®
`
`APPLICATION BULLETIN
`
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`PRINCIPLES OF DATA ACQUISITION AND CONVERSION
`
`Data acquisition and conversion systems are used to acquire
`analog signals from one or more sources and convert these
`signals into digital form for analysis or transmission by end
`devices such as digital computers, recorders, or communica-
`tions networks. The analog signal inputs to data acquisition
`systems are most often generated from sensors and transduc-
`ers which convert real-world parameters such as pressure,
`temperature, stress or strain, flow, etc., into equivalent
`electrical signals. The electrically equivalent signals are then
`converted by the data acquisition system and are then uti-
`lized by the end devices in digital form. The ability of the
`electronic system to preserve signal accuracy and integrity is
`the main measure of the quality of the system.
`The basic components required for the acquisition and
`conversion of analog signals into equivalent digital form are
`the following:
`1. Analog Multiplexer and Signal Conditioning
`2. Sample/Hold Amplifier
`3. Analog-to-Digital Converter
`4. Timing or Sequence Logic
`Typically, today’s data acquisition systems contain all the
`elements needed for data acquisition and conversion, except
`perhaps, for input filtering and signal conditioning prior to
`analog multiplexing. The analog signals are time multi-
`plexed by the analog multiplier; the multiplexer output
`signal is then usually applied to a very-linear fast-settling
`differential amplifier and/or to a fast-settling low aperture
`sample/hold. The sample/hold is programmed to acquire and
`hold each multiplexed data sample which is converted into
`digital form by an A/D converter. The converted sample is
`then presented at the output of the A/D converter in parallel
`and serial digital form for further processing by the end
`devices.
`
`SYSTEM SAMPLING RATE —
`Error Considerations
`The application and ultimate use of the converted data
`determines the required sampling and conversion rate of the
`data acquisition and conversion system. System sampling
`rate is determined, as shown in Figure 1, by the highest
`bandwidth channel, the number of data channels and the
`number of samples per cycle.
`
`Aliasing Error
`From the Nyquist sampling theorem, a minimum of two
`samples per cycle of the data bandwidth is required in an
`ideal sampled data system to reproduce sampled data with
`no loss of information. Thus, the first consideration for
`determining system sampling rate is aliasing error, i.e.,
`errors due to information being lost by not taking a sufficient
`number of samples per cycle of signal frequency.
`Figure 2 illustrates aliasing error caused from an insufficient
`number of samples per cycle of data bandwidth.
`
`How Many Samples per Cycle?
`The answer to this question depends on the allowable aver-
`age error tolerance, the method of reconstruction (if any),
`and the end use of the data. Regardless of the end use, the
`actual error of the discrete data samples will be equal to the
`throughput error of the data acquisition and conversion
`system plus any digital errors contributed by a digital com-
`puter or other digital end device.
`For incremental devices such as stepping motors and switches,
`the average error of sampled digital data is not as important
`
`Aliasing Error (cid:13)
`(not enough samples per frequency cycle –fS < 2fMAX)
`
`Wave Form
`
`Original Signal
`
`Reconstructed(cid:13)
`
`Highest(cid:13)
`Bandwidth(cid:13)
`Data Channel
`
`Number(cid:13)
`of(cid:13)
`Channels
`
`Number of(cid:13)
`Samples/Cycle
`
`Minimum(cid:13)
`System(cid:13)
`Sampling(cid:13)
`Rate
`
`Samples
`
`First Order(cid:13)
`Interpolation(cid:13)
`(Reconstruction Using(cid:13)
`Filter or Vector Generator)
`
`Zero Order(cid:13)
`Interpolation(cid:13)
`(Reconstruction Directly (cid:13)
`from D/A Converter)
`
`FIGURE 1. Determining Minimum System Sampling Rate.
`
`FIGURE 2. Aliasing Error vs Sampling Rate.
