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1 WestminsterResearch Development o planar ilters and diplexers or wireless transceiver ront ends. Damir ayniyev School o Electronics and Computer Science This is an electronic version o a PhD thesis awarded by the University o Westminster. The Author,. This is an exact reproduction o the paper copy held by the University o Westminster library. The WestminsterResearch online digital archive at the University o Westminster aims to make the research output o the University available to a wider audience. Copyright and Moral Rights remain with the authors and/or copyright owners. Users are permitted to download and/or print one copy or non-commercial private study or research. Further distribution and any use o material rom within this archive or proit-making enterprises or or commercial gain is strictly orbidden. Whilst urther distribution o speciic materials rom within this archive is orbidden, you may reely distribute the URL o WestminsterResearch: ( In case o abuse or copyright appearing without permission repository@westminster.ac.uk

2 DEVELOPMENT OF PLANAR FILTERS AND DIPLEXERS FOR WIRELESS TRANSCEIVER FRONT ENDS DAMIR AYNIYEV A thesis submitted in partial ulilment o the requirements o the University o Westminster or degree o Doctor o Philosophy May

3 ABSTRACT The central theme o this work is the design o compact microstrip bandpass ilters and diplexers and the investigation o applications o these circuits in integrated transceiver RF ront-end. The core o this thesis thereore presents the ollowing stages o the work: - Analysis o coupled pseudo-interdigital resonators and lines; ormulation o approximate transmission zero conditions and the investigation o coupling between these two resonators and related structures. - Development o compact, low loss and high selectivity microstrip pseudointerdigital bandpass ilters. The design procedure o the ilter consists o three simple steps, starting rom the design o a parallel-coupled bandpass ilter using the image parameter method applied to coupled microstrip lines. The development o compact microstrip diplexers composed o these ilters uses the optimized common-transormer diplexing technique. An experimental veriication o the developed ilters and diplexers is made. - Investigation o the use o stepped impedance resonators (SIR) or the design o pseudo-interdigital bandpass ilters with advanced characteristics. The design o compact dual-band ilter using SIR. The investigation o possible improvement o the stopband o bandpass ilters using bandstop generating structures. The application o SIR, deected ground structures (DGS), spur-lines, and opencircuited stubs in the design o compact bandpass ilters with improved stopband. - The application o the proposed ilters and diplexers in the design o integrated antenna ilters and antenna diplexers. Improvement o perormance o patch antennas, such as suppression o spurious harmonics o single-band antenna and improvement o bandwidth and selectivity o dual-band antenna, as a result o integration with ilters. Separation o antennas bands and reduction o component count in integrated antenna diplexers ii

4 ACKNOWELEDGEMENTS I would like to give my particular thanks to my director o studies, Dr. D. Budimir or his supervision, encouragement and guidelines throughout this research work. I would also like to thank my supervisor Dr. A. Tarczynski or his useul advice and support. The inancial support provided by School o Electronics and Computer Science, University o Westminster is grateully acknowledged. Also I would like to thank my mother Raisa and my brother Rashid or their aith in me, support and encouragement thought all our years o studying and working towards this degree. iii

5 CONTENTS. INTRODUCTION..... Filters or Wireless Applications..... Filters Design Microstrip Bandpass Filters Aims and Objectives o this Thesis Outline o the Thesis Reerences.... MICROSTRIP TRANSMISSION LINES AND RESONATORS Introduction Microstrip Lines Coupled Microstrip Lines Microstrip Transmission Line Resonators Coupled Resonators Reerences ANALYSIS OF PSEUDO-INTERDIGITAL LINES AND RESONATORS Introduction Analysis o Transmission ero Conditions o Coupled Pseudo- Interdigital Lines and Resonators Transmission ero Conditions o Parallel-Coupled Lines Transmission ero Conditions o Coupled Pseudo-Interdigital Lines and Resonators Coupling o Pseudo-Interdigital Resonators Summary Reerences...63 iv

