"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

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Fundamentals of Low-Pass Filters 16-4 |A| — Gain — dB φ — Phase — degrees 0 –10 –20 –30 –40 –50 –60 –70 1st Order Lowpass 4th Order Lowpass Ideal 4th Order Lowpass –80 0.01 0.1 1 Frequency — Ω 10 0 –90 –180 –270 Ideal 4th Order Lowpass 4th Order Lowpass 1st Order Lowpass –360 0.01 0.1 1 Frequency — Ω 10 Note: Curve 1: 1st-order partial low-pass filter, Curve 2: 4th-order overall low-pass filter, Curve 3: Ideal 4th-order low-pass filter Figure 16–4. Frequency and Phase Responses of a Fourth-Order Passive RC Low-Pass Filter The corner frequency of the overall filter is reduced by a factor of α ≈ 2.3 times versus the –3 dB frequency of partial filter stages. 100 100
A(s) Fundamentals of Low-Pass Filters In addition, Figure 16–4 shows the transfer function of an ideal fourth-order low-pass function (Curve 3). In comparison to the ideal low-pass, the RC low-pass lacks in the following characteristics: The passband gain varies long before the corner frequency, fC, thus amplifying the upper passband frequencies less than the lower passband. The transition from the passband into the stopband is not sharp, but happens gradually, moving the actual 80-dB roll off by 1.5 octaves above fC. The phase response is not linear, thus increasing the amount of signal distortion significantly. The gain and phase response of a low-pass filter can be optimized to satisfy one of the following three criteria: 1) A maximum passband flatness, 2) An immediate passband-to-stopband transition, 3) A linear phase response. For that purpose, the transfer function must allow for complex poles and needs to be of the following type: A0 1 a1s b1s21 a2s b2s2 A0 1 ans bns2 i 1 ais bis2 where A 0 is the passband gain at dc, and a i and b i are the filter coefficients. Since the denominator is a product of quadratic terms, the transfer function represents a series of cascaded second-order low-pass stages, with a i and b i being positive real coefficients. These coefficients define the complex pole locations for each second-order filter stage, thus determining the behavior of its transfer function. The following three types of predetermined filter coefficients are available listed in table format in Section 16.9: The Butterworth coefficients, optimizing the passband for maximum flatness The Tschebyscheff coefficients, sharpening the transition from passband into the stopband The Bessel coefficients, linearizing the phase response up to fC The transfer function of a passive RC filter does not allow further optimization, due to the lack of complex poles. The only possibility to produce conjugate complex poles using pas- Active Filter Design Techniques 16-5
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Operational Amplifier Chapter 1: Th
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1-2 problem. It seems that circuits
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1-4 you are looking in the wrong pl
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Laws of Physics 2-2 V IR (2-1) In
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Current Divider Rule 2-4 put voltag
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Thevenin’s Theorem 2-6 V theorem
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Superposition 2.6 Superposition 2-8
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Transistor Amplifier 2-10 I C I B
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Transistor Amplifier 2-12 approxima
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Ideal Op Amp Assumptions 3-2 a hard
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The Inverting Op Amp 3-4 in a curre
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The Differential Amplifier 3.5 The
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Complex Feedback Networks 3-8 Break
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Capacitors Figure 3-10. Low-Pass Fi
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3-12
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Single Supply versus Dual Supply 4-
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Circuit Analysis 4-4 VREF VIN Figur
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Circuit Analysis 4-6 Four op amps w
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Simultaneous Equations 4.3 Simultan
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Simultaneous Equations 4-10 VOUT V
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Simultaneous Equations 4-12 VIN = 0
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Simultaneous Equations 4-14 m R F
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Simultaneous Equations 4.3.3 Case 3
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Simultaneous Equations 4-18 - Input
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Simultaneous Equations 4-20 |b| V
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Summary 4.4 Summary 4-22 Single-sup
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Block Diagram Math and Manipulation
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Block Diagram Math and Manipulation
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Feedback Equation and Stability 5.3
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Bode Analysis of Feedback Circuits
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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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Loop Gain Plots are the Key to Unde
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References 5-16 M tangent 1 (2) (
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Review of the Canonical Equations 6
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Review of the Canonical Equations 6
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Inverting Op Amps 6-6 comparison al
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Differential Op Amps 6.5 Differenti
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6-10
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Internal Compensation 7-2 around in
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Internal Compensation 7-4 Damping R
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Internal Compensation AVD - Large-S
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External Compensation, Stability, a
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Dominant-Pole Compensation 7-10 VTH
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Gain Compensation 7-12 VOUT VIN a
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Lead Compensation 7-14 transfer fun
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Compensated Attenuator Applied to O
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Lead-Lag Compensation 7-18 FHASE (A
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Comparison of Compensation Schemes
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7-22
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Development of the Stability Equati
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The Noninverting CFA Figure 8-4. No
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The Inverting CFA 8-6 The current e
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Stability Analysis 8-8 The plot in
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Selection of the Feedback Resistor
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Stability and Feedback Capacitance
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Summary 8.11 Summary 8-14 A Z1 R
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Precision 9.2 Precision 9-2 The lon
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Bandwidth 9-4 A aR G R F R G (9-2
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Stability 9.4 Stability 9-6 Substit
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Equation Comparison 9-8 R G = 100
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9-10
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Characterization 10-2 Noise Signal
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Types of Noise 10.2.5 Noise Units 1
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Types of Noise 10-6 Shot noise is
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Types of Noise 10-8 Ith 4kTB R Wh
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Noise Colors Figure 10-4. Avalanche
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Op Amp Noise 10.4.3 Red/Brown Noise
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Op Amp Noise 10-14 E n Square it.
