Balanced Microwave Filters
Description
This book examines differential-mode, or balanced, microwave filters by discussing several implementations of practical realizations of these passive components. Topics covered include selective mode suppression, designs based on distributed and semi-lumped approaches, multilayer technologies, defect ground structures, coupled resonators, metamaterials, interference techniques, and substrate integrated waveguides, among others.
Divided into five parts, Balanced Microwave Filters begins with an introduction that presents the fundamentals of balanced lines, circuits, and networks. Part 2 covers balanced transmission lines with common-mode noise suppression, including several types of common-mode filters and the application of such filters to enhance common-mode suppression in balanced bandpass filters. Next, Part 3 examines wideband and ultra-wideband (UWB) balanced bandpass filters with intrinsic common-mode suppression. Narrowband and dual-band balanced bandpass filters with intrinsic common-mode suppression are discussed in Part 4. Finally, Part 5 covers other balanced circuits, such as balanced power dividers and combiners, and differential-mode equalizers with common-mode filtering. In addition, the book:
* Explores a research topic of increasing interest due to the growing demand of balanced transmission lines and circuits in modern communication systems
* Includes contributions from prominent worldwide experts in the field
* Provides readers with the necessary knowledge to analyze and synthesize balanced filters and circuits
Balanced Microwave Filters is an important text for R&D engineers, professionals, and specialists working on the topic of microwave filters. Post graduate students and Masters students in the field of microwave engineering and wireless communications, especially those involved in courses related to microwave filters, and balanced filters and circuits will also find it to be a vital resource.
More details
Other editions
Additional editions
Persons
Ferran Martín, IEEE Fellow, is a Full Professor of Electronics at Universitat Autònoma de Barcelona (UAB), Spain.
Lei Zhu, IEEE Fellow, is a Full Professor in the Faculty of Science and Technology at the University of Macau, Macau SAR, China.
Jiasheng Hong, IEEE Fellow, is a Full Professor in the Department of Electrical, Electronic and Computer Engineering at Heriot-Watt University, Edinburgh, UK.
Francisco Medina, IEEE Fellow, is a Full Professor of Electromagnetism at Universidad de Sevilla, Seville, Spain
Content
LIST OF CONTRIBUTORS xix
PREFACE xxiii
PART 1 INTRODUCTION 1
1 INTRODUCTION TO BALANCED TRANSMISSION LINES, CIRCUITS, AND NETWORKS 3
Ferran Martín, Jordi Naqui, Francisco Medina, Lei Zhu, and Jiasheng Hong
1.1 Introduction 3
1.2 Balanced Versus Single-Ended Transmission Lines and Circuits 4
1.3 Common-Mode Noise 5
1.4 Fundamentals of Differential Transmission Lines 6
1.4.1 Topology 6
1.4.2 Propagating Modes 8
1.4.2.1 Even and Odd Mode 8
1.4.2.2 Common and Differential Mode 11
1.5 Scattering Parameters 13
1.5.1 Single-Ended S-Parameters 13
1.5.2 Mixed-Mode S-Parameters 16
1.6 Summary 19
References 19
PART 2 BALANCED TRANSMISSION LINES WITH COMMON-MODE NOISE SUPPRESSION 21
2 STRATEGIES FOR COMMON-MODE SUPPRESSION IN BALANCED LINES 23
Ferran Martín, Paris Vélez, Armando Fernández-Prieto, Jordi Naqui, Francisco Medina, and Jiasheng Hong
2.1 Introduction 23
2.2 Selective Mode Suppression in Differential Transmission Lines 25
