determine the resolution, sensitivity, and accuracy of the measurement under each of these conditions.

First we must consider the usual trade-off between speed and resolution. For this example, we want to maximize resolution, so let’s select the slow conversion rate that will give us the best noise rejection (line cycle integration) and result in 22 bits of available resolution.

Accuracy

根据在15至35°C环境温度范围内的一年性能的规范，准确性为读取范围 + 0.002％的0.01％（不包括噪声）。这是绝对的准确性。我们包括了噪声注释，因为在图2中分别指定了噪声。

• With a 200-mV signal using the 250- mV range:
  0.01％×200 mV =±20 µV
• For percentage of range using the 250- mV range:
  0.002％×250 mV =±5 µV

The uncertainty due to the noise on this range, from Figure 2, is 1 µVrms or ±3 µV p-p, a fairly small value.

Unless we correct for it (a simple arithmetic subtraction of the measured offset), we also must include the input offset voltage uncertainty. The worst case specification is 20 µV for the Personal Daq/56.

The total uncertainty in the measurement for the 200-mV sensor output is

±(20 µV + 5 µV + 20 µV +3 µV) = ±48 µV

This implies that the 200-mV sensor output can be measured to an accuracy of ±48 µV.

Using the same methodology, we can calculate the accuracy for the 3-V sensor output. In this case, we must use the 4-V range.

Total Uncertainty = ±(300 µV + 80 µV + 20 µV + 12)
=±412 µV

因此，当传感器输出为3 V时，我们测量的准确性将保守地为±412 µV。

Resolution

表2显示了4V范围上指定的可用分辨率为22位RMS。让我们确定3V信号级别的分辨率。

请记住，分辨率是我们正在测量的最大信号与我们可以解决的最小部分之间的比率。4V范围的噪声规范为4 µVRM，这代表了我们可以解决的最小部分，除非我们平均。

4 µVrms/3 V = 1 part of 750,000, which is approximately 2²⁰，或20位RMS

This can be improved somewhat by averaging.

在200 mV示例中，1 µVRMS/200 mV = 200,000的1部分，约为2¹⁸, or 18 bits rms

对于两个示例，分辨率受噪声的限制。如果我们使用16位分辨率而不是22位分辨率，那么与噪声相比，类似于数字的转换器 - 将是限制因素，从而产生16位分辨率。

Sensitivity

我们最敏感的测量可以在250-mV范围内进行，其中噪声仅为1 µVRM。在这种情况下，我们的灵敏度为1 µVRM，或6 µV P-P（将峰值噪声计算为RMS值的〜6倍）。如果我们将测量局限于4V范围，则在这种情况下，我们的灵敏度为4 µVRM或24 µV P-P。

Observations

表3中找到了结果的摘要。这表明我们可以在最低范围内获得最佳灵敏度。但是，最低范围通常会限制我们测量的动态范围，在这种情况下为±250 mV。如果您不确定传感器输出的大小，请在设置测量时寻找最高范围，并具有最佳灵敏度。

Table 3. Actual Accuracy, Resolution and Sensitivity Values

Our measurement accuracy is determined largely by the value we are measuring (0.01% of reading) because the system’s range error is only 0.002%. On some data acquisition equipment, this spec is larger. If it is, then you compromise accuracy by selecting a range higher than what you need to make the measurement.

Conclusions

Different companies have different guidelines about how they derive their specifications, particularly when several components determine the specification—which often is the case concerning accuracy. Some companies simply add the accuracy errors and publish a worst-case specification. Other companies use a two-sigma calculation, which effectively is the square root of the sum of the squares of each of the error components. And other companies may simply add the typical accuracy specifications instead of worst case of each of the devices.

在为应用程序选择特定产品之前，可能有必要与您的供应商讨论规范理念。最终测试是在购买设备之前对设备进行评估，以确定其性能是否可以接受。

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