`
`©1994 Burr-Brown Corporation
`
`AB-082
`
`Printed in U.S.A. May, 1994
`
`SBAA051
`
`
`
`Apple 1021
`U.S. Pat. 9,189,437
`
`

`
`Zero Order Data(cid:13)
`Reconstruction(cid:13)
`(D/A Converter(cid:13)
`Output)
`
`First Order Data(cid:13)
`Reconstruction(cid:13)
`(Vector Connection(cid:13)
`of Sample)
`
`10
`
`100
`
`1000
`
`Samples/Cycle
`
`10(cid:13)
`
`1(cid:13)
`
`ccuracy (%)
`
`0.1A
`
`0.01
`
`1
`
`FIGURE 4. Reconstruction Accuracy vs Number of Samples
`Per Cycle.
`
`For sinusoidal data, maximum aperture error occurs at the
`zero crossing where the greatest dv/dt occurs, and is ex-
`pressed mathematically as:
`Aperture Error = d (A sin 2p
` ft) x tA x 100%
`dt
`= 2p
` ftA x 100% max
`where f = maximum data frequency
`tA = aperture time of system (This
`can be the conversion time of
`the A/D converter with no
`sample/hold, or the aperture
`time of a sample/hold if one is
`in front of an A/D converter).
`
`This expression is shown graphically in Figure 5 for
`frequencies of 1Hz to 10kHz with – 1/2LSB error high-
`lighted for 8-, 10- and 12-bit resolution A/D converters.
`The need for a sample/hold becomes readily apparent
`when data frequencies of 10Hz or higher are sampled,
`because the A/D converter conversion speed must be 2m s
`or faster for aperture errors less than – l/2LSB for l2-bit
`resolution, and high speed A/D converters are complicated
`and expensive when compared to slower A/D converters
`with a low aperture sample/hold.
`
`0 H z
`
`0
`
`1
`
`0 H z
`
`1
`
`1/2LSB of 10 Bits
`1/2LSB of 12 Bits
`
`1/2LSB of 13 Bits
`1/2LSB of 14 Bits
`1/2LSB of 16 Bits
`
`1 M H z
`
`k H z
`
`0
`
`0
`
`1
`
`k H z
`
`0
`
`1
`
`k H z
`
`1
`
`10(cid:13)
`
`1(cid:13)
`
`0.1(cid:13)
`
`.01(cid:13)
`
`.001
`
`.0001
`
`Aperture Error (% Full-Scale Range)
`
`1
`
`10
`
`100
`
`1µs
`
`Aperture Time (ns)
`
`FIGURE 5. Aperture Error vs Aperture Time for Data Fre-
`quencies from 10Hz to 1MHz.
`
`as it is for end devices that require continuous control
`signals. To illustrate average sampling error in sampled data
`systems, consider the case where the minimum of 2 samples
`per cycle of sinusoidal data are taken, and the data is
`reconstructed directly from an unfiltered D/A converter
`(zero-order reconstruction). The average error between the
`reconstructed data and the original signal is one-half the
`difference in area for one-half cycle divided by p
`, or 32% for
`zero order data, and 14% for first order reconstruction.
`However, the instantaneous accuracy at each sample point is
`equal to the accuracy of the acquisition and conversion
`system, and in many applications, this may be sufficient for
`driving band-limited end devices. The average accuracy of
`sampled data can be improved by (1) increasing the number
`of samples per cycle; (2) presample filtering prior to multi-
`plexing, or (3) filtering the D/A converter output.
`
`(1)
`
`(1)
`
`(1)
`
`(1)
`
`(1)
`
`(1)
`
`Original(cid:13)
`Data(cid:13)
`Signal
`
`(a)(cid:13)
`Zero Order(cid:13)
`Reconstructed(cid:13)
`Data(cid:13)
`(D/A Converter(cid:13)
`Output)
`
`(b)(cid:13)
`First Order(cid:13)
`Data(cid:13)
`Reconstruction(cid:13)
`(Filtered DAC(cid:13)
`or Vector Generator)
`
`Note: (1) Data samples of conversion(cid:13)
`
` system (2 samples per cycle). (cid:13)(cid:13)
`FIGURE 3. Reconstruction of Sampled Data Where fS =
`2fMAX.
`
`The improvement in average accuracy of sampled data is
`dramatic with only a slight increase in the number of
`samples per cycle as shown in Figure 4. The theoretical limit
`is the throughput accuracy of the acquisition and conversion
`system for continuous sampling.
