PERFORMANCE SPECIFICATION AND COMPONENT MATCHING

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PERFORMANCE SPECIFICATION AND COMPONENT MATCHING

• Presented by
• Balasubrahmanya P. Balusu
• Appala V. Surya Pradhan
• Vinay Kumar Bashaboina
• Muzamil Mohammed
• Shakeel Ahmed Syed

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INTRODUCTION

• Topic discusses about
• Instrument ratings.
• static and dynamic characteristics of the
  instruments.
• Parameters for performance specification of
  available components.
• Impedance and component matching.
• Error analysis.

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Measurement System

• All devices that assist in the measurement
  procedure can be interpreted as components of the
  measurement system.
• A measurement system is an essential component
  in any feedback control system and forms a vital
  link between the plant and the controller.
• A typical measurement system consists of one or
  more sensor- transducer units and associated
  signal-conditioning.

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Measurement system
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Sensors and Transducers

• These devices are analog components that generate
  analog signals.
• Analog signals are converted into digital signals
  using ADC for digital control. This process
  requires sampling of analog signals at discrete
  points.
• The changes in analog signal due to its transient
  nature should not affect this process of ADC, so
  we use sample and hold operation for each
  sampling period.

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Sensors and Transducers

• The encoded signal can be represented as either
  straight binary code, a gray code, BCD, ASCII.
• A multiplexer is employed for multiple
  measurement process, in order to pick one
  measured signal at a time from a bank of data
  channels for subsequent processing.
• The operation of multiplexing , sampling, and
  digitizing have to be properly synchronized under
  the control of an accurate timing device for
  proper operation of the control system.

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Sensors and Transducers

• The output variable that is being measured is
  termed the measurand and is usually analog
  signal.
• In a measuring device the measurand is first
  sensed and then, the measured signal is
  transduced into a suitable signal for
  transmitting, signal conditioning, processing or
  actuator.
• The output signal of the transducer stage is
  often a electrical signal.

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Sensors and Transducers
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Sensors and Transducers

• Let us consider operation of a piezoelectric
  accelerometer, where acceleration is measurand.
• Acceleration is first converted into an inertia
  force through a mass element and is exerted on a
  piezoelectric crystal within which a strain is
  generated. This stress generates a charge inside
  the crystal, which appears as an electric signal
  at the output of the accelerometer.
• A complex measuring device can have more than one
  sensing stage, in this case measurand goes
  through several transducer stages before it is
  available for control and actuating purposes.

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Classification Of Transducers

• Pure transducers depend on nondissipative
  coupling in the transduction stage.
• Passive transducers depend on their power
  transfer characteristics for operation, they are
  also called as self-generating transducers.
• Pure transducers are essentially passive
  transducers.
• Active transducers, on the other hand, do not
  depend on power transfer characteristics for
  operation.

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Classification Of Transducers

• In this classification we dealt with the power in
  the immediate transducer stage associated with
  the measurand, not the power used in the
  subsequent signal conditioning.
• Since passive transducers derive their energy
  entirely from the measurand, they generally tend
  to distort the measured signal to a greater
  extent than an active transducer would.
• Passive transducers are generally simple in
  design, more reliable, and less costly.

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Transfer Functions Models

• Majority of sensors-transducers can be
  interpreted as two-port elements
• Each port of a two-port transducer has a through
  variable, such as force current, and an across
  variable, such as velocity or voltage, associated
  with it.
• Through variables are also called flux variables
  and across variables are also called potential
  variables.

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Transfer Functions Models

• A two-port device can be modeled by the transfer
  function
• G
  
• Where vi and fi denote across and through
  variable at the input port, and v0 and f0 denote
  the corresponding variables at the output port.
• This representation essentially assumes a linear
  model for transducer. Such transducers are ideal
  transducers.

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Transfer Functions Models

• Using matrix transfer-function transduction
  process can be broken into two or simpler
  transducer stages.
• Generalized series element (electrical impedance)

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Transfer Functions Models

• Generalized parallel element (electrical
  admittance) is
• Generalized series element
• Generalized parallel element

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Transfer Functions Models

• A disadvantage of using through variables and
  across variables in the definition of impedance
  transfer function is apparent when comparing
  electrical impedance with mechanical impedance.
• The definition of mechanical impedance is force
  (through variable)/velocity (across variable).
• Whereas, electrical impedance is defined as ratio
  of voltage (across variable)/current (through
  variable).
• Impedance measures how much effort is needed to
  drive a system at unity flow .
• Impedance
  (effort/flow).

