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El. knyga: Continuous-Time Active Filter Design

(University of Northumbria, Newcastle upon Tyne, UK), (University of Hertfordshire, Herts, United Kingdom), (University of Patras, Patras, Greece)
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This book presents the design of active RC filters in continuous time. Topics include:

filter fundamentals

active elements

realization of functions using opamps

LC ladder filters

operational transconductance amplifier circuits (OTACs)

MOSFET-C filters Continuous-Time Active Filter Design uses wave variables to enable the reader to better understand the introduction of more complex variables created through linear transformations of voltages and currents. Intended for undergraduate students in electrical engineering, Continuous-Time Active Filter Design provides chapters as self-contained units, including introductory material leading to active RC filters.

Recenzijos

"Deliyannis, Sun, and Fidler present a comprehensive treatment highighting the most important new developments and focus on practical modern circuit implementations." -CHOICE, June 1999

Chapter 1 Filter Fundamentals
1(34)
1.1 Introduction
1(1)
1.2 Filter Characterization
1(3)
1.2.1 Lumped
1(1)
1.2.2 Linear
2(1)
1.2.3 Continuous-Time and Discrete-Time
3(1)
1.2.4 Time-Invariant
3(1)
1.2.5 Finite
3(1)
1.2.6 Passive and Active
3(1)
1.3 Types of Filters
4(2)
1.4 Steps in Filter Design
6(1)
1.5 Analysis
7(12)
1.5.1 Nodal Analysis
7(3)
1.5.2 Network Parameters
10(1)
1.5.2.1 One-Port Network
10(1)
1.5.2.2 Two-Port Network
11(3)
1.5.3 Two-Port Interconnections
14(1)
1.5.3.1 Series-Series Connection
14(1)
1.5.3.2 Parallel-Parallel Connection
15(1)
1.5.3.3 Series Input-Parallel Output Connection
16(1)
1.5.3.4 Parallel Input-Series Output Connection
16(1)
1.5.3.5 Cascade Connection
16(1)
1.5.4 Network Transfer Functions
17(2)
1.6 Continuous-Time Filter Functions
19(7)
1.6.1 Pole-Zero Locations
20(1)
1.6.2 Frequency Response
21(1)
1.6.3 Transient Response
22(1)
1.6.3.1 Impulse Response
22(1)
1.6.3.2 Step Response
23(1)
1.6.4 Step and Frequency Response
24(2)
1.7 Stability
26(3)
1.7.1 Short-Circuit and Open-Circuit Stability
27(1)
1.7.2 Absolute Stability and Potential Instability.
27(2)
1.8 Passivity Criterial for One-and Two-Port Networks
29(3)
1.8.1 One-Ports
29(1)
1.8.2 Two-Ports
30(1)
1.8.3 Activity
31(1)
1.8.4 Passivity and Stability
31(1)
1.9 Reciprocity
32(1)
1.10 Summary
33(1)
References and Further Reading
33(2)
Chapter 2 The Approximation problem
35(40)
2.1 Introduction
35(1)
2.2 Filter Specifications and Permitted Functions
35(2)
2.2.1 Causality
35(1)
2.2.2 Rational Functions
36(1)
2.2.3 Stability
36(1)
2.3 Formulation of the Approximation Problem
37(1)
2.4 Approximation of the Ideal Lowpass Filter
38(14)
2.4.1 Butterworth or Maximally Flat Approximation
39(3)
2.4.2 Chebyshev or Equiripple Approximation
42(3)
2.4.3 Inverse Chebyshev Approximation
45(2)
2.4.4 Papoulis Approximation
47(1)
2.4.5 Elliptic Function or Cauer Approximation
47(2)
2.4.6 Selecting the Filter from Its Specifications
