WELLOG DAQ CONCEPTS
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The following are a few important concepts to consider during Digital Acquisition of Analog Input signals.
Sampling rate is the rate at which data is sampled. Rapidly changing signals must be sampled more frequently in order to accurately represent the signal. Under-sampling may result in misrepresentation of the measured signal.
When a signal is under-sampled, data points are recorded that represent a lower frequency signal called an alias. Signals should be sampled at a rate that is at least twice their highest frequency to eliminate aliasing. This is based on the Nyquist-Shannon sampling theorem.
Logging of data should be performed at a sample rate that provides adequate measurement frequency to avoid missing relevant data.
The process of digitizing an analog signal involves representing the signal with a finite number of voltage levels. The resolution of a Data Acquisition system is controlled by the number of bits the analog to digital converter (ADC) uses to represent a signal. See our page on the power of two. The ADC voltage is divided into 2n divisions or levels. Each level is assigned a binary value which represents a discrete voltage. The ADC returns a digital value that best represents the analog voltage at its input. The higher the resolution, the higher the number of discrete voltage levels the ADC can represent. Resolution defines the precision with which a measurement is made.
Examples of resolution:
An 8 bit ADC can represent 256 discrete voltage levels. In a 5 volt system, the resolution is 5/256 = .0195 volts.
A 10 bit ADC can represent 1024 discrete voltage levels. In a 5 volt system, the resolution is 5/1024 = .00488 volts.
A 12 bit ADC can represent 4096 discrete voltage levels. In a 5 volt system, the resolution is 5/4096 = .00122 volts.
A 16 bit ADC can represent 65536 discrete voltage levels. In a 5 volt system, the resolution is 5/65536 = .000076 volts.
Dithering is a technique used in ADCs that improves their resolution beyond the hardware specification. Gaussian (white noise) is added to the input signal. The noise is random and averaging adds approximately .5 of the least significant bit to be added in resolution. For example a 12 bit board can perform with 14 bit resolution with dithering enabled. Dithering can be disabled in software in high speed applications.
Many signals measured in Data Acquisition systems are small when compared to the range of voltages the ADC is designed to measure. For example a signal that varies in the range of 0 to 1 volt when measured by an ADC having a 0 to 5 volt range will only be represented by 1/5 of the available ADC resolution. It is important to use an amplifier to increase or give gain to the input voltage. A 1 volt input signal given a gain of 5 will use the full resolution of the 5 volt ADC.
GAIN IMPROVES DYNAMIC RANGE:
Adding programmable gain amplifiers improves dynamic range. Very small voltages are difficult to resolve using 8 and 10 bit analog to digital converters. As shown above, a 10 bit a/d converter operating in a 5 volt system, has a resolution of .00488 volts. If a signal is less than the smallest amount of voltage that can be resolved, the a/d converter needs an amplifier to provide voltage gain. Programmable gain amplifiers can give a boost to these small voltages. An amplifier having a gain of 1000 will increase an input voltage of .00488 volts to 4.88 volts. This added gain gives the ability to resolve .00488 volts into 10 bit resolution – increasing the dynamic range of the 10 bit a/d converter to effectively 20 bit resolution.
Typical programmable gain amplifiers have selectable gains of 1, 2, 4, 5, 8, 10, 16, and 32. Two amplifiers in cascade can provide a gain of 32 x 32 = 1024. In a typical 5 volt system, a low level .00488 volt level (amplified by 1024) is increased to 4.99712 volts. This effectively increases the dynamic range of the ADC by an additional 8 bits. A 10 bit ADC therefore has an effective resolution equal to a 16 bit ADC. In this case there are eight gain ranges giving two (additional) non-binary gain options of x5 and x10.
The process of changing the voltage of an input signal is referred to as signal conditioning. Frequently input signals are too small compared to the input voltage range of the ADC. Other forms of signal conditioning may involve filtering, voltage shifting, voltage inversion.
In many instances, electrical noise may interfere with the measured signal. Noise may come from many different sources. Common 60 cycle power may introduce low frequency 60 cycle noise. A computer may generate unwanted high frequency noise. Atmospheric noise occurs from natural sources within the atmosphere. Terrestrial and exra-terrestrial sources of noise are abundant. Filtering can be used to reduce unwanted noise.
SIGNAL TO NOISE RATIO:
Acquisition of signals involves the capture of wanted and unwanted (noise) signals. It is preferable in most cases to acquire more of the wanted signal and less of the unwanted noise. The quality of an acquisition system is often measured by the ratio of signal to noise. The ratio of signal to noise is called the signal to noise ratio.
S/N ratio = signal/noise
Most often, S/N ratio is represented in dB (Decibels).
When signals are measure in terms of voltage, signal to noise (dB) = 10 (log10 of (S/N)).
When signals are measure in terms of power, signal to noise (dB) = 20 (log10 of (S/N)).
DC INPUT OFFSET CONTROL:
DC voltages may occur at an input that cause an undesired shift in voltage. WELLOG uses programmable Digital to Analog Converters for input offset trimming.
All measurements have a degree of uncertainty. It is therefore necessary to have knowledge of the instrumentation calibration before and after measurement in order to minimize uncertainty. Uncertainty has different forms and sources within any system. Because systems measure a given quantity that may have statistical change, repeat sections (when possible) of a logging interval provide a demonstration of repeatability.
Visit http://www.physics.nist.gov/cuu/ for more information on constants, units, and uncertainty.
For an example of an application using a DAQ in a well logging system go to our page on DAQ applications.
Further information on DAQ systems and concepts can be obtained from WELLOG.