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Transfer Functions Models

• Definitions of some mechanical
  transfer functions

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Parameters for performance specification

• A prefect measuring device can be defined as one
  that possesses the following characteristics
• 1.Output instantly reaches the measured
  value.
• 2.Transducer output is sufficiently large.
• 3.Output remains at the measured value
  unless the
• measurand itself changes.
• 4.The output signal level of the transducer
  varies in proportion to the
• signal level of the measurand.
• 5.connectionof measuring device does not
  distort the measurand itself.
• 6.power consumption is small.

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Time Domain Specifications
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• Rise Time This is often defined as the time
  taken to pass 90 percent the steady-state value
  of the steady state response and is measured from
  10 percent of the steady state value in order to
  leave up the start up irregularities and time
  lags.
• Rise time represents the speed of the system.
• Delay Time It is usually defined as the time
  taken to reach 50 percent of the steady state
  value for the first time. This parameter is also
  a measure of speed of the system.
• Peak Time This is the time at first peak. This
  parameter also represents speed of the system.

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• Settling Time This is the time taken for the
  device response to settle down within a certain
  percentage (e.g., 2 percent) of the steady state
  value.
• This parameter is related to the degree of
  damping present in the system as well as
  stability.
• Percentage Overshoot (P.O) This is defined as
• P.O 100(Mp-1)
• Where Mp is the peak value. This is also a
  measure of damping and relative stability.

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• Steady State Error This is the deviation of the
  actual steady state value from the desired value.
  Steady state error may be expressed as a
  percentage with respect to the desired value.

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Frequency Domain Specifications
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• Useful Frequency range This corresponds to the
  flat region in the gain curve and the
  zero-phase-lead region in the phase curve. It is
  determined by the dominant resonant frequency of
  the instrument. The maximum frequency in the
  frequency range is smaller than resonant
  frequency.
• Faithful measurement and fast response are
  guaranteed in this region.
• Instrument Bandwidth This is a measure of useful
  frequency range of the instrument. Larger the
  bandwidth faster the response of the device will
  be.
• Common definition may be stated as frequency
  range over which the response in flat.

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• Control Bandwidth This is used to specify speed
  of control.For a system to respond faithfully to
  a control action the control bandwidth has to be
  sufficiently small compared to the dominant
  resonant frequency of the system.
• Static Gain This is the gain ( transfer function
  gain) of a measuring instrument within the useful
  range.

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Impedance Characteristics

• When measuring instruments, control boards,
  process and signal conditioning equipment are
  connected, it is necessary to match impedances
  properly
• Adverse effect of impedance mismatch is Loading
  Effect
• Ex In measuring system, the measuring instrument
  can distort the signal that is being measured
• Loading errors result from connecting measuring
  device with low input impedance to a signal source

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Impedance Characteristics

• Depending on the signal being measured, impedance
  can be interpreted either in the traditional
  electrical sense or in the mechanical sense
• Ex A heavy accelerometer can introduce an
  additional dynamic load
• A thermocouple junction can modify the
  temperature that is being measured
• In mechanical and electrical systems, loading
  errors can appear as phase distortions as well

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Impedance Characteristics

• Improper impedance consideration leads to
  inadequate output signal levels, which make
  signal processing and transmission difficult
• Many types of transducers have high out put
  impedance, and they would require conditioning to
  step up the signal
• Impedance matching amplifiers are used for this
  purpose
• Low input devices extract high level of power
  from the preceding device. This is the reason for
  loading error

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Cascade Connection of Devices

• Out put impedance is defined as the ratio of
  the open circuit voltage at the output port to
  the short circuit current at the output port
• Open circuit voltage at the output is the output
  voltage present when there is no current flowing
  at the output port
• To measure open-circuit voltage, the rated input
  voltage is applied at the input port and
  maintained constant and the out put is measured
  using a voltmeter
• To measure short circuit current, a very low
  impedance ammeter is connected at the output port

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Cascade Connection of Devices

• The input impedance is defined as the ratio
  of the rated input voltage to the corresponding
  current through the input terminals while the
  output terminals are maintained as an open
  circuit
• These definitions are associated with electrical
  devices. A generalization is possible by
  interpreting voltage and velocity as across
  variables and current and force as through
  variables
• The mechanical mobility should be used in place
  of electrical impedance

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Cascade Connection of Devices

• The input impedance and output impedance can be
  represented schematically as shown below
• The corresponding transfer function under open
  circuit is

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Cascade Connections

• Consider two devices connected in cascade
• These relations can be combined to give
• We can note that cascading has resulted in
  distortion in the frequency response
  characteristics
• Cascading should be done such that the output
  impedance of the first device is much smaller
  than the input impedance of the second device

