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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
An in-depth look at the state-of-the-art in microwave filter design, implementation, and optimization Thoroughly revised and expanded, this second edition of the popular reference addresses the many important advances that have taken place in the field since the publication of the first edition and includes new chapters on Multiband Filters, Tunable Filters and a chapter devoted to Practical Considerations and Examples. One of the chief constraints in the evolution of wireless communication systems is the scarcity of the available frequency spectrum, thus making frequency spectrum a primary resource to be judiciously shared and optimally utilized. This fundamental limitation, along with atmospheric conditions and interference have long been drivers of intense research and development in the fields of signal processing and filter networks, the two technologies that govern the information capacity of a given frequency spectrum. Written by distinguished experts with a combined century of industrial and academic experience in the field, Microwave Filters for Communication Systems: * Provides a coherent, accessible description of system requirements and constraints for microwave filters * Covers fundamental considerations in the theory and design of microwave filters and the use of EM techniques to analyze and optimize filter structures * Chapters on Multiband Filters and Tunable Filters address the new markets emerging for wireless communication systems and flexible satellite payloads and * A chapter devoted to real-world examples and exercises that allow readers to test and fine-tune their grasp of the material covered in various chapters, in effect it provides the roadmap to develop a software laboratory, to analyze, design, and perform system level tradeoffs including EM based tolerance and sensitivity analysis for microwave filters and multiplexers for practical applications. Microwave Filters for Communication Systems provides students and practitioners alike with a solid grounding in the theoretical underpinnings of practical microwave filter and its physical realization using state-of-the-art EM-based techniques.
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Veröffentlichungsjahr: 2018
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
Chapter 1: Radio Frequency (RF) Filter Networks for Wireless Communications—The System Perspective
PART I Introduction to a Communication System, Radio Spectrum, and Information
1.1 Model of a Communication System
1.2 Radio Spectrum and its Utilization
1.3 Concept of Information
1.4 Communication Channel and Link Budgets
PART II Noise in a Communication Channel
1.5 Noise in Communication Systems
1.6 Modulation–Demodulation Schemes in a Communication System
1.7 Digital Transmission
PART III Impact of System Design on the Requirements of Filter Networks
1.8 Communication Channels in a Satellite System
1.9 RF Filters in Cellular Systems
1.10 Ultra Wideband (UWB) Wireless Communication
1.11 Impact of System Requirements on RF Filter Specifications
1.12 Impact of Satellite and Cellular Communications on Filter Technology
Summary
References
Appendix
Chapter 2: Fundamentals of Circuit Theory Approximation
2.1 Linear Systems
2.2 Classification of Systems
2.3 Evolution of Electrical Circuits: A Historical Perspective
2.4 Network Equation of Linear Systems in the Time Domain
2.5 Network Equation of Linear Systems in the Frequency-Domain Exponential Driving Function
2.6 Steady-State Response of Linear Systems to Sinusoidal Excitations
2.7 Circuit Theory Approximation
Summary
References
Chapter 3: Characterization of Lossless Lowpass Prototype Filter Functions
3.1 The Ideal Filter
3.2 Characterization of Polynomial Functions for Doubly Terminated Lossless Lowpass Prototype Filter Networks
3.3 Characteristic Polynomials for Idealized Lowpass Prototype Networks
3.4 Lowpass Prototype Characteristics
3.5 Characteristic Polynomials versus Response Shapes
3.6 Classical Prototype Filters
3.7 Unified Design Chart (UDC) Relationships
3.8 Lowpass Prototype Circuit Configurations
3.9 Effect of Dissipation
3.10 Asymmetric Response Filters
Summary
References
Appendix 3A
Chapter 4: Computer-Aided Synthesis of Characteristic Polynomials
4.1 Objective Function and Constraints for Symmetric Lowpass Prototype Filter Networks
4.2 Analytic Gradients of the Objective Function
4.3 Optimization Criteria for Classical Filters
4.4 Generation of Novel Classes of Filter Functions
4.5 Asymmetric Class of Filters
4.6 Linear Phase Filters
4.7 Critical Frequencies for Selected Filter Functions
Summary
References
Appendix 4A
Chapter 5: Analysis of Multiport Microwave Networks
5.1 Matrix Representation of Two-Port Networks
5.2 Cascade of Two Networks
5.3 Multiport Networks
5.4 Analysis of Multiport Networks
Summary
References
Chapter 6: Synthesis of a General Class of the Chebyshev Filter Function
6.1 Polynomial Forms of the Transfer and Reflection Parameters
S
21
(
S
) and
S
11
(
S
) for a Two-port network
6.2 Alternating Pole Method for the Determination of the Denominator Polynomial
E
(
s
)
6.3 General Polynomial Synthesis Methods for Chebyshev Filter Functions
6.4 Predistorted Filter Characteristics
6.5 Transformation for Symmetric Dual-Passband Filters
Summary
References
A6.1 Change of Termination Impedance
References
Chapter 7: Synthesis of Network-Circuit Approach
7.1 Circuit Synthesis Approach
7.2 Lowpass Prototype Circuits for Coupled-Resonator Microwave Bandpass Filters
7.3 Ladder Network Synthesis
7.4 Synthesis Example of an Asymmetric (4–2) Filter Network
Summary
References
Chapter 8: Synthesis of Networks: Direct Coupling Matrix Synthesis Methods
8.1 The Coupling Matrix
8.2 Direct Synthesis of the Coupling Matrix
8.3 Coupling Matrix Reduction
8.4 Synthesis of the
N
+ 2 Coupling Matrix
8.5 Even- and Odd-Mode Coupling Matrix Synthesis Technique: the Folded Lattice Array
Summary
References
Chapter 9: Reconfiguration of the Folded Coupling Matrix
9.1 Symmetric Realizations for Dual-Mode Filters
9.2 Asymmetric Realizations for Symmetric Characteristics
9.3 “Pfitzenmaier” Configurations
9.4 Cascaded Quartets (CQs): Two Quartets in Cascade for Degrees Eight and Above
9.5 Parallel-Connected Two-Port Networks
9.6 Cul-de-Sac Configuration
Summary
References
Chapter 10: Synthesis and Application of Extracted Pole and Trisection Elements
10.1 Extracted Pole Filter Synthesis
10.2 Synthesis of Bandstop Filters Using the Extracted Pole Technique
10.3 Trisections
10.4 Box Section and Extended Box Configurations
Summary
References
Chapter 11: Microwave Resonators
11.1 Microwave Resonator Configurations
11.2 Calculation of Resonant Frequency
11.3 Resonator Unloaded
Q
Factor
11.4 Measurement of Loaded and Unloaded
Q
Factor
Summary
References
Chapter 12: Waveguide and Coaxial Lowpass Filters
12.1 Commensurate-Line Building Elements
12.2 Lowpass Prototype Transfer Polynomials
12.3 Synthesis and Realization of the Distributed Stepped Impedance Lowpass Filter
12.4 Short-Step Transformers
12.5 Synthesis and Realization of Mixed Lumped/Distributed Lowpass Filters
Summary
References
Chapter 13: Waveguide Realization of Single- and Dual-Mode Resonator Filters
13.1 Synthesis Process
13.2 Design of the Filter Function
13.3 Realization and Analysis of the Microwave Filter Network
13.4 Dual-Mode Filters
13.5 Coupling Sign Correction
13.6 Dual-Mode Realizations for Some Typical Coupling Matrix Configurations
13.7 Phase- and Direct-Coupled Extracted Pole Filters
13.8 The “Full-Inductive” Dual-Mode Filter
Summary
References
Chapter 14: Design and Physical Realization of Coupled Resonator Filters
14.1 Circuit Models for Chebyshev Bandpass Filters
14.2 Calculation of Interresonator Coupling
14.3 Calculation of Input/Output Coupling
14.4 Design Example of Dielectric Resonator Filters Using the Coupling Matrix Model
14.5 Design Example of a Waveguide Iris Filter Using the Impedance Inverter Model
Summary
References
Chapter 15: Advanced EM-Based Design Techniques for Microwave Filters
15.1 EM-Based Synthesis Techniques
15.2 EM-Based Optimization Techniques
15.3 EM-Based Advanced Design Techniques
Summary
References
Chapter 16: Dielectric Resonator Filters
16.1 Resonant Frequency Calculation in Dielectric Resonators
16.2 Rigorous Analyses of Dielectric Resonators
16.3 Dielectric Resonator Filter Configurations
16.4 Design Considerations for Dielectric Resonator Filters
16.5 Other Dielectric Resonator Configurations
16.6 Cryogenic Dielectric Resonator Filters
16.7 Hybrid Dielectric/Superconductor Filters
16.8 Miniature Dielectric Resonators
Summary
References