6 4. COMPACT PSEUDO-INTERDIGITAL BANDPASS FILTERS Introduction Image Impedance o Coupled Microstrip Lines Design o Parallel Coupled Microstrip Bandpass Filters using Image Parameter Design o Hairpin-Line Microstrip Bandpass Filters Design o Compact Pseudo-Interdigital Microstrip Bandpass Filters Summary Reerences PSEUDO-INTERDIGITAL STEPPED IMPEDANCE BANDPASS FILTERS Introduction Description o Stepped Impedance Resonators Design o Compact Microstrip Dual-Band Pseudo-Interdigital Stepped Impedance Bandpass Filters Design o SIR Bandpass Filters with Improved Stopband Perormance Bandpass Filters with Extended Stopband Analysis o Spur-line and Open-Circuited Stubs Bandpass Filters with Improved Stopband Analysis o Deected Ground Structures Compact Pseudo-Interdigital SIR Bandpass Filters with Improved Stopband using DGS Summary Reerences... v

7 6. DESIGN OF COMPACT MICROSTRIP DIPLEXERS Introduction Microstrip Diplexer with Y-junction Miniaturised Microstrip Diplexers or Wireless Applications Microstrip Three-Port Four-Channel Diplexers Summary Reerences INTEGRATED ANTENNA FILTERS AND ANTENNA DIPLEXERS FOR WIRELESS APPLICATIONS Introduction Integrated Antenna Filter with Harmonic Rejection Microstrip Antenna Diplexers or Wireless Communications Integration o Microstrip Filters/Diplexers with Dual-band Multi-Resonator Microstrip-Fed Patch Antenna Summary Reerences CONCLUSION AND FUTURE WORK Introduction Contributions o the Thesis Development o Compact Microstrip Bandpass Filters and Diplexers Design o Stepped Impedance Pseudo-Interdigital Bandpass Filters Integration o Filters and Diplexer with Patch Antennas Suggestions or Future Work...54 vi

8 LIST OF ACRONYMS ABCD BPF CAD db DGS DSS EBG EM FBW GHz HTS IEEE IF IPM LCP LNA LTCC MEMS MIC MMIC PA RF SAW SIR SSS TEM T UIR WLAN WiMAX UWB Transer matrix Bandpass ilter Computer-Aided Design Decibel Deected ground structures Dumbbell-shaped slot Electromagnetic bandgap Electromagnetic Fractional bandwidth Gigahertz High Temperature Superconductor Institute o Electrical and Electronics Engineers Intermediate requency Image parameter method Liquid Crystal Polymers Low noise ampliier Low-Temperature Coired Ceramics Microelectromechanic Systems Microwave Integrated Circuits Monolithic Microwave Integrated Circuits Power ampliier Radio requency Surace acoustic waves Stepped impedance resonator Spiral-shaped slot Transverse electromagnetic propagation mode Transmission zero Uniorm impedance resonator Wireless local area network Worldwide Interoperability or Microwave Access Ultra wide band vii

9 LIST OF FIGURES AND TABLES Chapter Figure - Block diagram o ull-duplex superheterodyne transceiver with single conversion stage. Chapter Figure - Figure - Figure -3 Figure -4 Figure -5 Figure -6 Microstrip transmission line: (a) geometry; (b) electric and magnetic ield lines. Field distribution o coupled microstrip lines: (a) odd mode; (b) even mode. Characteristic impedances: even mode (black solid); odd mode (black dashed); single line (grey solid); arithmetic average (black dotted); geometric average(grey dashed). Distributed capacitances: (a) odd mode; (b) even mode. Equivalent circuit o coupled transmission lines. Coupling coeicients o coupled microstrip lines. Figure -7 Coupling coeicients o coupled microstrip lines with ixed slot width. Figure -8 Voltage distribution: (a) λg open-circuited line; (b) λg 4 short- circuited line; n= (solid), n= (dashed). Figure -9 Unloaded Q actor o microstrip open-circuited λ g resonator Figure - Figure - Figure - Figure -3 General coupled microwave resonators. Coupled resonators: (a) magnetic coupling; (b) electric coupling. Current in the coupled resonator circuit. Magnetically coupled synchronously tuned resonators. viii

