METROLOGY: TRANSDUCERS AND AMPLIFIERS
Eric Sanchez*, Rodrigo Barbosa*
The City College of New York, Florida International University
University of California Davis
Dr. Bruce Kutter* and Dr. Dan Wilson*
Abstract
During an earthquake simulation a lot of data is collected by computer data acquisition
programs. The main goal of this project is to make sure this data represents high levels of
accuracy during tests. Offset voltages, noise, and heat dissipation are just some of the problems
that transducers may encounter when a test is in progress. To get rid of these problems and to
ensure our best interpretation of the gathered data, researchers must calibrate devices before each
experiment. Indeed, the use of metrology plays an important role in this process. This science
will ensure that standards of measure meet specified degrees of accuracy and precision. Some of
the devices used in geotechnical modeling are amplifiers and sensor transducers, used to amplify
and translate signals. By improving and creating new ways of calibration for these devices
geotechnical modeling aims to achieve high standards.
Some devices used in modeling such as load cells and amplifiers need to be calibrated as
precise as possible. Using a BNC Flex unit through a Strain-Gage and PVL amplifiers allows
researchers to make analysis of sensor signals. The information gathered during this process is
colleted by complex analytical software called RESDAQ which guarantees a close analysis of
several factors concerning Geotechnical Modeling such as force, displacement, and pressure. If
at the end of this process researchers are able to fulfill these needs geotechnical modeling will
reach significant standards in engineering such as efficiency and time saving.
Introduction
More than 160 devices are use during a Geotechnical Modeling test. These devices are in
charge for collecting data to be analyzed by researchers. The more accurate these devices are the
better results researchers are going to get. To make sure that high accuracy data is collected, it is
imperative to use metrology. The latter is described as the science of measurement; the science
of accuracy and precision. In this way, we can say that metrology establishes standards for
measurements that are used by all countries in the world in both science and engineering. The
proper use of this science will assure high standards of calibrations.
The concept of calibration is applied to all devices use during a test simulation. In fact, all
those devices must be calibrated and ready to function as good as possible. Among these devices
it is found, amplifiers, load cells, accelerometers etc. These devices follow a common pattern in
which data flows. Sensors are based on electric resistance that react at specific physical stimulus,
for example, load cells (Pallas-Areney, 1998). In this way the sensor produces a signal that pass
through an amplifier to increase its strength. Then, a digitizer converts the signal into bits to get
the final result which is understandable knowledge. In this research we were able to analyze this
process by working with load cells and amplifiers.
To calibrate these devices, it is necessary to create the same environment conditions such
as temperature, atmospheric pressure among other, in which these devices are exposed during a
simulation (Interface, 2005). For instance, a load cell is a transducer that works in such way that
by applying a force by tension or compression will give a change of voltage in its output
(wikipedia, 2006). To calibrate this apparatus, it was created an actuator calibration system
which simulates the same condition from where the load cell is exposed in the centrifuge. The
same concept is used to calibrate amplifiers but the important point is to see how accurate those
devices behave in simulation, that way researcher would know what to expect from their results.
By creating the ideal environment conditions the only hope is not just building the
settings but improving efficiency, accuracy and time saving in this process. In the same way, it is
important to save information collected during the calibration process, so that researchers do not
have to go over the same procedure again. That is why it is significant to make a database in
which all the calibration data obtained is stored from the different amplifiers and transducers
used in metrology.
Procedure
An amplifier is an electronic device which increases or amplifies the size of a voltage or
current signal without altering the signal’s basic characteristics (Pallas-Areney, 1998).. Since
amplifiers play an important role in metrology therefore in earthquake simulation, it is essential
to know how they work before talking how they are actually calibrated. Operational amplifiers
are highly use in geotechnical modeling due to the fact that one of the important properties of
these devices is that their gain is very high and its impedance is infinite most of the times.
PVL amplifier is a high accuracy instrument that requires only external resistance to set
gains of 1 to 1000 (see figure 1). In addition, its low offset voltage is ideal for precision data
acquisition systems such as transducer interfaces.