Chapter 17: Allpass Phase and Group Delay Equalizer Networks
17.1 Characteristics of Allpass Networks
17.2 Lumped-Element Allpass Networks
17.3 Microwave Allpass Networks
17.4 Physical Realization of Allpass Networks
17.5 Synthesis of Reflection-Type Allpass Networks
17.6 Practical Narrowband Reflection-Type Allpass Networks
17.7 Optimization Criteria for Allpass Networks
17.8 Dissipation Loss
17.9 Equalization Tradeoffs
Summary
References
Chapter 18: Multiplexer Theory and Design
18.1 Background
18.2 Multiplexer Configurations
18.3 RF Channelizers (Demultiplexers)
18.4 RF Combiners
18.5 Transmit–Receive Diplexers
Summary
References
Chapter 19: Computer-Aided Diagnosis and Tuning of Microwave Filters
19.1 Sequential Tuning of Coupled Resonator Filters
19.2 Computer-Aided Tuning Based on Circuit Model Parameter Extraction
19.3 Computer-Aided Tuning Based on Poles and Zeros of the Input Reflection Coefficient
19.4 Time-Domain Tuning
19.5 Filter Tuning Based on Fuzzy Logic Techniques
19.6 Automated Setups for Filter Tuning
Summary
References
Chapter 20: High-Power Considerations in Microwave Filter Networks: (Revised and augmented by Chandra M. Kudsia, Vicente E. Boria, and Santiago Cogollos)
20.1 Background
20.2 High-Power Requirements in Wireless Systems
20.3 High-Power Amplifiers (HPAs)
20.4 Gas Discharge
20.5 Multipaction Breakdown
20.6 High-Power Bandpass Filters
20.7 Passive Intermodulation (PIM) Consideration for High-Power Equipment
Summary
Acknowledgment
References
Chapter 21: Multiband Filters
21.1 Introduction
21.2 Approach I: Multiband Filters Realized by Having Transmission Zeros Inside the Passband of a Bandpass Filter
21.3 Approach II: Multiband Filters Employing Multimode Resonators
21.4 Approach III: Multiband Filters Using Parallel Connected Filters
21.5 Approach IV: Multiband Filter Implemented Using Notch Filters Connected in Cascade with a Wideband Bandpass
21.6 Use of Dual-Band Filters in Diplexer and Multiplexer Applications
21.7 Synthesis of Multiband Filters
Summary
References
Chapter 22: Tunable Filters
22.1 Introduction
22.2 Major Challenges in Realizing High-
Q
3D Tunable Filters
22.3 Combline Tunable Filters
22.4 Tunable Dielectric Resonator Filters
22.5 Waveguide Tunable Filters
22.6 Filters with Tunable Bandwidth
Summary
References
Chapter 23: Practical Considerations and Design Examples
23.1 System Considerations for Filter Specifications in Communication Systems
23.2 Filter Synthesis Techniques and Topologies
23.3 Multiplexers
23.4 High-Power Considerations
23.5 Tolerance and Sensitivity Analysis in Filter Design
Summary
Acknowledgments
Appendix 23A
References
Appendix A: Physical Constants
Appendix B: Conductivities of Metals
Appendix C: Dielectric Constants and Loss Tangents of Some Materials
Appendix D: Rectangular Waveguide Designation
Appendix E: Impedance and Admittance Inverters
E.1 Filter Realization with Series Elements
E.2 Normalization of the Element Values
E.3 General Lowpass Prototype Case
E.4 Bandpass Prototype
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 2: Fundamentals of Circuit Theory Approximation
Figure 2.1 Block diagram of an electrical system.
Figure 2.2 Relationships between the idealized elements in an electrical network: (a) a resistor; (b) an inductor; (c) a capacitor.
Figure 2.3 Time-domain analysis of a series
RLC
circuit.
Figure 2.4 Complex frequency plane.
Figure 2.5 Electrical network with an exponential input function.
Chapter 3: Characterization of Lossless Lowpass Prototype Filter Functions
Figure 3.1 Lowpass filter amplitude response: (a) ideal filter and (b) practical filter. (Note that
ω
c
represents the passband cutoff frequency and
ω
s
represents the lower edge of stopband;
α
p
and
α
s
represent the maximum and minimum attenuation in the passband and stopband, respectively.)
Figure 3.2 Power transfer in a two-port network.
Figure 3.3 Doubly terminated lossless transmission network.
Figure 3.4 Permissible zero locations of lowpass prototype characteristic polynomials, (a) zero locations of
F
(
s
), and (b) zero locations of
P
(
s
) on the
jω
axis, real axis, and as a complex quad.
Figure 3.5 Lowpass amplitude response shape of an all-pole filter with an arbitrary distribution of reflection zeros.
Figure 3.6 Lowpass amplitude response of a fourth-order filter with and without a finite transmission zero.
Figure 3.7 Lowpass amplitude response of three-pole maximally flat filter.
Figure 3.8 Plot of a fourth-order Chebyshev polynomial.
Figure 3.9 Lowpass amplitude response of a third-order Chebyshev filter.
Figure 3.10 Amplitude response of a third-order lowpass prototype elliptic filter.
Figure 3.11 Lowpass amplitude response of four-pole elliptic filters: (a) class A, (b) class B, and (c) class C four elliptic filters.
Figure 3.12 Comparison of four-pole maximally flat, Chebyshev, and elliptic function filters.
Figure 3.19 UDC nomenclature for (a) Butterworth and (b) Chebyshev filters.
Figure 3.21 UDC nomenclature for quasielliptic filter with a single pair of transmission zeros.
Figure 3.13 General forms of lowpass prototype lossless all-pole ladder filters: (a) shunt–series configuration and (b) series–shunt configuration.
Figure 3.14 General forms of lowpass prototype lossless ladder filters with transmission zeros: (a) using parallel resonators and (b) using series resonators.
Figure 3.15 Scaling of prototype networks: (a) prototype network and (b) scaled network.
Figure 3.16 Different representations of the frequency-invariant reactance (FIR) element.
Figure 3.17 Permissible zero locations of
P
(
s
) to realize asymmetric response filters: (a) asymmetric transmission zero location in the upper band, (b) asymmetric transmission zero locations in the upper and lower bands, and (c) asymmetric zero locations to realize linear phase response.
Figure 3.18 Lowpass amplitude response of a four-pole asymmetric filter.
Chapter 4: Computer-Aided Synthesis of Characteristic Polynomials
Figure 4.1 Attenuation zeros and maxima of a sixth-order Chebyshev filter.
Figure 4.2 Attenuation poles and minima of a sixth-order inverse Chebyshev filter.
Figure 4.3 Attenuation maxima and minima of a sixth-order lowpass prototype class C elliptic function filter.
Figure 4.4 Lowpass prototype response of an eighth-order filter with two attenuation poles and a double zero at the origin.
Figure 4.5 Frequency response of an optimized lowpass prototype eight-pole filter with two attenuation poles and a double zero at the origin: (a) an equiripple stopband; (b) a 10 dB differential in stopband minima.
Figure 4.6 Lowpass prototype response of a four-pole asymmetric filter with two attenuation poles in the upper half of the stopband.
Figure 4.7 Lowpass prototype response of a fourth-order asymmetric filter with two attenuation poles in the upper half of the frequency band and optimized for an equiripple response.
Figure 4.8 Lowpass prototype response of a fourth-order asymmetric filter with a double zero at the origin and two attenuation poles in the upper half of the frequency band.
Figure 4.9 Lowpass prototype response of a four-pole asymmetric filter with a double zero at the origin, two attenuation poles in the upper half of the frequency band, and optimized for the equiripple response.
Chapter 5: Analysis of Multiport Microwave Networks
Figure 5.1 An example of a microwave circuit.
Figure 5.2 A two-port microwave network.
Figure 5.3 Equivalent
T
and
π
networks of a two-port microwave network.
Figure 5.4 The
ABCD
representation of a two-port network.
Figure 5.5 Two networks cascaded in series.
Figure 5.6 The
S
matrix of a two-port network.
Figure 5.7 A shunt admittance connected between two ports having the same characteristic impedance.
Figure 5.8 A shunt admittance connected between two ports having different characteristic impedances.
Figure 5.9
T
matrix representation of a two-port network.
Figure 5.10 Two networks connected in cascade.
Figure 5.11 A two-port network terminated in load
Z
L
.
Figure 5.12 A two-port network with extended reference planes.
Figure 5.13 Two networks connected in cascade.
Figure 5.14 A two-port symmetric network divided into two identical halves (EW, MW = electric, magnetic walls).
Figure 5.15 Applying superposition principle to a two-port symmetric network.
Figure 5.16 Four two-port networks connected in cascade.
Figure 5.17 Two-port networks
A
and
B
connected in series.
Figure 5.18 Half-network terminated by electric wall.
Figure 5.19 Half-network terminated by magnetic wall.
Figure 5.20 A multiport network of
N
ports.
Figure 5.21 A four-port network (a) decomposed into two 2-port networks, (b) with electric wall, and (c) magnetic wall termination.