10 Chapter 3 Figure 3- Layouts o coupled resonators: (a) pseudo-interdigital resonators; (b) hairpin resonators. Figure 3- Simulated S or coupled pseudo-interdigital lines (solid) and hairpin lines (dashed). Figure 3-3 Coupling o lines: (a) slot s coupling; (b) slot s coupling. Figure 3-4 Conventional parallel-coupled lines. Figure 3-5 Calculated S or conventional microstrip parallel-coupled lines. Figure 3-6 Asymmetrically terminated parallel-coupled lines. Figure 3-7 Calculated S or asymmetrically terminated coupled lines. Figure 3-8 Coupled pseudo-interdigital lines: (a) -port circuit; (b) 8-port circuit; (c) 8-port model. Figure 3-9 Simulated (solid) and calculated (dashed) S o coupled pseudo- interdigital lines. Figure 3- Simulated (solid) S o coupled pseudo-interdigital lines and calculated Figure 3- (dashed) coeicient describing T condition. Simulated T requencies. Figure 3- Simulated T requencies: s + s mm (black); s + s mm (grey). = = Figure 3-3 Coupled λ g resonators: (a) Pseudo-interdigital; (b) Hairpin; (c) Coupled through slot s ; (d) Coupled through slots s and s 3 ; (e) Coupled through slots s and s. Figure 3-4 Simulated S o resonators: Pseudo-interdigital (black dotted); Hairpin ` (black solid); Coupled through Slot s (grey solid); Coupled through slots s and s 3 (black dashed); Coupled through slots s and s (grey dotted). Figure 3-5 Simulated and calculated coupling coeicient as a unction o θ : Pseudo-interdigital (black dotted); Hairpin (black solid); Coupled through slot s (grey solid); Coupled through slots s and s 3 (black dashed). ix

11 Chapter 4 Figure 4- Figure 4- Figure 4-3 Figure 4-4 Figure 4-5 Figure 4-6 Figure 4-7 Figure 4-8 Figure 4-9 (a) Coupled microstrip lines; (b) two port network terminated in its image impedance. Normalized image impedance o coupled lines. Layout o parallel-coupled bandpass ilter with impedance transormers. Simulated S-parameters o edge-coupled ilter: (a) with impedance transormer; (b) without impedance transormer. Layout o hairpin bandpass ilter. Coupling coeicients o hairpin resonators. Simulated S-parameters o hairpin ilter. Layout o pseudo-interdigital bandpass ilter. Coupling coeicient o pseudo-interdigital resonators. Figure 4- Layout o compact microstrip bandpass ilter ( w =. mm, s =. 3 mm, Figure 4- Figure 4- g =.3 mm). Simulated (dashed) and measured (solid) S-parameters o pseudointerdigital bandpass ilter: (a) S coeicients; (b) S coeicients Photograph o abricated bandpass ilter. Chapter 5 Figure 5- Stepped impedance resonators: (a) quarter-wavelength type; (b) hal- wavelength type. Figure 5- Relationship between total electrical length and θ or resonant Figure 5-3 Figure 5-4 Figure 5-5 condition given or dierent impedance ratios. Relationship between normalized spurious resonance requency and impedance ratio. Simulated current distributions: (a) pseudo-interdigital resonators; (b) hairpin resonators. Layout o compact microstrip pseudo-interdigital SIR dual-band bandpass ilter. x

