ME 360 Lab 2

ME 360 Lab 2:
Op Amps

Your Name
Lab partners: Names of partner (s)

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September 16, 2018

Objective
The objective of this experiment is to condition the output signal of an electronic transducer using op-amps. The Op-amps will be used to remove the dc offset voltage associated with protractor potentiometer and to provide a gain of 0.01V/0. The conditioned signal will be measured, recorded and analyzed to ascertain its conformity with the desired expectation.
Background
A transducer is an electronic device that converts one form of energy into another for example angular position into voltage. There are several types of transducers depending on their functions. There is pressure transducers, speed transducers etc. Transducers are also referred to as sensors when their output is an electrical signal and they are widely used in industries to measure physical quantities. In order for the transducers to be suitably employed, their signals need to go through processing either to remove offsets or to amplify the signal which are usually quite small. For example, tachometers which are employed in aircraft instrumentation for measuring rotating speed of engine usually have outputs in millivolts (mV). For such small signal to be useful it must be amplified to certain desired magnitude. This process is called conditioning. Signal conditioning is basically the improvement of an electrical signal to enhance its applicability. Signal conditioners are measuring system elements that start with an electric sensor output signal and then yield a signal suitable for transmission, display or recording, or that better meet the requirements of a subsequent equipment or device (Sensors and Signal conditioning, 2001).
Commonly used signal conditioners in engineering practice is the operational amplifier (Op-amps). Op-amps are active circuit elements that are used to increase signal amplitudes. It is commonly referred to as a differential amplifier because it amplifies the difference between two input voltages. Op-amps can be used as an inverting or non-inverting amplifier depending on the desired application. The difference being the phase relationship between the input and output signal. For non-inverting amplifier, the output is in phase with the input but for inverting amplifier the output is 180 out of phase with its input. Figure 1a gives the Pin out for 741 Op-amp chip and Figure 1b and 1c shows the schematic for the inverting and non-inverting amplifiers.
Figure 1a
Pin outs for the 741 Op-amp

Figure 1b
Inverting amplifier configuration

VOUT = G x VIN (1)
G = – (R2/R1) (2)
Where
G = Gain
VOUT = Output voltage
VIN = Input Voltage
R1, R2 = Resistor values
For a differential Op-amp configuration, the gain

Figure 1c
Non-inverting amplifier configuration

VOUT = G x VIN (3)
G = {R1 /(R1 + R2)} (4)
Where
G = Gain
VOUT = Output voltage
VIN = Input Voltage
R1, R2 = Resistor values
For a differential Op-amp configuration, the gain
Experiment
A voltage follower circuit was first constructed and instrumented on a breadboard using the protractor potentiometer and a 741 Op-amp and as shown in the figure 1. This circuit was used to determine the necessary DC offset voltage and Gain. The pro-pot dial was varied in steps of 200 from 00 to 900 and the voltage follower output measured with an Agilent 34405A DMM and result recorded. The recorded value is shown in table 1. The DC offset and gain was determined by graphing the pro-pot output voltage versus the dial positions.
Table 1
Calibration data for determining circuit offset and gain
Input angle (0) Pro-pot output (V) Voltage follower output (V)
0 -2.570 -2.570
20 -3.596 -3.596
40 -4.756 -4.760
60 -5.891 -5.896
80 -6.875 -6.880

Figure 2
Plot of Pro-pot output Vs Angle

The Slope of the graph in figure 2 gave an experimental gain of -0.0546 and the pro-pot output voltage at 00 was taken as the dc offset Voff which was -2.57V.
Having obtained the actual gain and dc offset values of the pro-pot, the gain of the amplifier was then determined (see appendix) and this was found to be -0.181. The appropriate resistors (R1 and R2) required to achieve a gain 0.181 was then selected and measured using an Agilent 34405A DMM.
A circuit was then constructed on the same breadboard to remove the dc offset voltage and to also obtain the desired gain of 0.01V/0. This was done by incorporating another protractor potentiometer with a voltage follower and a summing amplifier on the same breadboard. The new potentiometer was adjusted to set its voltage follower output to -Voff. The final circuit connection is as show in figure 3a and 3b. The circuit was then powered up and the pro-pot dial was again rotated starting at 0 and in steps of 200 from 00 to 1000. The resulting output was measured and recorded for each angle position (see data in appendix section). Care was taken in approaching the angles on the first try to avoid backlash.
Figure 3a
Complete circuit schematic

Figure 3a
Snapshot of connected circuitry

Results
A plot of the summing amplifier output obtained from the experiment versus the pro-pot angle is shown in Figure 3.
Figure 3
Plot of summing amplifier output Vs. Input Angle

Note that the slope for the graph represents the gain for the entire circuit (that is volts per degree). From the graph the slope was determined and was found to be 0.0097. This value only differs from the desired gain of 0.01 by 0.0003 which is 0.03%. This error though very small and could be neglected can be attributed to factors such as backlash in turning the pro-pot dial and uncertainties in taking measurements.