49(3)
2.4.7 Ampulitude Equalization
52(1)
2.5 Filter with Linear Phase: Delays
52(7)
2.5.1 Bessel-Thomson Delay Approximation
54(4)
2.5.2 Other Delay Functions
58(1)
2.5.3 Delay Equalization
59(1)
2.6 Frequency Transformations
59(5)
2.6.1 Lowpass-to-Lowpass Transformation
60(1)
2.6.2 Lowpass-to-Highpass Transformation
61(1)
2.6.3 Lowpass-to-Bandpass Transformation
62(1)
2.6.4 Lowpass-to-Bandstop Transformation
63(1)
2.6.5 Delay Denormalization
64(1)
2.7 Design Tables for Passive LC Ladder Filters
64(6)
2.7.1 Transformation of Elements
65(1)
2.7.1.1 LC Filters
65(3)
2.7.1.2 Active RC Filters
68(2)
2.8 Impedance Scaling
70(1)
2.9 Predistortion
71(1)
2.10 Summary
72(1)
References
73(2)
Chapter 3 Active Elements
75(32)
3.1 Introduction
75(1)
3.2 Ideal Controlled Sources
75(1)
3.3 Impedance Transformation (Generalized Impedance Converters and Inverters)
76(6)
3.3.1 Generalized Impedance Converters
78(1)
3.3.1.1 The Ideal Active Transformer
78(1)
3.3.1.2 The Ideal Negative Impedance Converter
79(1)
3.3.1.3 The Positive Impedance Converter
79(1)
3.3.1.4 The Frequency-Dependent Negative Resistor
80(1)
3.3.2 Generalized Impedance Inverters
81(1)
3.3.2.1 The Gyrator
81(1)
3.3.2.2 Negative Impedance Inverter
82(1)
3.4 Negative Resistance
82(2)
3.5 Ideal Operational Amplifier
84(16)
3.5.1 Operations Using the Ideal Opamp
85(1)
3.5.1.1 Summation of Voltages
85(1)
3.5.1.2 Integration
86(1)
3.5.2 Realization of Some Active Elements Using Opamps
87(1)
3.5.2.1 Realization of Controlled Sources
87(1)
3.5.2.2 Realization of Negative-Impedance Converters
88(2)
3.5.2.3 Gyrator Realizations
90(1)
3.5.2.4 GIC Circuit Using Opamps
91(2)
3.5.3 Characterstics of IC Opamps
93(1)
3.5.3.1 Open-Loop Voltage Gain of Practical Opamps
93(1)
3.5.3.2 Input and Output Impedances
94(1)
3.5.3.3 Input Offset Voltage V(IO)
95(1)
3.5.3.4 Input Offset Current I(IO)
95(1)
3.5.3.5 Input Voltage Range V(I)
96(1)
3.5.3.6 Power Supply Sensitivity Delta V(IO) / Delta V(GG)
97(1)
3.5.3.7 Slew Rate SR
97(1)
3.5.3.8 Short-Circuit Output Current
97(1)
3.5.3.9 Maximum Peak-to-Peak Output Voltage Swing V(opp)
97(1)
3.5.3.10 Input Capacitance C(i)
98(1)
3.5.3.11 Common-Mode Rejection Ratio CMRR
98(1)
3.5.3.12 Total Power Dissipation
98(1)
3.5.3.13 Rise Time t(r)
98(1)
3.5.3.14 Overshoot
98(1)
3.5.4 Effect of the Single-Pole Compensation on the Finite Voltage Gain Controlled Sources
98(2)
3.6 The Ideal Operational Transconductance Amplifier (OTA)
100(6)
3.6.1 Voltage Amplification
100(1)
3.6.2 A Voltage-Variable Resistor (VVR)
101(1)
3.6.3 Voltage Summation
101(1)
3.6.4 Integration
102(1)
3.6.5 Gyrator Realization
102(1)
3.6.6 Practical OTAs
103(1)
3.6.7 Current Conveyor
104(2)
3.7 Summary
106(1)
References
106(1)
Chapter 4 Realization of First-and Second-Order Functions Using Opamps
107(44)
4.1 Introduction
107(1)
4.2 Realization of First-Order Functions
107(3)
4.2.1 Lowpass Circuits
108(1)
4.2.2 Highpass Circuits
109(1)
4.2.3 Allpas Circuits
110(1)
4.3 The General Second-Order Filter Function
110(1)
4.4 Sensitivity of Second-Order Filters
111(3)
4.5 Realization of Biquadratic Functions Using SABs
114(18)
