Next, we performed the lab titled "Temperature Measurement System Design", which is explained in more detail below under the "LAB" section.
After, we learned about digital-analog converters, which convert digital signals to analog forms. An example of such is the analog discovery kit we use in each lab. A digital analog converter at its core is simply a summing amplifier. Digital analog converters (DAC) can only have applied voltages of 0 V or 1 V. The amount of applied voltages and resistors in parallel is the number of bits. For example, a 4-bit DAC has 4 applied voltages and resistors in parallel. A DAC also has a most significant bit and a least significant bit. A most significant bit has the least resistance and a least significant bit has the most resistance.
Lastly, we learned about instrumentation amplifiers, which are cascaded op amp circuits at heart. It typically consists of three op amps, two being non-inverting and the third being a difference amplifier. When all of the resistors are made equal except for the gain-setting resistor Rg that connects the two non-inverting op amps, the gain of the instrumental amplifier is 1 + 2R/Rg. Instrumental amplifiers are really useful because they cancel out any offset voltages and any common-mode signals (i.e. noise).
LECTURE:
In this example, we simply determined the type of op amp in the cascaded op amp circuit. The op amps in boxes A and B were inverting and the one in box C was summing. The outputs of op amp A and op amp B were the input for op amp C. From there, the outputs of the op amps can be found and the total output of the cascade is the output of op amp C.
In this cascaded op amp circuit, the objective was to find the current io in the feedback resistor for the op amp to the right. To do so, the type of op amps used was determined. It was found that both op amps are non inverting. Then the output voltage of the op amp to the right was determined using the non-inverting op amp formula in order to find voltage at point a, which was found to be 1/10 V. Then, the same was done for the op amp to the right, and the voltage at point B was found, which was 7/20 V. Then, using nodal analysis the current io was found to be 1/40 mA.
In this problem, the output voltages for the DAC were determined at certain applied voltages in the three-bit DAC. In addition, the applied voltages were found for specific output voltages. When the applied voltages were [V1V2V3] = [010], the output voltage was found to be 0.5 V using nodal analysis. In addition, when [V1V2V3] = [110], the output voltage was 1.5 V. On the other hand, when the output voltage is 1.25 V, the applied voltages were found to be [V1V2V3] = [101] using nodal analysis. Lastly, when output voltage is 1.75 V, the applied voltages are [V1V2V3] = [111].
LAB:
Temperature Measurement System Design:
Purpose:
The objective of this experiment was to design a temperature measurement system that consists of a thermistor, a Wheatstone bridge and a difference amplifier connected together. The difference amplifier amplified the voltage difference between the two resistors on each branch in the Wheatstone bridge circuit. The thermistor was part of the Wheatstone bridge. In addition, the requirements of this design were as follows: The output voltage is 0 +/- 20 mV at room temperature, and as the thermistor is heated close to body temperature the output voltage should change by at least 2 V. Lastly, a temperature higher than room temperature should result in a positive output voltage, and a temperature below room temperature should result in a negative output voltage. The voltage will be an indicator of the temperature.
Prelab:
In the prelab, we designed the circuit consisting of the Wheatstone bridge and difference amplifier using an OP27. The Wheatstone bridge consists of four resistors total, a pair in series and both pairs parallel to each other, as shown above. The Wheatstone bridge we constructed contained a 5.6 kOhm resistor, a 12 kOhm resistor, the thermistor, and a potentiometer. The Wheatstone bridge used the change in resistance of the thermistor to convert the change to a change in voltage. On the other hand, the potentiometer was used to balance the Wheatstone bridge, meaning that to cause the voltages at point a and point b to be equal,resulting in an output of 0 V for the difference amplifier.
Using voltage dividers, the relationship between the voltage difference across points a and b and the applied power supply was derived, as shown below:
As can be seen, in order to obtain zero voltage across a and b, the potentiometer or a variable resistor will be needed. In order for the voltage Vab to be zero, the voltage across the potentiometer must be equal to the voltage across R1. To obtain this, the ratio between the resistances of R1 and R2 must be equal to the ratio of the resistances between Rp and Rt. Changing the resistance of the potentiometer until this ratio is achieved results in balancing of the Wheatstone bridge.
