Before entering my office, please turn your cell phone off.
The textbook "Design with Operational Amplifiers" by Sergio Franco is available in a much cheaper softcover international edition. Some of the cites selling this edition are listed at AbeBooks.com. To my knowledge, these books cannot be "sold back" to the Georgia Tech bookstore.
Circuit diagrams of operational amplifiers:
LM741 A workhourse general purpose op amp for many years. Not the best for new designs requiring high performance.
TL071 An example of a high performance general purpose op amp.
uA749 This is a very old op amp and is no longer made.
Click here to read a paper on the application of superposition to circuits containing controlled sources. The circuits courses say that you can't, but you can.
Here, here, and here are good tutorials on stain gauges.
Supplementary Class Notes - Chapter 1
Supplementary Class Notes - Chapter 2
The GTA for the class is Diana D. Fuertes. Her email address is:
dianafuertes@gatech.edu
Laboratory Design Project VIII - Because we have only one microphone setup in the lab, it is possible that more than one group will be ready to perform this part of the compressor/limiter experiment at the same time. In this case, it is OK if two groups join together using only one of the two compressor/limiter circuits. (You must have demonstrated previously that both circuits operate properly.) Each member of the two groups should talk into the microphone to see the operation of the circuit.
Assignment 1
PDF scan of Chapter 1 problems.
Problem 1.15
Set v_O - 4 = v_P to solve for v_O
Problem 1.16
For part (a) the 3k and 2k resistors have no effect on the answer. For part (b) make a Thévenin equivalent circuit, or use current division to solve for the fraction of the source current that flows in the original resistors of the circuit. (The latter is the easiest, just remember that the op amp has a virtual short between its inputs when using current division.)
Problem 1.18
Calculate v_P and v_N in terms of v_O and solve for v_O. For part (b) make a Thévenin equivalent circuit.
Problem 1.22
Calculate v_P in terms of v_I using voltage division for the voltage divider formed by kR_3 and (1-k)R_3. Use superposition of v_I and v_P to solve for v_O.
Problem 1.24
Solve for the output voltage of OA_2 in terms of v_O. Use this to solve for v_P for OA_1 and set this equal to v_I.
Problem 1.31
For the v_N inputs, use superposition for v_1, v_3, and v_5. Make Norton equivalents of the 3 sources connected to the v_P input and use superposition.
Problem 1.43
Let the op-amp output voltage be v_O. At the v_P node, look to the left through R_1 and make a Norton equivalent circuit as a function of v_I. Do the same looking to the right through R_2 as a function of v_O. Use these circuits to write the equation for v_P. Use voltage division to solve for v_N. Set v_P = v_N to solve for v_O. Calculate the input current i_I by dividing the voltage across R_1 by R_1. Calculate the input resistance by dividing the input current by v_I. The v_I should cancel from the equation.
Problem 1.44
Use the inverting amp equation to solve for v_O as a function of v_I. Use the inverting amp equation to solve for v_O2 as a function of v_O. Use the equations to calculate v_O2 as a function of v_I. Calculate the current through R_1 and R_3 as functions of v_I. Sum the currents to solve for the input current. Divide v_I by the input current to get the input resistance. The v_I should cancel out.
Assignment 2
Problem 2.5
Use the inverting amp gain to solve for the voltage across R_3. Solve for the currents through R_2 and R_3 and take their difference to get i_O.
Problem 2.9
Use Norton equivalents and superposition to solve for v_P as a function of v_2, v_O, and i_O. Let v_P = v_L in the equation. Solve it for v_O. Use Norton equivalents and superposition of v_1 and v_O to solve for v_N. Let v_N = v_P. Solve it for v_O. Equate the two equations for v_O and solve it for i_O as a function of v_I1, v_I2, and v_L. Use the equation to solve for the conditon that i_L be independent of v_L. This is the condition that the circuit act as a perfect current source.