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Op Amp Noise 10.5.4 Inverting Op Am
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Op Amp Noise 10.5.6 Differential Op
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Putting It All Together 10-20 Vn Vn
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Putting It All Together 10-22 volta
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10-24
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Operational Amplifier Parameter Glo
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Additional Parameter Information 11
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12-2 The ADC selection is based on
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12-4 (A) 4 V 3 V ADC 0 V Sensor Out
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12.2 Transducer Types 12-6 This is
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12-8 some value, and R X is switche
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12-10 Resolvers and synchros are po
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12-12 6) Scan the transducer and AD
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12-14 the worst case excursions of
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Table 12-3. Op Amp Selection 12-16
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12-18 this yields m = 16.16. The re
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12-20 0.97R 1 VREF(MIN) VREF 50 m
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12-22 ply contribution is reduced b
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12-24
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Wireless Systems 13-2 Signal @ - 10
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Wireless Systems 13-4 900 MHz Figur
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Selection of ADCs/DACs 13.3 Selecti
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Selection of ADCs/DACs 13-8 Therefo
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Factors Influencing the Choice of O
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Anti-Aliasing Filters 13-12 anti-al
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Communication D/A Converter Reconst
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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
Page 216 and 217: References 13.9 References 13-22 [1
Page 218 and 219: Understanding the D/A Converter and
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Page 222 and 223: D/A Converter Error Budget 14-6 rat
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Page 226 and 227: D/A Converter Errors and Parameters
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Page 236 and 237: Increasing Op Amp Buffer Amplifier
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Page 242 and 243: Requirements for Oscillation 15-2 u
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Page 246 and 247: Active Element (Op Amp) Impact on t
Page 248 and 249: Analysis of the Oscillator Operatio
Page 250 and 251: Sine Wave Oscillator Circuits 15-10
Page 262 and 263: References 15.8 References 15-22 [1
Page 264 and 265: Fundamentals of Low-Pass Filters 16
Page 274 and 275: Low-Pass Filter Design 16-12 1st or
Page 276 and 277: Low-Pass Filter Design Example 16-1
Page 278 and 279: Low-Pass Filter Design 16-16 In ord
Page 280 and 281: Low-Pass Filter Design 16.3.2.2 Mul
Page 282 and 283: Low-Pass Filter Design Second Filte
Page 284 and 285: High-Pass Filter Design 16-22 |A|
Page 286 and 287: High-Pass Filter Design 16-24 To di
Page 288 and 289: High-Pass Filter Design 16-26 Throu
Page 290 and 291: Band-Pass Filter Design 16-28 |A| [
Page 292 and 293: Band-Pass Filter Design 16-30 The g
Page 294 and 295: Band-Pass Filter Design 16-32 out a
Page 296 and 297: Band-Pass Filter Design 16-34 After
Page 298 and 299: Band-Rejection Filter Design 16-36
Page 304 and 305: All-Pass Filter Design 16-42 2 i
Page 306 and 307: All-Pass Filter Design 16.7.1 First
Page 308 and 309: All-Pass Filter Design 16-46 V IN f
Page 310 and 311: Practical Design Hints 16-48 low-pa
Page 312 and 313: Practical Design Hints V IN 16-50 C
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Practical Design Hints 16-54 f T 1
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Filter Coefficient Tables Table 16-
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16-64
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General Considerations 17.1.3 Noise
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PCB Mechanical Construction 17-4 Te
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PCB Mechanical Construction 17.2.2.
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Grounding 17-8 DIGITAL + DIGITAL -
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Grounding 17-10 CONNECTOR POWER SUP
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The Frequency Characteristics of Pa
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Decoupling 17-20 For example, a 0.4
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Decoupling 17-22 EQUIVALENT SERIES
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Packages 17.7 Packages 17-24 N1 IN-
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Packages 17-26 IN1 + OUT1 IN2 IN3 O
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Summary 17-28 HALF SUPPLY GOOD _ +
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17-30
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Introduction 18-2 swing at V CC = 5
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Dynamic Range 18-4 VIN VnR Figure 1
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Input Common-Mode Range 18-6 sible
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Input Common-Mode Range 18-8 VCC GN
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Input Common-Mode Range 18-10 V µ
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Shutdown and Low Current Drain 18-1
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Transducer to ADC Analog Interface
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DAC to Actuator Analog Interface 18
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DAC to Actuator Analog Interface 18
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Comparison of Op Amps 18-20 When DA
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Summary 18.11 Summary 18-22 Always
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18-24
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"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

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