Apparatus:
The apparatus for this experiment consisted of a thermistor, an OP27 op amp, Logger Pro with a temperature probe, and the usual equipment, such as resistors, wires, the analog discovery, a DMM, a breadboard, alligator clips, a laptop with Waveforms and a marker and a board. The temperature probe with Logger Pro was used to measure the change in temperature of the thermistor.
Procedure:
Thermistor Characterization:
First, the resistance of the thermistor at room temperature 22.3 degrees Celsius) was measured using an ohmmeter (11.21 kOhms). The thermistor was then grasped tightly between two fingers to heat it up to the desired body temperature. However, it was only heated to 31 degrees Celsius, and the resistance dropped to 6.65 kOhms.
Wheatstone bridge design and balance:
First of all, the resistances of each resistor used in the Wheatstone bridge was measured using an ohmmeter. These values are found in the data section below. Then, the actual Wheatstone bridge was built as seen below:
A closer look of the circuit is seen below, when the bridge is balanced. In it consists of the two resistors, the potentiometer, and the thermistor, as shown in the prelab design.
A voltage source of 1 V was applied to the Wheatstone bridge. It was found that the Wheatstone bridge is balanced when the potentiometer has a resistance of about 5.34 kOhms. Looking at the ratio between the potentiometer and the thermistor at room temp versus the ratio between R1 and R2, they are nearly equal, resulting in the near balancing of the circuit at about 6.3 mV more or less.
Next, the thermistor was heated to about 31 degrees Celsius, which was measured by Logger Pro and the temperature probe. This is shown below in the graph obtained of temperature over time:
At 31 degrees Celsius, the output voltage of the Wheatstone bridge was found to be 0.064 V. Below is a video showing the Wheatstone bridge in action:
Difference Amplifier:
First, the actual resistance values of the resistors used in the difference amplifier circuit were measured using an ohmmeter. The difference amplifier circuit, connected to the Wheatstone bridge, was built using the design made in the prelab. The total circuit is shown above. +5 V and -5 V were supplied to the OP27, and the same 1 V was added to the Wheatstone bridge. The inputs of the difference amplifier were placed at points a and b. When the Wheatstone bridge was balanced, the output voltage of the difference amplifier was 0.01 V. When the thermistor was gain heated to 31 degrees Celsius by firmly grasping it between two fingers, the output voltage increased to 2.05 V. All of this data is found below in the data section.
Below is a video of the entire circuit (difference amplifier and thermistor) in action:
Data:
In the picture below, the data obtained in the entire lab is contained, such as measured resistances, the resistance change of the thermistor at room and body temperatures, the reisstance of the potentimeter when the Wheatstone bridge is balanced and output voltages at room and body temperatures.
Data Analysis:
Looking at the Wheatstone bridge, the voltage across points a and b was zero when the ratio between the potentiometer (5.34 kOhms) and thermistor (11.21 kOhms) was nearly identical to the ratio between the first resistor (5.61 kOhms) and the second resistor (11.95 kOhms).
In addition, analyzing the difference amplifier, the ratio between the feedback resistor and the resistor seen by Va was the same as the ratio between the resistor going to ground and the resistor seen by Vb, as must be in a difference amplifier's design. In addition, looking at the theoretical gain and actual gain of the difference amplifier, they are not equal. The theoretical gain is the ratio between the feedback resistor and the resistor seen by voltage at point a (39.2) is not equal to the experimental gain, which can be found by dividing the output voltage of the difference amplifier by the voltage across points a and b. The experimental gain is calculated to be 32.0. This is due to the difference amplifier having offset voltages and generally noise. This is just a result of the design of the op amp and the quality of its build.
Conclusion:
Overall, the experiment was a success. The starting output voltages at room temperature were in the range of 0 +/- 20 mV. In addition, the output voltage of the difference amplifier increased by a minimum of 2 V over the temperature range between room and body temperatures. Lastly, when the temperature was increased, the output voltage was positive, and when it decreased, the output voltage was negative, which followed the design requirements. The only problem faced was that the experimental gain was not equivalent to the theoretical gain, which again is just due to the quality of the build of the op amp and any offset voltages or noise experienced by it.
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