Figure 5.22 An arbitrary microwave network consisting of several multiport networks connected together.
Figure 5.23 Schematic of the four-port network.
Figure 5.24 A three-channel multiplexer.
Chapter 6: Synthesis of a General Class of the Chebyshev Filter Function
Figure 6.1 Two-port network.
Figure 6.3 Angles of
S
21
(
s
),
S
11
(
s
), and
S
22
(
s
) numerator polynomials for an arbitrary position of the frequency variable
s
on the imaginary axis: (a) for a transmission zero pair; (b) for an
S
11
(
s
) zero and the complementary
S
22
(
s
) zero.
Figure 6.2 Possible positions for the finite-position roots of
P
(
s
), the numerator of
S
21
(
s
). (a) Two asymmetric imaginary-axis zeros, (b) real-axis pair, and (c) complex pair.
Figure 6.4 Pattern of the roots of
E
(
s
)
E
(
s
)* in the complex plane (symmetric about imaginary axis).
Figure 6.5 Zeros of the polynomials for a sixth-degree case where (
N
−
n
fz
) is even (equation (6.39b)): (a) and (b) .
Figure 6.6 Function
x
n
(
ω
) in the
ω
-plane with a prescribed transmission zero at
ω
n
= +1.3.
Figure 6.7 Lowpass prototype transfer and reflection characteristics of the 4–2 asymmetric Chebyshev filter with two prescribed transmission zeros at
s
1
= +
j
1.3217 and
s
2
= +
j
1.8082.
Figure 6.8 Transfer characteristics of a (4–2) bandpass filter with
Q
u
= infinity, 10,000, and 4000: (a) rejection, (b) in-band insertion loss.
Figure 6.9 Track of the frequency variable
s
in the complex plane with a finite-value
Q
u
.
Figure 6.10 Predistortion synthesis: (a) poles shifted to right by amount
σ
before synthesis. (b) Poles are now in correct nominal positions relative to the track of the frequency variable with loss (
s = σ + jω
) to give equivalent lossless response under analysis.
Figure 6.11 Predistorted 4–2 filter with
Q
act
= 4000 and
Q
eff
= 10,000. (a) Predistorted rejection characteristics with
Q
u
= infinity and
Q
act
= 4000 (effective
Q
of 10,000) and (b) in-band return loss and insertion loss compared with that of filter without predistortion.
Figure 6.12 Predistorted C-band (10–4–4) coaxial filter: (a) Comparison with unpredistorted dielectric filter. (b) Rejection performance. (c) In-band insertion loss performance. (
Source
: Courtesy ComDev).
Figure 6.13 Possible arrangements for the zeros
s
k
of
F
(
s
) for the symmetric 6–2 quasielliptic characteristic.
Figure 6.14 Dual-band filters: (a) (4–2) asymmetric lowpass prototype filter and (b) after transform to dual-band lowpass prototype with
x
1
= 0.4.
Figure 6.15 Coupling matrix for (8–4) dual-band filtering characteristic (folded-array configuration).
Chapter 7: Synthesis of Network-Circuit Approach
Figure 7.1 (a)
Y
in
= 0 when
s
=
s
0
= 0; therefore, this lowpass resonator resonates at zero frequency; (b) when
s
=
s
0
. Thus the resonant frequency is offset by from the nominal center frequency.
Figure 7.2 Basic lowpass prototype circuit (third-degree).
Figure 7.3 Lowpass prototype ladder networks: (a) where the leading component is a shunt capacitor; (b) the dual of the network.
Figure 7.4 Third-degree lowpass prototype ladder network: the form after addition of the unit inverters.
Figure 7.5 Steps in the synthesis process for a fourth-degree coaxial resonator bandpass filter.
Figure 7.6 Singly terminated filter network: (a) network with zero-impedance voltage source; (b) network replaced with equivalent
π
network; (c) Thévenin equivalent circuit with load impedance
Z
L
attached.
Figure 7.7 Second-degree ladder network with FIRs and inverters.
Figure 7.8 Extraction of the admittance inverter.
Figure 7.9 Extraction of a parallel-coupled inverter (PCI): (a) overall network as represented by [
ABCD
] matrix; (b) with an inverter of characteristic admittance
J
in parallel with the remainder matrix [
ABCD
]
rem
.
Figure 7.10 Cross-coupled array components and their extraction formulas: (a) transmission line and special case where and
Y
0
= 1 (unit inverter); (b) shunt-connected frequency-variant capacitor; (c) shunt-connected frequency-invariant reactance; (d) parallel cross-coupling inverter.
Figure 7.11 Folded cross-coupled network for the (4–2) asymmetric prototype.
Figure 7.12 Lumped-element lowpass prototype ladder networks.
Chapter 8: Synthesis of Networks: Direct Coupling Matrix Synthesis Methods
Figure 8.1 Multi-coupled series-resonator “bandpass prototype” network: (a) classical representation
Figure 8.2 Bandpass to lowpass frequency mapping.
Figure 8.3 Lowpass prototype equivalent of the bandpass network as shown in Figure 8.1b with inverter coupling elements.
Figure 8.4 Overall impedance matrix [
z
′] of the series-resonator circuits of Figure 8.3 operating between a source impedance
R
S
and a load impedance
R
L
.
Figure 8.5 Configurations of the input and output circuits for the
N
×
N
and
N
+ 2 coupling matrices. (a) The series-resonator circuit in Figure 8.4 represented as an (
N
×
N
) impedance coupling matrix between terminations
R
S
and
R
L
. (b) The circuit in (a) withinverters to normalize the terminations to unity. (c)
N
+ 2 matrix (parallel resonators) and normalized terminating conductances
G
S
and
G
L
. (d)
N
+ 2 impedance matrix with series resonators and normalized terminating resistances
R
S
and
R
L
, the dual network of (c).
Figure 8.6
N
+ 2 multi-coupled network with parallel “lowpass resonators.”
Figure 8.7 Fourth-degree
N
+ 2 coupling matrix with all possible cross-couplings. The “core”
N
×
N
matrix is indicated within the double lines. The matrix is symmetric about the principal diagonal, that is,
M
ij
=
M
ji
.
Figure 8.8 Network between source
e
g
of impedance
R
S
and load of impedance
R
L
.
Figure 8.9
N
×
N
folded canonical network coupling matrix form—seventh-degree example. “s” and “xa” couplings are zero for symmetric characteristics.
Figure 8.10 Example of seventh-degree rotation matrix
R
r
—pivot [3, 5], angle
θ
r
.
Figure 8.11 Seventh-degree coupling matrix: reduction sequence for folded canonical form. The shaded elements are those that may be affected by a similarity transform at pivot [3, 5], angle
θ
r
(≠0). All others remain unchanged.
Figure 8.12 7-1-2 asymmetric single-terminated filter—
N
×
N
coupling matrix before application of reduction process. Element values are symmetric about the principal diagonal. .
Figure 8.13 7-1-2 asymmetric single-terminated filter—
N
×
N
coupling matrix after reduction to folded form (
M
10
).
Figure 8.14 7-1-2 asymmetric single-terminated filter synthesis example—analysis of folded coupling matrix: (a) rejection and return loss and (b) group delay.
Figure 8.15 Realization in folded configuration: (a) folded network coupling and routing schematic and (b) corresponding realization in coaxial-resonator technology.
Figure 8.16 Canonical transversal array. (a)
N
—resonator transversal array including direct source–load coupling
M
SL
; (b) equivalent circuit of the
k
th “lowpass resonator” in the transversal array.
Figure 8.17 Equivalent circuit of transversal array at .
Figure 8.18
N
+ 2 fully canonical coupling matrix
M
for the transversal array. The “core”
N
×
N
matrix is indicated within the double lines. The matrix is symmetric about the principal diagonal, that is,
M
ij
=
M
ji
.
Figure 8.19 Folded
N
+ 2 canonical network coupling matrix form—fifth-degree example: (a) folded coupling matrix form. “s” and “xa” couplings are in general zero for symmetric characteristics; (b) coupling and routing schematic.
Figure 8.20 Transversal coupling matrix for a 4-4 fully canonical filtering function. The matrix is symmetric about the principal diagonal.
Figure 8.21 Fully canonical synthesis example. Folded coupling matrix for 4-4 filtering function. (a) Coupling matrix. Matrix is symmetric about the principal diagonal. (b) Coupling and routing schematic.
Figure 8.22 4-4 fully canonical synthesis example: analysis of folded coupling matrix. Rejection as .
Figure 8.23 4-2 asymmetric filtering function. (a) Coupling matrix with complex source and load terminations
Z
S
= 0.5 +
j
0.6 and
Z
L
= 1.3 −
j
0.8. (b) For comparison, the equivalent coupling matrix with source and load values
Z
S
=
Z
L
= 1.0.
Figure 8.24 4-4 fully canonical asymmetric coupling matrix with complex source and load terminations
Z
S
= 0.5 +
j
0.6 and
Z
L
= 1.3 −
j
0.8.
