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    1. General: Device that communicates, denotes, detects, indicates, measures,

    observes, records, or signals a quantity or phenomenon, or controls or

    manipulates another device.

    2. Law: Formally executeddocument that evidences a legally enforceable

    agreement between two or more parties, and expresses a contractual duty,

    obligation, or right. Practically all documents used in borrowing, lending,

    investing, and sale and purchase on credit, are legal instruments.

    Definition: Measurement is collection of quantitative data. A measurement is made by comparing

    a quantity with a standard unit. Since this comparison cannot be perfect, measurements inherently

    include error.

    accuracy: The degree of conformity of a measured or calculated value to its actual or specified value

    precision: 1. The degree of mutual agreement among a series of individual measurements, values,

    or results; often, but not necessarily, expressed by the standard deviation. 2. With respect to aset of

    independent devices of the same design, the ability of these devices to produce the same value or

    result, given the sameinput conditions and operating in the same environment. 3. With respect to a

    single device, put into operationrepeatedly without adjustments, the ability to produce the same

    value or result, given the same input conditions and operating in the same environment. Synonym (for

    defs. 1, 2, and 3)reproducibility. 4. In computer science, a measure of the ability to distinguish

    between nearly equal values. (188) 5. The degree of discrimination with which a quantity is stated; for

    example, a three-digit numeral to the base 10 discriminates among 1000 possibilities.

    Expected value

    1. The sum of all possible values for a random variable, each value multiplied by its

    probability of occurrence.

    2. The integral of the probability density function and a continuous random variable over

    its range of values.

    error

    3. 1. An act, assertion, or belief that unintentionally deviates from what is correct, right, or true.

    4. 2. The condition of having incorrect or false knowledge.

    5. 3. The act or an instance of deviating from an accepted code of behavior.

    6. 4. A mistake.

    7. 5. Mathematics The difference between a computed or measured value and a true or

    theoretically correct value.

    8. 6.Abbr. EBaseballA defensive fielding or throwing misplay by a player when a play normally

    should have resulted in an out or prevented an advance by a base runner.

    9.

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    10.Resolution -- the smallest amount of input signal change that the instrument can

    detect reliably. This term is determined by the instrument noise (either circuit or

    quantization noise). For example, if you have a noiseless voltmeter that has 5 1/2

    digits displayed and is set to the 20 V input range, the resolution of this voltmeter is

    100 V. This can be determined by looking at the change associated with the least

    significant digit.

    Now, if this same voltmeter had 10 counts of peak-to-peak noise, the effective resolution

    would be decreased because of the presence of the noise. Because of the Gaussian

    distribution of the noise, in this case the effective resolution would be 0.52 1 mV. In general

    when you have a measurement system that has X counts of Gaussian noise, the effective

    resolution of the system is given by

    Error Calculation or Accuracy Determination

    DC Measurement

    Error Type

    Reading-Dependent

    Errors

    Noise and Range-

    Dependent Errors

    Specified Accuracy % of reading x

    reading/100

    offset

    Nonlinearity % nonlinearity x

    range/100System Noise rms noise x 6.6 (to

    find peak-to-peak

    value)

    Settling Time % settled x Step

    change/100 (this must

    be added for scanning

    systems unless it is

    included in the

    accuracy

    specifications)NM Noise Normal Mode Noise x

    10^(-NMRR/20)

    CMV Common mode

    Voltage x 10^(-CMRR/20)

    Temperature Drift

    (this must be added if

    your temperature

    range is outside the

    specified range for the

    given accuracy tables)

    (% of reading/C) xX

    C x reading/100

    Xis the temperature

    difference between

    the specified

    temperature range andthe actual operating

    (offset /C) xXC

    Xis the temperature

    difference between the

    specified temperature

    range and the actual

    operating temperature.

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    temperature.

    Let us consider the National Instruments NI 4350 Series 5 1/2 digit Temperature and Voltage

    Data Logger. We will calculate the total accuracy of a 1 V reading. Let us also assume that

    the instrument is at an ambient temperature between 15 and 35 C, and it has been less than a

    year since the last calibration was performed but more than 90 days. The total accuracy based

    on the error budget determined above is:

    Error Type

    Percent of Reading

    Errors

    Range-Dependent

    Errors

    Specified Accuracy 1 V x 0.0131% = 131

    mV

    3 V

    Nonlinearity 0, included in accuracy

    System Noise 0, included in offset

    Settling Time not needed asspecification table

    included any errors

    due to scanning

    NM Noise, assume 1

    mVrms of

    environmental noise

    1 mV x 1.4 x l0^(-100/20)

    = 0.01 V

    CMV, assume

    maximum CMV of

    2.5 V

    2.5 x 10^(-100/20) = 25 V

    Temperature Drift N/A (because the NI4350 specification

    tables cover 15 to 35

    C)

    N/A (because the NI4350 specification

    tables cover 15 to 35

    C)

    Subtotal 131 V 28.01 V

    Total Maximum Error 159.01 V or 0.016% of reading

    AC Measurement

    Error Type

    Reading-Dependent

    Errors

    Range-Dependent

    Errors

    Specified Accuracy at

    a Given Signal

    Frequency Range

    % of reading x

    reading/100

    offset

    Nonlinearity % nonlinearity x

    range/100

    System Noise rms noise x 3.46 (to

    find peak to peak

    value x assumegaussian noise)

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    Settling Time % settled x Step

    change/100 (this must

    be added for scanning

    systems unless it is

    included in the

    accuracyspecifications)

    CMV Common mode

    voltage x 10^(-CMRR/20)

    Temperature Drift

    (this must be added if

    your temperature

    range is outside the

    specified range for the

    given accuracy tables)

    (% of reading/C) xX

    C x reading/100

    Xis the amount of

    temperature drift from

    the specified

    temperature range.

    offset /C xXC

    Xis the amount of

    temperature drift from

    the specified

    temperature range.

    Crest Factor Error Xx reading/100

    AddX% additional

    error based on the

    type of waveform.

    Let us consider the NI 4050 5 1/2 digit multimeter and calculate the total accuracy of a 1

    Vrms reading. Let us also assume that the instrument is at an ambient temperature between

    15 and 35 C, and it has been one year since the last calibration was performed. Because this

    is an AC measurement, we need to specify the frequency of the signal measured and the crest

    factor. Let us assume a frequency of 1 kHz and a crest factor of 2. The total accuracy based

    on the error budget determined above is:

    Error Type

    Reading-Dependent

    Errors

    Range-Dependent

    Errors

    Specified Accuracy at

    a Given Signal

    Frequency Range

    0.42% x 1 V = 4.2

    mV

    1.2 mV

    Nonlinearity Included in

    specification table

    Included in

    specification table

    System Noise Included in

    specification table

    Settling Time This is not a scanning

    DMM and let us

    assume that the signal

    is not changing

    CMV assume

    maximum allowable

    CMV of 250 V

    250 10^(-100/20) = 2.5

    mV

    Temperature Drift Not applicable

    because the

    temperature range is

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    included in the

    specification table

    Crest Factor Error 0% x 1 V/100 = 0 mV

    Subtotal 4.2 mV 3.7 mV

    Total Maximum Error 7.9 mV or 0.79% of reading