26-Mar-2015: Inverting Voltage Amplifier

PURPOSE

The purpose of this experiment was to use the relationship of Vout and Vin we learned about inverting amplifiers and implement this newfound knowledge in an experiment.

PRE-LAB

Figure 1: Mathematical process of the pre-lab

Before starting the experiment, we were given the task of designing an inverting amplifier that resulted in a gain of approximately 2. In order to do this, we used the equation shown in Figure 1 and plugged in two arbitrary resistance values. We chose 1.8 kΩ and 3.6 kΩ as resistors R1 and R2, respectively, because they divided nicely into 2.

PROCEDURES

Figure 2: Schematic of our design

Figure 3: Measured resistance values of the resistors used in our design

After figuring out which resistors to use, we drew out the schematic of our design. We also measured the actual resistance values of the resistors before proceeding with our experiment.

Figure 4: Set-up of our designed circuit

The actual set-up of our circuit is shown above in Figure 4. After setting up our circuit, we applied a voltage to the amplifier and measured its output voltage. We repeated this process for a range of voltages, from -3 V to +4V, in increments of 0.5 V.

Figure 5: Data table of Vin and Vout

All the input voltages and their corresponding output voltages in this experiment are shown in the data table above (Figure 5).

Figure 6: Graph of Vout vs Vin

We then plotted the data with Vout on the y-axis and Vin on the x-axis. From this graph, it can be seen that our design was successful. This is because the slope of the linear portion of the graph is -1.97 (this is how Vout was changing with respect to Vin). This is very close to the -2 we solved for in the pre-lab. In fact, the percent error was only 1.5 percent.

Another thing that can be observed from this graph is the voltages at which the amplifier reached saturation. This can be seen from the areas where the graph level out and do not change. The saturation voltages were approximately 3.0 V on the positive end and -2.5 V on the negative end.

CONCLUSION

As mentioned before, our percent error between the expected and measured values was only 1.5 percent. Therefore, it can be concluded that our experiment was successful. This is pretty much the closest to the expected value that we can get because no experiment is perfect. There are always random errors that we cannot account for. The results are especially impressive considering that our experiments are relatively low-budget when compared to the experiments conducted by researchers that work for big corporations.

24-Mar-2015: Non-ideal Power Sources/Maximum Power Transfer

Non-ideal Power Sources

PURPOSE

PRE-LAB

Figure 1: Expected values of Vout, Is, and P

Before conducting our experiment, we determined the expected values for the measured voltage (Vout), source current (Is), and the power dissipated by the resistor (P). We calculated these values for both an ideal voltage source (right) and a non-ideal source (left). The work is shown above in Figure 1.

PROCEDURES

Figure 2: Set-up of circuit

Figure 3: Measured values of Vout and R

Figure 2 shows the actual set-up of the circuit. After setting up our circuit, we turned on the voltage source and made sure that it was actually outputting 1 V with our multimeter. Then, we applied the voltage onto the circuit and measured the Vout. We repeated this process for three different resistors. The measured values are displayed above in Figure 3, including the actual resistances of the resistors.

Figure 4: Measured (Vout and R) and calculated (Rs, Is, and P) values

From these measured values, we calculated the internal resistance of the voltage source by using the formula shown earlier in Figure 1. We also found the source current and the power dissipated by the resistor for each trial. The resulting values are illustrated in Figure 4. 

CONCLUSION

From looking at the values in Figure 4, we noticed that the internal resistance of the voltage source decreased as we increased the resistance value of the resistor in our circuit. One of the possible reasons that we think that this may have occurred is because the higher resistance values made the internal resistance more and more negligible.

19-Mar-2015: Thevenin's Theorem

PURPOSE

The purpose of this lab was to apply our knowledge on Thevenin equivalent circuits in a real-world situation.

PRE-LAB

For the pre-lab, we analyzed the circuit shown in Figure 1 (click to enlarge), marked with the red circle. We found the open circuit voltage by examining the Thevenin equivalent circuit displayed in Figure 1 with the blue circle. We found this voltage to be 0.45 V. Then, we found the Thevenin resistance (Rth) by utilizing the circuit labeled with the green circle. We ended up with a value of 7.198 kΩ.

PROCEDURES

Figure 2: Set-up of our circuit

After finishing the pre-lab, we constructed the circuit as shown in Figure 2 above. We then proceeded to measure Thevenin resistance of the circuit (Figure 3). We found this value to 14.83 kΩ.