2.3 Common-Mode Suppression Filters Based on Patterned Ground Planes 27
2.3.1 Common-Mode Filter Based on Dumbbell-Shaped Patterned Ground Plane 27
2.3.2 Common-Mode Filter Based on Complementary Split Ring Resonators (CSRRs) 30
2.3.3 Common-Mode Filter Based on Defected Ground Plane Artificial Line 40
2.3.4 Common-Mode Filter Based on C-Shaped Patterned Ground Structures 44
2.4 Common-Mode Suppression Filters Based on Electromagnetic Bandgaps (EBGs) 49
2.4.1 Common-Mode Filter Based on Nonuniform Coupled Lines 50
2.4.2 Common-Mode Filter Based on Uniplanar Compact Photonic Bandgap (UC-PBG) Structure 55
2.5 Other Approaches for Common-Mode Suppression 55
2.6 Comparison of Common-Mode Filters 60
2.7 Summary 61
Appendix 2.A: Dispersion Relation for Common-Mode Rejection Filters with Coupled CSRRs or DS-CSRRs 61
Appendix 2.B: Dispersion Relation for Common-Mode Rejection Filters with Coupled Patches Grounded through Inductive Strips 64
References 65
3 COUPLED-RESONATOR BALANCED BANDPASS FILTERS WITH COMMON-MODE SUPPRESSION DIFFERENTIAL LINES 73
Armando Fernández-Prieto, Jordi Naqui, Jesús Martel, Ferran Martín, and Francisco Medina
3.1 Introduction 73
3.2 Balanced Coupled-Resonator Filters 74
3.2.1 Single-Band Balanced Bandpass Filter Based on Folded Stepped-Impedance Resonators 75
3.2.2 Balanced Filter Loaded with Common-Mode Rejection Sections 79
3.2.3 Balanced Dual-Band Bandpass Filter Loaded with Common-Mode Rejection Sections 82
3.3 Summary 88
References 88
PART 3 WIDEBAND AND ULTRA-WIDEBAND (UWB) BALANCED BAND PASS FILTERS WITH INTRINSIC COMMON-MODE SUPPRESSION 91
4 WIDEBAND AND UWB BALANCED BANDPASS FILTERS BASED ON BRANCH-LINE TOPOLOGY 93
Teck Beng Lim and Lei Zhu
4.1 Introduction 93
4.2 Branch-Line Balanced Wideband Bandpass Filter 97
4.3 Balanced Bandpass Filter for UWB Application 105
4.4 Balanced Wideband Bandpass Filter with Good Common-Mode Suppression 111
4.5 Highly Selective Balanced Wideband Bandpass Filters 116
4.6 Summary 131
References 131
5 WIDEBAND AND UWB COMMON-MODE SUPPRESSED DIFFERENTIAL-MODE FILTERS BASED ON COUPLED LINE SECTIONS 135
Qing-Xin Chu, Shi-Xuan Zhang, and Fu-Chang Chen
5.1 Balanced UWB Filter by Combining UWB BPF with UWB BSF 135
5.2 Balanced Wideband Bandpass Filter Using Coupled Line Stubs 142
5.3 Balanced Wideband Filter Using Internal Cross-Coupling 148
5.4 Balanced Wideband Filter Using Stub-Loaded Ring Resonator 155
5.5 Balanced Wideband Filter Using Modified Coupled Feed Lines and Coupled Line Stubs 161
5.6 Summary 173
References 174
6 WIDEBAND DIFFERENTIAL CIRCUITS USING T-SHAPED STRUCTURES AND RING RESONATORS 177
Wenquan Che and Wenjie Feng
6.1 Introduction 177
6.2 Wideband Differential Bandpass Filters Using T-Shaped Resonators 179
6.2.1 Mixed-Mode S-Parameters for Four-Port Balanced Circuits 179
6.2.2 T-Shaped Structures with Open/Shorted Stubs 184
6.2.2.1 T-Shaped Structure with Shorted Stubs 184
6.2.2.2 T-Shaped Structure with Open Stubs 185
6.2.3 Wideband Bandpass Filters without Cross Coupling 187
6.2.3.1 Differential-Mode Excitation 189
6.2.3.2 Common-Mode Excitation 191
6.2.4 Wideband Bandpass Filter with Cross Coupling 193
6.3 Wideband Differential Bandpass Filters Using Half-/Full-Wavelength Ring Resonators 201
6.3.1 Differential Filter Using Half-Wavelength Ring Resonators 201
6.3.2 Differential Filter Using Full-Wavelength Ring Resonators 206
6.3.3 Differential Filter Using Open/Shorted Coupled Lines 215
6.3.4 Comparisons of Several Wideband Balanced Filters Based on Different Techniques 220