4.5.1 Classification of SABs
115(1)
4.5.2 A Lowpass SAB
116(4)
4.5.3 A Highpass SAB
120(1)
4.5.4 A Bandpass SAB
121(5)
4.5.5 Lowpass-and Highpass-Notch Biquads
126(1)
4.5.6 Lowpass Notch (R(6) = Infinity)
127(2)
4.5.7 Highpass Notch (R(7) = Infinity)
129(1)
4.5.8 An Allpass SAB
129(3)
4.6 Realization of a Quadratic with a Positive Real Zero
132(2)
4.7 Biquads Obtained Using the Twin-T RC Network
134(2)
4.8 Two-Opamp Biquads
136(5)
4.8.1 Biquads by Inductance Simulation
136(2)
4.8.2 Two-Opamp Allpass Biquads
138(1)
4.8.3 Selectivity Enhancement
139(2)
4.9 Three-Opamp Biquads
141(6)
4.9.1 The Tow-Thomas [ 25-27] Three-Opamp Biquad
144(1)
4.9.2 Excess Phase and Its Compensation in Three-Opamp Biquads
145(1)
4.9.3 The Akerberg-Mossberg Three-Opamp Biquad
146(1)
4.10 Summary
147(1)
References
148(3)
Chapter 5 Realization of High-Order Functions
151(32)
5.1 Introduction
151(1)
5.2 Selection Criteria for High-Order Function Realizations
151(2)
5.3 Multiparameter Sensitivity
153(1)
5.4 High-Order Function Realization Methods
154(1)
5.5 Cascade Connection of Second-Order Sections
155(7)
5.5.1 Pole-Zero Pairing
156(2)
5.5.2 Cascade Sequence
158(1)
5.5.3 Gain Distribution
159(3)
5.6 Multiple-Loop Feedback Filters
162(9)
5.6.1 The Shifted-Companion-Form (SCF) Design Method
166(2)
5.6.2 Follow-the-Leader Feedback Design (FLF)
168(3)
5.7 Cascade of Biquartics
171(9)
5.7.1 The BR Section
171(2)
5.7.2 Effect of Eta on Omega'(i) and Q'(i)
173(2)
5.7.3 Cascading Biquartic Sections
175(1)
5.7.4 Realization of Biquartic Sections
175(1)
5.7.4.1 Design Example
176(2)
5.7.5 Sensitivity of CBR Filters
178(2)
5.8 Summary
180(1)
References
180(1)
Further Reading
181(2)
Chapter 6 Simulation of LC Ladder Filters Using Opamps
183(22)
6.1 Introduction
183(1)
6.2 Resistively-Terminated Lossless LC Ladder Filters
184(1)
6.3 Methods of LC Ladder Simulation
184(1)
6.4 The Gyrator
185(5)
6.4.1 Gyrator Imprefections
186(2)
6.4.2 Use of Gyrator in Filter Synthesis
188(2)
6.5 Generalized Impedance Converter, GIC
190(3)
6.5.1 Use of GICs in Filter Synthesis
190(3)
6.6 FDNRs: Complex Impedance Scaling
193(2)
6.7 Functional Simulation
195(7)
6.7.1 Example
198(1)
6.7.2 Bandpass Filters
199(2)
6.7.3 Dynamic Range of LF Filters
201(1)
6.8 Summary
202(1)
References
202(3)
Chapter 7 Wave Active Filters
205(26)
7.1 Introduction
205(1)
7.2 Wave Active Filters
205(3)
7.3 Wave Active Equivalents (WAEs)
208(9)
7.3.1 Wave Active Equivalent of a Series-Arm Impedance
208(1)
7.3.2 Wave Active Equivalent of a Shunt-Arm Admittance
209(1)
7.3.3 WAEs for Equal Port Normalization Resistances
209(1)
7.3.4 Wave Active Equivalent of the Signal Source
210(1)
7.3.5 Wave Active Equivalent of the Terminating Resistance
211(1)
7.3.6 WAEs of Shunt-Arm Admittances
212(1)
7.3.7 Interconnection Rules
212(2)
7.3.8 WAEs of Tuned Circuits
214(2)
7.3.9 WA Simulation Example
216(1)
7.3.10 Comments on the Wave Active Filter Approach
216(1)
7.4 Economical Wave Active Filters
217(3)
7.5 Sensitivity of WAFs
220(1)
7.6 Operation of WAFs at Higher Frequencies
221(2)
7.7 Complementary Transfer Functions
223(1)
7.8 Wave Simulation of Inductance
