Chapter 6: Data Recording and Presentation

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Chapter 6 Data Recording and Presentation

• Agenda
• Recording of Data
• Presentation of data
• Fitting Curves Techniques

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Galvalnometric Recorders

• Cheap, simple, reliability, poor dynamic response
• Galvanometric (80) the displacement y of the
  pen across the chart recorder is yRsin?
• error of 0.7 for deflection of ?10o
• resolution of 1
• difficult translation the measurement results
• Knife-edge galvanometric recorder y Rtan? ?
  still non-linear and error 0.7 for ?10o but
  easier interpolation

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Potentiometric Recorders

• Accuracy can achieve an inaccuracy of ??0.1
  full scale
• Resolution 0.2 f.s.
• Slow response in the range of 0.2-2.0 second ?
  d.c. and slow signals

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Ultra-Violet Recorder

• Principle pen of galvanometric beam of
  ultraviolet light mirror
• Accuracyresolution bandwidth ?13 kHz and
  inaccuracy ??0.2f.s.

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Other Types of Recorders

• Fiber-optic recorders
• Principle direct light onto light sensitive
  paper(similar to oscilloscopes)
• Expensive, high bandwidth
• Magnetic tape recorders
• Record analog signals up to 80kHz
• Signals can be recorded at high speed and
  replayed at a lower speed?hard copy for
  ultraviolet or galvanometric recorders
• Two types of analog tape recorder direct
  recording and frequency-modulated recording.
• Direct recording high data bandwidth, low
  accuracy
• Frequency-modulated recording higher accuracy,
  80kHz bandwidth
• Computer data logging
• Can record signals higher than 80kHz
• Need analog-to-digital converter

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Presentation of Data

• Tabular Data Presentation Present precise
  values, Further calculations
• Graphical Data Presentation
• Low accuracy
• Easy to comprehend
• Express quantitative significance of results
• Show relationship between parameters

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Fitting Curves Techniques

• Fitting curves approximate to draw a smooth
  curve close to all data points with lowest total
  errors
• Regression techniques find a mathematical
  relationship between two variables
• Linear least-squares regression y bx a
• Find a b such that
• Solution ?S/?a 0 and ?S/?b 0
• Result

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Example

• From theoretical consideration, it is known that
  the voltage (V) across a charged capacitor decays
  with time (t) according to the relationship V
  Kexp(-t/t). Estimate value for K and t if the
  following values of V and t are measured

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Solution

• We have VKexp(-t/t) then lnVlnK-t/t
• Let y lnV a lnK b -1/t x t. then
• y abx
• Apply least-squares method, we have
• a 1.4718 b - 0.4364
• Thus K 4.35707 and t 2.29