Figure 1
This is the most common amplifier used in the Geotechnical Modeling Facilities at UC
Davis. There are 3 amplifiers, each one with 16 channels. Two of them have variable gains
change by a potentiometer that is connected between pin 1 and 8, the graph shows this resistance
as RG. The other amplifier has the same circuit but its gain does not change (It has a gain of 100).
Variable amplifiers were the one studied during this research.
As talked before in order for us to calibrate this amplifier, it is necessary to create the
proper conditions to do so. Therefore, a CX-0404 interface box is used to accomplish this
purpose. This interface has calibrated values going from 0 to 4.4mV/V. The purpose of the
interface is to simulate a sensor which is going to behave if as it was in the centrifuge. To start
the simulation, some essential components are required:




DC supply:
It will supply voltage to the amplifier (it is not important how
much voltage is used)
Interface CX-0404: it will simulate sensors going from 0 to 4.4 calibrated values.
Flex interface: This arm, which is attached to the computer, will have a lost of inputs in
which we will place cables to be able to read output, inputs and excitation voltages
coming from the amplifiers.
Computer Station:
Loaded with Labview7.1 Software. The latter will show up the
actual data coming from the flex interface.
The first step to start the calibration process is to connect the power supply to the
amplifier, it does not matter which voltage is used since these PVL amplifiers are set to use 5V
excitation voltage. Once, that is done the next step is to connect a ground. Then, the CX-0404
interface is going to be connected to the amplifier input; here is where input voltage is going to
vary. However, it is really important to know our excitation voltage, so that using the same cable
for the input connection between pins 1 and 2 is made to establish this voltage. To be clear about
the cables use in this process it is important to say that there are many cables used in calibration,
choosing which cable to use depends on the device and on the type of measure (see figure 3). In
this way, for this research our input cable was configured as follow:
CABLE FOR CALBRATING AMPLIFIERS
8 pin conf.
1- +5 exc. V
2- 0V or return
3- Signal +
4- Signal –
5- Shield
6- -5V exc. V
7- not connected
8- not connected
2
5
1
1
4
8
7
2
3
3
1- Excitation +
2- Excitation –
3- Signal +
4- Signal -
6
4
Figure 3 (Interface Force)
In this way, the Flex Interface has two cables, one to read the excitation voltage and the
other one to read the input. The flex interface is also connected to the computer, so that, the
computer has all the information that is needed to complete the calibration (see connections in
figure 4).
Now the computer is configure to read voltages depending on the channels that are going
to be measured. In this case, as an example the computer is going to read voltages from channels
1 through 16. For the excitation voltage and for the input voltage it is needed to create two more
channels in the program. In other words, 16 channels to read output voltages, one for excitation
and the other one for input voltages.
Figure 4
After everything is set up, now it is time to get data. This data will help to find out the
gain, the offset voltage and also it is important to know how accurate the calibration is. To find
the gain, first it is essential to define gain. Gain of an amplifier is the amount by which it
increases the size of a signal, that is, the ratio of the output signal to the input signal. If the gain
is grater that 1 the output will be bigger that the input. In this way, by dividing the ratio of the
output that the computer shows, over input which is going to be gotten by multiplying the
excitation voltage times the interface input, then, that is going to be our gain.
Even though, the offset voltage does not affect the accuracy of the amplifier, it is really
important to know this value, due to the fact that researchers need to take it into account when
they are making conclusion of the tests. Ideally an amplifier does not have to have an offset
voltage, in other words, an amplifiers is suppose to intercept at 0V. However, offset voltages are
almost impossible so eliminate, so that, it is important to record it. In addition to that, it is also
necessary to know how accurate our measurements are, that is why the use of R2-value becomes
important (see equation 1). Gain, offset voltage and R2-value are number easy to get with the
help of Microsoft Excel software.
(1)
The final calibration results are presented in a certificate designed with the aim of
identifying and shows in a friendly way all the vital data. This is show in figure 5.
