ELEG 205 Analog Circuits Laboratory Manual Fall 2017 University of Delaware Dr. Mark Mirotznik Kaleb Burd Aric Lu Patrick Nicholson Colby Banbury
Table of Contents Policies Policy Page 3 Labs Lab 1: Intro duction 4 Lab 2: DC Circuits Part 2 11 Lab 3: Op Amps 15 Lab 4: Transient Circuits 20 Lab 5: AC Circuits 26 Index Component Fact Sheets 31 Sample Lab Report 33 2
Lab Policies I. Every lab report should have the following sections: A. Heading - to identify who you are and what lab it is B. Purpose - a brief synopsis of the topics discussed in the lab C. Results - all of the data collected and work performed D. Design (for Labs 2-5) II. Demos take place Tuesday and Thursday between 3:30 pm and 7:30 pm. You can sign up here. You will have the same demo time every week unless specifically told by a TA otherwise. III. Demos last five minutes and consist of demonstrating a circuit you were required to keep on the board and answering two questions to test your understanding of material covered in the lab. IV. All Labs are weighted equal but may be out of a different amount of points. Demos are worth approximately one third of your lab grade. V. If you are tardy to your demo, there will be a half credit deduction on your demo grade. If you are late by more than 15 minutes to your scheduled demo time, you will receive a zero for the lab. VI. Lab reports are to be submitted on sakai by 11:55 pm the Monday night before demos. If submitted late, you will receive a zero for the lab. 3
Lab One: Introduction Lab reports are to be submitted on sakai by 11:55 pm the Monday night before demos. Components: One LED One 100 Ω Resistor One 1 kω Resistor One 100 kω Resistor Jumper Wires MultiMeter Digilent Board & Software (Waveforms) If you don t have these parts, go to Evans 129. 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. They can be purchased online or at any home improvement store. There are multimeters for use in the isuite, but they are not portable. Your multimeter should look a little something like the image below. 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. Follow this link to download the waveforms software http://store.digilentinc.com/waveforms-2015-download-only/ 4. Click the Download Here button and then choose the link that matches with your operating system under Latest Downloads (3.6.8). Keep this software, you will need it in later labs and in other classes as well. If you have any difficulty with downloading the software, contact a TA immediately. 5. Now turn to the Digilent EExplorer board: 6. You should have check one out from Evans 129 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
7. Measure and record the resistance between A1 and A5 (two holes in the same column). To do this, you may have to place a wire in each hole, touching the leads of the multimeter to the alternate end of each wire. In the case the resistance is too high to measure, your multimeter may return OL, a one followed by no other digits, or dashes for each digit. 8. Now measure and record the resistance between A1 and B1 (two holes in the same row). 9. Measure and record the resistance between A1 and B2 (two holes in different rows & columns). 10. Connect Row A to Row B with a wire and again measure and record the resistance between A1 and B2. 11. Based on these measurements, how are the rows and columns connected to each other in the breadboard? 12. 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. (The holes in the red column are connected to each other and the holes in the blue column are connected to each other, but these columns are NOT connected to each other.) 13. Additionally, holes that are marked with a small line/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 connected to ground, connect it to one of these holes. 6
14. Connect the Digilent Board to your computer and a power outlet. Then open up the Digilent Waveforms software. Click the Supplies button on the left. Turn the physical board power switch on. The following window should open up: 15. Press the green triangle button next to Supplies at the top to turn the power supplies on. Change the positive supply setting to 5 V. The voltage supplies in waveforms correlate with different pins on the board: 7
Breadboarding 16. 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 17. 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. 18. 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. 19. Diodes must be placed in a circuit in a certain orientation to work. Make sure the side of the LED with the shorter leg and the flat part of the body corresponds to the flat line in the LED schematic signal. 8
