ELEG 205 Analog Circuits Laboratory Manual Fall 2016

ELEG 205 Analog Circuits Laboratory Manual Fall 2016 University of Delaware Dr. Mark Mirotznik Kaleb Burd Patrick Nicholson Aric Lu Kaeini Ekong 1

Table of Contents Lab 1: Intro 3 Lab 2: Resistive Circuits 10 Lab 3: Op Amps 14 Lab 4: Capacitors 19 Lab 5: Phasors and Passive Filters 25 Lab 6: Active Filters 29 2

Lab One: Introduction Lab reports are to be submitted separately and in paper. Components: Three LEDs 100 Ω Resistor 1 kω Resistor 100 kω Resistor Jumper Wires MultiMeter Digilent Board & Software (Waveforms) If you don t have these parts, go to Evans 127. A multimeter can be bought online or at Home Depot, you will need one for the rest of your college career. Waveforms software: http://store.digilentinc.com/waveforms-2015-download-only/ Click the Download Here button Then click the link that matches with your operating system in the v3.3.5 category Keep this software, you will need this software for all of the labs and labs in later classes 3

Procedure: Multimeters 1. We ll start with an introduction to multimeters. If you do not have one, buy one: you ll need it every year in this major. There are multimeters for use in Evans 134, but they are not portable. Your multimeter should look a little something like this: Yours may have different settings or a slightly different layout, but they are all operated in a similar fashion. 2. You only need to know how to use three settings on the multimeter for now: DC voltage is measured using any setting under this symbol: DC current is measured using any settings under this symbol: Resistance is measured using any setting under this symbol: 4

Digilent Board & WaveForms Software 3. Now turn to the Digilent EExplorer board: You should have check one out from Evans 127 by now. If you haven t, go right now. This is where you will be building and testing all the circuits for the labs this semester and in other classes next semester. Columns are labeled alphabetically and rows are labeled numerically. 5

4. Place wires in two different holes in the same row. Set the multimeter to measure resistance and measure the resistance between the two holes in the same row. Record the measurement in your lab report and the units. In the case the resistance is too high to measure, your multimeter may return OL, a one followed by no other digits, dashes for each digit, etc.. 5. Then measure the resistance between two holes in the same column. Record the measurements and units. Make sure you do not touch the leads with your fingers, this will cause the multimeter to measure the resistance between your fingers instead. 6. Measure and record the resistance between two holes in different rows & columns and record the units. 7. Connect the two rows from part 6 with a wire. Then measure and record the value and setting. 8. Based on these measurements, how are the rows and columns connected to each other in the breadboard? A note about the red and blue columns: all of the holes are connected in the column direction, not row direction. These are useful in future labs to give power to multiple devices. (i.e: all the holes in one red column are connected to each other, all the holes in one blue column are connected to each other, but these columns are NOT connected to the other red and blue columns within the breadboard.) Additionally, holes that are marked with a small arrow are connected to the internal ground of the board. All voltages produced by the board are in reference to this ground. Whenever a component is to be connected to ground, we mean connect it to one of these holes. The voltage supplies on the board are already connected to ground, so you don t have to connect those to ground. 6

Connect the breadboard to your computer and open up the Digilent Waveforms software. Click the Supplies button. Turn the board power switch on. The following window should open up: 9. Press the green triangle button next to Supplies to turn the power supplies on. Change the positive supply setting to 5 V and measure this voltage with your multimeter. Be sure to change the setting on the multimeter to an appropriate value. You can measure this voltage by placing one probe in one of the 6 holes next to VP+ and the other probe in a ground. Does your measurement match the setting on the board? Record the voltage you read. (If the sign is flipped, don t worry, it means you have your probes mixed up. Passive sign convention is applied here.) 7

The only thing you need to know about this supplies page is in the picture below: The voltage supplies in waveforms correlate with different pins on the board: Breadboarding 10. Familiarize yourself with the resistor color code. Here is a picture, for additional help, here is a video. https://www.youtube.com/watch?v=o-b_awt-7fum 8