Problem 2.14
Use superposition of v_2 and v_L to solve for v_P1. Use superposition of v_1 and v_P1 to solve for v_O1 as a function of v_1, v_2, and v_L. Set this voltage equal to v_L + i_O x R_5. Solve this equation for i_O as a function of v_1, v_2, and v_L. Use the equation to solve for the conditon that i_L be independent of v_L. This is the condition that the circuit act as a perfect current source.
Problem 2.15
Use superposition of v_I and v_O2 to solve for v_O1. Set v_L = v_O1 and v_O2 = v_L + i_O x R_5. Use the equation to solve for i_L as a function of v_I and v_L. Use the equation to solve for the conditon that i_L be independent of v_L. This is the condition that the circuit act as a perfect current source.
Problem 2.16
Solve for v_O2 as a function of v_I and v_L. Set this equal to (I_L + v_L/R_2) x R_3. Use the equation to solve for i_L as a function of v_I and v_L. Use the equation to solve for the conditon that i_L be independent of v_L. This is the condition that the circuit act as a perfect current source.
Problem 2.21
Use superposition to solve for v_P as a function of i_S and v_L. Set v_N = v_P. Calculate i_L as (v_P - v_L)(1/R_1 + R_2). Use this equation to solve for i_L as a function of i_S and v_L. The equation should be of the form i_L = A_I x v_S - v_L/R_o, where R_o is the output resistance.
Problem 2.25
Use the inverting gain formulas and superposition to write the answer by inspection. I think the figure should have been drawn with v_P1 grounded and R connected from v_O1 to v_N2. You get the same answer either way.
Problem 2.39
This is tricky. Set v_P1 = v_1. Use superposition and the inverting and non-inverting formulas to write v_O2 as a function of v_1, v_2, and v_O. Set v_N2 = v_2. Use superposition of v2 and v_O2 to write the equation for v_P1. Set this equal to v_1. Eliminate v_O1 between the equations and solve for v_O as a function of v_1 and v_2.
Problem 2.52
Use superposition of V_REF and v_O to solve for v_N. Use voltage division to solve for v_P. Equate the two and solve for v_O.
Problem 2.54
Use the inverting gain formula to solve for v_O1 as a function of V_REF. Use superposition of V_REF and v_O1 to solve for v_O. Note that someone holds a patent on this simple little circuit.
Assignment 3
Problem 3.27
Write node equations at the upper nodes of C1 and C2. Uce the inverting op-amp gain formula for V_o.
Problem 3.28
Write a node equation at the node to the right of R1. Use the inverting op-amp bain formula for V_o.
Problem 3.33
Use superposition of Vi and Vo to solve for Vo1. Use the transfer function of the BPF to write Vo as a function of Vo1. The Vo will be on both sides of the equal sign. Solve for Vo.
Problem 3.37
Replace Vi, R, and mR with a Thévenin equivlent circuit. Use superposition to solve for VBP as a function of Vi and VLP. Write VLP as a function of VBP. VLP will be on both sides of the equal sign. Solve for VBP. Solve for VLP. Solve for VBP.
Assignment 4
Problem 4.11
Calculate ε using the equation on page 12 of the Filter Potpourri (FP). Use this to calculate h on page 14. Use the value of h and n = 5 to calculate the ai and the bi on page 15. Use these values to write TLP(s) as a product of 2 second-order LPFs and one first-order LPF. Use the low-pass to high-pass frequency transformation on page 6 to solve for THP(s). Note that the ai stay in the denominator when replacing p with 1/p in ths frequency transformation. Realize the filters using two KRC second-order HPF, one first-order HPF, and a variable gain stage with a 10 kΩ potentiometer to vary the gain from 1 to 10. To calculate numerical values for the elements, first specify values for the capacitors. Then calculate the resistor values. Convenient values of capacitors are 0.001 μF, 0.01 μF, and 0.1 μF if possible.
Problem 4.18
Use voltage division to solve for the voltage at the top of L. Note that the impedance (R + 1/Cs) is in parallel with Ls in the voltage divider. Use voltage division again to solve for the output voltage. Impose the condition R = sqrt(2L/C) for the transfer function to be Butterworth. The -3 dB frequency is equal to the resonance frequency for the Butterworth filter. Calculate the element values in the circuit for the specified -3 dB frequency. Realize the circuit with the GIC filter topology. Because a value for R is not given, the values for the other elements in the circuit must be expressed as a function of R.