12 Figure 5-6 Figure 5-7 Figure 5-8 Figure 5-9 Figure 5- Figure 5- Figure 5- Figure 5-3 Figure 5-4 Figure 5-5 Figure 5-6: Figure 5-7 Figure 5-8 Figure 5-9 Figure 5- Figure 5- Figure 5- Simulated (dashed) and measured (solid) S-parameters o pseudointerdigital SIR dual-band bandpass ilter: (a) S coeicients; (b) S coeicients Photograph o the abricated bandpass ilter. Layout o compact microstrip pseudo-interdigital SIR bandpass ilter with extended stopband. Simulated S-parameters o compact microstrip pseudo-interdigital SIR bandpass ilter with extended stopband. Spur-line section: (a) Layout; (b) Terminal conditions. Equivalent circuit o spur-line. Microstrip open-circuited stub: (a) layout. (b) equivalent circuit. Layout o bandpass ilter with spur-line and open-circuited stubs. Simulated S-parameters o spur-line section and open-circuited stub. Simulated S-parameters o compact microstrip pseudo-interdigital SIR bandpass ilter with improved stopband. Structure and equivalent circuit o DGS: (a) dumbbell-shaped slot; (b) spiral shaped slot. Simulated S-parameters o SSS (black lines) and DSS (grey lines). Layout o bandpass ilter with one SSS. Simulated S-parameters o bandpass ilter with one SSS. Layout o bandpass ilter with two SSS. Simulated S-parameters o two SSS. Simulated S-parameters o bandpass ilter with two SSS. Chapter 6 Figure 6- Figure 6- Figure 6-3 Figure 6-4 Figure 6-5 Simulated S-parameters o bandpass ilters: with passband centered at.44 GHz (black lines); with passband centered at 3.5 GHz (grey lines). Layout o microstrip diplexer with Y-junction. Simulated S-parameters o microstrip diplexer with Y-junction. Common-transormer diplexer with interdigital ilters. Layout o miniaturised microstrip diplexer. xi

13 Figure 6-6 Figure 6-7 Figure 6-8 Figure 6-9 Figure 6- Figure 6- Simulated (dashed) and measured (solid) S-parameters o miniaturized microstrip diplexer: (a) S coeicients; (b) S coeicients; (b) S 3 coeicients Photograph o abricated miniaturized microstrip diplexer. Architecture o diplexer: (a) using our single band ilters; (b) using two Dual-band ilters. Layout o three-port our-channels diplexer. Simulated S-parameters o port to port 3 bandpass ilter. Simulated S-parameters o three-port our-channel diplexer. Chapter 7 Figure 7- Figure 7- Figure 7-3 Figure 7-4 Figure 7-5 Figure 7-6 Figure 7-7 Figure 7-8 Figure 7-9 Figure 7- Figure 7- Figure 7- Figure 7-3 Figure 7-4 Layout o microstrip inset-ed patch antenna. Layout o microstrip antenna ilter. Simulated S o inset-ed antenna (dashed) and antenna-ilter (solid). Simulated radiation patterns, E-plane (red) and H-plane (blue): (a) Patch antenna; (b) Integrated Antenna Filter. Layout o proposed microstrip antenna diplexer. Simulated S loss o proposed antenna. Simulated S-parameters o microstrip diplexer. Simulated S-parameters o microstrip antenna diplexer. Layout o proposed antenna diplexer. Simulated return loss o multi-resonator patch antenna. Simulated S-parameters o microstrip diplexer. Simulated S-parameters o integrated antenna diplexer. Layout o integrated dual-band antenna ilter. Simulated return loss o integrated dual band antenna ilter. Chapter 3 Table 3- Table 3- Table 3-3 Dimensions o coupled resonators. T requencies or coupled microstrip lines with dierent size T requencies or dierent eeding o coupled pseudo-interdigital resonators. xii

14 . INTRODUCTION.. Filters or Wireless Applications Electronic ilters are circuits that have signal processing unctions. i.e. they transorm an input signal to obtain an output signal with the required characteristics. In the requency domain ilters are used to reject unwanted signal requencies and to pass signals o desired requencies. Filters are indispensable devices, in many systems and applications including wireless broadband, mobile, and satellite communications, radar, navigation, sensing and other systems [-]-[-5]. With the development o these systems, mostly induced by great commercial interests, limited electromagnetic spectrum has to be shared among more and more systems. Thus, there is an increasing demand or RF, microwave, and millimetre wave ilters with more stringent requirements. These ilters are employed in various systems to select or conine signals within speciied spectral limits. Typical application o ilters and variety o unction perormed by them can be illustrated in conventional superheterodyne transceiver. The block diagram o ullduplex superheterodyne transceiver with single conversion stage is shown in Figure - [-6]-[-8]. Figure -: Block diagram o ull-duplex superheterodyne transceiver with single conversion stage.

