Download Lecture January 27

2/1/2010
Analog Measurements & Signal
Conditioning
• Module goals…
–
–
–
–
Obtain a basic understanding of bridge circuits
Learn concepts related to sampling frequency
Review basics of filters and amplifiers
Explore use of filters in Labview
Motivation…
• Many sensors respond to the sensed variable via a
change in electrical resistance (e.g., strain gauges,
RTDs, thermistors)
• Computer data acquisition systems are able to sample
voltages of incoming signals.
• Thus
Thus, the electrical resistance signal of sensors must be
converted into a corresponding voltage signal.
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Voltage Dividers… a review
• Ohm’s law: V=iR
• Current through each
resistor is the same
• Ei= i(R1+R2)
• V1=i(R1)
• V2=i(R2)
• But i= Ei/(R1+R2)
• So…
V1  Ei
R1
R2
V1
V2
Ei
R1
R1  R2 
V2  Ei
R2
R1  R2 
Prof. Sailor
Wheatstone Bridges
• Useful for measuring small changes in resistance
– Strain gages have a nominal resistance of 120 or 350 ohms.
This resistance changes under loading, but not by much…
R1
iG
R2
G
R3
R4
Ei
Prof. Sailor
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Wheatstone Bridges
• Under a “balanced” condition iG = 0
R2 R4

R1 R3
R1
iG
R2
G
R3
R4
Ei
Prof. Sailor
Wheatstone Bridges – Null Method
• Suppose R1 is a sensor with varying resistance
• Balance bridge by changing a variable resistor (R2)
R2
R4

R1
R3
R
1

R2R
R4
so...
R1
3
Requires active balancing of
circuit to obtain no current flow
through G. But, the input voltage
does not need to be constant.
iG
R2
G
R3
R4
Ei
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Wheatstone Bridges – Deflection Method
• Suppose R1 is a sensor with varying resistance
• Balance bridge by changing a variable resistor (R2)
R1
R2
V
R3
R4
Measure voltage across this leg
of the bridge
bridge.
Use eqn. 6.15… or (if resistances
are initially equal… 6.16 to determine
the change in R1
Ei
Wheatstone bridge – deflection method
(general)
 R1R4  R3 R2 

Eo  Eo  Ei 




R

R
R

R
2
3
4 
 1
(6.15)
R1
R2
This equation can be simplified if
we set all resistances initially equal…
Eo
R3
R4
Ei
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Wheatstone bridge – deflection method
(all resistances initially equal)
Eo
Ei

R / R
4  2(R / R )
((6.16))
R
R
A useful approach as the response
(voltage) can track high frequency
variations in the sensor resistance.
This approach does require accurate
control of the input voltage as well as
accurate measurement of the output
voltage.
Eo
R
R
Ei
Why use a Wheatstone Bridge rather than a
simple Voltage Divider?
• Consider the case of a 120 Ohm strain gage used to
measure strain. If a small applied strain results in a 0.1
Ohm increase in resistance what would be the voltage
signal that one would get from each circuit?
Voltage Divider
Wheatstone Bridge
Eo  Ei
R1
R1  R2 
Eo  Eo  Ei
and,
R1  R1
R1  R1  R2 
Eo
Ei