Figure 8.25 Folded lattice network: (a) circuit schematic—sixth-degree example; (b) corresponding coupling and routing diagram; (c) fifth (odd)-degree coupling and routing diagram. All components are equal-valued about the plane of symmetry.
Figure 8.26 Bisection of “straight” cross-couplings through plane of symmetry: (a) even mode; (b) odd mode.
Figure 8.27 Bisection of diagonal cross-couplings through plane of symmetry: (a) first section of lattice network (sixth-degree example); (b) equivalent for even mode; (c) equivalent for odd mode.
Figure 8.28 Bisection of central resonant node for an odd degree case—fifth-degree example. Because of symmetry,
M
23
=
M
34
.
Figure 8.29 Even and odd-mode one-port networks; (a) even mode; (b) odd mode.
Figure 8.30 Synthesis of even- and odd-mode admittance functions from the Hurwitz zeros of
E
(
s
) [poles of
S
21
(
s
) and
S
11
(
s
)].
Figure 8.31 Coupling matrix for sixth-degree example synthesized as a symmetric lattice network, showing the two planes of symmetry.
Figure 8.32 Sixth-degree example—folded (reflex) coupling matrix topology after two similarity transforms (rotations).
Figure 8.33 Analysis of sixth-degree symmetric lattice coupling matrix—transfer and reflection characteristics.
Chapter 9: Reconfiguration of the Folded Coupling Matrix
Figure 9.1 Sixth-degree network: (a) cross-coupled folded configuration; (b) after conversion to inline topology.
Figure 9.2 Stages in the transformation of a sixth-degree folded coupling matrix to the symmetric inline form.
Figure 9.3 Eighth-degree network: (a) cross-coupled folded configuration; (b) after conversion to inline topology.
Figure 9.4 10th-degree network: (a) cross-coupled folded configuration; (b) after conversion to inline topology.
Figure 9.5 12th-degree network: (a) cross-coupled folded configuration; (b) after conversion to inline topology.
Figure 9.6 Pfitzenmaier configuration for (6–4) symmetric filtering characteristic: (a) original folded configuration; (b) after transformation to the Pfitzenmaier configuration.
Figure 9.7 Formation of Pfitzenmaier topology: (a) original folded CM; (b) pivot at [2, 6] to annihilate
M
27
, creating
M
16
and
M
25
; (c) pivot at [3, 5] to annihilate
M
36
.
Figure 9.8 Pfitzenmaier configuration for 8th-degree symmetric filtering characteristic: (a) original folded configuration; (b) after transformation to Pfitzenmaier configuration.
Figure 9.9 Cascade quartet (CQ) configuration with the eighth-degree symmetric filtering characteristic: (a) original folded configuration; (b) after the transformation to form two CQs.
Figure 9.10 Quasi-Pfitzenmaier topology for canonical 8th-degree symmetric filtering characteristic: (a) original folded configuration; (b) after transformation to form two CQs and retaining the
M
18
coupling.
Figure 9.11 Coupling submatrix (a) and coupling–routing diagram (b) for residues
k =
1 and 6.
Figure 9.12 Coupling submatrix (a) and coupling–routing diagram (b) for residue group
k =
2, 3, 4, 5.
Figure 9.13 Superimposed 2nd- and 4th-degree submatrices: (a) coupling matrix; (b) coupling–routing diagram.
Figure 9.14 Analysis of parallel-connected two-port coupling matrix: (a) rejection and return loss; (b) group delay.
Figure 9.15 Symmetric (6–2–2) filter configured as parallel-coupled pairs: (a) coupling matrix; (b) coupling–routing diagram; (c) multilayer dual-mode patch resonator realization.
Figure 9.16 Cul-de-sac network configurations: (a) (10–3–4) filter network; (b) (7–1–2) filter network.
Figure 9.17 Example of the seventh-degree filter in cul-de-sac configuration: (a) original folded coupling matrix; (b) after transformation to cul-de-sac configuration.
Figure 9.18 Example of the simulated performance of a (7–1–2) asymmetric filter: (a) rejection and return loss; (b) group delay.
Figure 9.19 Example of a (7–1–2) asymmetric filter in coaxial cavity configurations: (a) folded network configuration; (b) cul-de-sac configuration.
Figure 9.20 Three alternative forms for the cul-de-sac configuration: (a) the indirect-coupled, (b) fully canonical form, and (c) rat-race coupled even- and odd-mode one-port networks.
Figure 9.21 Canonical cul-de-sac coupling matrix for symmetric (6–2) characteristic.
Figure 9.22 (8–3) asymmetric filter example: (a) folded coupling matrix; (b) same matrix after transformation to the indirect cul-de-sac configuration.
Figure 9.23 Simulated and measured performance of the (8–3) cul-de-sac filter.
Figure 9.24 Indirect-coupled cul-de-sac configuration for the (8–3) asymmetric filter.
Figure 9.25 Sensitivity to variations in the coupling value: (a) nominal 11–3 characteristic; (b) cul-de-sac—random variations to all the couplings; (c) cul-de-sac—0.2% increase to the self-couplings, 0.2% decrease to all others; (d) box filter—0.2% increase to self-couplings, 0.2% decrease to all others.
Chapter 10: Synthesis and Application of Extracted Pole and Trisection Elements
Figure 10.1 Shunt-connected series pair producing a short circuit at
s = s
0
.
Figure 10.2 Input impedance/admittance as
s
approaches
s
0
.
Figure 10.6 (4–2) extracted pole filter in cylindrical TE
011
-mode resonator cavities: (a) both poles cavities on the input side; (b) one pole cavity synthesized within the main body.
Figure 10.3 (4–2) extracted pole filter, synthesized network with both poles on input side.
Figure 10.4 Possible realizations for the extracted pole: (a) parallel-connected (waveguide
H
plane); (b) series-connected (waveguide
E
plane).
Figure 10.5 Development of the shunt resonant pair into an inverter and short-circuited half-wavelength transmission line.
Figure 10.7 Admittance submatrices: (a) phase length + extracted pole; (b) phase length + coupling inverter; (c) prototype resonator node + inverter; (d) prototype resonator node + inverter + phase length.
Figure 10.8 Superimposition of the admittance submatrices to form an overall admittance matrix.
Figure 10.9 Equivalence of phase length with inverter surrounded by two FIRs.
Figure 10.10 (4–2) asymmetric filter—phase-coupled extracted pole network.
Figure 10.11 (4–2) asymmetric filter—direct-coupled extracted pole realization.
Figure 10.12 (4–2) asymmetric filter, the direct-coupled extracted pole realization: (a) coupling matrix. Nodes N1 and N2 (as well as the
S
and
L
nodes) are NRNs; (b) coupling and routing diagram; (c) realization in waveguide cavities; (d) alternative realization with waveguide resonant cavities.
Figure 10.13 Fourth-degree bandstop filter realized in a rectangular waveguide.
Figure 10.14 (4–4) bandstop filter network.
Figure 10.15 Direct-coupled (4–2) bandstop filter: (a) coupling–routing diagram; (b) possible realization with coaxial cavities.
Figure 10.16 Cul-de-sac forms for direct-coupled bandstop filters: (a) sixth degree; (b) seventh degree. (c) seventh degree bandstop filter—hybrid-coupled even- and odd-mode networks.
Figure 10.17 (4–2) Direct-coupled cul-de-sac bandstop filter: (a) coupling and routing diagram; (b) possible realization with waveguide cavities; (c) rejection and return loss performance.
Figure 10.18 Coupling–routing diagram for trisections: (a) internal; (b) source connected; (c) load connected; (d) canonical; (e) nonconjoined cascaded; (f) conjoined cascaded.
Figure 10.19 Trisection realization for the (4–2) asymmetric filter characteristic.
Figure 10.20
N
+ 2 coupling matrix for the (4–2) asymmetric characteristic synthesized with trisections: (a) coupling matrix; (b) possible realization with two dual-mode dielectric resonator cavities.
Figure 10.21 Fifth-degree wheel or arrow canonical circuit: (a) coupling–routing diagram (wheel); (b)
N
+ 2 coupling matrix (arrow).
Figure 10.22 (8–2–2) filter synthesis example: (a) initial arrow coupling matrix; (b) corresponding coupling–routing diagram; (c) rotation 1 creates first trisection at index position 7; (d) rotation 2 pulls the trisection to index position 6; (e) rotation 6 positions the first trisection at index position 2.
Figure 10.23 (8–2–2) asymmetric filter function: (a) coupling matrix after synthesis of two trisections; (b) coupling–routing diagram; (c) coupling–routing diagram after formation of two quartets.
Figure 10.24 Complex zero pairs: realization with cascade quartets.