11. All resistors have a tolerance given as a percentage. The 100 Ω resistor you are using most likely has a tolerance of 5%, meaning the manufacturer guarantees the resistance between 95 Ω and 105 Ω. Measure the resistance of the 100 Ω resistor and record. 12. Next, turn off the power switch on the board. (As a general rule, turn off the power switch whenever you are working directly on the board, and turn it back on when you are ready to make measurements.) Assemble the following circuit on the breadboard, using the 100 Ω resistor, an LED, and VP+ in place of the power supply. There is a flat part on the physical LED bulb, make sure it correlates with the line of the diode in this schematic. Otherwise it won t work. 13. Measure the voltages across the resistor and LED and record them in the lab report. To measure voltage, place the probes so that one probe is on each leg of the component. Also record whether or not the LED is lit and the brightness of the LED. 14. Measure the current traveling through the Resistor. To do this, you need to ensure all current is flowing in series with the multimeter. One way you can accomplish this is to remove the jumper wire connecting the resistor and LED. Making sure your multimeter is set to read current. Place one lead on the resistor and the other lead on the LED. The LED should light up and the meter should read a current. Record this value. 15. Repeat steps 11-13 with the 1k Ω and 100k Ω resistors and record the resistance of the resistor, voltage across the resistor, and voltage across the LED for both resistances. Make sure you build a new circuit each time. You should have three circuits on your board when finished. Please bring all three circuits to lab and show to the TA for credit. 9

Lab Two: Resistive Circuits Lab reports are to be submitted separately and in paper. Components: Two LEDs Five 1kΩ resistors 100Ω resistor 3.3kΩ resistor If you don t have these parts, go to Evans 127. Procedure: Voltage Divider 1. Derive the Voltage Divider equation for the series combination shown below. Show your work. A diagram is provided below. Assume V 1 is the voltage across R 1, V 2 is the voltage across R 2, and I is the current through both resistors. 2. Make R 1 = 1 kω, R 2 = 3.3 kω, and V s = 5V. Calculate the voltage across and current through both resistors and record. 3. Build this circuit on your breadboard. Measure the voltage across and current through both resistors and record. How do your calculations and measurements compare? Provide a table in your report for measured versus calculated values and the % error. If they do not agree, what could be responsible? Current Divider 10

4. Derive the Current Divider equation for the parallel combination shown below. Show your work. A diagram is provided below. Assume I 1 is the current through R 1, I 2 is the current through R 2, and V s is the voltage across both resistors. 5. Make R 1 =1 kω, R 2 =3.3kΩ, and V s =5V. Calculate the current through and voltage across each resistor. 6. Build the circuit with your breadboard. Measure the current through and voltage across each resistor. How do your calculations and measurements compare? Provide a table in your report for measured versus calculated values and the % error. If they do not agree, what could be responsible? 7. For a visual aid, place a LED in each branch as in the figure below. This will help you visualize the current divider. Resistor Combinations 8. What is the largest resistance you can make using all of the resistors listed in the parts list? 9. What is the smallest resistance you can make using all of the resistors in the parts list? 10. Now, construct the circuit shown below: 11

Measure and record the voltages across the 3.3 kω and the 100 Ω resistors. 11. What is the equivalent resistance of the combination of all resistors in the circuit? 12. What would be the power absorbed by this equivalent resistor? Now, consider the following circuit: 13. What value should the unlabeled resistor be to make this circuit have the same equivalent resistance as the one from Question 10? 12

Design Problem The 3V battery to your drill suddenly dies while assembling a new desk for your dorm room. You have a 5V battery still but unfortunately the drill will be fried if you use the 5V battery. With the resistors from the parts list, design a voltage divider circuit to supply the drill with the 3V (± 0.2V) it requires. (Hint: R1 and R2 may or may not be a combination of resistors) Draw a schematic of your circuit, write down the resistances of R1 and R2, and the voltages across R1 and R2. Also, keep this circuit on your board for your Lab Demo. 13

Lab Three: Op Amps Lab reports are to be submitted separately and in paper. Components: 22 μf Capacitor Six 10 kω Resistors Four 20 kω Resistors 100 Ω Resistor Four RC4558 Op-Amps If you don t have these parts, go to Evans 127. Procedure: Difference Amplifier 1. Derive the output voltage to input voltage relationship of the circuit below using your knowledge of ideal operational amplifiers. Keep the terms R 1, R 2, R 3, R f, and R L,throughout the derivation. Show your work. 14