Figure 3: Measured Thevenin resistance

Percent error = (|expected value - measured value| ÷ expected value) x 100%

= (|7.198 kΩ - 14.830 kΩ| ÷ 7.198) x 100%

= (|-7.632| ÷ 7.198) x 100 %

= (7.632 ÷ 7.198) x 100 %

= (1.060) x 100 %

= 106.0 %

CONCLUSION

This experiment was a useful learning experience because it allowed us to implement what we learned during lecture in an actual experiment. This allows us to achieve a deeper understanding of the concepts that we learn in class.

When we measured the actual resistance of our Thevenin equivalent circuit, we found that the measured value was much bigger than the expected value. In fact, when we calculated the percent error, it was 106 percent. This is most likely due to two factors. The first possible reason for this error is that we made a mistake when performing the mathematical process. We could have taken the wrong steps when finding the value or we could have simply added wrong. The second factor that most likely caused this huge error is the fact that we could have set up the circuit incorrectly.

17-Mar-2015: Time-varying Signals/A BJT Curve Tracer

Time-varying Signals

PURPOSE

The purpose of this lab was to examine the relationship between the input and output voltages (Vin and Vout) for time-varying signals.

PRE-LAB

Figure 1: Relationship between Vin and Vout

Figure 2: Graphs of Vin and Vout

Prior to commencing with our lab, we drew our predictions for the shapes of the Vin and Vout graphs based on the given criteria. We were able to do this by using the equation shown in Figure 1 and assuming that R1 and R2 were equal. The resulting graphs are shown in Figure 2.

PROCEDURES

Figure 3: Input sinusoidal graph

Figure 4: Output sinusoidal graph

Figure 5: Input triangular graph

Figure 6: Output triangular graph

Figure 7: Input square graph

Figure 8: Output square graph

Following the pre-lab, we implemented our set-up and captured the resulting input and output voltage graphs using the WaveGen instrument. We repeated this process for three different graph shapes: sinusoidal, triangular, and square. These graphs are displayed above in Figures 3 through 8 (the input graph is shown first and then the output for each case).

CONCLUSION

According to the results, this experiment was successful. This can be seen by observing the frequency and amplitude of the Vout graphs. For example, the output square graph has a frequency of 1.00001 kHz and an amplitude of 996.8 mV. These values are considerably close to the expected values of 1 kHz and 1 V. In fact, the percent error for these values are only .001 and .32 percent, respectively.

A BJT Curve Tracer

PURPOSE

The purpose of this experiment was to observe the relationship between the base-emitter voltage (Vbe) and collector current (Ic) by utilizing the WaveGen instrument.

PROCEDURES

We began this experiment by setting up our circuit as shown in Figure 1. This set-up consisted of a 2N3904 NPN transistor, a 100 Ω resistor, a 100 kΩ, and some wires to connect the elements. Before proceeding with the experiment, we measured the actual resistances of these resistors as shown in Figures 2 and 3.

Figure 4: Stair-step function graph

Figure 5: Triangular function graph

Next, we generated two curves: a stair-step wave and a triangular wave. These graphs are shown in Figures 4 and 5. 

Figure 6: Collector current (Ic) vs base-emitter voltage (Vbe)

Figure 7: Scaled graph of Ic vs Vbe

After plotting the previous graphs, we constructed another with collector current with respect to base-emitter voltage of the transistor. This graph is shown in Figure 6. Then, we fit the graph to a different scale to get a better view of what was happening. The resulting graph is illustrated in Figure 7 above.

CONCLUSION

This experiment gave us a better understanding of the relationship between the base-emitter voltage and collector current. This allowed us achieve a deeper understanding of how BJT transistors function.

12-Mar-2015: Mesh analysis

Today, we further developed our understanding of mesh analysis. We applied this newly acquired knowledge by solving for the current across a resistor and the voltage across another. Then, we set up a circuit to compare the theoretical and experimental values.

(Figure 1)

We began the day by taking a quiz during which we solved for i1 and i using mesh analysis (Figure 1). We found i1 by solving for the system of equations that we got from applying KVL across each mesh, or independent loop. From this system of equation, we also found i2 and i3. We solved for i from these values by subtracting i2 from i3. We did this because we saw that i3 went in the same direction as i, while i2 went in the opposite direction.

(Figure 2)

After the quiz, we learned about supermeshes. A supermesh is composed of two meshes that have a common current source. Then, we learned about diodes, which are semiconductor devices that are made up of (to be continued...) For more information on supermeshes, diodes, and transistors, refer to the Day 6 lecture posted on profmason.com. After the lecture, we did a lab in which we implemented the concepts that we studied in class to a real-life situation. Before setting up the circuit, we first calculated I1 and V1 by utilizing mesh analysis, shown on the left side of Figure 2. We then used a multimeter to measure the actual resistance values of the 1.8 Ω, 22 Ω, 6.8 Ω, and 4.7 Ω resistors, respectively, shown on the right side of Figure 2.