`For zero order reconstruction of data, it can be seen from
`Figure 4 that more than 10 samples per cycle of data
`bandwidth are required to reconstruct sampled data to aver-
`age accuracies of 90% or better. A commonly used range is
`7 to 10 samples per cycle.
`
`Aperture Error
`Aperture error is defined as the amplitude and time errors of
`the sampled data points due to the uncertainty of the dy-
`namic data changes during sampling. In data acquisition and
`conversion systems, aperture error can be reduced or made
`insignificant either by the use of a sample/hold or with a
`very fast A/D converter.
`
`2
`
`

`
`A sample/ hold with an aperture time of 50ns to 60ns
`produces negligible aperture error for data frequencies up to
`100Hz for 10- and 12-bit resolution A/ D converters, and is
`less than – 1/2LSB for 8-bit resolution for data frequencies
`near 5kHz. Use Figure 5 to determine your system aperture
`error for each data channel versus the desired resolution
`
`A FEW A/D CONVERTER POINTS
`A brief discussion of A/D converter terminology will help
`the reader understand system resolution and accuracy a little
`better.
`
`Accuracy
`All analog values are presumed to exist at the input to the
`A/D converter. The A/D converter quantizes or encodes
`specific values of the analog input into equivalent digital
`codes as an output. These digital codes have an inherent
`uncertainty or quantization error of –1/2LSB. That is, the
`quantized digital code represents an analog voltage that can
`be anywhere within –1/2LSB from the mid-point between
`adjacent digital codes. An A/D converter can never be more
`accurate than the inherant –1/2LSB quantizing error. Ana-
`log errors such as gain, offset, and linearity errors also
`affect A/D converter accuracy. Usually, gain and offset
`errors can be trimmed to zero, but linearity error is
`unadjustable because it is caused by the fixed-value ladder
`resistor network and network switch matching. Most qual-
`ity A/D converters have less than –1/2LSB linearity error.
`Another major error consideration is differential linearity
`error. The size of steps between adjacent transition points
`in an ideal A/D converter is one LSB. Differential linearity
`error is the difference between adjacent transition points in
`an actual A/D converter and an ideal one LSB step. This
`error must be less than one LSB in order to guarantee that
`there are no missing codes. An A/D converter with –1/
`2LSB linearity error does not necessarily imply that there
`are no missing codes.
`
`Selecting the Resolution
`The number of bits in the A/D converter determines the
`resolution of the system. System resolution is determined by
`the channel(s) having the widest dynamic range and/or the
`channel(s) that require measurement of the smallest data
`increment. For example, assume a channel that measures
`pressure has a dynamic range of 4000psi that must be
`measured to the nearest pound. This will require an A/D
`converter with a minimum resolution of 4000 digital codes.
`A 12-bit A/D converter will provide a resolution of 212 or
`4096 codes—adequate for this requirement. The actual reso-
`lution of this channel will be 4000/4096 or 0.976 psi.
`The A/D converter can resolve this measurement to within
`– 0.488 psi (– 1/2LSB).
`
`Resolution
`The number of bits in an A/D converter determines the
`resolution of the data acquisition system. A/D converter
`resolution is defined as:
`
`VFSR
`Resolution = One LSB = , for binary A/D converters
`2n
`VFSR
`= , for decimal A/D converters
`10D
`LSB = Least Significant Bit
`VFSR = Full Scale Input Voltage Range
`where n = number of bits
`D = numbers of decimal digits
`The number of bits defines the number of digital codes and
`is 2n discrete digital codes for A/D converters.
`For this discussion, we will use binary successive-approxi-
`mation A/D converters. Table I shows resolutions and LSB
`values for typical A/D converters.
`
`A/D Converter Resol-
`ution (Binary Code)
`
`Value of 1LSB
`
`Value of 1/2LSB
`
`Number
`of Bits
`(n)
`
`Number
`Of Incre-
`ments (2n)
`
`0 to +10V
`Range
`(mV)
`
`16
`12
`11
`10
`9
`8
`
`65536
`4096
`2048
`1024
`512
`256
`
`0.152
`2.44
`4.88
`9.77
`19.5
`39.1
`
`+10V
`Range
`(mV)
`
`0.305
`4.88
`9.77
`19.5
`39.1
`78.2
`
`0 to +10V
`Range
`(mV)
`
`+10V
`Range
`(mV)
`
`0.076
`1.22
`2.44
`4.88
`9.77
`19.5
`
`0.152
`2.44
`4.88
`9.77
`19.5
`39.1
`
`TABLE I. Relationship of A/D Converter LSB Values and
`Resolutions for Binary Codes.