2. If R 1 = R 2 = R 3 = R f = 10 kω, and R L = 20 kω, calculate what V out would be in terms of V 1 and V 2. 3. Build the above circuit using: R 1 = R 2 = R f = 10kΩ, R L = 20kΩ, V REF1 = 1.5V, V REF2 = 2V. Leave this circuit completed on your board to be used in a later problem. 4. Measure V out 5. Compare your measured value to the calculated value, by percent difference. Summing Amplifier 6. Derive the output to input voltage relationship of the circuit below using your knowledge of ideal operational amplifiers, nodal analysis and voltage divider techniques. Show your work. 15

7. If R 1b, R 2b = R express the new output to input voltage relationship. 8. Build this circuit by borrowing the V ref1 voltage source from the previously built circuit to supply this one. Use 2V for your new V ref2 value, NOT the 3.3V V cc depicted in the schematic. Use R 1b = R 2b = 10kΩ, R fb = R Lb = 20kΩ. Leave this circuit completed on your board to be used in a later problem. 9. Measure the value for V out using V mtr on the board. 10. Compare the measured value to the calculated value, by percent difference. 16

Cascaded Amplifiers 11. Build the circuit above using your two previously built op amp circuits. 12. Use 1.5V, 2V, and 3.3V, as V ref1, V ref2, and V cc respectively. 13. Calculate and measure the total output voltage,, using your derived equations and a multimeter.additionally, write out a general formula for the output voltage of the second amplifier. 14. Leave connected to demonstrate to the TAs. 17

Op-Amp Design Problem 12. Design, measure and test an op-amp circuit that performs the following operation Where V 1 and V 2 are input voltages and V out is the output voltage. Show your work as to how you derived the resistor values you used. Do this before attempting to to build the circuit. Use resistor values greater than 1 kω. Test the circuit using at least 3 different combinations of V 1 and V 2. Provide a table in your lab report that gives the expected and measured results, and include a schematic of the circuit. 13. Leave this circuit connected to demonstrate to the TAs. 18

Lab Four: Capacitors Lab reports are to be submitted separately and in paper. Components: One LED Two 10 μf Capacitors 4.7 μf Capacitors 20 kω Resistor 10 kω Resistor 1 kω Resistor If you don t have these parts go to Evans 127. Procedure: Oscilloscope and AWG introduction 1. To begin, open up Waveforms and click on Scope to open up the oscilloscope. Also click on Wavegen to open up the Arbitrary Waveform Generator (AWG). You will be using both instruments simultaneously. The following screens should pop up. 19

2. In the Wavegen window, change the type to Square, the frequency to 1 Hz, amplitude to 2.5 V, and offset to 2.5 V. Leave symmetry and phase alone for now. 3. Next, build the following circuit on the board. Use AWG as the voltage source, and a 1 kω resistor. 4. Turn on the Waveform generator. You should see the LED blink on and off every second. 5. Now connect the oscilloscope. The scopes are all with respect to the internal ground of the board, and can therefore be treated like a multimeter. Place a wire in one of the scope 1 holes marked for DC. Place the other end of the wire at the connection of the resistor and the LED. This will allow you to measure the voltage across the resistor. Turn on the oscilloscope and record and measure the amplitude and period of the voltage. You can use the autoscaling function to get a better view of the waveform. 20

Additionally, you can use another probe (in say, channel 2) and place a probe at another point. This will allow you to measure voltage differences between two points by using the math operations on the oscilloscope. To do this, click add channel, Simple, and set up the math operation desired. This can be used to find voltage drops across specific components. Custom can be used for more complex operations, but is not necessary for these labs. Capacitors and TIme Constants 6. Build a circuit using a 10 microfarad capacitor and a 10 kohm resistor. Connect this circuit to the AWG. Change the period of the square wave to 2 seconds. 21

7. Use the oscilloscope to look at the voltage across the capacitor. Look at the waveform, and find where the voltage across the capacitor reaches 63% of its final voltage as it charges. The difference between this time and the time at which the voltage is applied to the circuit is the time constant. Record this time. 8. Why do we use 63% as the voltage for finding the time constant? 9. Calculate the time constant and compare this value to the measured time constant. 10. Use another probe and scope to measure AWG. Take a screenshot of your Waveforms displaying your AWG and the voltage across the capacitor. It should look something like the picture below. 22