(Figure 3)

Next, we set up the circuit on a breadboard. The completed circuit is shown above (Figure 3). Note that we labeled the two voltage sources and the ground cable above the circuit in terms of the color of the wires and the color of the clips, respectively.

(Figure 4)

(Figure 5)

After completing the circuit, we turned on the voltage sources and measured the current running through the 1.8 Ω resistor and the voltage across the 22 Ω resistor. Figure 4 shows us measuring the current across 1.8 Ω resistor, while Figure 5 lists the experimental and theoretical voltage values across the 22 Ω resistor, respectively.

10-Mar-2015: Nodal analysis

Today, we continued our studies on nodal analysis. We employed what we learned about this topic by predicting the voltages across two different resistors and comparing them to the values that we found experimentally. We were also introduced to the concept of mesh analysis.

PRE-LAB

Figure 1: Application of nodal analysis

To begin our process, we calculated V1 and V2 by applying nodal analysis to the circuit shown in Figure 1. Since there are multiple variables called V1 and V2 in our work, the V1 and V2 we are referring to was circled in black.

PROCEDURES

Figure 2: Set-up of our circuit

After finding the theoretical values for V1 and V2, we constructed the circuit as shown in Figure 2. This set-up consisted of a 6.8 kΩ resistor, a 10 kΩ resistor, a 22 kΩ resistor, two 5 V voltage sources, and a 3 V voltage source.

Figure 3: Measured resistances

Next, we measured the actual resistances of each resistor. The measured values are shown in Figure 3.

Figure 4: Measured voltages

Finally, we turned on the voltage sources and measured the voltages across the 6.8 kΩ resistor and the 22 kΩ resistor. We labeled the voltage across the 6.8 kΩ resistor as V1 and the voltage across the 22 kΩ resistor as V2. The measured values are shown in Figure 4.

CONCLUSION

We found that our expected values and measured values were very different. In fact, the percent error for V1 was 454 percent. The reason for this enormous error can most likely be attributed to the fact that we carried out our calculations incorrectly. Another factor could have been that the set-up of our circuit was wrong.

Even though we were not able to find measured values that were close to the expected values, we still gained valuable experience in applying our knowledge about nodal analysis to an actual circuit.

5-Mar-2015: Temperature Measurement System

QUIZ

PURPOSE

The purpose of this experiment was to build our skills in constructing a design and implementing it in an experiment.

PRE-LAB

Figure 1: Graph of the thermistor's resistance vs temperature

We began this experiment by looking at the graph in Figure 1. From this examining this graph, we estimated that the resistance of the thermistor was around 11 kΩ at 25°C and 7 kΩ at 37°C. We used these values and voltage division to calculate the theoretical values of Vout, shown on the top side of the red line in Figure 2 (click to enlarge).

Figure 2: Mathematical process of finding the desire R value

The resultant value was in terms of R, which was the value of the resistor that we had to select for our design. To decide which value of R to use, we had to consider the constraint of this experiment: Vout has to increase by a minimum of 0.5 V with the temperature increase. Therefore, we set the difference of the voltages at 25°C and 37°C equal to 0.5 V, and solved for R. This process is shown in the bottom half of Figure 2. When we solved for the quadratic equation shown in Figure 2 (circled in blue), we got two values for R: 17.633 kΩ and 4.367 kΩ. Since we did not have resistors that were close 17.633 kΩ, we decided to go with a 4.7 kΩ resistor in our design as it was relatively close to 4.367 kΩ. The measured value of the resistor is shown below in Figure 3.

Figure 3: Actual fixed resistance value

PROCEDURES

Figure 4: Measured resistance values of the thermistor at ~25°C and ~37°C, respectively

Before implementing our design, we measured the actual resistance values of the thermistor used in our setup. We first measured its resistance at room temperature, which we assumed to be around 25°C. Then, we measured its value after holding the thermistor in our hands until the number displayed on the multimeter stabilized. We believed that this was when the thermistor had reached the same temperature as our hands, which we approximated to be 37°C. The measured values are shown in Figure 4 above. The percent difference between these values and the theoretical values calculated in the pre-lab was 1.36 percent and 1.29 percent for the 25°C and 37°C resistances, respectively. Since the percent differences were not very large, we believed that the system was going to be effective in achieving our goal.