6.4 Wideband Differential Networks Using Marchand Balun 223
6.4.1 S-Parameter for Six-Port Differential Network 223
6.4.2 Wideband In-Phase Differential Network 227
6.4.3 Wideband Out-of-Phase Differential Network 236
6.5 Summary 244
References 245
7 UWB AND NOTCHED-BAND UWB DIFFERENTIAL FILTERS USING MULTILAYER AND DEFECTED GROUND STRUCTURES (DGSS) 249
Jian-Xin Chen, Li-Heng Zhou, and Quan Xue
7.1 Conventional Multilayer Microstrip-to-Slotline Transition (MST) 250
7.2 Differential MST 251
7.2.1 Differential MST with a Two-Layer Structure 251
7.2.2 Differential MST with Three-Layer Structure 252
7.3 UWB Differential Filters Based on the MST 253
7.3.1 Differential Wideband Filters Based on the Conventional MST 253
7.3.2 Differential Wideband Filters Based on the Differential MST 255
7.4 Differential Wideband Filters Based on the Strip-Loaded Slotline Resonator 262
7.4.1 Differential Wideband Filters Using Triple-Mode Slotline Resonator 265
7.4.2 Differential Wideband Filters Using Quadruple-Mode Slotline Resonator 267
7.5 UWB Differential Notched-Band Filter 270
7.5.1 UWB Differential Notched-Band Filter Based on the Traditional MST 270
7.5.2 UWB Differential Notched-Band Filter Based on the Differential MST 272
7.6 Differential UWB Filters with Enhanced Stopband Suppression 277
7.7 Summary 280
References 281
8 APPLICATION OF SIGNAL INTERFERENCE TECHNIQUE TO THE IMPLEMENTATION OF WIDEBAND DIFFERENTIAL FILTERS 283
Wei Qin and Quan Xue
8.1 Basic Concept of the Signal Interference Technique 283
8.1.1 Fundamental Theory 284
8.1.2 One Filter Example Based on Ring Resonator 287
8.1.3 Simplified Circuit Model 288
8.2 Signal Interference Technique for Wideband Differential Filters 290
8.2.1 Circuit Model of Wideband Differential Bandpass Filter 290
8.2.2 S-Matrix for Differential Bandpass Filters 292
8.3 Several Designs of Wideband Differential Bandpass Filters 293
8.3.1 Differential Bandpass Filter Based on Wideband Marchand Baluns 293
8.3.2 Differential Bandpass Filter Based on p-Type UWB 180 Phase Shifters 299
8.3.3 Differential Bandpass Filter Based on DSPSL UWB 180 Phase Inverter 302
8.3.3.1 Differential-Mode Analysis 305
8.3.3.2 Common-Mode Analysis 305
8.3.3.3 Filter Design and Measurement 308
8.4 Summary 308
References 309
9 WIDEBAND BALANCED FILTERS BASED ON MULTI-SECTION MIRRORED STEPPED IMPEDANCE RESONATORS (SIRs) 311
Ferran Martín, Jordi Selga, Paris Vélez, Marc Sans, Jordi Bonache, Ana Rodríguez, Vicente E. Boria, Armando Fernández-Prieto, and Francisco Medina
9.1 Introduction 311
9.2 The Multi-Section Mirrored Stepped Impedance Resonator (SIR) 312
9.3 Wideband Balanced Bandpass Filters Based on
7-Section Mirrored SIRs Coupled Through Admittance Inverters 317
9.3.1 Finding the Optimum Filter Schematic 319
9.3.2 Layout Synthesis 325
9.3.2.1 Resonator Synthesis 325
9.3.2.2 Determination of the Line Width 327
9.3.2.3 Optimization of the Line Length (Filter Cell Synthesis) 327
9.3.3 A Seventh-Order Filter Example 330
9.3.4 Comparison with Other Approaches 334
9.4 Compact Ultra-Wideband (UWB) Balanced Bandpass Filters Based on 5-Section Mirrored SIRs and Patch Capacitors 336
9.4.1 Topology and Circuit Model of the Series Resonators 337
9.4.2 Filter Design 341
9.4.3 Comparison with Other Approaches 345
9.5 Summary 346
Appendix 9.A: General Formulation of Aggressive Space Mapping (ASM) 347
References 349
10 METAMATERIAL-INSPIRED BALANCED FILTERS 353
Ferran Martín, Paris Vélez, Ali Karami-Horestani, Francisco Medina, and Christophe Fumeaux