11. Now place another 10 microfarad capacitor in parallel with the other capacitor. Repeat steps 7 and 10 for this new circuit. 12. Add another 4.7 microfarad capacitor in series with the capacitors from the previous circuit. Repeat steps 7 and 10, this time measuring the total voltage drop across the capacitors. 13. For the previous circuit, change the resistor to a 20 kohm resistor and measure and record the new time constant. Additionally, save a copy of the waveform as the circuit charges and submit it with the lab report. 23

Thevenin Equivalent Circuit 14. Next, construct the following circuit. Use a square wave ranging from 0 V to 2 V with a 2 second period in place of the voltage source. 15. Calculate the time constant for this circuit and record it in your lab report. Show your work. You may need to use Thevenin s Theorem to find the time constant. 16. Measure the time constant and compare to your calculated value. Design 17. Voltage dividers can be constructed using capacitors instead of resistors. Using the capacitors in the kit, create a voltage divider where the applied voltage splits 80/20. This means that the voltage across C1 is 80% of the applied voltage, and the voltage across C2 is 20%. Bring this circuit to the lab and record what capacitors you used to create the voltage divider. 24

Lab Five: Phasors and Passive Filters Lab reports are to be submitted separately and in paper. Components: Two 1 μf Capacitors 1 kω Resistor 20 kω Resistor 10 kω Resistor 100 Ω Resistor Two 500 Ω Resistors If you don t have these parts, go to Evans 127. Procedure: Concept 1. For the provided time varying voltage, V 1 (t) = 16 sin (3πt + 30 ) V, determine the following: a. Amplitude b. Phase c. Frequency (Hz) d. Period (s) e. The equivalent cosine function expressing V 1, then list the cosine function in phasor form. 2. Using V 2 = 33-70, does V 1 lag or lead V 2, and by how much? Answer in terms of phase. Phasors 3. Build a RC circuit with a 1kΩ resistor and a 1μF capacitor in series with one another. Use AWG1 to power the circuit. Keep this circuit on your board for use in step 8. 4. Set AWG1 to provide a 1 khz sine wave with an amplitude of 2.5 V, and an offset of 0 V. 25

5. Use an oscilloscope to measure the voltage across the capacitor. Display both Awg and scope1 on the same screen. Take a screenshot. 6. Measure and record the time difference between the input signal (AWG1) and the output signal (Scope1). Then, convert the time difference into the phase shift. You can use the equation φ = t T * 360, where φ is the phase shift, t is the time difference, and T is the period. 7. Build another RC circuit, this time with a 100 Ω resistor and a 1 μf capacitor. 8. Measure and record the phase angle. 9. Use the oscilloscope to measure the voltages across the capacitors in both of the circuits. You should see both waveforms on the oscilloscope at the same time. Take a screenshot. 10. Finally, measure and record the phase angle between the two capacitors. 11. Build the following circuit: Filters 12. Set the input voltage to a 1 Hz sine wave with a 5 V amplitude and an offset of 0 V. 13. Measure the input voltage and the voltage on the second capacitor (C2) using the oscilloscope. 14. Record the maximum amplitude of the output voltage on the capacitor. 15. Change the frequency to 10 Hz, and record the maximum amplitude again. Do this for 10 Hz, 100 Hz, 500 Hz, 1 khz, and 5 khz. 16. Find the frequency that produces the highest amplitude, and record both the frequency and amplitude in your lab report. 26

17. What kind of filter is this? How do you know? Design One of the major problems in signal processing is electronic noise. Your challenge is to build a circuit that eliminates all other frequencies except the 2 KHz signal you are using to transmit information. Tune the following circuit to accomplish this. You may adjust any of the resistor or capacitor values, as long as you have the parts to do so. You can read ahead to the next lab, which includes instructions on how to use the network analyzer instrument on the Digilent board, which may be helpful in finishing this lab. Include a schematic drawing in your lab report and bring your circuit into the demo. 27