Figure 10.25 Formation of cascade quartet: (a) realization of TZs with two trisections (see Figure 10.26a) (trisection cross-couplings shown in bold); (b) annihilation of
M
35
, creating
M
14
and
M
24
(Figure 10.26b); (c) rotation at [2, 3] to annihilate
M
13
and thus create first quartet in Figure 10.26c.
Figure 10.26 Transformation of two conjoined trisections to form a quartet section.
Figure 10.27 Formation of cascade quintet: (a) realization of TZs with three trisections (trisection cross-couplings shown in bold); (b) annihilation of
M
S
2
and
M
46
; (c) after series of three rotations to create the folded network in submatrix.
Figure 10.28 Transformation of three conjoined trisections to form a quintet section.
Figure 10.29 Formation of cascade sextet: (a) realization of TZs with four trisections (trisection cross-couplings are shown in bold); (b) annihilation of
M
S
2
and
M
68
; (c) after series of six rotations to create a folded network within the submatrix.
Figure 10.30 Transformation of four conjoined trisections to form a sextet section. Rotation 2 annihilates
M
68
and creates
M
57
and
M
47
, which are annihilated by rotations 3 and 4.
Figure 10.31 (4–1) asymmetric filter function: (a) realized with the conventional diagonal cross-coupling (
M
13
); and (b) realized with the box configuration.
Figure 10.32 Formation of the box section for the (4–1) filter: (a) the trisection; (b) annihilation of
M
23
and creation of
M
24
; (c) untwisting to obtain box section.
Figure 10.33 (4–1) filter coupling matrices: (a) the trisection; (b) after transformation to box section (TZ on upper side of passband); (c) TZ on lower side of passband.
Figure 10.34 Measured results of the (4–1) filter: (a) transmission zero on upper side; (b) transmission zero on lower side.
Figure 10.35 Coupling and routing diagrams of the (10–2) asymmetric filter: (a) synthesized with two trisections; (b) after transformation of trisections to two box sections by application of two cross-pivot rotations at pivots [2, 3] and [8, 9]. This form is suitable for realization in a dual-mode technology.
Figure 10.36 Simulated and measured return loss and rejection of the (10–2) asymmetric filter.
Figure 10.37 8th-degree network—two box sections conjoined at one corner.
Figure 10.38 Coupling and routing diagrams for extended box section networks (a) 4th degree (basic box section); (b) 6th degree; (c) 8th degree; (d) 10th degree.
Figure 10.39 Extended box section configuration of an 8th-degree example: (a) original folded coupling matrix; (b) after transformation to extended box section configuration.
Figure 10.40 (8–3) asymmetric filter in an extended box section configuration—simulated rejection and return loss performance.
Figure 10.41 Stages in the synthesis of an (11–3) network with cascaded box sections: (a) initial synthesis with trisections; (b) formation of cascaded quad section; (c) formation of the 6th-degree extended box section in cascade with a basic box section.
Chapter 11: Microwave Resonators
Figure 11.1 Lumped-element resonators realized by (a) a chip inductor and a chip capacitor and (b) spiral inductor and interdigital capacitor.
Figure 11.2 Examples of microstrip resonator configurations: (a) half-wavelength resonator; (b) ring resonator; (c) rectangular patch resonator.
Figure 11.3 Examples of three-dimensional cavity resonators: (a) coaxial resonator; (b) rectangular waveguide resonator; (c) circular waveguide resonator; (d) dielectric resonator.
Figure 11.4 Application of the various resonator configurations.
Figure 11.5 Typical relative size and insertion loss of various resonators.
Figure 11.6 A transmission line terminated in short circuit at both ends.
Figure 11.7 Mode chart for the resonant modes in circular waveguide resonators [1].
Figure 11.8 A microstrip transmission line loaded with a rectangular strip.
Figure 11.9 A two-port representation of the discontinuity shown in Figure 11.8.
Figure 11.10 The field distribution of the first eigenmode solution of a top-loaded coaxial resonator.
Figure 11.11 One-port
S
-parameter analysis of a top-loaded coaxial resonator.
Figure 11.12 Comparison between the one-port
S
-parameter analysis and the two-port
S
-parameter analysis for a microstrip resonator as calculated by HFSS.
Figure 11.13 One-port analysis of a dielectric resonator illustrating the resonant frequencies of single and dual modes.
Figure 11.14 (a) A
λ
/2 short-circuit transmission line; (b)
λ
/2 open-circuit transmission line.
Figure 11.15 A plot of
Q
for various modes for circular waveguide cavities [1].
Figure 11.16 A resonator inductively coupled to an input port.
Figure 11.17 Resonator loading caused by input coupling.
Figure 11.18 The
Q
circle on the Smith chart.
Figure 11.19 A
λ
/2 transmission-line resonator capacitively coupled to an input port.
Figure 11.20 The
Q
circles for the circuit shown in Figure 11.19: (a) , undercoupled; (b) , overcoupled; (c) , critical coupled; (d) , critical coupled.
Figure 11.21 The reflection coefficient at two frequencies around
f
L
on the
Q
circle [20].
Figure 11.22 The reflection coefficient on a linear scale.
Chapter 12: Waveguide and Coaxial Lowpass Filters
Figure 12.1 Commensurate-line equivalents for (a) lumped inductor and (b) lumped capacitor.
Figure 12.2 Unit element (UE) and associated [
A B C D
] transfer and admittance matrix.
Figure 12.3 Comparison of Chebyshev functions of the first and second kinds, with a full-zero pair (first kind), and a half-zero pair (second kind).
Figure 12.4 In-band (voltage) amplitude of (a) an eighth-degree function and (b) a ninth-degree Zolotarev function.
Figure 12.5 Comparison of seventh-degree Chebyshev and Zolotarev functions: (a) in-band amplitude and (b) out-of-band rejection.
Figure 12.6 Stepped impedance LPF mapping of an all-pole transfer and reflection function from the
ω
plane to the
θ
plane through the mapping function .
Figure 12.7 Commensurate-line lengths (UEs): (a) single UE and (b) two UEs in cascade.
Figure 12.8 Sixth-degree stepped impedance LPF prototype circuit and direct rectangular waveguide realization.
Figure 12.9 Introduction of redundant inverters and impedance scaling.
Figure 12.10 Sixth-degree stepped impedance LPF in a rectangular waveguide.
Figure 12.11 Rejection and return loss of the sixth-degree 26 dB return loss stepped impedance lowpass filter, with and .
Figure 12.12 Equivalent circuits: (a) impedance inverter and (b) capacitive iris in a rectangular waveguide.
Figure 12.13 Comparison of the rejection performance of a sixth-degree stepped impedance LPF with and without frequency variation in the UEs.
Figure 12.14 Insertion loss and return loss characteristics of the 1:4 short-step transformer: (a) and (b) .
Figure 12.15 Basic prototype elements of the lumped/distributed filter: (a) double-length unit element with a shunt-connected open-circuited UE at each end (distributed capacitors) and (b) with the distributed capacitors represented by their lumped equivalents.
Figure 12.16 Mapping of the seventh-degree Zolotarev transfer and reflection functions from the
ω
plane (a) to the
θ
plane (b) through the mapping function , where . In this case , , and the return loss = 30 dB.
Figure 12.17 Components of the tapered–corrugated LPF: (a) double unit element and (b) distributed shunt capacitor.
Figure 12.18 Initial synthesis cycle for the lumped/distributed LPF ladder network; the original matrix comprises a shunt capacitor + double UE + remainder matrix [
A B C D
]
(2)
.
Figure 12.19 Relationships of the components of the prototype lumped/distributed LPF network to a waveguide structure (o/c = open circuit).
Figure 12.20 Equivalent circuits: (a) shunt-distributed capacitor and (b) capacitive iris in rectangular waveguide.
Figure 12.21 Rejection and return loss performance of a degree 49 Zolotarev LPF, designed by extrapolation from a degree 31 prototype.
Figure 12.22 Theoretical passbands of the lowpass filter to higher-order TE modes. The TE
10
mode forms the primary passband.
Figure 12.23 Seventeenth-degree lumped/distributed lowpass filter with transformers.
Figure 12.24 Mode-matching analysis of the 17th-degree Chebyshev lumped/distributed LPF.
Chapter 13: Waveguide Realization of Single- and Dual-Mode Resonator Filters
Figure 13.1 Plot of function
F
(
s
)/
P
(
s
) for a (4–2) asymmetric filtering function.
Figure 13.2 Flow diagram for the group delay equalization process.
Figure 13.3 An eighth-degree filter function with two rejection lobes and a group delay compensation slope: (a) rejection and return loss; (b) group delay.
Figure 13.4 Realization process, from prototype filtering function via a coupling matrix to the realization in a rectangular waveguide.
Figure 13.5 Equivalence of impedance inverter and shunt reactance symmetrically placed in a length of transmission line.
Figure 13.6 Rectangular waveguide resonators where the endwall is coupled: (a) rectangular waveguide resonator
R
j
; (b) open-wire electrical equivalent circuit.