10.1 Introduction 353
10.2 Balanced Bandpass Filters Based on Open Split Ring ResonatorS (OSRRS) and Open Complementary Split Ring Resonators (OCSRRS) 354
10.2.1 Topology of the OSRR and OCSRR 354
10.2.2 Filter Design and Illustrative Example 356
10.3 Balanced Filters Based on S-Shaped Complementary Split Ring Resonators (S-CSRRs) 363
10.3.1 Principle for Balanced Bandpass Filter Design and Modeling 365
10.3.2 Illustrative Example 367
10.4 Summary 369
References 369
11 WIDEBAND BALANCED FILTERS ON SLOTLINE RESONATOR WITH INTRINSIC COMMON-MODE REJECTION 373
Xin Guo, Lei Zhu, and Wen Wu
11.1 Introduction 373
11.2 Wideband Balanced Bandpass Filter on Slotline MMR 375
11.2.1 Working Mechanism 375
11.2.2 Synthesis Method 378
11.2.3 Geometry and Layout 382
11.2.4 Fabrication and Experimental Verification 388
11.3 Wideband Balanced BPF on Strip-Loaded Slotline Resonator 392
11.3.1 Strip-Loaded Slotline Resonator 392
11.3.2 Wideband Balanced Bandpass Filters 396
11.3.2.1 Wideband Balanced BPF on Strip-Loaded Triple-Mode Slotline Resonator 397
11.3.2.2 Wideband Balanced BPF on Strip-Loaded Quadruple-Mode Slotline Resonator 403
11.4 Wideband Balanced Bandpass Filter on Hybrid MMR 408
11.4.1 Hybrid MMR 408
11.4.2 Wideband Balanced Bandpass Filters 416
11.5 Summary 420
References 420
PART 4 NARROWBAND AND DUAL-BAND BALANCED BANDPASS FILTERS WITH INTRINSIC COMMON-MODE SUPPRESSION 423
12 NARROWBAND COUPLED-RESONATOR BALANCED BANDPASS FILTERS AND DIPLEXERS 425
Armando Fernández-Prieto, Francisco Medina, and Jesús Martel
12.1 Introduction 425
12.2 Coupled-Resonator Balanced Filters with Intrinsic Common-Mode Rejection 426
12.2.1 Loop and SIR Resonator Filters with Mixed Coupling 427
12.2.1.1 Quasi-elliptic Response BPF: First Example 428
12.2.1.2 Quasi-elliptic Response BPF: Second Example 434
12.2.2 Magnetically Coupled Open-Loop and FSIR Balanced Filters 439
12.2.2.1 Filters with Magnetic Coupling: First Example 439
12.2.2.2 Filters with Magnetic Coupling: Second Example 447
12.2.3 Interdigital Line Resonators Filters 449
12.2.3.1 ILR Filter Design Example 450
12.2.4 Dual-Mode and Dual-Behavior Resonators for Balanced Filter Design 451
12.2.4.1 Dual-Mode Square Patch Resonator Filters 453
12.2.4.2 Filters Based on Dual-Behavior Resonators 458
12.2.5 LTCC-Based Multilayer Balanced Filter 464
12.2.6 Balanced Bandpass Filters Based on Dielectric Resonators 466
12.3 Loaded Resonators for Common-Mode Suppression Improvement 469
12.3.1 Capacitively, Inductively, and Resistively Center-Loaded Resonators 470
12.3.1.1 Open-Loop UIR-Loaded Filter 470
12.3.1.2 Folded SIR Loaded Filter 476
12.3.2 Filters with Defected Ground Structures (DGS) 484
12.3.2.1 Control of the Transmission Zeros 488
12.3.3 Multilayer Loaded Resonators 490
12.3.3.1 Design Example 492
12.4 Coupled Line Balanced Bandpass Filter 493
12.4.1 Type-II Design Example 495
12.5 Balanced Diplexers 499
12.5.1 Unbalanced-to-Balanced Diplexer Based on Uniform Impedance Stub-Loaded Coupled Resonators 500
12.5.1.1 Resonator Geometry 500
12.5.1.2 Unbalanced-to-Balanced Diplexer Design 502
12.5.2 Example Two: Balanced-to-Balanced Diplexer Based on UIRs and Short-Ended Parallel-Coupled Lines 505
12.6 Summary 508
References 510
13 DUAL-BAND BALANCED FILTERS BASED ON LOADED AND COUPLED RESONATORS 515
Jin Shi and Quan Xue
13.1 Dual-Band Balanced Filter with Loaded Uniform Impedance Resonators 516
13.1.1 Center-Loaded Uniform Impedance Resonator 516