R / R
4  2(R / R )
• If R1 = R2 we can show that the voltage divider sensitivity
is the same as the Wheatstone bridge.
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Why use a Wheatstone Bridge rather than a
simple Voltage Divider?
• You can set up a bridge circuit so that the voltage is
ZERO at the nominal conditions.
• Consider a strain gage installed on a beam. Under no
load conditions you’d like the output to read 0.0. You’d
also like the sign of the output voltage to correspond to
whether the gage is in tension or compression.
• The output of a bridge circuit can be centered on 0.0
• The output of a voltage divider circuit will necessarily
read between 0.0 and the supply voltage.
Sampling and Data Acquisition (Ch 7)
• Sampling theorem – to reconstruct the frequency
content of a measured signal the sample rate must be
more than twice the highest frequency (fm) within the
signal.
• Alias frequencies – apparent (lower) frequency
response of a signal measured at less than 2fm
• Nyquist frequency – if fs is the sampling frequency,
fN = fs/2 is the frequency level above which any
frequency components will show up as alias
frequencies.
Prof. Sailor
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DATA ACQUISITION AND SAMPLING FREQUENCY
1.2
1
0.8
0.6
0.4
0.2
0
-0.2 0
0.5
1
1.5
2
2.5
3
-0.4
-0.6
-0.8
-1
Prof. Sailor
Original Signal to Sample (4 Hz)
Original Signal: y=sin(2Pi*f*t) (frequency= 4hz; Period = 0.25sec)
1.5
1
0.5
0
0
0.5
1
1.5
2
-0.5
-1
-1.5
1 second
2 seconds
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Sampling theorem requires that we sample at more than
2* 4hz = 8hz in order to reconstruct the signal…
Alias Signal (under-sampled)
Original Signal: y=sin(2Pi*f*t) (frequency= 4hz; Period = 0.25sec)
1.5
1
0.5
0
0
0.5
1
1.5
2
-0.5
-1
-1.5
1 second
2 seconds
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Sample at ~2 Hz
Original Signal: y=sin(2Pi*f*t) (frequency= 4hz; Period = 0.25sec)
1.5
1
0.5
0
0
0.5
1
1.5
2
-0.5
-1
-1.5
Sample at 4 Hz
Original Signal: y=sin(2Pi*f*t) (frequency= 4hz; Period = 0.25sec)
1.5
1
0.5
0
0
0.5
1
1.5
2
-0.5
-1
-1.5
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Sample at 4 Hz (offset)
Original Signal: y=sin(2Pi*f*t) (frequency= 4hz; Period = 0.25sec)
1.5
1
0.5
0
0
0.5
1
1.5
2
-0.5
-1
-1.5
Sample at 8 Hz
Original Signal: y=sin(2Pi*f*t) (frequency= 4hz; Period = 0.25sec)
1.5
1
0.5
0
0
0.5
1
1.5
2
-0.5
-1
-1.5
Now Sample Frequency = 2* Fm and we get the right frequency content
Of the signal. Of course, we miss the amplitude…
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Sample at 12 Hz
Original Signal: y=sin(2Pi*f*t) (frequency= 4hz; Period = 0.25sec)
1.5
1
0.5
0
0
0.5
1
1.5
2
-0.5
-1
-1.5
Now Sample Frequency > 2* Fm and we get the right frequency content,
And most of the amplitude content…
Estimating Alias Frequencies
(folding diagram of Figliola/Beasley Fig 7.3)
Input frequency= f Nyquist frequency = fN
32
3.2
3.0 fN
2.6
2.2
2.8
2.4
2 0 fN
2.0
1.8
1.6
1.4
1.2
0
0.2
0.4
0.6
0.8
1.0 fN
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Estimating Alias Frequency from the
example
• We are sampling at 6 Hz so the Nyquist frequency is 3
Hz.
• We expect an alias frequency based on the folding
diagram…
• The signal is at 4 Hz or f/fN = 4/3 = 1.33. Thus, the
signal frequency is too high to resolve and will result in
an alias frequency.
• According to the folding diagram the alias frequency is
0.67*fN or 2 Hz.
ME 411/511
Prof. Sailor
Avoiding Alias Frequencies
• If you are sampling at a particular rate fs you can avoid
aliasing, simply by filtering out all frequencies at or
above the Nyquist frequency.
• For example, if your sampling rate is 100 Hz, the Nyquist
frequency is 50 Hz.
• You should apply a filter to remove all frequencies in the
signal that are above 50 Hz.
ME 411/511
Prof. Sailor
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Basics of Filters
• Filters remove undesired frequency content from a dynamic signal.
This “undesired” frequency content is generally noise in the signal
that can arise from a variety of influences, including the 60 Hz “hum”
of AC circuits.
• A filter can be thought of as a selective amplifier in which the Gain is
frequency dependent.
• Passband – frequency range where signal is passed through the
