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Oscillators A.5.4 Quadrature Oscillator Quadrature oscillators produce sine waves 90° out of phase, so they output sine/cosine, or quadrature waves. When R 1 C 1 = R 2 C 2 = R 3 C 3 , the circuit oscillates at ω = 2πf = 1/RC. Both op amps act as integrators causing two poles at 1/RC, thus the circuit oscillates when the loop gain crosses the 0-dB axis. The integrators ensure that gain is always sufficient for oscillation. There is a slight bit of distortion at the sine output, and it is very hard to eliminate this distortion. C 1 R 1 C 3 +V CC _ V OUT(SINE) + V CC 2 R 3 C 2 R 2 + _ +V CC V OUT(COSINE) Figure A–40. Quadrature Oscillator A-40
Oscillators A.5.5 Classical Phase Shift Oscillator Theoretically, the three RC sections do not load each other, thus the loop gain has three identical poles multiplied by the op amp gain. The loop phase shift is –180° when the phase shift of each section is –60°, and this occurs when ω = 2πf = 1.732/RC because the tangent of 60° = 1.73. The magnitude of β at this point is (1/2) 3 , so the gain, A = R F /R G , must be greater or equal to 8 for the system gain to be equal to 1. The assumption that the RC sections do not load each other is not entirely valid, thus the circuit does not oscillate at the specified frequency, and the gain required for oscillation is more than 8. This circuit configuration was very popular when an active component was large and expensive, but now that op amps are inexpensive, small, and come quad packages, the classical phase shift oscillator is losing popularity. The classical phase shift oscillator has an undistorted sine wave available at the output of the third RC section. This is not a low-impedance output, and the signal amplitude is smallest here, but these sacrifices have to be made to get away from distortion. An undistorted output can be obtained from the op amp if an AGC circuit similar to the one shown in Figure A–39 is employed. The reference voltage is set according to the equation V REF = V CC / 2(1+R F /R G ) to center the output voltage at V CC /2. A 1 RCs 1 3 A–46 R F +V CC R G _ R R R V OUT + V CC 18 C C C Figure A–41. Classical Phase Shift Oscillator Single-Supply Circuit Collection A-41
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Design Reference August 2002 Advanc
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Forward Everyone interested in anal
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Contents Contents 1 The Op Amp’s
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Contents 10 Op Amp Noise Theory and
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Contents 14.4.3 AC Application Erro
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Contents 17.7.1 Through-Hole Consid
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Figures Figures 2-1 Ohm’s Law App
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Figures 7-5 TL08X Frequency and Tim
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Figures 13-12 Differential Amplifie
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Figures 16-41 Comparison of Q Betwe
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Figures A-37 Basic Wien Bridge Osci
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Examples Examples 16-1 First-Order
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Chapter 1 The Op Amp’s Place In T
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The first signal conditioning op am
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Chapter 2 Review of Circuit Theory
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Voltage Divider Rule source, throug
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Thevenin’s Theorem 2.5 Thevenin
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Thevenin’s Theorem V OUT V TH R
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Calculation of a Saturated Transist
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Transistor Amplifier 2 V (from 8 V
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Chapter 3 Development of the Ideal
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The Noninverting Op Amp 3.2 The Non
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The Adder 3-5, and if R F = 100 k a
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Complex Feedback Networks portion o
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Video Amplifiers 3.7 Video Amplifie
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Summary 3.9 Summary When the proper
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Chapter 4 Single-Supply Op Amp Desi
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Circuit Analysis R G R F +V V IN _
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Circuit Analysis V OUT VCC -V IN
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Circuit Analysis R G R F V CC V REF
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Simultaneous Equations m 2 1 0.1
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Simultaneous Equations R F R G R G
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Simultaneous Equations measured 4.5
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Simultaneous Equations +5V R 2 820
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Simultaneous Equations |m| 5.56 R
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Simultaneous Equations 4.3.4 Case 4
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Simultaneous Equations -0.10 -0.15
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Chapter 5 Feedback and Stability Th
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Block Diagram Math and Manipulation
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Block Diagram Math and Manipulation
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Bode Analysis of Feedback Circuits
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Loop Gain Plots are the Key to Unde
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The Second Order Equation and Ringi
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Chapter 6 Development of the Non Id
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Review of the Canonical Equations T
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Noninverting Op Amps 6.3 Noninverti
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Inverting Op Amps The transfer equa
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Differential Op Amps A aZ G Z G Z
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Chapter 7 Voltage-Feedback Op Amp C
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Internal Compensation Figure 7-2 sh
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Internal Compensation AVD - Large-S
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Internal Compensation - Large-Signa