13.1.2 Dual-Band Balanced Filter Using the Uniform Impedance Resonator with Center-Loaded Lumped Elements 520
13.1.3 Dual-Band Balanced Filter Using Stub-Loaded Uniform Impedance Resonators 526
13.2 Dual-Band Balanced Filter with Loaded Stepped-Impedance Resonators 528
13.2.1 Center-Loaded Stepped-Impedance Resonator 528
13.2.2 Dual-Band Balanced Filter Using Stepped-Impedance Resonators with Center-Loaded Lumped Elements 531
13.2.3 Dual-Band Balanced Filter Using Stub-Loaded Stepped-Impedance Resonators 535
13.3 Dual-Band Balanced Filter Based on Coupled Resonators 538
13.3.1 Dual-Band Balanced Filter with Coupled Stepped-Impedance Resonators 538
13.3.2 Dual-Band Balanced Filter with Coupled Stub-Loaded Short-Ended Resonators 542
13.4 Summary 546
References 547
14 DUAL-BAND BALANCED FILTERS IMPLEMENTED IN SUBSTRATE INTEGRATED WAVEGUIDE (SIW) TECHNOLOGY 549
Wen Wu, Jianpeng Wang, and Chunxia Zhou
14.1 Substrate Integrated Waveguide (SIW) Cavity 550
14.2 Closely Proximate Dual-Band Balanced Filter Design 551
14.3 Dual-Band Balanced Filter Design Utilizing High-Order Modes in SIW Cavities 555
14.4 Summary 563
References 563
PART 5 OTHER BALANCED CIRCUITS 565
15 BALANCED POWER DIVIDERS/COMBINERS 567
Lin-Sheng Wu, Bin Xia, and Jun-Fa Mao
15.1 Introduction 567
15.2 Balanced-to-Balanced Wilkinson Power Divider with Microstrip Line 569
15.2.1 Mixed-Mode Analysis 569
15.2.1.1 Mixed-Mode Scattering Matrix of a Balanced-to-Balanced Power Divider 569
15.2.1.2 Constraint Rules of Balanced-to-Balanced Power Divider 571
15.2.1.3 Odd- and Even-Mode Scattering Matrices of Balanced-to-Balanced Power Divider 572
15.2.2 A Transmission-Line Balanced-to-Balanced Power Divider 572
15.2.2.1 Even-Mode Circuit Model 572
15.2.2.2 Odd-Mode Circuit Model 573
15.2.2.3 Scattering Matrix of the Balanced-to-Balanced Power Divider 575
15.2.3 Theoretical Result 575
15.2.4 Simulated and Measured Results 576
15.3 Balanced-to-Balanced Gysel Power Divider with Half-Mode Substrate Integrated Waveguide (SIW) 580
15.3.1 Conversion from Single-Ended Circuit to Balanced Form 580
15.3.2 Half-Mode SIW Ring Structure 581
15.3.3 Results and Discussion 583
15.4 Balanced-to-Balanced Gysel Power Divider with Arbitrary Power Division 585
15.4.1 Analysis and Design 585
15.4.2 Results and Discussion 587
15.5 Balanced-to-Balanced Gysel Power Divider with Bandpass Filtering Response 590
15.5.1 Coupled-Resonator Circuit Model 590
15.5.2 Realization in Transmission Lines 591
15.5.2.1 Internal Coupling Coefficient 592
15.5.2.2 External Q Factor 594
15.5.3 Results and Discussion 595
15.6 Filtering Balanced-to-Balanced Power Divider with Unequal Power Division 598
15.7 Dual-Band Balanced-to-Balanced Power Divider 599
15.7.1 Analysis and Design 599
15.7.2 Results and Discussion 601
15.8 Summary 603
References 603
16 DIFFERENTIAL-MODE EQUALIZERS WITH COMMON-MODE FILTERING 607
Tzong-Lin Wu and Chiu-Chih Chou
16.1 Introduction 607
16.2 Design Considerations 610
16.2.1 Equalizer Design 610
16.2.2 Common-Mode Filter Design 612
16.3 First Design 613
16.3.1 Proposed Topology 613
16.3.2 Odd-Mode Analysis 616
16.3.2.1 Equalizer Optimization in Time Domain 617
16.3.3 Even-Mode Analysis 623
16.3.4 Measurement Validation 628
16.4 Second Design 633
16.4.1 Proposed Circuit and Analysis 633
16.4.2 Realization and Measurement 637
16.4.2.1 Realization 637
16.4.2.2 Common-Mode Noise Suppression 638
16.4.2.3 Differential-Mode Equalization 640
16.5 Summary 641
References 641
INDEX 645
CHAPTER 1
INTRODUCTION TO BALANCED TRANSMISSION LINES, CIRCUITS, AND NETWORKS