Figure 5
The certificates show the entire information gather during he calibration process. In
addition to this it also shows three values that are really important to see if the amplifiers are
working properly. The intercept values illustrate the offset voltage of the amplifier, the slope will
show the gain and the R2-value will say how accurate the calculations were (the closes to one the
better.). In addition to this certificate it was created a data base for the researchers to take a look
in the computer if they need the gain and R2-value of each channel (see figure 6).
Figure 7
Figure 6
In this data base there are two pages, one showing the R2-value for the different gains and
the other one for the actual gains in each amplifier. Sixteen lines means sixteen channels in the
amplifier.
On the other hand there are the load cells. Indeed load cells need amplifiers with the aim
of increase the signal amplitude. These are able to detect changes in force and are fundamental
tools in geotechnical modeling as well as full-scale modeling. Load cells are part of metrology
because with these, it is possible to measure with precision changes in the forces involved.
However, to do so, it is imperative to have the correct sensitivity for each load cell, which
implies to have them calibrated.
First, it is important to understand how a load cell is connected to the amplifier and at the
same time how this transmits the data to the computer station. Figure 7 shows the connection
between the load cell and a Strain-Gage amplifier.
Figure 7 (Phoenix Contact, 2001)
The process of calibration can be done by finding the slope of relationship between the
force applied (in tension or compression) and the output voltage of the load cell.
Slope 
Voltage(mV )
Force(lbf )
(2)
Then, having the slope, the gain of the amplifier, the excitation voltage, and the range of
load cell, the following formula is applied to find the sensitivity:
Sensitivity 
Slope Range 
(Gain)( Ex.V .)
(3)
The sensitivity is given in mV/V and this represents the multiplication factor for future
measurements done with this load cell.
Now, knowing how to obtain the different variables to get the sensitivity, the first test is
done. In this, an Interface load cell model 1500AZB-100 is tested. Its serial number is 202431A
with a factory sensitivity of 2.539mV/V and a range of 100lbf. For this purpose standard weights
are used to apply force in tension mode over the load cell. It is used an excitation voltage of 5V
with a PVL amplifier with a gain of 100. The following data is obtained:
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0.0
-20.0
Table 1
-40.0
Voltage (mV)
-60.0
-80.0
-100.0
-120.0
R2 = 0.997
-140.0
-160.0
Force
(lbf)
0.00
0.50
1.00
2.00
3.00
3.50
5.00
Output
(mV)
-97.0
-105.4
-111.0
-123.6
-137.6
-144.5
-160.1
-180.0
Force (lbf)
Figure 8
By applying equation 3 it is found that the slope is -0.1271mV/lbf. Then, using the information
above, it is applied equation 4 to find the sensitivity. This gives that the current sensitivity of the
load cell is 2.542mV/V. Figure 9 shows the final certificate of this load cell.
Now, the next step to do is to build a calibration system in which the entire range can be
analyzed. To do so, it is necessary to make a design of how this system actually works. In figure
10 an approximation of the possible design is sketched.
Figure 9
Figure 10
In this process, the following materials are used:





T-Slot table
Actuator
Air regulator
Reference load cell
Tested load cell
As a reference load cell is used a calibration load cell from Interface 1610AJH-1K with a
range of 1000lbf and a sensitivity of 2.103mV/V. the serial number of the calibration load cell is
205036A. The actuator is a FABCO-AIR cylinder model GTND-100-050. Using this actuator, a
pressure of maximum 50psi can be applied, which gives a force of around 600lbf.
The final calibration system is what is shown in figure 11.
Figure 11
With this actuator calibration system 3 different load cells are going to be tested and
calibrated. It is important to keep in mind that per 1psi applied to the actuator a force of more or
less 12lbf is produced through the piston.
For the test, three different load cells are used. However, for one of them two different
amplifiers are used. That is a total of three load cells tested with Strain-Gage amplifiers and one
with a PVL amplifier. The purpose of this is to observe if there is notable variation in the results
by using different amplifiers.
