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Measurements &
Electrical Analog
Devices (Part 2)
Introduction
Analog Signal Conditioning: Amplifiers
 Analog Signal Conditioning: Filters
 Grounds, Shielding & Connecting Wires
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Amplifiers
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Amplifier - device that scales the magnitude of an
analog input signal according to
E0(t) = h{Ei(t)}
Simplest amplifier = linear scaling amplifier:
h{Ei(t)} = GEi(t)
Have finite frequency response & limited input voltage
range
Most widely used – solid-state operational amplifier
Amplifiers
Amplifiers
Operational Amplifier
Amplifiers
High internal gain, A:
E0 = A [Ei2(t) – Ei1(t)]
 A – flat at low frequencies, falls off rapidly
at high frequencies but can overcome
using external input and feedback
resistors (control G)
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Amplifiers
Filters
Filter = used to remove undesirable
frequency information from a dynamic
signal
 Classified as low pass, high pass,
bandpass and notch
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An introduction to signal…
Measurement system – takes input
quantity / signal & transforms into
measurable output quantity / signal
 Shape / form of signal = waveform
 Waveform – information on magnitude,
amplitude, frequency
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Definition of signal
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Signal = physical information about a
measured variable being transmitted from
one place to another (between a process
and the measurement system, between
the stages of a measurement system, or
the output from a measurement system)
Classification of signals
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Signals – analog, discrete time, digital
Analog signals = continuous in time
Classification of signals (2)
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Discrete time signals – information about the
magnitude of signal is available only at discrete
points in time
Results from sampling of continuous variable at
finite time intervals
Classification of signals (3)
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Digital signals – 1) exist at discrete values in time; 2)
discrete magnitude determined by quantization (assigns
single number to represent a range of magnitudes of
continuous signal)
Signal Waveforms
Static signal = does not vary with time
 Dynamic signal = time-dependent signal
 Deterministic signal = varies in time in
predictable manner
i) Periodic = variation of magnitude repeats at
regular intervals in time
ii) Aperiodic = do not repeat at regular intervals
 Nondeterministic = has no discernible pattern of
repitition
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Signal Waveforms (2)
Filters
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Low-pass filter:
Permits frequencies
below a prescribed cut-off
frequency to pass while
blocking the passage of
frequency information
above the cut-off
frequency, fc
Filters
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High-pass filter:
Permits only
frequencies above the
cutoff frequency to
pass
Filters
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Bandpass filter:
Combines features of
both low & high pass
filters
Described by a low cutoff
frequency, fc1 and high
cutoff frequency, fc2, to
define a band of
frequencies that are
permitted to pass through
the filter
Filters
Notch filter:
- Permits passage of all
frequencies except
those within a narrow
frequency band
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Filters
Passive filters – combinations of resistors,
capacitors and inductors
 Active filters – incorporate operational
amplifiers
 Important terms – roll-off (rate of transition
where the magnitude ratio decreases
relative to the frequency – dB/decade);
phase shift (between input & output signal)
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Filters
Butterworth Filter Design
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Characteristics –
relatively flat
magnitude ratio over
its passband,
moderately steep
initial roll-off and
acceptable phase
response
Butterworth Filter Design
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For first-order RC filter system:
Magnitude ratio, M = 1 / (1+ ()2), where
 = RC = 1/2fc,  = 2f
Phase shift,  () = -tan-1 
Roll-off slope = 20 dB/decade
Cutoff frequency, fc(dB) = 20 log M(f) =
-3dB
Butterworth Filter Design
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Roll-off slope can be improved by staging filters
in series (cascading filters) – adding additional
reactive elements (L / R)
Butterworth Filter Design
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For k-stage low-pass Butterworth filter:
Magnitude ratio, M = 1 / [1 + (f/fc)2k]1/2
Phase shift,  (f) =  i (k)
Attenuation (dB) = 10 log [1 + (f/fc)2k]
Roll-off slope = 20 x k [dB/decade]
Butterworth Filter Design
For other values, L = Li Rs / 2fc and C = Ci / (Rs 2fc)
High-pass Butterworth Filter
(Li)HP = (1/Ci)LP and (Ci)HP = (1/Li)LP
Magnitude ratio, M(f) = f/fc / [1 + (fc/f)2k]1/2
Bessel Filter Design
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Sacrifices a flat gain over its passband with a
gradual initial rolloff in exchange for a very linear
phase shift
Active Filters
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Uses high frequency gain characteristics of opamp to form an effective analog filter
First order, single-stage, low-pass Butterworth
filter:
fc = 1 / 2R2C2
Gain, K = R2 / R1
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First-order, single-stage, high-pass Butterworth
active filter:
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fc = 1 / 2R1C1
Gain, K = R2 / R1
Magnitude ratio, M(f) = f/fc / [1 + (f/fc)2]1/2
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Active bandpass filter – combining high- & lowpass filters:
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Low cutoff, fc1 = 1 / 2R1C1
High cutoff, fc2 = 1 / 2R2C2
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Grounds, Shielding & Connecting
Wires
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1)
2)
3)
4)
Rules to keep noise levels low:
Keep the connecting wires as short as
possible
Keep signal wires away from noise
sources
Use a wire shield and proper ground
Twist wire pairs along their lengths
Ground & Ground Loops
Ground = a return path to earth
 Ground loops = caused by connecting a
signal circuit to two / more grounds that
are at different potentials
 Ensure a system has only one ground
point
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Shields & Connecting Wires
Shield = a piece of metal foil or wire braid
wrapped around the signal wires and
connected to ground
 Different type of wires – single cable, flat
cable, twisted pair of wires, coaxial cable,
optical cable
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