filter
• Stopband – frequency range where signal is stopped
• Cut-off frequency (fc) – frequency where the filter magnitude ratio
(M(f)) transitions from a value of 1.0 to 0.0
Ideal filters
M(f)
1.0
fc
• Low-pass
f
M(f)
1.0
fc
• High-pass
f
M(f)
1.0
• Band-pass
fc2
fc1
f
M(f)
• Notch filter
1.0
fc1
fc2
f
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Real filters
• Butterworth Low-pass
RC filter
• Cut-off frequency
q
y – fc is
frequency at which M(fc)
= 0.5
1.0
M(f)
fc
f
R
fc 
1
RC
C
Ei(t)
Eo(t)
Better filters
1.0
• Multistage filters – RC
and LC components
• Active filters
• Numerical filters
M(f)
fc
f
Prof. Sailor
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Amplifier Basics
• An amplifier scales the magnitude of an analog input signal:
Eo(t) = h { Ei(t) }
• For a linear amplifier
p
Eo(t) = G * Ei(t)
where G is the “gain”
• Amplifiers have many flavors:
–
–
–
–
Non inverting
Inverting
Differential
Integrating and differentiating
• One can build an amplifier circuit using an op-amp and
several resistors from a local electronics supply store.
Signal Conditioning – a broader perspective
• Many data acquisition systems will have aspects of
signal conditioning (filtering and amplification) built
into the system
• In some cases filtering can be taken care of within
the data analysis phase.
• Build it or buy it?
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Labview Filter Examples
• Start a Blank VI in LabView
• Use the “SIMULATE SIGNAL” sub-VI that can be found
on the Input list under the Express category on the
Functions palette to create 3 separate sine waves with
differing frequencies (say 10, 50, and 150 Hz) and
magnitudes (say 1.0, 2.0, and 5.0).
• Use a few addition operators to add the signals and then
pipe them into a Waveform Graph indicator.
g
Analysis
y
menu within the
• Use a Filter from the Signal
Express category.
• Create another Waveform Graph to display the filtered
signal.
• Explore…
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Data Acquisition Overview
Software (e.g. LabView) and
“virtual instrument”
Data Acquisition card
Terminals and/or
signal conditioning
Experimental apparatus
and sensors
Prof. Sailor
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Data Acquisition Issues
• Accuracy
–
–
–
–
8 bit (28 or 256 possible states)
8-bit
12-bit (4096 possible states)
16-bit (65536 possible states)
24-bit (16.8 Million possible states)
• Speed
– ~100,000 samples per second
– ~10,000,000
10,000,000 samples per second
• Digital and analog I/O, counters, etc.
• Software for automated DAQ/analysis
Digital representation of analog signals
255=“11111111”
0 =“00000000”
“00000000”
Discrete digital
reading
10 volts
0 volts
Continuous analog
signal
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255=“11111111”
10 volts
For an 8-bit card with a 10 Volt range
the uncertainty in the voltage reading
will be +/- (10v/256) * ½
… or +// 0.02
0 02 volts
lt
In this example the DAQ would represent
a 0.5000 volt signal as “00001101”=13.
This would be converted by software into:
0.51 +/- 0.02 volts
“.508v”
“.467v”
13=“00001101”
12=“00001100”
0 =“00000000”
Discrete digital
reading
Signal = 0.5000 volts
0 volts
Continuous analog
signal
Can we use a 16-bit DAQ card to read
temperatures from a thermocouple?
• Answer this question in terms of zero-order uncertainty.
• Could be a good in-class assignment if time allows…
?
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Can we use a 16-bit DAQ card to read
temperatures from a thermocouple?
• Answer this question in terms of zero-order uncertainty.
• The resolution of the 16
16-bit
bit card is as follows:
– Assume the 10 volt range is represented by 216 possible values.
– The scale resolution of the DAQ is 10V/216 = 10V/(65536-1) or
0.153 mV
– So, the zero-order uncertainty (in terms of voltage) is 0.075 mV
– Chapter 8 in Figliola and Beasley has a table for J-type
thermocouples. If we are interested in a temperature range
around 20 to 30 C, the sensitivity of the thermocouple is 0.052
mV/deg C
– So, the zero-order sensitivity of the DAQ for J-type thermocouple
readings is about 0.075 mV / 0.052 mV/degC = 1.4 deg. C.
ME 411/511
Prof. Sailor
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