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Dominant-Pole Compensation 7.4 Domi
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Dominant-Pole Compensation 100 dB D
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Lead Compensation Gain compensation
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Lead Compensation slopes down at -2
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Compensated Attenuator Applied to O
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Lead-Lag Compensation C R + _ V OUT
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Conclusions Dominant pole compensat
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Chapter 8 Current-Feedback Op Amp A
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The Noninverting CFA output impedan
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The Inverting CFA V OUT V IN Z1 Z
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Stability Analysis 8.6 Stability An
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Selection of the Feedback Resistor
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Stability and Input Capacitance Tab
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Compensation of CF and CG Z F A R
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Chapter 9 Voltage- and Current-Feed
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Bandwidth The noninverting input of
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Bandwidth The CFA is a current oper
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Impedance The CFA stability is not
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Equation Comparison Table 9-1. Tabu
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Chapter 10 Op Amp Noise Theory and
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Characterization 10.2.2 Noise Floor
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Types of Noise 10.3.1 Shot Noise Th
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Types of Noise as average dc curren
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Types of Noise Some characteristics
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Noise Colors There are an infinite
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Op Amp Noise 1000 Hz V n - Input No
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Op Amp Noise can be represented bet
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Op Amp Noise This simplifies the ga
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Putting It All Together 10.6 Puttin
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Putting It All Together When it is
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References +5 V 100 k +5 V 100 k V
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Chapter 11 Understanding Op Amp Par
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Operational Amplifier Parameter Glo
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Additional Parameter Information 10
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Additional Parameter Information +V
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Additional Parameter Information of
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Chapter 12 Instrumentation: Sensors
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The system definition specifies the
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pends heavily on test conditions su
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the bias resistor, R 1 , is selecte
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V OUT I D R F (12-6) The phototran
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the semiconductor in a direction pe
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eference has a temperature drift of
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impedance of the transducer. The te
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Y mX b (12-14) Two pairs of data
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Table 12-5. Offset and Gain Error B
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R G 23.7 kΩ R FB 280 kΩ R FA 200
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12.10 Test The final circuit is rea
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Chapter 13 Wireless Communication:
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Wireless Systems ality. Image rejec
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Wireless Systems of the DAC, is usu
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Selection of ADCs/DACs The mean squ
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Selection of ADCs/DACs fication. Wi
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Anti-Aliasing Filters The op amp dy
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Communication D/A Converter Reconst
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External Vref Circuits for ADCs/DAC
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External Vref Circuits for ADCs/DAC
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High-Speed Analog Input Drive Circu
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High-Speed Analog Input Drive Circu
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Chapter 14 Interfacing D/A Converte
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Understanding the D/A Converter and
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Understanding the D/A Converter and
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D/A Converter Error Budget 14.4.1 A
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D/A Converter Error Budget 20 Ampli
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D/A Converter Errors and Parameters
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Increasing Op Amp Buffer Amplifier
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Chapter 15 Sine Wave Oscillators Ro
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Phase Shift in the Oscillator 15.3
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Active Element (Op Amp) Impact on t
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Analysis of the Oscillator Operatio
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Sine Wave Oscillator Circuits Phase
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Sine Wave Oscillator Circuits large
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Sine Wave Oscillator Circuits The i
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Sine Wave Oscillator Circuits R F 1
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Sine Wave Oscillator Circuits V OUT
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Sine Wave Oscillator Circuits resis
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Sine Wave Oscillator Circuits 15.7.