Ferran Martín,1 Jordi Naqui,1 Francisco Medina,2 Lei Zhu,3 and Jiasheng Hong4
1CIMITEC, Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Spain
2Departamento de Electrónica y Electromagnetismo, Universidad de Sevilla, Sevilla, Spain
3Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Macau SAR, China
4Institute of Sensors, Signals and Systems, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK
1.1 INTRODUCTION
This chapter is an introduction to the topic of balanced lines, circuits, and networks. The main objectives are (i) to point out the advantages and limitations of balanced versus unbalanced systems; (ii) to analyze the origin and effects of the main source of noise in differential systems, that is, the common-mode noise; (iii) to provide the fundamentals of differential transmission lines, with special emphasis on microstrip lines (the most common), including the main topologies and fundamental propagating modes; and (iv) to present the mixed-mode scattering parameters, suitable for microwave differential circuit characterization. We will also point out the two main approaches for the implementation of balanced microwave filters with common-mode noise suppression (end of Section 1.3), which will be further discussed along this book.
1.2 BALANCED VERSUS SINGLE-ENDED TRANSMISSION LINES AND CIRCUITS
Unbalanced systems transmit single-ended signals. In such systems, one of the two conductors is connected to the common ground, being the signal referenced to ground. Alternatively, signal propagation can be made on the basis of balanced or differential systems, where each wire (or conductor) has the same impedance to the circuit common, which is typically grounded. Differential signals are transmitted as complementary pairs, driving a positive voltage on one wire and an equal but opposite voltage on the other wire. The signal of interest is the potential difference between the two conductors, called differential-mode signal, which is no longer referenced to ground [1].
The main advantages of differential over single-ended signals are lower electromagnetic interference (EMI) and higher immunity to electromagnetic noise and crosstalk. Due to the previous advantages, a better signal integrity and a higher signal-to-noise ratio (SNR) can be achieved in differential systems [2, 3]. The cancelation of the fields, resulting from opposite current flowing, is the reason for the low EMI in differential systems [4]. The high noise immunity is related to the fact that voltages and currents induced from interfering sources (noise) tend to be identical on both conductors, and hence this noise couples to the differential line as a common-mode signal (to be discussed later in this chapter) [1, 3, 5]. The main drawback of differential systems is the need for balanced circuits and interconnects (transmission lines),1 representing further complexity in terms of layout and number of elements [6].
Traditionally, differential circuits have been used in low-frequency analog and digital systems. In radio-frequency (RF) and microwave applications, unbalanced structures have dominated the designs for decades and are still more common than differential circuits. Nevertheless, recent technological advances are pushing differential circuits into the RF and microwave frequency domain [7]. Thus, balanced lines and devices are becoming increasingly common in high-speed digital circuits, as well as in modern balanced communication systems [8, 9].
