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MECH 373
Instrumentation and Measurements
Lecture 6
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Measurement Systems with Electrical Signals
(Chapter 3)
• Electrical signal measurement systems
• Signal conditioners
Filtering
Indicating and recording devices
Lecture 6
Lecture Notes on MECH 373 – Instrumentation and Measurements
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Components of Measurement Systems
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Lecture Notes on MECH 373 – Instrumentation and Measurements
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Outlines of Filter Design
input
Filter
output
Filtering:
Certain desirable features are retained
Other undesirable features are suppressed
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Lecture Notes on MECH 373 – Instrumentation and Measurements
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Classification of Filters
Signal Filter
Analog Filter
Element Type
Active
Passive
Digital Filter
Frequency Band
Low-Pass
Band-Pass
High-Pass
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All-Pass
Band-Reject
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Classification of Filters
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Classification of Filters
Butterworth filters have the characteristic that they are maximally flat in the
passband. This means that the gain is essentially constant in the passband. For
lowpass Butterworth filters with unity dc gain, the gain as a function of frequency
f and order n is given by
where n is the order of the
filter.
For a first-order filter
(n=1) this means that
each time the frequency
doubles, the gain will be
reduced by a factor of 2.
http://en.wikipedia.org/wiki/Butterworth_filter
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Classification of Filters
Chebyshev filters have a much crisper change in slope but at the price of
ripple in the passband gain, as shown in Figure 3.18.
Chebyshev filters with no
passband ripple have the same
frequency response as the
Butterworth filters.
High-order Chebyshev filters
are more satisfactory than
Butterworth designs for notch
filters.
http://en.wikipedia.org/wiki/Chebyshev_filter
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Classification of Filters
Elliptic filters have a very crisp transition between the
passband and the stopband but allow ripples in the stopband
as well as the passband.
http://en.wikipedia.org/wiki/Elliptic_filter
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Classification of Filters
As with amplifiers, filters alter the phase of components of the signal as a function
of frequency. For example, the phase-angle shift for an eighth-order Butterworth
filter is 360° at the cutoff frequency. For higher-order filters, this phase response
can introduce serious phase distortion.
Bessel filters are often used because they
have a more nearly linear variation of
phase angle with frequency in the
passband than that of higher-order filters of
other classes.
http://en.wikipedia.org/wiki/Bessel_filter
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Terminology in Filter Design

Signal-To-Noise Ratio (S/N)
S
W
 10  log  S
N
 WN

dB


Bandwidth
the range of frequencies of |G(jw)|>0.707

Cutoff Frequency
the end of pass-band frequency
Break-point of a filter

the point with a gain of -3dB
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Passive Low-Pass Filter
H ( jw )
Vout
Vin
wp
ws
C
Vout
w
R
Vin
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 The pass-band is from 0
to some frequency wp.
 Its stop-band extends
from some frequency ws,
to infinity.
 In practical circuit design,
engineers often choose
amplitude gain of 0.95 for
passive RC filters:
RL
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Passive High-Pass Filter
 Its stop-band is from 0 to
some frequency ws
 The pass-band is from
some frequency wp to
infinity.
H ( jw )
Vout
Vin
ws
w
wp
C
Vin
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R
Vout
 In practical circuit design,
engineers choose
amplitude gain of 0.95 for
passive CR filters:
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Design of Passive Filters
R
The amplitude response:
C
Vin
Vout
RL
Vout

Vin
1
1   RCw 
2
The amplitude gain:
Transfer Function
H  jw  
H s  
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1
jRCw  1
1
RCs  1
ZL
G
ZF  ZL
The 3dB break-point is at:
f 3dB 
1
1

2RC 2 
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Guideline of Pass Filter Design
Select resistor based on amplitude gain:
R
C
Vin
Vout
RL
G
ZL
 0.95
ZF  ZL
ZF  R 
Transfer Function
1
H s  
s  1
Time Constant
0.05
Z L  0.053  RL
0.95
Select capacitor based on cut-off freq:

1
C 
R 2Rf 3dB
  RC
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Higher Order Filters
R
Vin
R1
C
Vout
First Order RC Low Pass
Vin
R2
C1
C2
Vout
Second Order RC Low Pass
The higher the order of the filter,
the closer it approaches ideal characteristics.
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Indicating and Recording Devices
Digital Voltmeters and Multimeters
Figure 3.26 shows a typical hand-held
digital multimeter (DMM)
An important component of a digital
voltmeter is an analog-to-digital (A/D)
converter, which converts the input analog
voltage signal to a digital code that can be
used to operate the display.
Digital multimeters can be used to display
other types of input signals, such as
current or resistance or frequency.
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Indicating and Recording Devices
Oscilloscopes
If the output of a
sensor is varying
rapidly, a digital
voltmeter is not a
suitable indicating
device and an
oscilloscope (scope) is
more appropriate.
In this device, shown
in Figure 3.27, the
voltage output of the
signal conditioner is
used to deflect the
electron beam in a
cathode ray tube
(CRT).
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Oscilloscopes
The CRT consists of a heated cathode
that generates free electrons, an anode
used to accelerate an electron beam, two
sets of deflection plates, and a front face
(screen) that is coated with phosphor
When voltages of suitable amplitude are
applied to the deflection plates, the
electron beam will be deflected and cause
the phosphors to glow at a particular
position on the screen. The deflection plate
voltage is proportional to the input voltage,
and so the visible deflection is proportional
to the input voltage.
A block diagram of the basic circuit
elements used to control the CRT is
shown in Figure 3.29.
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Indicating and Recording Devices
Strip-Chart Recorders
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Data Acquisition Systems
A measurement system could consist of a single sensor, appropriate signal
conditioning, and an indicating device such as a digital voltmeter.
Then a data acquisition system can be used for accepting the outputs from
several sensors and record them.
Each of the inputs to the acquisition system is called a channel.
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