224(1)
7.9 Linear Transformation Active Filters (LTA Filters)
224(5)
7.9.1 Interconnection Rule
227(2)
7.9.2 General Remarks on the Method
229(1)
7.10 Summary
229(1)
References
229(2)
Chapter 8 Single Operational Transconductance Amplifier (OTA) Filters
231(38)
8.1 Introduction
231(1)
8.2 Single OTA Filters Derived from Three-Admittance Model
232(9)
8.2.1 First-Order Filter Structures
232(1)
8.2.1.1 First-Order Filters with One or Two Passive Components
233(1)
8.2.1.2 First-Order Filters with Three Passive Components
234(1)
8.2.2 Lowpass Second-Order Filter with Three Passive Components
235(1)
8.2.3 Lowpass Second-Order Filters with Four Passive Components
236(2)
8.2.4 Bandpass Second-Order Filters with Four Passive Components
238(3)
8.3 Second-Order Filters Derived from Four-Admittance Model
241(8)
8.3.1 Filter Structures and Design
241(1)
8.3.1.1 Lowpass Filter
241(2)
8.3.1.2 Bandpass Filter
243(1)
8.3.1.3 Other Considerations on Structure Generation
244(1)
8.3.2 Second-Order Filters with the OTA Transposed
245(1)
8.3.2.1 Highpass Filter
245(2)
8.3.2.2 Lowpass Filter
247(1)
8.3.2.3 Bandpass Filter
247(2)
8.4 Tunability of Active Filters Using Single OTA
249(1)
8.5 OTA Nonideality Effects
249(5)
8.5.1 Direct Analysis Using Practical OTA Macro-Model
249(4)
8.5.2 Simple Formula Method
253(1)
8.5.3 Reduction and Elimination of Parasitic Effects
253(1)
8.6 OTA-C Filters Derived from Single OTA Filters
254(4)
8.6.1 Simulated OTA Resistors and OTA-C Filters
254(1)
8.6.2 Design Considerations of OY Structures
255(3)
8.7 Second-Ordre Filters Derived from Five-Admittance Model
258(6)
8.7.1 Highpass Filter
259(1)
8.7.2 Bandpass Filters
260(2)
8.7.3 Lowpass Filter
262(1)
8.7.4 Comment and Comparison
263(1)
8.8 Summary
264(1)
References
264(5)
Chapter 9 Two Integer Loop OTA-C Filters
269(40)
9.1 Introduction
269(1)
9.2 OTA-C Building Blocks and First-Order OTA-C Filters
270(2)
9.3 Two Integrator Loop Configurations and Performance
272(2)
9.3.1 Configurations
272(1)
9.3.2 Pole Equations
272(2)
9.3.3 Design
273(1)
9.3.4 Sensitivity
273(1)
9.3.5 Tuning
273(1)
9.3.6 Biquadratic Specifications
273(1)
9.4 OTA-C Realization of Distributed-Feedback (DF) Configuration
274(6)
9.4.1 DF OTA-C Circuit and Equations
274(2)
9.4.2 Filter Functions
276(1)
9.4.3 Design Examples
277(1)
9.4.4 DF OTA-C Realizations with Special Feedback Coefficients
278(2)
9.5 OTA-C Filters Based on Summed-Feedback (SF) Configuration
280(3)
9.5.1 SF OTA-C Realization with Arbitrary k(12) and k(11)
281(1)
9.5.1.1 Design Example of KHN OTA-C Biquad
282(1)
9.5.2 SF OTA-C Realization with k(12) = k(11) = k
282(1)
9.6 Biquadratic OTA-C Filters Using Lossy Integrators
283(2)
9.6.1 Tow-Thomas OTA-C Structure
284(1)
9.6.2 Feedback Lossy Integrator Biquad
284(1)
9.7 Comparison of Basic OY Filter Structures
285(2)
9.7.1 Multifunctionality and Number of OTA
285(1)
9.7.2 Sensitivity
286(1)
9.7.3 Tunability
286(1)
9.8 Versatile Filter Functions Based on Node Current Injection
287(4)
9.8.1 DF Structures with Node Current Injection
288(1)
9.8.2 SF Structures with Node Current Injection
289(2)