20. 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 (dim, bright, etc). 21. Measure the current traveling through the Resistor. To do this, you need to ensure your components are in series with the multimeter. One way you can accomplish this is to set your multimeter to read current and then connect the resistor and LED with your multimeter instead of using a jumper wire. The LED should light up and the meter should read a current. Record this value. 22. Replace the 100Ω resistor with a 1kΩ resistor. Remeasure and record: a. Resistance of the resistor b. Voltage across the LED c. Voltage across the resistor d. Current through the resistor e. Brightness of the LED 23. Rebuild the circuit again, this time replacing the 1kΩ resistor with the 100kΩ and take the same measurements listed above. Please bring the circuit and all three resistors to the demo and show to the TA for credit. 24. Which parameter(s), Resistance, LED Voltage, Resistor Voltage, and/or Current, may be the cause of the change in the Brightness of the LED, and which is/are not. Look for strong correlations. Explain. 9
Summary The Results section of your Lab Report should include the following: Table for measured resistances for the bread board Explanation of breadboard connections Table for the three LED resistor circuits (100Ω, 1kΩ, 100kΩ) that includes Resistance of the resistor Voltage across the LED Voltage across the resistor Current through the resistor Brightness of the LED Explanation to cause of LED brightness 10
Lab Two: DC Circuits Lab reports are to be submitted on sakai by 11:55 pm the Monday night before demos. Components: Five 1kΩ resistors One 2.2kΩ resistor One 100Ω resistor One 6.8kΩ resistor One 470Ω resistor If you don t have these parts, go to Evans 129. 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 = 2.2 kω, and V s = 5V. Calculate the voltage across each resistor and current through each resistor 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? %EEEEEEEEEE = 100 CCCCCCCCCCCCCCCCCCCC EEEEEEEEEEEEEEEEEEEEEEEE CCCCCCCCCCCCCCCCCCCC 11
Current Divider 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=2.2kΩ, 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? Complex Circuitry 7. Using either Nodal or Mesh Analysis and show your work to find V x. 8. Now build the circuit on your breadboard and measure V x. 9. Compare your calculated value and experimental value using percent difference. 12
Design Problem Build the above circuit. Pick a value for R so that as little current flows as possible through the 100 Ω resistor ( < 1 ma ). Use VP+ for the source and connect Vtmr1 to one side of the 100Ω resistor and Vtmr2 to the otherside. Draw a schematic of your circuit, write down the resistance of R, and the current through the 100Ω resistor. Also, give a brief explanation to how you solved the design challenge. Keep this circuit on your board for your Lab Demo. (Keep the design problem circuit on your board to show the TAs) 13
Summary The Results section of your Lab Report should include the following: Voltage Divider Calculation derivations Table of experimental / calculated / %error values Current Divider Calculation derivations Table of experimental / calculated / %error values Complex Circuitry Nodal or Mesh analysis work Calc Vx / Exper Vx / %error Design Problem Circuit schematic Resistance and current values Short explanation of how you tackled the problem 14
Lab Three: Op Amps Lab reports are to be submitted on sakai by 11:55 pm the Monday night before demos. Components: Six 10 kω Resistors Three 20 kω Resistors Two LM833P Op-Amps (One op-amp chip, see index) If you don t have these parts, go to Evans 129. Procedure: Difference Amplifier 1. Derive the output voltage to input voltage equation of the circuit below using your knowledge of ideal op-amps. Keep the terms R 1, R 2, R 3, R f, and R L,throughout the derivation.show your work. 2. Make R 1 = R 2 = R 3 = R f = 10 kω, and R L = 20 kω. Calculate V out would be in terms of V 1 and V 2. 3. Build the above circuit using: R 1 = R 2 = R 3 = R f = 10kΩ, R L = 20kΩ, V 1 = 2V, V 2 = 5V. To supply these voltages, use V ref1 for V 1 and use V ref2 for V 2. This circuit is used in a later problem. Do not disassemble. 4. Measure V out 5. Compare your measured value to the calculated value, by percent difference. 15
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. 7. Make R 1 = R 2 = 10kΩ, R f = R L = 20kΩ. Calculate V out in terms of V 1 and V 2. 8. Build the above circuit using: R 1 = R 2 = 10kΩ, R f = R L = 20kΩ, V 1 = 1V, and V 2 = 2V. Again, use V ref1 for V 1 and use V ref2 for V 2 to supply these voltages. This circuit is used in a later problem. 9. Measure V out 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. Set V 1 = 2V, V 2 = 1V, and V 3 = 3.3V using V ref1, V ref2, and V cc respectively. 13. Using your simplified equations for the previous two amplifiers, derive an equation relating V 1 = 2V, V 2 = 1V, and V 3 = 3.3V using V ref1. 14. Calculate the total output voltage using your formula. 15. Measure the output of the amplifier and compare using percent difference. 17