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Chapter 16 Active Filter Design Tec
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Fundamentals of Low-Pass Filters V
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Fundamentals of Low-Pass Filters A(
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Fundamentals of Low-Pass Filters 16
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Fundamentals of Low-Pass Filters 10
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Low-Pass Filter Design The multipli
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Low-Pass Filter Design C 1 R 1 R 2
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Low-Pass Filter Design V IN R 1 R 2
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Low-Pass Filter Design The general
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Low-Pass Filter Design In order to
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High-Pass Filter Design With C 1 =
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High-Pass Filter Design 16.4.1 Firs
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High-Pass Filter Design To simplify
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Band-Pass Filter Design R 1 1 1 2
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Band-Pass Filter Design 16.5.1 Seco
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Band-Pass Filter Design Because of
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Band-Pass Filter Design A mi is
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Band-Pass Filter Design In accordan
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Band-Rejection Filter Design |A| [d
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Band-Rejection Filter Design or to
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All-Pass Filter Design 0 |A| — Ga
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All-Pass Filter Design Inserting th
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All-Pass Filter Design The transfer
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Practical Design Hints 16.8 Practic
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Practical Design Hints +V CC +V CC
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Practical Design Hints The differen
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Practical Design Hints 16.8.4 Op Am
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Filter Coefficient Tables 16.9 Filt
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Filter Coefficient Tables Table 16-
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References 16.10 References D.Johns
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Chapter 17 Circuit Board Layout Tec
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PCB Mechanical Construction 17.2 PC
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PCB Mechanical Construction V+ IN -
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Grounding ponents and feed-throughs
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Grounding components carefully if t
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The Frequency Characteristics of Pa
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Decoupling + Figure 17-15. Logic Ga
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Input and Output Isolation A decoup
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Packages SINGLE DUAL SHORT TRACES L
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Packages and other passive componen
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References 17.8.4 Routing 17.
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Chapter 18 Designing Low-Voltage Op
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Dynamic Range The trick to designin
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Signal-to-Noise Ratio Table 18-1. C
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Input Common-Mode Range Many low vo
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Input Common-Mode Range The input s
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Output Voltage Swing Op amps always
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Page 393 and 394: Transducer to ADC Analog Interface
Page 395 and 396: DAC to Actuator Analog Interface is
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Page 399 and 400: Comparison of Op Amps Table 18-2. O
Page 401 and 402: Summary mon-mode range of the op am
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Page 405 and 406: Introduction + 5 V R G R F +V CC _
Page 407 and 408: Amplifiers A.3 Amplifiers Many type
Page 409 and 410: Amplifiers A.3.3 Inverting Op Amp w
Page 411 and 412: Amplifiers A.3.5 Noninverting Op Am
Page 413 and 414: Amplifiers A.3.7 Noninverting Op Am
Page 415 and 416: Amplifiers A.3.9 Differential Ampli
Page 417 and 418: Amplifiers A.3.11 High Input Impeda
Page 419 and 420: Amplifiers A.3.13 High-Precision Di
Page 421 and 422: Amplifiers A.3.15 Variable Gain Dif
Page 423 and 424: Amplifiers A.3.17 Buffer The buffer
Page 425 and 426: Amplifiers A.3.19 Noninverting AC A
Page 427 and 428: Computing Circuits A.4.2 Noninverti
Page 429 and 430: Computing Circuits A.4.4 Inverting
Page 435 and 436: Computing Circuits A.4.10 Noninvert
Page 439 and 440: Oscillators A.5 Oscillators This se
Page 441: Oscillators A.5.3 Wien Bridge Oscil
Page 445 and 446: Oscillators A.5.7 Bubba Oscillator
Page 447 and 448: Appendix BA Single-Supply Op Amp Se
Page 449 and 450: Table B-1. Single-Supply Operationa
Page 451 and 452: A AC loads, DAC, 14-2 AC parameters
Page 453 and 454: low pass filter, 16-1 low-pass filt
Page 455 and 456: esistor ladder, 14-2 to 14-4 resist
Page 457 and 458: phase shift for TL07x, 7-5 phase sh
Page 459 and 460: N Noise, 10-8 to 10-10 avalanche, 1
Page 461 and 462: packages, 17-24 to 17-27 parallel s
Page 463 and 464: Theorem Norton’s, 2-5 Superpositi
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