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Lecture 2: Measurement and Instrumentation

This document discusses time domain vs frequency domain analysis of signals and provides examples of various signal types in both domains. It also describes key aspects of measurement systems including: 1) Transducers convert physical quantities to electrical signals, signal conditioners modify signals, and ADCs convert to digital; 2) Transfer functions describe linear time-invariant systems using Laplace transforms; 3) Frequency response curves show amplitude ratios vs input frequency and bandwidth is the range where input is attenuated less than -3dB.

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Deepali Kundnani
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71 views16 pages

Lecture 2: Measurement and Instrumentation

This document discusses time domain vs frequency domain analysis of signals and provides examples of various signal types in both domains. It also describes key aspects of measurement systems including: 1) Transducers convert physical quantities to electrical signals, signal conditioners modify signals, and ADCs convert to digital; 2) Transfer functions describe linear time-invariant systems using Laplace transforms; 3) Frequency response curves show amplitude ratios vs input frequency and bandwidth is the range where input is attenuated less than -3dB.

Uploaded by

Deepali Kundnani
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPT, PDF, TXT or read online on Scribd
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Lecture 2: Measurement and Instrumentation

Time vs. Frequency Domain


Different ways of looking at a problem
Interchangeable: no information is lost in changing from one domain to another Benefits from changing perspective: the solution to difficult problems can often become quite clear in the other domain

Time Domain Analysis The traditional way of observing signals is to view them in the time domain. Record in the time domain typically describes the variation of system output or system parameter over time.

Record from Seismograph


This record (of displacement, also called seismogram) displays 24 hours of data, beginning approximately 8 hours before the mainshock, recorded by the BDSN station BKS at a distance of 525 km.

Frequency Domain Analysis


It was shown over one hundred years ago by Jean B. Fourier that any waveform that exists in the real world can be generated by adding up sine waves.

n =1 where the Fourier coefficients of f(x) can be calculated using the so-called Euler formulas

f ( x) = a0 + (an cos nx + bn sin nx)

1 a0 = f ( x )dx 2

1 f ( x ) cos nxdx 1 bn = f ( x ) sin nxdx an =

Frequency Component of a Signal


This frequency domain representation of our signal is called the spectrum of the signal, in which every sine wave from the signal appears as a vertical line. Its height represents its amplitude and its position represents its frequency. Each sine wave line of the spectrum is called a component of the total signal.

Spectrum of Various Signal Types Figures on the right show a few common signals in both the time and frequency domains.

Laplace Transformation

Measurement System Components


Transducer: convert a physical quantity into a timevarying electrical signal, i.e. analog signal Signal conditioner: modify/enhance the analog signal (profiltering, amplification, etc) Analog-to-digital converter: convert analog signal into digital format Digital signal processing Recorder: display or data storage
Actual Input Measurement System Recorder output

Transfer Function
Block diagram and transfer function provide an efficient way to describe a dynamic system
Input, r(t) System Output, y(t)

Transfer Function
Used to describe linear time-invariant systems Can be expressed using the Laplace transform of the ratio of the output and input variables of the system Can be experimentally determined by curve-fitting
Frequency response (sinusoidal input) Impulse response (short-duration pulse input)

Frequency Response of a System

L[ y (t )] Y ( s ) G (s) = = L[r (t )] R ( s )

Characteristics of a Good Measurement System

y (t ) = A sin( 2ft + )
A: Amplitude f: frequency Amplitude Linearity Adequate Bandwidth Phase Linearity

: phase

Amplitude Linearity

Vout (t ) Vou t (0) = [Vin (t ) Vin (0)]

: proportion constant

Factors impact linearity Limited range of input amplitude Bandwidth

Frequency Bandwidth
Requirement: a measurement system should replica all frequency components Unit-Decibel scale:

Aout dB = 20 log10 A in

Bode plot: frequency response curve of a system, i.e. a plot of amplitude ratio Aout/Ain, vs. the input frequency

Bode Plot
Amplitude (dB)

fL

fc

fH

Frequency

Bandwidth
Bandwidth: the range of frequencies where the input of the system is not attenuated by morn than -3dB Low & high cutoff frequency: Bandwidth: BW = f f H L Questions:
what happen if a square wave is measured with a limited BW system How to determine the BW of a measurement system

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