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Impedance Matching Amplifiers

• The signal conditioning circuitry should have a
  considerably large input impedance in comparison
  to the output impedance of the sensor-transducer
  unit in order to reduce loading errors
• In piezoelectric sensors, where the input
  impedance of the signal-conditioning unit might
  be inadequate to reduce loading effects, we
  introduce several stages of amplifier circuitry
  between sensor output and the data acquisition
  unit input
• The first stage is an impedance-matching
  amplifier and the last stage is a stable high
  gain amplifier stage to step up the signal level

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Operational Amplifiers

• They have high gain, high input impedance and low
  output impedance
• A schematic diagram is shown below

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Operational Amplifiers

• If one of the two input lead is grounded, it is a
  single-ended amplifier
• If neither lead is grounded, it is a differential
  amplifier
• But the operational amplifier in its basic form
  has poor stability.
• For these reasons, additional passive elements
  such as feedback resistors are used in
  conjunction with op-amps in practical applications

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Voltage Followers

• They are impedance matching amplifiers with very
  high input impedance, very low output impedance,
  and almost unity gain
• They are suitable for use with high output
  impedance sensors such as piezoelectric devices
• The schematic diagram is as shown

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Voltage Followers

• Equivalent circuit for voltage follower
• Charge amplifier

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Voltage Followers

• From the above, the input impedance is given as
• The output impedance is given as
• Since gtgt , we can neglect
  .Consequently, we get

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CHARGE AMPLIFIERS

• Basic principle used here is CAPACITANCE
  FEEDBACK
• These are commonly used for conditioning output
  signals from piezoelectric
  transducers.
• Charge voltage x capacitance

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Measurement of Across Variables and Through
Variables

• Across variables voltage, velocity, pressure
  etc..
• Through variables current, force, flow rate etc

• Zi Input Impedance Zo Output Impedance
• Zl Load Impedance G System Transfer Function

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Ground Loop Noise

• Devices that handle low-level signals gets easily
  effected by electrical noise around, which create
  excessive error.
• Other form of noise is caused by fluctuating
  magnetic fields due to nearby AC lines
• Another cause of electrical noise is ground loops.

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Instrument Ratings

• Instrument ratings, these are available as
  parameter values, tables, charts, calibration
  curves and empirical equations.
• Typical rating parameters supplied by instrument
  manufacturers are
• 1. Sensitivity 6. Useful frequency range
• 2. Dynamic range 7. Bandwidth
• 3. Resolution 8. Input and output
• 4. Linearity impedances
• 5. Zero drift and full-scale drift.

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Definitions

• Sensitivity of a transducer is measured by the
  magnitude of the output signal corresponding to a
  unit of the measurand.
• In other words ratio of (incremental
  output)/(incremental input).
• However for better operation of a device
  sensitivity to parameter changes and noise has to
  be small.
• Dynamic range of an instrument is determined by
  the allowed lower and upper limits of its input
  or output.
• This range is usually expressed as a ratio in
  Decibels.
• Resolution is the smallest change in a signal
  that can be detected and accurately indicated by
  a transducer or any instrument
• Usually expressed as the inverse of the dynamic
  range ratio.

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Contd.

• Linearity is determined by the calibration curve
  of an instrument.
• The curve of output amplitude versus input
  amplitude under static conditions within the
  dynamic range of an instrument is known as the
  static calibration curve.
• Zero drift is defined as the drift from the null
  reading of the instrument when the measurand is
  maintained stady for a long period.
• Similarly, full-scale drift is defined with
  respect to the full-scale reading.

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Contd

• Useful frequency range corresponds to a flat gain
  curve and a zero phase curve in the frequency
  response characteristics of an instrument.
• Bandwidth of an instrument determines the maximum
  speed or frequency at which the instrument is
  capable of operating.
• High bandwidth implies faster speed of response.
• Bandwidth of a measuring device is important,
  particularly when measuring transient signal.

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Precision

• Reproducibility if an instrument reading
  determines the precision of an instrument.
• The precision of an instrument is determined by
  the standard deviation of error in the instrument
  response.
• Quantitative definition for precision
• Precision (measurement range)/
• Lack of precision originates from random cause
  and poor construction practices.
• It cannot be compensated for by recalibration,
  just as precision of a clock cannot be improved
  by resetting the time.