Design Problem 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 and use V mtr1 to measure output. Provide a table in your lab report that gives the expected and measured results, and include a schematic of the circuit. Also, give a brief explanation to how you solved the design challenge. (Keep the design problem circuit on your board to show the TAs) 18
Summary The Results section of your Lab Report should include the following: Difference Amp Derivation Simplified Derivation Real/Calculated Values and percent difference Summing Amp Derivation Simplified Derivation Real/Calculated Values and percent difference Cascading Amp Derivation Real/Calculated Values and percent difference Design Problem Brief Explanation Resistor value derivations Schematic of circuit Table of Results 19
Lab Four: Transient Circuits Lab reports are to be submitted on sakai by 11:55 pm the Monday night before demos. Components: One LED One Diode One 10 μf Capacitor One 1 μf Capacitors One 20 kω Resistor Two 10 kω Resistor One 2.2 kω Resistor One 1 kω Resistor If you don t have these parts go to Evans 129. Procedure: Oscilloscope and AWG introduction 1. To begin, open up Waveforms and click on Scope to open up the oscilloscope. The following screen should pop up. 2. Also click on Wavegen to open up the Arbitrary Waveform Generator (AWG). The following screen should pop up. You will be using both instruments simultaneously. 20
3. In the Wavegen window, change the type to Square, the frequency to 1 Hz, amplitude to 2.5 V, offset to 2.5 V, and symmetry to 50%. Leave phase alone for now. 4. Next, build the following circuit on the board. Use AWG as the voltage source, and a 1 kω resistor. 5. Turn on the Waveform generator. You should see the LED blink on and off every second. 21
6. 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 view the voltage across the resistor. You can use the autoscaling function to get a better view of the waveform. Capacitors and TIme Constants 7. 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. 8. Use the DC pin of 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. 9. Why do we use 63% as the voltage for finding the time constant? 10. Calculate the time constant and compare this value to the measured time constant using percent difference. 22
11. 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. 12. Now replace the 10uF capacitor with a 1uF capacitor. Again calculate the time constant, measure the time constant, compare them using percent difference, and take a screenshot of the waveform. 13. For the previous circuit, change the resistor to a 20 kohm resistor. Your circuit should still contain the 1uF capacitor. Again calculate the time constant, measure the time constant, compare them using percent difference, and take a screenshot of the waveform. 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 using percent difference 23
Design Problem Design a RC circuit that holds 55 C of charge and has a time constant of about 800 ms. You may use any capacitors, resistors, or any combination of these that are listed in your parts kit. Keep the design problem circuit on your board to show the TAs. 24
Summary The Results section of your Lab Report should include the following: Time Constant Explanation Capacitive Circuit (10uF, 10 kohm) Calculations Table of calculated time constant, measured time constant, and percent difference Screenshot of waveform Capacitive Circuit (1uF, 10 kohm) Calculations Table of calculated time constant, measured time constant, and percent difference Screenshot of waveform Capacitive Circuit (1uF, 20 kohm) Calculations Table of calculated time constant, measured time constant, and percent difference Screenshot of waveform Thevenin Equivalent Calculations Table of calculated time constant, measured time constant, and percent difference Design Problem Schematic Explanation Circuit 25
Lab Five: AC Circuits Lab reports are to be submitted on sakai by 11:55 pm the Monday night before demos. Components: One 10 μf Capacitor Two 1 μf Capacitors Two 10 kω Resistors Two 1 kω Resistors One 2.2 kω Resistor One 4.7 kω Resistor One LM833P Op-Amp If you don t have these parts, go to Evans 129. Procedure: Filters 1. Build the circuit below with a R1 = 10 kω resistor, C1 = 1 μf, R2 = 1 kω, and R3 = 4.7 kω. Use AWG1 to power the circuit, and drive the op-amp with +/- 9V. 26