`
`INCREASING SYSTEM THROUGHPUT RATE
`The throughput rate of the system is determined by the
`settling times required in the analog multiplexer and input
`amplifier, sample/hold acquisition time and A/D converter
`settling and conversion time.
`Two programming modes that are commonly used in data
`acquisition systems are normal serial programming (Figure
`6a) and overlap mode programming (Figure 6b). The range
`of typical system throughput rates for these types of modes
`are shown in Table II for the Burr-Brown SDM857KG
`modular data acquisition systems.
`A wide range of throughput speeds can be achieved by
`“short cycling” the A/D converter to lower resolutions and
`by overlap programming the data acquisition system.
`The multiplexer and amplifier settling time is eliminated by
`selecting the next sample (channel n + 1) while the held
`sample (channel n) is being converted. This requires a
`sample/hold with very low feed-through error.
`
`3
`
`

`
`Channel Period
`
`Multiplier(cid:13)
`and Amplifier(cid:13)
`Settling(cid:13)
`Time
`
`S/H(cid:13)
`Acquisi-(cid:13)
`tion and(cid:13)
`Settling(cid:13)
`Time
`
`A/D Converter(cid:13)
`Settling and(cid:13)
`Conversion Time
`
`Channel In
`
`Channel Period
`
`A/D Converter(cid:13)
`Settling and(cid:13)
`Conversion Time
`
`S/H(cid:13)
`Acquisi-(cid:13)
`tion and(cid:13)
`Settling(cid:13)
`Time
`
`Channel In
`
`(A)
`
`(B)
`
`FIGURE 6a. System Throughput Rate-Signal Programming
`and, 6b, System Throughput Rate-Overlap
`Mode.
`
`NORMAL
`PROGRAMMING
`Max System
`Throughput
`Rate
`
`RSS
`Accuracy
`
`OVERLAP
`MODE
`Max System
`Throughput
`Rate
`
`RSS
`Accuracy
`
`18kHz
`
`19.5kHz
`
`21.1kHz
`
`0.025%
`
`0.08%
`
`0.30%
`
`27kHz
`
`30kHz
`
`34.1kHz
`
`0.025%
`
`0.08%
`
`0.30%
`
` Resolution
`
`12 Bits
`
`10 Bits
`
`8 Bits
`
`TABLE II. System Throughput Rates and RSS Accuracy for
`Normal and Overlap Mode Programming for
`Burr-Brown Model SDM857KG Modular Data
`Acquisition System.
`
`Error Source
`
`8 Bits
`
`MUX Error
`
`AMP Error
`S/H Error
`
`ADC Errors
`Analog
`Quantizing
`
`0.0025%
`
`0.01%
`0.01%
`
`0.2%
`0.2%
`
`RESOLUTIONS
`
`10 Bits
`
`0.0025%
`
`0.01%
`0.01%
`
`0.05%
`0.05%
`
`12 Bits
`
`0.0025%
`
`0.01%
`0.01%
`
`0.012%
`0.012%
`
`RSS Error
`0.283%
`0.072%
`0.022%
`TABLE III. System Error Contribution and RSS Error vs
`Resolution for Burr-Brown Model857KG
`Modular Data Acquisition System.
`
`DIGITAL CODES
`One final consideration in data acquisition and conversion
`systems is the digital coding of the data at the output of the
`A/D converter. Data is usually encoded in either binary or
`binary-coded-decimal (BCD) form.
`Binary encoded data formats are most commonly employed
`for digital computer-oriented applications where the pro-
`cessing is normally performed in binary notation. BCD data
`encoding is usually required in applications where the data
`is fed to decimal end devices such as digital readouts and
`printers. The majority of applications require binary encod-
`ing.
`The most commonly used binary codes in A/D converters
`are:
`1. Unipolar Straight Binary (USB)—used for unipolar ana-
`log signal ranges, i.e., 0 to – 5V, 0 to – 10V, etc.