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Accuracy

• The instrument ratings discussed affect the
  overall accuracy of an instrument.
• Usually, the instrument accuracy is given with
  respect to a standard set of operating conditions
  by the manufacturer.
• Measurement accuracy determines the closeness of
  the measured value to true value.
• Instrument accuracy is related to the worst
  accuracy obtained with in the dynamic range of
  the instrument .
• Error (measured value) - (true value)
• Correction (true value) (measured value)

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Error Analysis

• Analysis of an error is very challenging task.
  Particularly in the following reasons
• 1. True value is usually unknown.
• 2. The instrument reading may contain random
  error that cannot be determined accurately.
• 3. The error may be complex function of many
  variables.
• 4. The instrument may be made up of many
  components that have many complex inter relations
  and each might contribute to overall error.

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Statistical representation

• Error (instrument reading)-True value.
• Random associated with a measurand can be
  interpreted in two ways,
• 1.when the true value is known and a fixed
  quantity, then the randomness can be interpreted
  as the randomness in error that is generally due
  to random factors in instrument response.
• 2. When the true value is unknown, which is
  obtained from large set of known readings error
  analysis can be interpreted as estimation problem.

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Cumulative probability distribution function

• If X is a random variable and if x is a specific
  value then the probability that Xltx is given as
  cumulative distribution function.
• Random variable X is always less than infinity
  and never equal to negative infinity. The graph
  of cumulative function always shows an increasing
  curve.

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Probability density function

• If X is a continuous random variable and F(x) is
  a continuous function of x then the probability
  density function f(x) is given by
• The graph of PDF is as shown, where
• area under the curve is Unity.
• The probability that the random variable
• falls within two values is given by
• area under the density curve between the
  two points.

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Contd..

• Mean value For a random variable X which is
  measured repeatedly a large number of times,
  average of this gives the mean value
• Root Mean Square Value The mean square value of
  a random variable X is given by
• Variance Variance of a random variable is the
  mean square value of the deviation from the mean
  and is given by

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Contd

• Standard Deviation Square root of variance gives
  the standard deviation.
• Standard deviation is a measure of statistical
  spread of a random variable.
• A random variable with smaller SD is less random
  and its density curve exhibits a sharp curve.
• Independent random variable When
• two random variables X1 X2 are
• independent

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Contd

• Sample mean and sample variance For a data
  sample X1, X2,.Xn of random variable X we
  cannot extract the whole information about
  probability distribution, but we can make useful
  estimates.
• Sample mean Sample Variance
• Unbiased Estimates If N measurements are taken
  at one time and the same measurements are
  repeated, then the values of corresponding data
  samples might differ due to random origin of X

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Gaussian Distribution

• This distribution function is most extensively
  used because of its simplicity and central limit
  theorem which states that a random variable is
  formed by summing a very large number independent
  variables.
• A closed algebraic expression cannot be given for
  cumulative probability distribution function. The
  random variable X should be normalized with
  respect to Mean and SD.
• Probability density function of Z is

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Contd

• Statistical process control This is used to
  generate control actions and enhance the
  performance of a system.
• Control Limits and Action Lines A very high
  percentage of readings from a instrument should
  lie between 3 and -3 drawn about the mean
  value otherwise corrective measures like
  recalibration and controller adjustments should
  be done.

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Steps of SPC

• 1. Collect the measurements of response variables
  of the process.
• 2. Compute mean upper control limit and lower
  control limit
• 3. Plot the graph.
• 4. If the readings lie outside the control limits
  corrective action should be taken.
• Confidence Interval The probability that random
  variable lies within specified interval is called
  confidence level

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Contd..

• Sign test and Binomial Distribution This is
  useful in comparing the accuracies of two similar
  instruments.
• The probability of getting exactly r positive
  signs among n entries is given by
• Least Square Fit An instrument linearity may be
  measured by largest deviation of input output
  data from the least squares straight line fit of
  data. This line is referred as linear regression
  line

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Contd

• Error Combination Error in a response variable
  of an instrument or in an estimated parameter
  would depend on individual variable errors and
  parameter values.
• These errors all together give rise to total
  system error.
• Absolute Error Since can be positive or
  negative an upper bound for an overall error is
  obtained by summing the absolute value of each
  right hand term of above equation.

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Contd

• SRSS error Square root sum of errors Since
  absolute error is an upper bound estimate it is
  not precise and has high conservatism this is
  overcome by SRSS error which is very precise.

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Conclusion

• Thus the paper discusses the parameters,
  performance specifications and characteristics,
  of various components which help in the
  selection of available components for a
  particular application. It also highlights the
  time domain and frequency domain performances.
  Further it explains the importance of component
  matching (impedance characteristics) and
  instrument ratings. Lastly it briefs the various
  types of errors and their analysis.