Figure 13.7 Rectangular waveguide resonators with sidewall coupling: (a) sidewall coupling between rectangular waveguide resonators
R
j
and
R
l
; (b) open-wire electrical equivalent circuit.
Figure 13.9 Realization of (6–2) extended box filter in rectangular waveguide TE
103
-mode cavities.
Figure 13.8 Extended box (6–2) filter prototype: (a) prototype coupling matrix; (b) coupling–routing diagram.
Figure 13.10 RF analysis of open-wire circuit model of (6–2) asymmetric filter in extended box configuration.
Figure 13.11 Dual-mode resonator cavities: (a) two cylindrical waveguide dual-mode cavities and interconnecting iris plate; (b) corresponding coupling–routing diagram; (c) relations between the mode polarization vectors and tuning screws, coupling screws, and coupling irises.
Figure 13.12 Creation of a virtual negative coupling between dual-mode cavities: (a)
M
14
positive; (b)
M
14
negative.
Figure 13.13 Coupling sign correction by the method of enclosures: (a) negative sign on
M
56
; (b) moving the negative sign to iris couplings—every coupling the enclosure cuts changes the sign; (c) dual-mode realization.
Figure 13.14 Two examples of multiple sign corrections on coupling–routing diagrams by the method of enclosures: (a)
M
34
and
M
56
negative; (b)
M
12
,
M
34
, and
M
56
negative.
Figure 13.15 Realization of an eighth-degree folded configuration coupling matrix in dual-mode filter structure: (a) folded
N
×
N
coupling matrix; (b) corresponding coupling–routing diagram; (c) dual-mode cavity arrangement; (d) cavity–iris arrangement.
Figure 13.16 Pfitzenmaier dual-mode filter arrangement—eighth-degree example: (a) coupling–routing diagram; (b) dual-mode structure; and (c) cavity–iris relationships.
Figure 13.17 “Propagating” dual-mode filter arrangement for an eighth-degree filter; (a) coupling–routing diagram; (b) dual-mode structure; (c) cavity–iris relationships.
Figure 13.18 Cascade quartet dual-mode filter arrangement for an eighth-degree filter: (a) coupling–routing diagram; (b) dual-mode structure; (c) cavity–iris relationships.
Figure 13.19 Extended box dual-mode filter arrangement for a sixth-degree filter: (a) dual-mode structure; (b) cavity–iris relationships.
Figure 13.20 Sixth-degree rectangular waveguide filter with two
E
-plane extracted poles: (a) waveguide realization; (b) development of one of the prototype extracted poles to the waveguide equivalent circuit.
Figure 13.21 Dual-mode rectangular waveguide resonant cavity.
Figure 13.22 An example of a fourth-degree filter with two full-inductive dual-mode resonator cavities.
Figure 13.23 Full-inductive dual-mode filter equivalent circuits: (a) two cascaded cavities (4th degree) with TE
102
/TE
201
-mode dual resonances; (b) three cascaded cavities (6th degree) with TE
m
0
n
/TE
p
0
q
-mode dual resonances.
Figure 13.24 Full-inductive dual-mode realization for asymmetric (6–2) filter characteristic: (a) the coupling matrix; (b) analysis of an equivalent circuit at RF.
Chapter 14: Design and Physical Realization of Coupled Resonator Filters
Figure 14.1 Several waveguide, dielectric resonator, and coaxial and microstrip filter components illustrating interresonator coupling and input/output coupling.
Figure 14.2 (a) Coupling matrix model for Chebyshev filters, (b) impedance inverter model for Chebyshev filters, and (c) admittance inverter model for Chebyshev filters.
Figure 14.3 (a) Impedance inverter—equivalent circuit of two resonators separated by an inductive coupling, (b) half of the circuit terminated in a magnetic wall (even mode; open circuit), and (c) half of the circuit terminated in an electric wall (odd mode; short circuit).
Figure 14.4 (a) Admittance inverter—equivalent circuit of two resonators capacitively coupled, (b) magnetic wall (even mode), and (c) electric wall (odd mode).
Figure 14.5 Measurement of interresonator coupling using a two-port network and a one-port network.
Figure 14.6 The return loss of the circuits shown in Figure 14.5.
Figure 14.7 Interresonator coupling calculation using
S
-parameters: (a) coupling iris in a rectangular waveguide, (b) equivalent
S
matrix, and (c) equivalent T network that is used to calculate the coupling between two resonators.
Figure 14.8 Equivalent circuit of the input coupling and first resonator.
Figure 14.9 The four-pole dielectric resonator filter.
Figure 14.10 The simulated ideal response of the filter based on the coupling matrix model.
Figure 14.11 Dielectric resonator configuration, ; ; ; support, ; ; ; cavity, ; ; mode 1, (HFSS version 8.5); and mode 2, (HFSS version 8.5).
Figure 14.12 The two-coupled dielectric resonator structure.
Figure 14.13 Resonator coupling (
k
) versus iris window (
W
), calculated from the data given in Table 14.2.
Figure 14.14 Calculation of the resonance frequency of the resonator including the effect of the iris. The adjacent cavities are detuned by removing the dielectric resonators.
Figure 14.15 Calculation of the
Q
e
and resonance frequency of the first resonator, factoring in the effect of iris loading.
Figure 14.16 Physical dimensions of probe used for the first and last cavities:
a
= 0.044 in.;
b
= 0.1 in.;
G
= 0.01 in.,
F
= 7.47 mm;
H
= length of the probe inside cavity. (a) Top view and (b) side view.
Figure 14.17 (a) HFSS simulation results based on physical dimensions given in Table 14.5 and (b) comparison with ideal response.
Figure 14.18 Four-pole waveguide iris filter: (a) top view of filter, (b) equivalent circuit, and (c) modified equivalent circuit.
Figure 14.19 A comparison between the ideal response and the mode matching EM simulation results of the designed filter whose dimensions are given in Table 14.6.
Figure 14.21 The equivalent circuit of the capacitive microstrip discontinuity.
Figure 14.20 The six-pole capacitive coupled microstrip filter: (a) top view of filter, (b) equivalent circuit, and (c) modified equivalent circuit.
Figure 14.22 Agilent ADS circuit simulation of the design given in Table 14.7.
Figure 14.23 Agilent Momentum EM simulation results of the design given in Table 14.10.
Chapter 15: Advanced EM-Based Design Techniques for Microwave Filters
Figure 15.1 EM-based optimization process.
Figure 15.2 Sample frequency points taken over the passband and stopband.
Figure 15.3 (a) The complete filter circuit; (b) the filter circuit divided into subsections cascaded by transmission lines.
Figure 15.4 (a) The EM simulation results of circuit shown in Figure 15.3a; (b) the simulation results obtained using the semi-EM simulation approach for the circuit shown Figure 15.3b.
Figure 15.5 Comparison between Cauchy (a) and spline (b) interpolation for four-pole filter.
Figure 15.6 Adaptive frequency sampling (num—numerator; denom—denominator).
Figure 15.7 A neural network consisting of three layers.
Figure 15.8 An inset-fed microstrip patch resonator.
Figure 15.9 Correlation between the
S
11
results obtained by the neural network and EM simulator (exact solution) for the resonator shown Figure 15.8 [21].
Figure 15.10 Schematic of a three-pole microstrip filter designed by the multidimensional Cauchy technique [17].
Figure 15.11 Simulation results for the three-pole microstrip filter shown in Figure 15.10 [17].
Figure 15.12 Representation of the fine and coarse models.
Figure 15.13 The original space mapping technique.
Figure 15.14 The Rosenbrock functions: (a) the fine model
R
f
(
x
1
,
x
2
); (b) the coarse model
R
c
(
x
1
,
x
2
).
Figure 15.15 The six-pole filter layout.
Figure 15.16 The coarse model of the microstrip filter shown in Figure 15.15.
Figure 15.17 The optimized filter response using the coarse model.
Figure 15.18 The filter responses after each iteration of the ASM technique.
Figure 15.19 Fine and coarse model functions.
Figure 15.20 The fine EM model of the three-pole microstrip filter.
Figure 15.21 The coarse model of the three-pole filter.
Figure 15.22 Comparison between results of the coarse model and the fine model.
Figure 15.23 The calibrated coarse model (CCM) technique.
Figure 15.24 A comparison between the fine model (solid line) and the calibrated coarse model (+ + +).
Figure 15.25 The calibrated coupling matrix technique.
Figure 15.27 The coarse model.
Figure 15.26 A six-pole filter designed using the generalized CCM technique. The EM simulation of the whole filter represents the fine model.
Figure 15.28 Coupling between various resonators of the microstrip filter shown in Figure 15.20.
Figure 15.29 Comparison between the solution of the calibrated model (corrected model) and the fine model [40].
Figure 15.30 Photograph of a superconductive filter designed using the CCM technique [40].