9.9 Universal Biquads Using Output Summation Approach
291(3)
9.9.1 DF-Type Universal Biquads
292(1)
9.9.2 SF Type Universal Biquads
292(1)
9.9.3 Universal Biquads Based on Node Current Injection and Output Summation
293(1)
9.9.4 Comments on Universal Biquads
294(1)
9.10 Universal Biquads Based on Canonical and TT Circuits
294(1)
9.11 Effects and Compensation of OTA Nonidealities
295(8)
9.11.1 General Model and Equations
295(3)
9.11.2 Finite Impedance Effects and Compensation
298(1)
9.11.3 Finite Bandwidth Effects and Compensation
299(2)
9.11.4 Selection of OTA-C Filter Structures
301(1)
9.11.5 Selection of Input and Output Methods
302(1)
9.11.6 Dynamic Range Problem
302(1)
9.12 Summary
303(1)
References
304(5)
Chapter 10 OTA-C Filters Based on Ladder Simulation
309(40)
10.1 Introduction
309(1)
10.2 Component Substitution Method
310(10)
10.2.1 Direct Inductor Substitution
310(1)
10.2.1.1 OTA-C Inductors
310(1)
10.2.1.2 Tolerance Sensitivity of Filter Function
311(1)
10.2.1.3 Parasitic Effects on Simulated Inductor
312(1)
10.2.1.4 Parasitic Effects on Filter Function
313(2)
10.2.2 Application Examples of Inductor Substitution
315(1)
10.2.2.1 OTA-C Biquad Derived from RLC Resonator Circuit
315(1)
10.2.2.2 A Lowpass OTA-C Filter
316(1)
10.2.3 Bruton Transformation and FDNR Simulation
317(3)
10.3 Admittance/Impedance Simulation
320(5)
10.3.1 General Description of the Method
320(1)
10.3.2 Application Examples and Comparison
321(3)
10.3.3 Parial Floating Admittance Concept
324(1)
10.4 Signal Flow Simulation and Leapfrog Structures
325(11)
10.4.1 Leapfrog Simulation Structures of General Ladder
325(3)
10.4.2 OTA-C Lowpass LF Filters
328(2)
10.4.2.1 Example
330(2)
10.4.3 OTA-C Bandpass LF Filter Design
332(1)
10.4.4 Partial Floating Admittance Block Diagram and OTA-C Realization
332(2)
10.4.5 Alternative Leapfrog Structures and OTA-C Realizations
334(2)
10.5 Equivalence of Admittance and Signal Simulation Methods
336(2)
10.6 OTA-C Simulation of LC Ladders Using Matrix Methods
338(2)
10.7 Coupled Biquad OTA Structures
340(2)
10.8 Some General Practical Design Considerations
342(1)
10.8.1 Selection of Capacitors and OTAs
342(1)
10.8.2 Tolerance Sensitivity and Parasitic Effects
343(1)
10.8.3 OTA Finite Impedances and Frequency-Dependent Transconductance
343(1)
10.9 Summary
343(1)
References
344(5)
Chapter 11 Multiple Integrator Loop Feedback OTA-C Filters
349(38)
11.1 Introduction
349(1)
11.2 General Design Theory of All-Pole Structures
350(5)
11.2.1 Multiple Loop Feedback OTA-C Model
350(1)
11.2.2 System Equations and Transfer Function
350(3)
11.2.3 Feedback Coefficient Matrix and Systematic Structure Generation
353(1)
11.2.4 Filter Synthesis Prcedure Based on Coefficient Matching
354(1)
11.3 Structure Generation and Design of All-Pole Filters
355(8)
11.3.1 First-and Second-Order Filters
355(1)
11.3.2 Third-Order Filters
356(1)
11.3.3 Fourth-Order Filters
357(2)
11.3.4 Design Examples of Fourth-Order Filters
359(1)
11.3.5 General nth-Order Architectures
360(1)
11.3.5.1 General IFLF Configuration
360(1)
11.3.5.2 General LF Configureation
361(1)
11.3.6 Other Types of Realization
362(1)