2. Solve for the transfer function (Vout/Vin) using AC circuit analysis and record it in the lab report. Keep everything in terms of R1, R2, etc.. 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. In Waveforms, open the network analyzer instrument (by clicking the network button). Set the start frequency (labeled Start ) to 10 Hz and the stop frequency (labeled Stop ) to 1 MHz. Use the network analyser to measure the input waveform as well as the voltage across the capacitor with scopes 1 and 2. 5. 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. 6. You should also be able to see the -3 db point on the graph. Compare this value to your calculate -3dB value from earlier using percent difference. 7. Take a screenshot of the network analyzer and include this in you report. 27
Superposition 8. Set V 1 to 1V at 10 Hz and set V 2 to 3.3V at 20 Hz. Calculate the voltage across R2. Record the calculation in phasor form. 9. Build the circuit and measure the voltage across R2. Take a screenshot of the waveform on the oscilloscope. Hint, you may have to use the Math function on the oscilloscope to measure the voltage across the resistor. 28
Design Problem For the design problem, you will be using two inputs: V 1(t) = cos( 1t) at 10 khz, and V 2(t) = cos( 2t) at 20 khz. Both inputs are sinusoidal waves. Design a circuit that takes these two voltages as inputs and produces V out(t) = 2*cos( 1t) + cos( 2t + /4). Use schematics from previous labs to help. Include a schematic of your circuit and a screenshot of the circuit output in your lab report. For reference, your output should look something like this: (Keep the design problem circuit on your board to show the TAs) 29
Summary Filters Derivation for Transfer Function Calculation for -3dB point Table for measured, calculated, and percent difference of -3db values Bode Plot screenshot Superposition Calculations Screenshot of Waveform Design Problem Schematic Output Screenshot Explanation 30
Components Resistor Units: Ohms ( Ω ) Purpose: To provide a specific resistance between two parts of a circuit Schematic Symbol: How to Use: Image of Component: Place each lead into its own distinct hole to create a path for current to travel between said two holes. Purpose: To transform current into light LED Schematic Symbol: Image of Component: How to Use: Place the cathode lead ( the longer lead or the lead on the flat side of the LED ) into the more negative of the two hole you are connecting and the anode in the more positive hole. If the LED does not light up, try flipping the leads as you may have the polarities wrong. If it does still not light up, you may have a defective LED. 31
Capacitor Units: Farads ( F ) Purpose: Store charge. Schematic Symbol: Image of Component: Electrolytic (polarized) capacitor: : Ceramic capacitor How to Use: Place each lead into its own distinct hole to create a path for current to travel between said two holes. If the capacitor is an electrolytic or polarized capacitor, make sure the negative end is where the current flows out and the positive end is where current flows in. Op Amp 32
Purpose: To provide a controllable gain based on a differential between inputs Schematic Symbol: Image of Component: Pin Out: How to Use: Supply 9V to V CC+ and -9V to V CC- to power the device.make sure you insert the op amp into the breadboard so that it straddles the center ridge, as in the image below. There are two op amps in 1 chip. 33
Sample Lab Format Lab Title <Name> <Date> <lab number> Purpose: Give a very brief description of the topics discussed in the lab Example: To prove basic circuit analysis techniques by comparing calculated and measured values Results: Present the data in an organized fashion and follow with text to explain the data. Example1: If you need to make a table Circuit 1 Calculated Measured Percent Error 5V 4.75V 5% After calculating the values with circuit analysis techniques, build the circuit, and measuring actual values, the percent difference was calculated to be 5%. This is well within reason and can be contributed to the tolerances of the components. Example2: If there is only one value needed 34
Output Voltage: 10V After building the circuit, the measured value was as expected. Example3: Derivations and Calculations Neatly recopy your work onto a new piece of paper. Take an image and include in your lab report. Only use this method if work it is required, otherwise use example1 or example2. Points WILL be taken off if your answers and tables are reported by hand. Example4. Excel Graph Noise 1 and 2 both have linear trends. However, Noise 2 does not increase at the same rate as Noise 1. Design: 35
*For Labs 2-5 **Schematics are allowed to be NEATLY hand drawn Example1: Resistor Values Schematic R1 R2 R3 10Ω 15Ω 100Ω Based on the parameters given in the problem, R1, R2, and R3 were calculated using current divider. R2 and R3 are summed to give the correct voltage for the output load. 36