Chapter 16: Dielectric Resonator Filters
Figure 16.1 Various dielectric materials commercially available for dielectric resonator filter applications: (a) resonators and (b) resonators, supports, and substrates.
Figure 16.2 A dielectric resonator consisting of a dielectric puck mounted inside a metal enclosure.
Figure 16.3 Cylindrical dielectric resonator.
Figure 16.4 Analytic solution of diameter versus resonant frequency,
D
/
L
= 3 and
ϵ
r
= 45.
Figure 16.5 Comparison plot of resonant frequency versus diameter,
D
/
L
= 3 and
ϵ
r
= 45.
Figure 16.6 Dielectric resonator.
Figure 16.7 Electric field distribution of the TEH mode.
Figure 16.10 Electric field distribution of the HEE mode.
Figure 16.11 The mode chart for the first four modes of the dielectric resonator. (Generated from Table 16.2.)
Figure 16.12 A dielectric resonator filter in a planar configuration.
Figure 16.13 A dielectric resonator filter in an axial configuration.
Figure 16.14 An eight-pole dual-mode filter for CDMA applications [20].
Figure 16.15 A triple-mode dielectric resonator.
Figure 16.16 The quadruple-mode dielectric resonator illustrating the four orthogonal modes.
Figure 16.17 The typical support structure of a DR resonator.
Figure 16.18 Mixing of dielectric resonators with coaxial resonators to improve the filter spurious performance.
Figure 16.19 A coaxial cavity filter is added to improve the filter spurious performance [20].
Figure 16.20 Modified resonator configuration to improve the spurious performance of resonators operating in dual HEH modes.
Figure 16.21 Field distribution in dielectric resonators: (a) HE dual modes; (b) half-cut resonator terminated in a perfect electric wall; (c) half-cut resonator terminated in a perfect magnetic wall; and (d) half-cut resonator, with dielectric–air interface equivalent to termination with a nonperfect magnetic wall.
Figure 16.22 Size comparison between traditional single-mode DR resonator filters and single-mode half-cut DR resonator filters.
Figure 16.23 A four-pole quasi-dual-mode DR resonator filter constructed by using two half-cut DR resonators in each cavity.
Figure 16.24 A coaxial TM dielectric resonator filter [20].
Figure 16.25 A TM dielectric resonator filter.
Figure 16.26 Trans-Tech high-
K
ceramic substrates used to construct low-cost DR filters [25].
Figure 16.27 An assembled four-pole filter made of high-
K
ceramic substrates [25].
Figure 16.28 The measured loss tangent versus temperature of BMT material.
Figure 16.29 A dielectric resonator cavity for measuring unloaded
Q
.
Figure 16.30 Transition from conventional DR cavity to an image DR cavity: (a) conventional DR resonator; (b) field distribution; (c) image DR resonator; and (d) image DR resonator with a dielectric support [28].
Figure 16.31 A hybrid DR/HTS filter. Components: 38s, dielectric resonators; 40s, HTS wafers diced from a standard 2 in. wafer; 36s, dielectric supports; 44s, spring washers; 26s-24, 102, 104, elements of filter housing; 28s, input/output probes.
Figure 16.32 A layout of an eight-pole dual-mode hybrid DR/HTS filter at 4 GHz. The filter volume is one eighth the size of a conventional dual-mode DR filter [28, 30].
Figure 16.33 Mode chart of a cylindrical dielectric resonator.
D
= 17.78 mm,
ϵ
r
= 38, cavity size; 25.4 mm × 25.4 mm × 25.4 mm. The EM simulation results are obtained by varying resonator height
L
.
Figure 16.34 (a) Top view of E-field distribution of the dual-mode HEH
11
and HEE
11
. Each mode has two orthogonal components, which are rotated 90°; (b) side view of E-field of HEH
11
mode that is concentrated mainly near the middle and that of the HEE
11
mode that is concentrated mainly at the top and bottom of the resonator.
Figure 16.35 Structure of the quad-mode four-pole filter.
Source
: Memarian [32] 2009. Reproduced with the permission of IEEE.
Figure 16.36 (a) A four-pole filter realized using a quad-mode DR resonator, (b) the measured results.
Source
: Memarian [32] 2009. Reproduced with the permission of IEEE.
Figure 16.37 Views of the E-field distribution of ½HEH
11
and ½HEE
11
modes of the half-cylinder dielectric resonator. The modes are orthogonal.
Figure 16.38 (a) Front view, (b) top view, and (c) 3D view of the dual-mode cavity with coupling and tuning mechanisms. Screw 1 for coupling the two modes, Screw 2 for tuning the ½HEH
11
mode, and Screw 3 for tuning the ½HEE
11
mode. The
I
/
O
probe placement as shown only couples mostly to the ½HEH
11
mode, (d) vertical iris to couple the ½HEH
11
modes in adjacent cavities, and (e) horizontal iris to couple ½HEE
11
modes in adjacent cavities.
Source
: Memarian [32] 2009. Reproduced with the permission of IEEE.
Figure 16.39 (a) Fabricated four-pole filter using half-cut dual-mode resonators with the two cavities attached, (b) with the two cavities separated to illustrate half-cut resonator mounting and iris coupling.
Source
: Memarian [32] 2009. Reproduced with the permission of IEEE.
Figure 16.40 The measured results of the four-pole half-cut dual-mode resonator shown in Figure 16.39.
Source
: Memarian [32] 2009. Reproduced with the permission of IEEE.
Chapter 17: Allpass Phase and Group Delay Equalizer Networks
Figure 17.1 Pole–zero location of lumped-element allpass networks: (a) first-order network; (b) second-order network.
Figure 17.2 Lumped-element symmetric lattice networks: (a) standard representation of symmetric lattice; (b) bridge form of symmetric lattice.
Figure 17.3 General network terminated in the resistor,
R
.
Figure 17.4 Cascade connection of constant-resistance lumped-element lattice networks.
Figure 17.5 Constant-resistance lumped-element lattice network.
Figure 17.6 Lumped-element lattice forms of (a) first-order and (b) second-order allpass network.
Figure 17.7 Pole–zero location of distributed allpass networks: (a) first-order allpass C section; (b) second-order allpass D section.
Figure 17.8 Normalized time delay of C-section TEM equalizer.
Figure 17.9 Normalized time delay of D-section waveguide equalizer.
Figure 17.10 Circulator-coupled reflection-type allpass equalizer network.
Figure 17.11 Hybrid-coupled reflection-type equalizer network.
Figure 17.12 One-cavity reactance network.
Figure 17.13 Two-cavity reactance network.
Figure 17.14 Capacitive coupled two-resonator reactance network for a second-order TEM transmission-line equalizer.
Figure 17.15 Optimization criteria for the equalizer: (a) when the system group delay is constant across the desired band and the constant itself either has a preassigned value or is allowed to float; (b) when the system group delay lies between the curves
T
1
and
T
2
designated as the region of acceptance.
Figure 17.16 Amplitude response of a nine-pole Chebyshev filter.
Figure 17.17 Optimized group delay of the equalized filter (a) using C-section equalizer; (b) using D-section equalizer; (c) using CD-section equalizer; and (d) comparison of the equalized group delays.
Figure 17.18 Schematic of the D-section equalizer.
Figure 17.19 Physical realization of the D-section equalizer (top view).
Chapter 18: Multiplexer Theory and Design
Figure 18.1 A simplified block diagram of a satellite payload.
Figure 18.2 A simplified block diagram of the front end in base stations.
Figure 18.3 Layout of a hybrid-coupled multiplexer.
Figure 18.4 A circulator-coupled multiplexer.
Figure 18.5 A four-channel circulator-coupled multiplexer.
Figure 18.6 A directional filter multiplexer.
Figure 18.7 (a) A waveguide directional filter and (b) microstrip directional filter.
Figure 18.8 A manifold-coupled multiplexer.
Figure 18.9 A C-band four-channel waveguide multiplexer compared with a four-channel multiplexer implemented using superconductor technology.
Figure 18.10 A three-channel planar multiplexer.
Figure 18.11 Hybrid branching input multiplexer (IMUX).
Figure 18.12 Circulator-coupled or channel dropping input demultiplexer.
Figure 18.13 Circulator-coupled input demultiplexer subsystem.
Figure 18.14 En passant distortion with (a) noncontiguous channels and (b) contiguous channels.
Figure 18.15 In-band distortions for channel 3: (a) insertion loss and (b) group delay.
Figure 18.16 Hybrid-coupled filter module (HCFM).
Figure 18.17 Output multiplexer with hybrid-coupled filter modules.
Figure 18.18 Possible HCFM configurations: (a) using dual-mode filters and (b) using extracted pole filters.
Figure 18.19 HCFM directional multiplexer with four contiguous channels: (a) overall transfer characteristics, (b) in-band insertion loss characteristic, (c) in-band group delay characteristic, and (d) effect on channel 1 rejection characteristic of removing channel 2 module.