The following load cells are used in the tests:

Interface Load Cell SML-500
Capacity: 500lbf,
S/N: E17023

Interface Load Cell SML-1000
Capacity: 1000lbf,
S/N: 181363

Interface Load Cell SML-1000
Capacity: 1000lbf,
S/N: 181325
For the first test a PVL amplifier is used. Using the load cell SML-500 S/N: E17023 and
an excitation voltage of 5V. The gain is set to 100. Unlike the test with weights, this is done in
compression mode. For analytical purposes also a National Instruments interface Flex BNC-2120
is used, and this is connected to the computer station. The pressure applied as well as the data
obtained from the outputs is shown in table 2 in the three first columns.
Table 2
Pressure
(psi)
0
8.5
10
16
21
23
25
30
34
34.5
Calibrator
(V)
0.00419
-0.0991
-0.11906
-0.19012
-0.2485
-0.2709
-0.2915
-0.3495
-0.399
-0.4095
Load Cell
(V)
-0.051
0.3432
0.41
0.682
0.9
0.982
1.0605
1.278
1.4665
1.4931
Force
(lbf)
0.00
98.23
117.21
184.79
240.31
261.62
281.21
336.37
383.44
393.43
Output
(mV)
-51.00
343.20
410.00
682.00
900.00
982.00
1060.50
1278.00
1466.50
1493.10
In order to convert the reference load cell output voltage into the exact equivalent force
applied to the tested load cell it is necessary to apply the following formula:
Force 
V
Gain
x
Range 
Ex.V .Sensitivity 
(4)
To apply equation 4, it is necessary to have the reference load cell excitation voltage, the
gain in its amplifier, sensitivity and its range. After doing that, the fourth and fifth columns of
table 2 are found. Furthermore, also helps to understand the load cell behavior by finding the
relationship between the outputs voltages of the load cell versus the force applied.
1600.0
R2 = 0.9999
1400.0
1200.0
Voltage (mV)
1000.0
800.0
600.0
400.0
200.0
0.0
0.00
-200.0
100.00
200.00
300.00
400.00
500.00
Force (lbf)
Figure 12
By taken two points from figure 12, (using values form table 2) and applying equation 3
the slope is obtained. This is computed in equation 4 to obtain the sensitivity which is
1.969mV/V. also the r-squared value is found to figure out the reliability of the measurements
taken. This latter is shown in figure 12.
The second test is done with the same load cell but with different amplifier. Instead the
PVL, a Strain-Gage amplifier is used. Almost all the conditions remain the same except the
excitation voltage for the calibration load cell which now is 10V. This was done in a different
day therefore atmospheric conditions also are different.
The test performed gives the following data shown in table 3:
Table 3
Pressure
(psi)
0
5
8.5
10
15
20
21
25
30
34.5
Calibrator
(V)
0.00335
-0.056
-0.1071
-0.1191
-0.18276
-0.2455
-0.2568
-0.3055
-0.365
-0.4193
Load Cell
(V)
0.00442
0.223
0.4071
0.4541
0.6907
0.9225
0.9646
1.1485
1.3707
1.572
Force
(lbf)
0.00
56.44
105.04
116.45
176.99
236.66
247.41
293.72
350.31
401.95
Output
(mV)
4.42
223.00
407.10
454.10
690.70
922.50
964.60
1148.50
1370.70
1572.00
The relationship between the force applied and the output voltage of the tested load cell is
sketched in the following figure:
1800.0
1600.0
1400.0
Voltage (mV)
1200.0
1000.0
800.0
600.0
400.0
200.0
0.0
0.00
100.00
200.00
300.00
400.00
500.00
Force (lbf)
Figure 13
The sensitivity found by applying equation 3 to figure 13 and the equation 4 to this test is
1.953mV/V. Now keeping in mind that in this test both of the excitation voltages were 10V and
the fact that Strain-Gage amplifiers are more accurate and reliable than PVL amplifiers the
slightly difference is about 16µV which is equivalent to 0.8%. The certificate for this load cell is
shown in figure 14.
For the third test the load cell SML-1000 S/N: 181363 is used. Unlike the SML-500 this
has a capacity of 1000lbf. However, the same test conditions are applied to this load cell. The
test is done and the data shown in table 4 is obtained in its process.