Conclusion
The output of a protractor potentiometer was conditioned by removing its offset dc voltage and creating a positive relationship between the pro-pot angle and its output voltage. The relationship is such that when the pro-pot dial is at 00, its output voltage reads zero volts and at 1000 it is 1V. A load follower and summing amplifier was employed to accomplish this result and they were constructed using the 741 operational amplifiers. A second pro-pot connected to a load follower was employed to provide dc offset voltage. By appropriately selecting feedback and input resistances for the summing amplifier, the desired gain was obtained. Analysis of the output from the summing amplifier indicated that the summing amplifier provided a gain of 0.0097V/0 which can be approximated to 0.01V/0. Thus, the objective of the experiment was adequately met and a successful signal conditioning of the protractor potentiometer was achieved using 741 operational amplifiers.

References
Ramon, Pallas-Areny. John G. Webster (2001). Sensors and Signal Conditioning, 2nd Edition. John Wiley & Sons
Mathew N.O. Sadiku, Charles K. Alexander (1999). Fundamentals of Electric Circuits, 5th Edition. McGraw-Hill Education.
Tarun Agarwal. The IC 741 Op-Amp tutorial and characteristics. Retrieved from
https://www.elrpocus.com/ic-741-op-amp-tutorial-and-sharacteristics

Appendix
Contents
Assumption for uncertainty values – page 10
Calculation to determine the amplifier voltage gain and resistors required – page 10.
Raw data – page 12
Assumption for uncertainty values
Measurement made with Agelent 34405A DMM, (Note, the uncertainties is obtained from the data sheet of the Agilent 34405A DMM)
Resistance uncertainty
Uncertainies for 1k range is 0.05% of reading + 0.005% of range
Uncertainies for 10k range is 0.05% of reading + 0.006% of range
Voltage Uncertainty
Uncertainies for 1V range is 0.025% of reading + 0.006% of range
Uncertainies for 10V range is 0.025% of reading + 0.005% of range
Calculation to determine the amplifier voltage gain and resistors require
The gain of the protractor-potentiometer was found to be -0.0546V/0
The required gain is 0.01V/0.
Therefore, the Voltage gain (Amplifier gain-G) required to achieve a gain of 0.01V/0 can be found by the ratio the required gain to the pro-pot gain.
That is, G = 0.01/(-0.0546) = -0.183
Since the G = – Rref/Ri
Where
Rref is the feedback resistor on the amplifier and Ri is the input resistor. The two resistors were selected so that an amplifier gain of -0.183 is obtained. In our circuit, Rref = R2 and Ri = R1.
R1 and R2 were selected and their values measured as 5.501K and 0.9944K respectively.
Thus, R2/R1 = 0.9944/5.501 = 0.181. This is closed enough to the desired gain earlier calculated.

Raw Data
Measurements recorded
Input angle (0) Pro-pot (V) Fixed Potentiometer (V) Summing Amp output (V)
0 -2.559 2.57 0.000333
20 -3.61 2.57 0.199000
40 -4.726 2.57 0.404000
60 -5.77 2.57 0.598000
80 -6.77 2.57 0.787000
100 -7.77 2.57 0.978000
80 -6.78 2.57 0.788000
60 -5.8 2.57 0.604000
40 -4.79 2.57 0.416000
20 -3.64 2.57 0.205000
0 -2.59 2.57 0.012600
20 -3.65 2.57 0.207000
40 -4.76 2.57 0.410000
60 -5.77 2.57 0.599000
80 -6.76 2.57 0.784000
100 -7.82 2.57 0.982000
80 -6.74 2.57 0.781000
60 -5.73 2.57 0.591000
40 -4.74 2.57 0.408000
20 -3.68 2.57 0.212000
0 -2.64 2.57 0.021700

Resistances Measured
Resistors Rmeasured Range, Ohms
R1 1K 0.9944K 1K
R2 5.6K 5.501K 10K