Figure 18.20 Types of star combining junctions: (a) basic star combining junction, (b) staged star junction, and (c) internal star junction in coaxial diplexer housing.
Figure 18.21 Common configurations for manifold multiplexers: (a) comb, (b) herringbone, and (c) one filter feeding directly into the manifold.
Figure 18.22 12 Channel C - Band Output Multiplexer with dual-mode filters.
Figure 18.23 Typical sampling points for the evaluation of the optimization cost function: (a) return loss zeros and maxima and (b) close-to-band rejection points.
Figure 18.24 Open-wire model of waveguide manifold multiplexer (three channels).
Figure 18.25
E
-plane and
H
-plane waveguide junctions and
S
-parameter matrix representation.
Figure 18.26 Common port return loss computation.
Figure 18.27 Channel 2 transfer function calculation.
Figure 18.28 Real and Imaginary parts of input admittance of a sixth order prototype quasielliptic filter, (a) singly terminated filter, (b) doubly terminated filter.
Figure 18.29 Singly terminated filter with two contiguous neighbors—composite admittances as seen from the common port of the manifold.
Figure 18.30 Preoptimization performance of a four-channel contiguous manifold multiplexer, (a) superimposed channel amplitude response, (b) common port return loss.
Figure 18.31 Four-channel manifold multiplexer after optimization of manifold lengths: (a) superimposed channel transfer characteristics and (b) common port return loss.
Figure 18.32 Four-channel manifold multiplexer after the first optimization of filter parameters: (a) superimposed channel transfer characteristics and (b) common port return loss.
Figure 18.33 Four-channel manifold multiplexer and final performance: (a) superimposed channel transfer characteristics and (b) common port return loss.
Figure 18.34 Twenty-channel manifold multiplexer superimposed channel transfer characteristics and common port return loss (RL is return loss and IL is insertion loss).
Figure 18.35 A diplexer implemented using the 90° hybrid approach.
Figure 18.36 Transmit–receive diplexer configurations: (a) implemented using two coaxial filters and a wire T junction and (b) implemented using two waveguide iris filters and T waveguide junction.
Figure 18.37 Outline sketch of a (12–3) filter realized with one sixth-degree extended box section (two TZs) and one fourth-degree box section (one TZ).
Figure 18.38 Simulated and measured rejection characteristics of a transmit–receive diplexer (duplexer) of a cellular telephony base station.
Figure 18.39 Transmit–receive diplexer with two complementary (6–2) asymmetric filters: (a) rejection characteristics, (b) voltage characteristics in transmit filter cavities, and (c) voltage characteristics in receive filter cavities.
Chapter 19: Computer-Aided Diagnosis and Tuning of Microwave Filters
Figure 19.1 Lowpass prototype circuit.
Figure 19.2 Phase of input reflection coefficient of an eight-pole filter as successive resonators are tuned.
Figure 19.3 Group delay of input reflection coefficient of an eight-pole filter as successive resonators are tuned.
Figure 19.4 A generalized model for coupled resonator filters.
Figure 19.5 Equivalent circuit of two cascaded resonators terminated in a short circuit.
Figure 19.6 The equivalent circuit of
N
-cascaded resonators terminated in a short circuit.
Figure 19.7 Frequency response and
S
11
time-domain response of a five-pole bandpass filter [27].
Figure 19.8 Frequency response and
S
11
time-domain response when resonator 2 is detuned (the lighter trace is the ideal response; the darker trace is after detuning) [27].
Figure 19.9 The frequency response and
S
11
time-domain response when resonator 3 is detuned (lighter trace indicates ideal response; darker trace, after detuning) [27].
Figure 19.10 The frequency response and
S
11
time-domain response when
M
12
is increased by 10% (the lighter trace indicates the ideal response before increasing
M
12
) [27].
Figure 19.11 The frequency response and
S
11
time-domain response when
M
23
is reduced by 10% (the lighter trace indicates the ideal response before decreasing
M
23
) [27].
Figure 19.12 A block diagram of the fuzzy logic system.
Figure 19.13 Functions for
X
(age) = {very young, young, middle age, old, very old}.
Figure 19.14 Potential membership functions for the elements of the coupling matrix.
Figure 19.15 The membership function for variable
x
1
.
Figure 19.17 The membership function for variable
y
.
Figure 19.16 The membership function for variable
x
2
.
Figure 19.18 Function approximation using Boolean logic.
Figure 19.19 Function approximation using fuzzy logic.
Figure 19.20 Function approximation using fuzzy logic with optimization.
Figure 19.21 Percentage error of three different function approximators.
Figure 19.22 Examples of slightly detuned and highly detuned four-pole Chebyshev filter characteristics [29].
Figure 19.23 Output membership functions for the four-pole filter.
Figure 19.24 A comparison between experimental and extracted performance using fuzzy logic for the slightly detuned filter.
Figure 19.25 A comparison between experimental and extracted performance using fuzzy logic for the highly detuned filter.
Figure 19.26 The automated tuning station.
Figure 19.27 COM DEV's RoboCat.
Figure 19.28 An automated filter tuning setup.
Chapter 20: High-Power Considerations in Microwave Filter Networks: (Revised and augmented by Chandra M. Kudsia, Vicente E. Boria, and Santiago Cogollos)
Figure 20.1 Approximate limits of microwave power sources: solid state, TWTA, and klystron.
Figure 20.2 Variation of electron concentration versus electric field.
Figure 20.3 Breakdown strength of air at 9.4 GHz.
Figure 20.4 CW breakdown in air, oxygen, and nitrogen at 992 MHz.
Figure 20.5 CW breakdown in air, nitrogen, and oxygen at 9.4 GHz.
Figure 20.6 Derating factors affecting the high-power capability in waveguide structures (voltage standing-wave ratio) from Ref. [9].
Figure 20.7 Theoretical curves of the average power rating for a copper rectangular waveguide operating in the TE
10
mode with unity VSWR at an ambient temperature of 40°C: (a) for a temperature rise of 62°C and (b) temperature rise of 110°C.
Figure 20.8 Secondary emission parameters: (a)
δ
versus
W
and (b)
δ
versus
θ
.
Figure 20.9 Possible regions of multipaction between parallel plates.
Figure 20.10 Evolution of electron population versus time for a six-carrier signal. The first carrier is at 3.57 GHz and the frequency spacing is 100 MHz. The geometry is a simple parallel-plate case with a critical gap of 0.43 mm.
Figure 20.11 Five-channel high-power (100 W per channel) S-band multiplexer assembly.
Figure 20.12 An eight-channel high-power (300 W per channel), low PIM (−140 dBm) Ku-band multiplexer. (
Figure 20.13 Test setup of for measuring RF breakdown effects (i.e., multipaction and gas discharge).
Figure 20.14 General admittance inverter cross-coupled lowpass filter prototype.
Figure 20.15 Five-pole H-plane iris filter (WR75).
Figure 20.16 Five-pole H-plane iris filter response using FEM and prototype,
f
0
= 12026 MHz, BW = 470 MHz. Couplings:
M
01
=
M
56
= 1.078,
M
12
=
M
45
= 0.928,
M
23
=
M
34
= 0.662.
Figure 20.17 Resonator voltage ratios [equation (10)] as a function of frequency.
Figure 20.18 Voltage ratio distribution along the center line of the filter using FEM and comparison of the peak values to the values obtained using the prototype.
Figure 20.19 PIM measurement setup.
Chapter 21: Multiband Filters
Figure 21.1 A diplexer employing (a) single-band filters and (b) dual-band filters.
Figure 21.2 Multiple bandwidths transmitted by one beam through the use of multiband filters.
Figure 21.3 Filter structure, coupling matrix, and associated simulation results of a 12-pole dual-band filter having two passbands with equal widths.
Figure 21.4 Coupling matrix and simulation results of a 12-pole dual-band filter having two passbands with nonequal widths.
Figure 21.5 Coupling matrix, filter structure, and simulation results of a dual-band filter employing cylindrical dual-mode cavities.
Figure 21.6 A six-pole dual-band wideband filter implemented in ridge waveguide technology. (a) Filter structure and (b) measured results.
Figure 21.7 A schematic of the coupling matrix of the 16-pole dual-band filter.
Figure 21.8 Mechanical assembly of the ridge waveguide realization of the filter: two identical parts with a metal plate in between.
Figure 21.9 The measured response of the fabricated filter shown in Figure 21.8.
Figure 21.10 The triple-conductor combline resonator.
Figure 21.11 Field distribution in triple-conductor combline cavity. (a) Inner conductor is shorter in height than the intermediate conductor. (b) Inner conductor is longer in height than the intermediate conductor.
Figure 21.12 A three-dimensional cross section of the filter and schematic illustrating a technique to manufacture it from three separate parts.
Figure 21.13 Two prototype units for three-pole and five-pole dual-band filters built using triple-conductor combline resonators.