Problem 4.20
Let V1 be the applied input voltage, V2 the voltage across Z2, Voa1 the output voltage of OA1, and Voa2 the output voltage of OA2. Calculate Voa1 in terms of V1. Use this to calculate the current I1 = (V1 - Voa1)/R that flows into the resistor from input to output of OA1. Calculate the admittance Y1 = I1/V1 seen looking into this resistor. Use superposition of Voa1 and V2 to write an equation for Voa2. Use superpositon of Voa2 and V1 to write an equation for V2. The equation has V2 on both sides. Solve it for V2. Solve for the current I2 = (V1 - V2)/R that flows from V1 to V2 through the resistor R. Calculate the admittance Y2 = I2/V1 seen looking into this resistor. The admittance seen looking into the input is Y1 + Y2. Solve for this and take the reciprocal for the impedance seen looking into the input.
Problem 4.21
This should be straightforward because all the element values are given.
Problem 4.25
Replace the switched capacitors with their equivalent resistances. Use superposition of V_i and V_o to solve for V_oa1. Use superpositon of V_i and V_oa1 to write an equation for V_o. The equation will have V_o on both sides. Solve it for V_o and put the transfer function obtained into the standard form for a notch filter. You must solve for C_1, C_2, and C_3 as functions of C_0 for part (b).
Project 2. Procedure Part 2 added. Here are some reference papers on analog computers: Paper 1, Paper 2, Paper 3.
The Class-D Amplifier. This document explains the theory of operation of the class-d amplifier and gives some of the design equtions. The object of this project is to design a mock class-d amplifier with op amps. You can omit the MOSFET output stage and take the output from the comparator. To obtain a non-inverting amplifier, you should interchange the two inputs of the comparator. This is because the MOSFET output stage has an inverting gain. The op amp used for the comparator should have a high slew rate. The passive filter at the output is to be replaced with a 4th-order active Butterworth low-pass filter. The switching frequency should be as high as possible, but not so high that the output of the comparator shows excessive slewing. The first step in this project is to design the basic circuit consisting of the triangle wave generator and the comparator. After this part is completed, design the filter and verify that a clean sine wave is obtained at its output. The last step is to add the integrator which provides negative feedback. The overall voltage gain of the amplifier should be 10.
| Homework Assignments for Fall 2005 | |
|---|---|
| Chapter in Book | Problems |
| 01 | 1.07, 1.12, 1.13, 1.15, 1.16, 1.17, 1.18, 1.19, 1.20, 1.21, 1.22, 1.24, 1.31, 1.33, 1.41, 1.43, 1.44, 1.74 |
| 02 | 2.5, 2.9, 2.12 (there are 2 equations to derive), 2.14, 2.15, 2.16, 2.21, 2.25, 2.39, 2.52, 2.54 |
| 03 | 3.2, 3.3, 3.6, 3.7, 3.8, 3.11, 3.15, 3.16 |
Design Project 1 Preliminaries
Problems 1.7, 1.12, 1.13, 1.15, 1.16, 1.17, 1.18, 1.19, 1.20, 1.21, 1.33, 1.41, 1.44, 1.74
Problems 2.5, 2.9, 2.12 (there are 2 equations to derive), 2.14, 2.15, 2.16, 2.21, 2.39, 2.52, 2.54
Problems 3.2, 3.3, 3.6, 3.7, 3.8, 3.11, 3.15, 3.16
Problems 3.20, 3.22, 3.26, 3.27, 3.28, 3.37
Homework Assignment 4 - Physical Characteristics of Op Amps, See Supplementary Class Notes Chapter 2
Laboratory Procedures and Instructions
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Fall 2001 FilesSample QuizzesThis page is not a publication of the Georgia Institute of Technology and the Georgia Institute of Technology has not edited or examined the content. The author of this page is solely responsible for the content.
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