Table 4
Pressure
(psi)
0
5
8.5
10
15
20
21
25
30
34.5
Calibrator
(V)
0.0035
-0.0556
-0.1
-0.117
-0.1791
-0.2428
-0.2555
-0.3037
-0.366
-0.41
Load Cell
(V)
0.0073
-0.1044
-0.1862
-0.2211
-0.3393
-0.4589
-0.482
-0.574
-0.691
-0.771
Force
(lbf)
0.00
56.21
98.43
114.60
173.66
234.24
246.31
292.15
351.40
393.25
Output
(mV)
7.30
-104.40
-186.20
-221.10
-339.30
-458.90
-482.00
-574.00
-691.00
-771.00
Figure 14
Then, it is proceed to apply the equation 3 to the data and the following graph (figure 15)
is obtained from the forth and fifth column of table 4.
100.0
0.0
0.00
-100.0
100.00
200.00
300.00
400.00
500.00
Voltage (mV)
-200.0
-300.0
-400.0
-500.0
-600.0
-700.0
R2 = 1
-800.0
-900.0
Force (lbf)
Figure 15
The sensitivity obtained by applying equation 4 is 1.984mV/V. as it’s shown in figure 15;
the R2-value is 1, which implies that there is total linearity and the measurement process was
highly accurate. The final certificate for this load cell is found in figure 16.
The fourth test is performed with a load cell SML-1000 S/N 181325. This is the same
model than the latter. Nevertheless, that does not implies that its sensitivity actually the same.
However, a closed sensitivity is expected.
This test is given with a gain of 100 for the tested load cell as well for the reference load
cell. The excitation voltage for the load cell is 5V and the voltage for the tested load cell is 10V.
Figure 16
During the test the following data is get it:
Table 5
Pressure
(psi)
0
5
8.5
10
15
20
21
25
30
34.5
Calibrator
(V)
0.0027
-0.0545
-0.0975
-0.1155
-0.1784
-0.242
-0.2544
-0.303
-0.365
-0.422
Load Cell
(V)
0.017
-0.0903
-0.17
-0.20256
-0.377
-0.4401
-0.4638
-0.5567
-0.674
-0.783
Force
(lbf)
0.00
54.40
95.29
112.41
172.23
232.72
244.51
290.73
349.69
403.90
Output
(mV)
17.00
-90.30
-170.00
-202.56
-377.00
-440.10
-463.80
-556.70
-674.00
-783.00
The graph of the relationship between force applied and output voltage from the tested
load cell is shown in figure 17. The latter also shows a point of great significance. The reason is
that such point is positioned on the line. This also is confirmed when the R 2-value of such
function is taken. Even though the R2-value is close to 1, this is not as accurate as the one for the
past tests. However, this single value does not affect dramatically the sensitivity of the load cell.
100.0
0.0
0.00
-100.0
100.00
200.00
300.00
400.00
500.00
Voltage (mV)
-200.0
-300.0
-400.0
-500.0
-600.0
-700.0
R2 = 0.9956
-800.0
-900.0
Force (lbf)
Figure 17
In figure 18 is found the complete certificate as well as the information for this load cell.
Figure 18
Acknowledgements
We thank the Network for Earthquake Simulation (NEES) Inc. REU program for the
opportunity to participate in this research project. Special thanks go to our mentors Dr. Bruce
Kutter and Dr. Dan Wilson for his dedication and interest. We also thank Ray Gerhard, Assistant
Development Engineer for his time and patience in collaborating us, Mr. Chad Justice, technician
and Ms. Cypress Winter, Safely Officer, for supplying any kind of additional help.
References




Interface Force, Load Cell Terms and Definitions, Scottsdale, AZ, 2005.
Pallas-Areny, Ramon, JGW, Sensor and Signal Conditioning, Barcelona, Spain, 1998.
Phoenix Contact, MCR Strain-Gage Amplifier, Harrisburg, PA, 2001.
Wikipedia, Transducer, www.wikepedia.com, 2006.