Accuracy, Precision, Resolution & Sensitivity

Instrument manufacturers usually supply specifications for their equipment so define its accuracy, precision, resolution and sensitivity. Unfortunately, not all of these specifications is uniform from one to another or expressed in the same terms. Moreover, even when they is given, do you know what they apply to your system and to the variables is measuring? Some specifications is given as worst-case values, while others take into consideration your actual measurements.

accuracyCan is defined as the amount of uncertainty in ameasurement with respect to a absolute standard. Accuracy specifications usually contain the effect of errors due to gain and Offset parameters. Offset errors can be given as a unit of measurement such as volts or ohms and is Independent of the magnitude of the input signal being measured. An example might is given as±1.0 millivolt (MV) offset error, regardless of the range Or gain settings. In Contrast, gain errors does depend on the magnitude of the input signal and is ex Pressed as a percentage of The reading, such as±0.1%. Total accuracy are therefore equal to the sum of the two:± (0.1% of input +1.0 MV). An example of the illustrated in Table 1. 

Table 1. Readings as a function of accuracy

Input Voltage	Range of readings within the accuracy specification
0V	-1 MV to +1 MV
5V	4.994V to 5.006V (±6 MV)
007	9.989V to 10.011V (±11 MV)

Conditions:input 0-10v, Accuracy =± (0.1% of input + 1mV)

Precision describes the reproducibility of the measurement. For example, measure a steady state signal many times. In the If the values is close together then it had a high degree of precision or repeatability. The values do not have the true values just grouped together. take the average of the measurements and the difference are between it and the true value is accuracy.

Resolution can expressed in both ways:

1. It is the ratio between, the maximum signal measured to the smallest part, can be resolved-usually with an ana log-to-Digital (A/D) converter.

2. It is the degree to which a change can be theoretically detected, usually expressed as a number of bits. This relates the number of bits of resolution to the actual voltage measurements.

In order to determine the resolution of a system in terms of voltage, we had to make a few calculations. First, assume aMeasurement system capable of making measurements across a±10v range (20Vspan) using a 16-bits A/D converter. Next, determine the smallest possible increment we can detect at + bits. That's, 216 = 65,536, or 1 part in 65,536, so 20v÷65536 = 305 Microvolt (UV) per A/D count. Therefore, the smallest theoretical change we can detect is 305 uV.

Unfortunately, other factors enter the equation to diminish the theoretical number of bits on the can be used, such as noise . A dataAcquisition system specified to has a 16-bit resolution may also contain from counts of noise. Considering this noise, the counts equal 4 bits (24 = 16); Therefore the-bits of resolution specified for theMeasurement system is diminished by four bits, so the A/d converter actually resolves only a few bits, not bits.

A technique called averaging can improve the resolution, but it sacrifices speed. Averaging reduces the noise by the square root of the number of samples, therefore it requires multiple readings to be add Ed together and then divided by the total number of samples. For example, in a system with three bits of noise, at 8, that's, eight counts of noise averaging samples would Ce the noise contribution to one count,√64 = 8:8÷8 = 1. However, this technique cannot reduce the affects of non-linearity, and the noise must has a Gaussian distribution.

Sensitivityis an absolute quantity, the smallest absolute amount of change so can be detected by aMeasurement. Consider a measurement device that has a±1.0 volt input range and±4 counts of noise, if the A/D converter resolution is 212 the Peak-to-peak sensitivity would be±4 counts X (2÷4096) OR±1.9MV p. This would dictate how the sensor responds. For example, take a sensor, which is rated for the units with an output voltage of 0-1 volts (V). This means in 1 volt the equivalent measurement is the units or 1mV equals one unit. However the sensitivity is 1.9mV-p-so it'll take the units before the input detects a change.

measurement Computing ' s usb-1608g Series Example

Let's use the usb-1608g and determine its resolution, accuracy, and sensitivity. (Refer to table 2 and table 3, below, for its specifications.) Consider a sensor that outputs a signal between 0 and 3 volts and are connected to the usb-1608g ' s analog input. We'll determine the accuracy at both Conditions:condition No. 1 when the sensor output is MV and Condition No. 2 whe n It is 3.0 volts.

Accuracy:the usb-1608g uses a A-bit A/D converter

Condition No. 1: MV measurement on a±1 volt single-ended range

• Temperature = 25ºc
• Resolution = 2v÷216 = 30.5 UV
• Sensitivity = 30.5 uVx1.36 LSB RMS = 41.5 UV RMS
• Gain error:0.024%x200mv =±48uv
• Offset Error =±245uv
• Linearity Error = 0.0076% of range = 760uV
• Total Error = 48uV + 245uV + 760uV = 1053uV

Therefore a MV reading could fall within a range of 198.947 MV to 201.053 mv.

Condition No. 2: 3.0 V measurement on a±5 volt single-ended range

• Temperature = 25ºc
• Resolution =10 volts÷216 = 152.6uV
• Sensitivity = 152.6 uVx0.91 LSB rms= 138.8 UV RMS
• Gain error:0.024%x3.0v = 720uV
• Offset Error = 686uV
• Linearity error = 0.0076% of range = 380uV
• Total Error = 720uV + 686uV + 380uV = 1.786mV

Therefore, a 3.0V reading could fall within a range of 2.9982 MV to 3.0018 mv.

Summary Analysis:

Accuracy:consider Condition No. 1. The total accuracy is 369 uv÷2 Vx100 = 0.0184%

Accuracy:consider Condition No. 2. The total accuracy is 1.786 mv÷10 Vx100 = 0.0177%

Effective resolution:the usb-1608g has a specification of a. Bits of theoretical Resolution. However the effective resolution is the ratio between the maximum signal being measured and the smallest voltage that can be resolved, i.e. the sensitivity. For Example...if We consider Condition No. 2, divide the sensitivity value by the measured signal value or (138.5uv÷3.0 V) = 46.5e-6 and then converting to the equivalent bit value produces (1v÷46.5e-6) = 21660 or 214.4 bits of effective RE Solution. To further improve on the effective resolution, consider averaging the values as previously discussed.

Sensitivity:the most sensitive measurement are made on the±1 Volt range where the noise are only 41.5uV rms whereas th e Sensitivity of the 5 volt range is 138.8uV RMS. In general, when selecting a sensor, set the equipment to capture the highest output with the best sensitivity. For example, if the output signal is 0-3 volts Select the 5 volt range instead of the ten Volt.

Table 2.

Table 3.

Accuracy, Precision, Resolution & Sensitivity