1.3 COMMON-MODE NOISE
In differential transmission lines and circuits, the main contribution to noise is the so-called common-mode noise [1]. Common-mode noise is originated from electromagnetic radiation (through crosstalk or through an external source) and from the ground terminal [3, 10, 11]. Moreover, common-mode signals (also viewed as noise for the differential signals) can also be generated as consequence of time skew, amplitude unbalance, and/or different rising/falling times of the differential signals. These latter effects are ultimately caused by imperfect balance, resulting in conversion from the differential mode to the common mode. Similarly, in practice, conversion from the common mode to the differential mode always exists. Therefore, a perfect balance of the two signal conductors with respect to the reference conductor is necessary to avoid (or minimize) the conversion from common-mode noise to differential-mode noise (always representing a degradation in signal integrity).
Although, ideally, the differential mode is fully independent of the common mode, in actual differential systems, the circuits are sensitive to the common mode (e.g., in differential-mode receivers, the common-mode noise is rejected up to a certain limit that defines the ability of the receiver to work properly up to a defined amount of common-mode noise) [3]. The presence of common-mode signals in differential lines and circuits may also cause radiated emission [3]. The reason is that common-mode currents flow in the same direction (contrary to differential-mode currents, which flow in opposite directions, thus preventing far-field radiation, provided the two conductors are closely spaced). A method to reduce dramatically common-mode radiated emission is to place a metallic plane beneath and parallel to the differential line pair [3]. Such metallic plane produces image currents flowing in opposite direction to the original common-mode currents, generating fields that tend to cancel the fields resulting from the original wires. Nevertheless, due to the limited dimensions of the ground plane, a perfect image is not achieved, causing the ground plane to radiate.
Due to the negative effects of common-mode noise in differential systems (mainly signal integrity degradation and common-mode radiation), it must be reduced as much as possible. Traditionally, solutions that use common-mode chokes with high permeability ferrite cores have been proposed [12-14], but chokes represent a penalty in terms of size and frequency operating range, not being useful for high-speed, high-density, and microwave systems. Recently, many approaches fully compatible with planar fabrication technology for the design of differential lines able to suppress the common mode in the range of interest, and simultaneously preserving the integrity of the differential signals, have been reported. These common-mode filters are exhaustively reviewed in Chapter 2. Such filters may be used not only for differential-mode interconnects but also to improve the common-mode rejection of balanced bandpass filters by cascading both components, as will be pointed out in Chapter 3. Nevertheless, the design of balanced filters with inherent (and efficient) common-mode suppression without the need to cascade common-mode filters is by far the optimum solution for common-mode suppressed microwave filters, the main objective of this book (Parts III and IV of this book are dedicated to this topic).
1.4 FUNDAMENTALS OF DIFFERENTIAL TRANSMISSION LINES
Since most of the balanced filters and circuits studied in this book are implemented in microstrip technology, the present analysis is entirely focused on microstrip differential lines. Such lines are able to propagate both differential- and common-mode signals. Therefore, a comprehensive analysis of both modes is carried out in this section. The first part of the section is devoted to the topology of these lines.
1.4.1 Topology
Transmission lines may be classified according to the currents flowing on it. For comparative purposes let us first consider a two-wire unbalanced transmission line (see Figure 1.1a). In such lines, the conductors have different impedance to ground, and they are fed by single-ended ports in which there are an active terminal and a ground terminal (or, equivalently, one of the conductors is fed, whereas the other one is tied to ground potential) [15]. One conductor is used for transporting signal current and the other one is the return current path. By contrast, in a two-wire balanced line (Figure 1.1b), the conductors have equal potential respect to ground with 180° phase shift [16]. The signal on one line is referenced to the other, which means that each conductor provides the signal return path for the other and the currents flowing on the conductors have the same magnitude but opposite direction. Such lines are fed by differential ports consisting of two terminals, neither of which is explicitly tied to ground. In a balanced line, also called differential line, the conductors have the same impedance to ground, if it exists. It is important to highlight that the nature (balanced or unbalanced) of a transmission line is determined by the currents, not only by the physical structure. Essentially, a balanced line carries balanced currents. Microstrip lines (Figure 1.2a), coplanar waveguides (CPW), and coaxial lines are well-known examples of two-wire unbalanced lines. Conversely, coplanar strips (CPS), such as those depicted in Figure 1.2(b), or slotlines are balanced structures by nature. Nevertheless, these...