11.4 Generation and Synthesis of Transmission Zeros
363(10)
11.4.1 Output Summation of OTA Network
364(1)
11.4.2 Input Distribution of OTA Network
364(2)
11.4.3 Universal and Special Third-Order OTA-C Filters
366(1)
11.4.3.1 IFLF and Output Summation Structure in Fig. 11.10(a)
367(1)
11.4.3.2 IFLF and Input Distribution Structure in Fig.11.10(b)
367(1)
11.4.3.3 LF and Output Summation Structure in Fig. 11.10(c)
367(1)
11.4.3.4 LF and Input Distribution Structure in Fig. 11.10(d)
368(1)
11.4.3.5 Realization of Special Characteristics
368(1)
11.4.3.6 Design of Elliptic Filters
368(2)
11.4.4 General nth-Order OTA-C Filters
370(2)
11.4.4.1 Universal IFLF Architectures
370(2)
11.4.4.2 Universal LF Architectures
372(1)
11.5 General Formulation of Sensitivity Analysis
373(4)
11.5.1 General Sensitivity Relations
373(2)
11.5.2 Sensitivity of Different Filter Structures
375(2)
11.6 Determination of Maximum Signal Magnitude
377(2)
11.7 Effects of OTA Frequency Response Nonidealities
379(2)
11.8 Summary
381(1)
References
382(5)
Chapter 12 Current-Mode Filters and Other Architectures
387(44)
12.1 Introduction
387(1)
12.2 Current-Mode Filters Based on Single DO-OTA Model
388(8)
12.2.1 General Model and Filter Architecture Generation
389(1)
12.2.1.1 First-Order Filter Structures
389(1)
12.2.1.2 Second-Order Filter Architectures
390(1)
12.2.2 Passive Resistor and Active Resistor
390(1)
12.2.3 Design of Second-Order Filters
391(3)
12.2.4 Effects of DO-OTA Nonidealities
394(2)
12.3 Current-Mode Two Integrator Loop DO-OTA-C Filters
396(9)
12.3.1 Basic Building Blocks and First-Order Filters
396(1)
12.3.2 Current-Mode DO-OTA-C Configurations with Arbitrary k(ij)
397(1)
12.3.3 Current-Mode DO-OTA-C Biquadratic Architectures with k(12) = k(ij)
398(1)
12.3.4 Current-Mode DO-OTA-C Biquadratic Architectures with k(12) = 1
399(2)
12.3.5 DO-OTA Nonideality Effects
401(1)
12.3.6 Universal Current-Mode DO-OTA-C Filters
401(4)
12.4 Current-Mode DO-OTA-C Ladder Simulation Filters
405(6)
12.4.1 Leapfrog Simulation Structures of General Ladder
405(2)
12.4.2 Current-Mode DO-OTA-C Lowpass LF Filters
407(2)
12.4.3 Current-Mode DO-OTA-C Bandpass LF Filter Design
409(1)
12.4.4 Alternative Current-Mode Leapfrog DO-OTA-C Structure
410(1)
12.5 Current-Mode Multiple Loop Feedback DO-OTA-C Filters
411(8)
12.5.1 Design of All-Pole Filters
411(4)
12.5.2 Realization of Transmission Zeros
415(1)
12.5.2.1 Multiple Loop Feedback with Input Distribution
415(1)
12.5.2.2 Multiple Loop Feedback with Output Summation
416(1)
12.5.2.3 Filter Structures and Design Formulas
417(2)
12.6 Other Continous-Time Filter Structures
419(6)
12.6.1 Balanced Opamp-RC and OTA-C Structures
419(1)
12.6.2 MOSFET-C Filters
420(2)
12.6.3 OTA-C Opamp Filter Design
422(1)
12.6.4 Active Filters Using Current Conveyors
423(2)
12.6.5 Log-Domain, Current Amplifier, and Integrated-RLC Filters
425(1)
12.7 Summary
425(1)
References
426(5)
Appendix A A Sample of Filter Functions 431(6)
Index 437
T. Deliyannis, Yichuang Sun, J.K. Fidler
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
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