Figure 5: Setup of our circuit

After measuring the resistances of the thermistor, we set up the circuit as shown above in Figure 5. In Figure 5, the voltage source of the circuit is illustrated with the red circles and the multimeter used to measure Vout is marked with green ones. Then, we applied 5 V to the circuit and measured Vout for the two different temperatures. First, we measured Vout at room temperature. The measured value is shown below in Figure 6. Next, we held the thermistor in our hands to warm it up to approximately 37 °C. The resulting voltage is shown in Figure 7.

Figure 7: Vout at 25°C

Figure 8: Vout at 37°C

Percent error = |expected value - measured value|/expected value x 100%

Since the difference between these values was 0.53 V, our design met the minimum constraints. In fact, the percent error of this value was 6 percent. Considering the limitations that we had, we believed that the experiment was successful.

POST-LAB

After performing the lab, we did a post-lab exercise in which we attempted to design an experiment in which the output voltage increased by 0.1 V per °C change. Since the overall temperature increase was 12°C, we concluded that our design had to result in a voltage increase of 1.2 V. However, we when we tried to solve for R, we got imaginary values. Therefore, we were unable to come up with a design that met the design specifications. Our process is illustrated in Figure 8.

CONCLUSION

In this experiment, we learned how to come up with a design for a circuit and implement the design successfully. We also acquired valuable experience in dealing with variable resistors. In this particular case, we saw how a certain type of variable resistor reacted to temperature changes.

The design that we implemented in this experiment was successful in meeting the minimum constraints. The results could have been even more accurate if we had been exact in getting the thermistor to be exactly 25°C and 37°C.

3-Mar-2015: Dusk-to-Dawn Light

DEMONSTRATION

At the beginning of class, we had a demonstration in which a current was applied across a hot dog with LEDs connected to it. Some were positioned perpendicularly from the hot dog, while others were positioned parallel to it. The ones that were positioned parallel to the hot dog lit up from the current, while the perpendicular LEDs did not. This is because the ones that were parallel with the hot dog were actually in series with the hot dog/circuit, while the perpendicular ones were parallel to the hot dog/circuit. As a result, the parallel LEDs received the current, while the perpendicular ones did not (at least not enough).

PURPOSE

The purpose of this experiment was to become familiar a type of variable resistor known as the photocell and a current-controlled current source called a bipolar junction transistor (BJT).

PRE-LAB

Figure 1: Mathematical process for pre-lab

Before starting our experiment, we solved for the theoretical values of the voltage across the photocell (Vb). We did this by applying KVL across the circuit displayed within the red circle in Figure 1. Also included in Figure 1 is the mathematical process for solving for Vb when we assumed the resistance of the photocell to be 5kΩ. We found this value to be 1.667. We followed the same process to solve for Vb when the resistance of the photocell was assumed to be 20 kΩ. We found this value to be 3.333 V.

PROCEDURES

After solving for the theoretical values in the pre-lab, we set up the circuit as shown below in Figure 2. The photocell is labeled with the red circle, the BJT with the green circle, the fixed resistor with the purple circle, and the LED with the blue. In addition, the black and red clips represent the 5 V voltage source.

Figure 2: Set-up of our circuit consisting of a photocell, a BJT, a fixed resistor,
an LED, and a voltage source

Next, we applied 5 V to the circuit and measured the voltage across the photocell and the LED when the photocell was allowed to receive light and when it was not. In the pre-lab, we assumed that the resistance of the photocell was 20 kΩ when the light was on and 5 kΩ when it was off. The measured values are shown below in Figure 3.

Figure 3: Measured voltages across the photocell and the LED, respectively

When the photocell was exposed to light, the LED remained off. However, when the light was cut off from the photocell, the LED lit up. This is due to the fact that the photocell's resistance is much higher when it is exposed to light. As a result, the photocell behaves like a on/off switch that is regulated by light. A video of this process is shown below.

CONCLUSION

In this experiment, we became familiar with two circuit elements: the BJT and the photocell. This will be a valuable lesson because these are commonly used in circuits. Moreover, this experiment allowed us to apply what we learned about KVL and voltage division.

Furthermore, we compared these measured values to the values that we found in the pre-lab by calculating the percent difference between the expected values and measured values. We found the percent difference to be 10.6 percent for when the light was off and 94.0 percent when the light was on. We noticed that the percent difference for when the light was on was incredibly high. We believe this may be due to the fact that resistance of the photocell was not actually 20 kΩ when it was exposed to light. It also could have been due to a mathematical error in our calculations.