Lab Six: Active Filters Lab reports are to be submitted separately and in paper. Components: Three 1 μf Capacitors Three 10 kω Resistors Two RC4558 Op-Amps If you don t have these parts, go to Evans 127. This is a long lab, we recommend you work on this sooner rather than later. Procedure: 1st Order Passive Filter 1. Build a RC circuit with a 10 kω resistor and a 1 μf capacitor. Use AWG1 to power the circuit. 2. Solve for the transfer function (Vout/Vin) using AC circuit analysis and record it in the lab report. 3. Using your transfer function, find the -3 db frequency for this circuit. Record this in the lab report and keep this number in mind for future parts of the lab. 4. Set AWG1 to provide a 1 KHz, 1 V peak to peak sine wave centered around 0 V. 28

5. Measure the input waveform and the voltage across the capacitor with the oscilloscope. Make sure the input waveform is in Channel 1 and the capacitor output is in Channel 2. 6. In Waveforms, open the network analyzer instrument (by clicking the network button). Set the start frequency (labeled Start ) to 1 Hz and the stop frequency (labeled Stop ) to 1 MHz. 7. Click run. The top graph displays Vout/Vin as a function of frequency, and the bottom graph displays the phase difference between Vout and Vin as a function of frequency. We are primarily interested in Vout/Vin. --A quick note: The units on the y-axis are decibels (db) and follow a logarithmic scale. The actual graph is known as a Bode Plot. Both decibels and Bode Plots will show up in other classes. 8. You should also be able to see the -3 db point on the graph. Is this the same value as what you calculated in part 3? 9. Click File -> Export to save the data as a.csv file in your computer. You can open this file in Excel or any other spreadsheet application. 1st Order Active Filter 10. Connect a non-inverting op amp based amplifier to the output of the previous step. 11. Set R1 and R2 to create a gain of 2.5 within the Op-Amp portion of the circuit(use a resistor or resistor combination from your kit that allows you to achieve a gain of 2.5). 12. Run the network analyzer on this new circuit and save the data as a.csv file. 29

13. Compare the results to the passive filter from earlier. What is the -3 db value of the new filter? How do they perform differently? What are the advantages of this active circuit over the passive circuit? 14. Plot the results from the passive and the active circuits on the same graph in Excel and turn this in with the lab report. If you already know how to plot two sets of y values on the same graph, skip ahead to step 21. Leave this circuit intact; you will need it later in the lab. 15. Open your passive filter.csv file in Excel. Copy your x values, in this case frequency, and paste them in a new column. 16. Repeat this for your first set of y values, in this case Channel 1 Magnitude of your passive filter data. Rename the column Passive. 17. Repeat for as many sets of y as you have, in this case you only have two sets of y. Rename the second set to Active. 18. Highlight all three columns. Click Insert-Charts-Scatter Plots-Scatter with Smooth Curves. 30

19. Double click on x-axis and change to a log-scale. 20. Double click on the Chart Title and rename it. Higher Order Filters 21. The circuit above is a second order filter. Use 10 kω resistors for R3 and R4 and 1 μf capacitors for C1 and C2. Adjust R1 and R2 so that the amplifier has a gain of 1. 22. Run the spectrum analyzer on this circuit and record the -3dB point. Save the data as a.csv file. 23. Now attach the output of the first order filter you built in steps 10-14 to the input of the second order filter you just created. This will create and even more efficient third order filter. 31

24. Run the network analyzer one last time, calculate the -3dB point, and save as a.csv file. 25. Plot all three active filter transfer functions on the same graph and submit this with the lab report. You will notice some noise at higher frequencies. Disregard this data and simply calculate the slope of the initial drop off. 26. Calculate the slope of each order of amplifier in db/decade. Below is a formula you can use to calculate the slopes. y2 y1 x2 Log( x1) Design Problem http://www.electronics-tutorials.ws/filter/filter_7.html This design problem is very similar to the one from the last lab. Your goal is to make a bandpass filter with a center frequency of 2 khz. The filter must be an active second order filter, and the input and output amplitudes must be the same (to a reasonable degree). You may look up designs online to use for this problem; a link that you can use is included above. Include a copy of a labeled schematic of the circuit and bring this circuit to the demonstration. Set up the circuit so that we can test it during the lab demo. 32