`2. Bipolar Offset Binary (BOB)—used for bipolar analog
`signal ranges, i.e., – 5V, – 10V, etc.
`3. Bipolar Two’s Complement (BTC)—used for bipolar
`analog signal ranges in many digital computer applica-
`tions.
`Two BCD codes, unipolar BCD and sign-magnitude BCD
`(SMD) are used in A/D converters. The definition of these
`codes is shown in Table IV and V.
`
`2
`
`ADC
`
`OUTPUT
`DIGITAL
`CODE
`
`MSB LSB
`111....11f
`(1)
`
`DEFINITION
`
`+Full Scale
`
`Mid Scale
`
`–Full Scale
`
`USB
`CODE
`
`BOB(2)
`CODE
`
`+VFSR –1/2LSB
`
`100....00f
`000....00f
`
`+VFSR/2
`+1/2LSB
`
`+VFSR –1/2LSB
`2
`
`Zero
`
`–VFSR +1/2LSB
`2
`
`– VFSR
`One Least
`VFSR
`Significant Bit
`2n
`2n
`NOTES: (1) f is the transition value of the LSB. (2) BTC Code–invert the
`MSB (sign bit) of the digital code—ranges same as BOB codes.
`
`TABLE IV. Definition of Binary Codes.
`
`4
`
`SYSTEM THROUGHPUT ACCURACY
`The most common method used to describe data acquisition
`and conversion system accuracy is to compute the root-sum
`squared (RSS) errors of the system components. The RSS
`error is a statistical value which is equivalent to the standard
`deviation (1s ), and represents the square root of the sum of
`the squares of the peak errors of each system component,
`including ADC quantization error:
`= e
`2 + e
`2 + e
`
`where e
`
`2 + e
`
`RSS
`MUX
`AMP
`SH
`MUX = analog multiplexer error
`AMP = input amplifier error
`SH = sample/hold error
`ADC = A/D converter error
`The source irnpedance, data bandwidth, A/D converter reso-
`lution and system throughput rate affect these error calcula-
`tions. To simplify, errors can be calculated by assuming the
`following:
`1. Aperture error is negligible - i.e., less than 1/10LSB.
`2. Source impedance is less than 1000W
`.
`3. Signal range is – 10 volts.
`4. Throughput rate is equal to or less than the maximum
`shown in Table III.
`
`e
`e
`e
`e
`

`
`DEFINITION
`
`OUTPUT
`DIGITAL CODE
`(3 DIGITS)
`
` Sign
`
`MSD(1)
`
`LSD
`
`+ Full Scale
`
`1 1001 1001 1001
`
`Zero
`
`1 0000 0000 0000
`
`–Full Scale
`
`0 1001 1001 1001
`
`One Least
`Significant Bit
`
`DECIMAL VALUE
`
`BCD
`CODE
`
`999
`
`000
`
`N/A
`
`( 2)
`
`VFSR
`10n
`
`SMD
`CODE
`
`+999
`
`+000
`
`–999
`– VFSR
`10n
`
`( 2)
`
`NOTES: (1) MSD = Most Significat Digit. (2) n represents number of
`digits—4 bits per digit.
`
`TABLE V. Definition of Decimal Codes.
`
`SUMMARY
`The criteria that determine the key parameters and perfor-
`mance requirements of a data acquisition and conversion
`system are:
`1. Number of analog input channels;
`2. Amplitude of data source signals;
`3. Bandwidth of data;
`4. Desired resolution of data; and,
`5. End use of converted data.
`Although this discussion did not treat all system criteria
`from a rigorous mathematical point of view, it does not
`identify and attempt to shed insight on the most important
`considerations from a practical viewpoint.
`
`The information provided herein is believed to be reliable; however, BURR-BROWN assumes no responsibility for inaccuracies or omissions. BURR-BROWN assumes
`no responsibility for the use of this information, and all use of such information shall be entirely at the user’s own risk. Prices and specifications are subject to change
`without notice. No patent rights or licenses to any of the circuits described herein are implied or granted to any third party. BURR-BROWN does not authorize or warrant
`any BURR-BROWN product for use in life support devices and/or systems.
`
`5
`
`

`
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