Physics of Transducers Definitions

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Physics of Transducers Definitions

• Transducer device that converts a signal to one
  physical form to different physical form
• Sensor A device which converts a signal in one
  physical form to an electrical signal.
• Actuator An output device which produces an
  output which displays or controls a device.

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Definitions and Properties

• A Transducer may be a sensor.
• Sensors usually detect physical quantities which
  are more subtle than the human senses.
• A transducer may be a sensor.
• A sensor may not be a transducer.
• Sensors amplify voltage.
• Actuators amplify power.

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Definitions and Properties

• Actuators may have either an analog or digital
  output.
• Signal conditioning --are measuring system
  elements that use the output of sensors and
  produce an output suitable that is suitable for
  recording, display or transmitting.
• Signal conditioning involves amplification,
  filtering, impedance matching, level shifting,
  modulation and demodulation.

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Definitions and Properties

• Interface signal-modifying elements that
  usually change from one data domain to another.
• Data Domain a quantity used to represent or
  transmit information. (Fig1.2)
• Analog Domain information is carried by the
  amplitude of voltage, current, charge or power.

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Definitions and Properties

• Digital Domain information is carried by
  signals having two values
• Time Domain information is carried by period,
  phase, pulse width or frequency.
• Measurements can be either direct or indirect.
  Indirect example power is measured by the
  product of voltage and current.

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Sensor Classification

• In addition to the classification of sensors by
  the power supply as Modulating or
  Self-generating. There are two other criteria
• OUTPUT SIGNAL sensors are either Analog or
  Digital.
• OPERATION MODE sensors are either Deflection or
  Null types.

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General Input-Output Configuration

• Let xs be the desired input signal
• Let y be the output
• Let xi be an interfering input signal
• Let xM be a modifying input signal
• the modifying signal both affect the
• desired signal xs and xi

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Compensation Techniques

• The interfering and modifying inputs can be
  reduced by adding Negative Feedback to the
  measuring system. If G(s) is the transfer
  function between the input and output and if H(s)
  is the transfer function for the negative
  feedback, then the ratio of the output to the
  input is
• Y(s) G(s) __1___
• X(s) 1 G(s) H(s) H(s)

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Compensating Techniques

• One can also construct the circuit with
• More ideal components. Such as low drift
  capacitors, low temperature coefficient
  resistors, etc.
• Also one can put in compensating elements, such
  as bucking potentials, opposite temperature
  coefficient to the part which are changing
  positively.

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Static CharacteristicsAccuracy, Precision and
Sensitivity

• Need for static calibration with standard
  quantities through NIST.
• Any discrepancy between the accepted value and
  the instrument is error.
• Absolute error Experiment Accepted
• Relative error Absolute error
• Accepted Value

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Static CharacteristicsAccuracy, Precision and
Sensitivity

• Accuracy Class all sensors belonging to the
  same class have the same measurement error (in
  working range)
• Index of class normally 1 , so error of a
  thermometer of 25oC /- 1oC , likewise for
• One reading 30oC. If in class 0.2 then 25oC would
  be 25oC /- 0.5oC and the
• 30oC /- 0.6oC.

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Static CharacteristicsAccuracy, Precision and
Sensitivity

• Precision high ability to be repeatable
• (agreement among different readings)
• Repeatability repeatable during short time
  interval with probability of 95
• Reproducibility repeatable over a long
  
  interval using
  different instruments in different laboratories,
  also assumes 95.

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Static CharacteristicsAccuracy, Precision and
Sensitivity

• Other parameters affecting error
• Zero drift Output drifts when input is zero
• Scale factor drifts affects sensitivity
• Sensitivity (scale factor) is slope of the
• calibration curve.
• S(xa) dy/dx xa
• for y kx b S k (a constant)

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Linearity and Resolution

• Linearity closeness between the calibration
  curve and a straight line.
• Independent linearity least squares fit
• Zero based linearity least squares zero
• Terminal based linearity straight line based on
  minimum input and theoretical high output.
• End-Points Linearity straight line based on
  input zero and full scale output.
• Theoretical Linearity based on theory when
  designed.

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Resolution and Hysteresis

• Resolution the minimal change in the input that
  makes a just detectable output change.
• If the input starts at zero, then it is called
  the Threshold.
• If the sensor respond rapidly, then the noise
  floor (random fluctuations) determines the
  resolution.
• Hysteresis is the difference in the output
  compared for the same input when the input was
  either increasing or decreasing

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Systematic Errors

• Systematic errors Under same circumstances of
  measurement the same absolute value of error
  occurs or varies according to known measurement
  conditions or laws.
• Discovered by measuring the same quantity using
  different devices or different methods or
  different operators.

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Systematic Errors

• Indirect measurements with errors that propagate,
  and are less accurate than direct measurements.
• V I R Direct measurement dV/V 0.1
• dV dI dR
• So dV dI dR If dI 0.1, dR 0.1
• V I R I
  R
• Then dV/V 0.2

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Random Errors

• Random (accidental) errors are those errors
  remaining after systematic errors have been
  eliminated.
• Characteristics Positive and negative with same
  occurrence probability for same absolute value of
  the signal.
• Less probable as magnitude of the absolute value
  increases.

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Random Errors

• Approaches zero as the number of measurements
  increase.
• For a given measurement method, random errors do
  not exceed a fixed value. If random errors do
  exceed a fixed value, that experiment should be
  repeated and studied separately.

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Random Errors

• Random errors imply one measures n times to have
  a set of x (datum) that can be averaged (xn) . If
  the set of values is finite then each average is
  different. The averages follow a Gaussian
  Distribution
• Having a variance of s2/n and s2 is the variance
  of x.
• Confidence interval for x is
• xn uncertainty x xn uncertainty

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Random Errors

• And the uncertainty is k times the square root of
  the variance or
• ks/vn
• One can obtain k from the tables of the normal
  Gaussian Distribution tables.
• The confidence interval has a probability of
• Conf. Interval Probability 1 a where a is
  also found from the Gaussian Distribution tables.
  

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Random Errors

• The normalized Gaussian Distribution is shown at
  the following site
• http//www.itl.nist.gov/div898/handbook/eda/sectio
  n3/eda3661.htm
• In normalized functions, the total probability
  is 1. So 1-a is the total probability minus the
  tail of the Gaussian Distribution.

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Random Errors

• See Example 1.2 page 19 of the text.