Before coming into 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 strain gauges.
Supplementary Class Notes - Chapter 1
Supplementary Class Notes - Chapter 2
LTSpice is distributed by Linear Technology and has become the defacto standard for the "do it yourself" electronics and audio communities. Unlike other free versions, there are no limits on the number of devices in a circuit. Here are the links:
Linear Technology Software Page
LTSpice Tutorial
LTSpice Guide
The GTA for the class is James Barfield. His hours in the Tutotial Lab are Thursday from 9:00 am to noon. His email address is jbarfield3_at_gatech_dot_edu.
Project I - A Wien-bridge Oscillator
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 1.21
With the switch closed, v_P = 0. Use the gain formula for the inverting amplifier to solve for v_O. With the switch open, divide the source v_I into two equal parallel sources, one connected to R_1 and the other connected to R_3. Erase the lead that connects the two sources. There is no drop across R_3 so that v_P = v_I. Use superposition of the two input sources, the non-inverting gain formula, and the inverting gain formula to solve for v_O. Repeat the same procedure with the added resistor. You only need the inverting and non-inverting gain formulas to write the answer by inspection.
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.
Assignment 2
Problem 1.31
For the v_N inputs, use the inverting gain formula and superposition for v_1, v_3, and v_5 to solve for v_O. For the v_P inputs, make Norton equivalents of the 3 sources connected to the v_P input to obtain 3 current sources in parallel with a single resistor. Solve for v_P and use the non-inverting gain formula to solve for v_O.
Problem 1.43
Let v_I be the input voltage and v_O be the op-amp output voltage. At the v_P node, make a Norton equivalent of v_I,R_1 and v_O,R_2. Use the circuit obtained to write the equation for v_P. Use voltage division to solve for v_N. Set v_P = v_N and solve for v_O. Use the value of v_O to solve for v_N. Set v_P = v_N to obtain an equation for v_P in terms of v_I alone. 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. The answer is independent of the second op amp and the resistors connected to it. Use the inverting amp equation to solve for v_O2 as a function of v_O. Use the two equations to solve for v_O2 as a function of v_I. Use the equations to calculate the currents through R_1 and R_3 as functions of v_I alone. 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.
Problem 2.5
Let v_3 be the voltage across R_3. Solve for the currents into the v_N node in terms of v_I and v_3. Solve the equation for v_3 as a function of v_I. Solve for the currents through R_2 and R_3 and take their difference to get i_O.
Problem 2.9
At the v_L (v_P) node, make Norton equivalents of v_2,R_1 and v_O,R_2. Use the circuit obtained to write the equation for v_L in terms of v_2 and v_O. Solve the equation for v_L. At the v_N node, make Norton equivalents of v_1,R_3 and v_O,R_4. Use the circuit to write the equation for v_N. Set the equations for v_N and v_L equal to each other and solve the equation for v_O as a function of v_1, v_2, and i_O. Now use the equation for v_O in the first equation for v_L and solve the equation obtained for i_O as a function of v_1, v_2, and v_L. To obtain the condition that i_O be independent of v_L, set the coefficient of v_L equal to zero. This makes the circuit a perfect current source.
Problem 2.14
Make Norton equivalent circuits at the v_P1 node and write the equation for v_P1 as a function of v_2 and v_L = v_O2. 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 * 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.
Assignment 3
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. The figure in some books might have the (1 + δ) term on the wrong resistor. Note that someone holds a patent on this simple little circuit.
Part One
The Class-D Amplifier. The linked 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, comparators, and complementary MOS transistors. Do not use the 741 op amp for any of the circuits. It has too low a slew rate to be used in this project.
The first step is to assemble the triangle wave generator using an op amp in place of the comparator. The design of this circuit is covered in the course textbook. Design the circuit for an initial 50kHz triangle-wave frequency. The peak voltage of the triangle wave is to be 10V. This voltage sets the clipping voltage of the class-D amplifier at 10V. If you cannot get the triangle wave generator to work properly at 50kHz, it may be necessary to lower its frequency. However, the class-D amplifier requires this frequency to be as high as possible.
The second step is to connect the triangle wave and the test signal from a function generator to the two inputs of an op amp that is used as a comparator. You should see an output that looks like a square wave with a modulation of the widths of its positive and negative peaks. If the op-amp comparator will not switch at 50kHz, it may be necessary to reduce the triangle wave frequency.
An IC chip containing the MOS transistors for the CMOS inverter will be provided in the lab. The third step is to connect this to the output of the op-amp comparator. The inverter may not switch properly without a resistive load on it, so it might be necessary to connect a resistor from its output to ground. You might try a 10kohm resistor. The value may have to be reduced for the circuit to work properly.
In the first lab, you should be able to get the basic circuit to work using op amps for the comparators.
Part B
Until I can see if I can make the CMOS inverter output stage work, you can omit it from the circuit. I will try to see if I can make it work properly this afternoon (Jan. 22). If I can, you can add it to the last part of the experiment next week.
The object this week is to design an active filter to recover the audio signal from the pulse-width modulated signal output of the comparator. The document linked in Part One that describes the class-D amplifier shows a passive 2nd-order LC filter for this. Although a passive filter must be used if the amplifier is to drive a loudspeaker, we can replace it with an active filter for purposes of this lab. The filter is to be a 3rd-order Chebyshev filter with a db ripple of 1 dB. The design of this filter is described starting on page 30 of this document. You will probably not be able to find exact capacitor values, but you should be able to come close. For a "first cut" design, a cutoff frequency of 1/10 of the triangle wave frequency is suggested. For example, if you were able to make the pulse-width modulator work properly with a triangle wave frequency of 50 kHz, you might choose the filter cutoff frequency to be 5 kHz. The cutoff frequency can easily be changed later if desired to optimize the amplifier performance. The filter circuit diagram shows only one op amp in the circuit. A second op amp should be added to the input that is operated as a non-inverting, unity-gain buffer. Measure and document the frequency response of the filter before connecting it to the comparator output.
Part Three
The last part of the experiment is to add negative feedback to the circuit. This is done by implementing an inverting integrator as an input stage to the amplifier. In order for the feedback to be negative, you should adhere to the op-amp polarities shown in Figure 5 of the document on the Class-D Amplifier. The amplifier should exhibit an overall closed-loop gain of 10 (20 dB). This might be achieved with R1 = 10 kohm and RF = 100 kohm. See page 3 of the Class-D Amplifier document for suggestions on picking a value for CF. If this capacitor is too small, the circuit could oscillate. If it is too large, the bandwidth will be limited.
You should document the operation of your circuit by capturing time waveforms from various points in the system using sine-wave and square-wave input signals. Because the Butterworth filter has complex poles, you should observe some ringing at its output with a square wave in. With a sine-wave input signal, the distortion can be measured using the FFT facility in the oscilloscope. The FFT can also be used to obtain the spectrum of the v′o output, i.e. the signal before the low-pass filter. Your report should include all calculations, derivations, and measurements. It does not have to be a formal report.
Part One
A JFET Voltage Controlled Attenuator. This part involves the design, assmebly, and testing of a voltage controlled attenuator that uses a JFET as a variable resistor. You should complete this part during the first lab meeting for this design project. Before using them, you should check the equations given in the instructions to be sure there are no errors.
Part Two
Peak Detector Circuit. This is a continuation of Part One. It involves the design of a precision full-wave rectifier circuit with voltage in and current out. The circuit is to be used as the detector circuit for the compressor/limiter.
Part Three
Final Assembly of the Circuit. This is a continuation of Part Two. It involves the connection of the output of the peak dectector to the JFET gate to close the control loop for the compressor/limiter.
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.
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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