15 The block diagram o the receiver is on the top and block diagram o the transmitter is on the bottom o the scheme. Both these systems share antenna, voltage-controlled oscillator, and duplexer which consists o two bandpass ilters (BPF). BPF has a passband at the receiver band and it is used to select signal or the receiver and to remove intererence caused by them leakage o the output signal rom transmitter. It should have low insertion loss, which aects the sensitivity o receiver, and high attenuation, especially at the transmitter band. BPF 6, the second ilters o duplexer, is employed to reduce spurious radiation power rom transmitter. It also should attenuate noise at the receiver band. Thereore, a bandpass ilter with low insertion loss and wide stopband is required. At the receiver part, BPF, placed ater low noise ampliier (LNA), is an image rejection ilter. It is used to suppress the signal at the image requency, which ater down-conversion will appear at the same intermediate requency (IF) as the main signal and will degrade signal-to-noise ratio. The channel selection ilter BPF 3 is a narrow band ilter with steep attenuation which operates at IF requency. In the transmitter part, BPF 5, is placed beore power ampliier (PA) to select the required signal and to reject mixing products generated by up-converter. The baseband signal is iltered by BPF 4 beore upconversion. For particular applications, the number and type o employed ilters can vary, but still ilters are essential components in these systems. The advancement in the design o microwave ilters was inluenced by the requirements o dierent systems they were developed or. Mainly these are military systems, satellite communications systems, cellular communication base-stations, and cellular radio handsets [-3]. The main requency bands used by these and other wireless communication systems are spread throughout a wide range, rom several tens o MHz to several tens o GHz. Hence a wide range o resonators and ilters can be applied to these requency bands in order to provide the most optimal solution to the various application requirements. For example at the requencies below GHz, surace acoustic wave (SAW) and helical resonators are used [-4]. SAW ilters have extremely sharp selectivity and they are used in cases when miniaturisation and low loss are required. Moreover, SAW resonators show outstanding temperature characteristics satisying conditions or applications o narrow band ilters. Helical resonator ilters are used when a high level o power handling is required.

16 For the requency range rom RF to microwave, various types o ilters are employed, including coaxial, dielectric, waveguide, and stripline/microstrip resonator ilters [-4]. Coaxial ilters are very attractive ilters with low insertion loss and compact size, but abrication o these ilters or high requency bands is diicult. Dielectric resonator ilters also have small size and low insertion loss. However, their application is limited by cost and complexity o the processing techniques. Waveguide ilters, which have been used in this requency range or a long time, have low insertion loss, high power capability, and practical application easibility up to GHz. The size o waveguide ilters is much larger than the size o others types o ilters. Stripline/microstrip resonators and ilters are commonly used in wireless communications due to their small size, low cost o production, and possibility to integrate with other lumped passive and active microwave devices. These ilters can be used on wide range o requency bands by employing various kinds o substrate materials. The main disadvantage o this type o ilter is high insertion loss, due to signiicantly lower Q actor o stripline/microstrip resonators, compared to other types o resonators. The rapid development o microstrip and other planar ilters is mainly driven by two actors. First is the recent advance o new materials and abrications technologies, such as high-temperature superconductors (HTS), low-temperature coired ceramics (LTCC), monolithic microwave integrated circuits (MMIC) and others. The second actor is the improvement and urther development o computeraided design (CAD) tools. Full-wave electromagnetic simulators (EM) are requently used in the design and optimisation o novel microwave ilters with advanced iltering perormance [-]. 3

17 .. Filters Design The basic concept o ilters was proposed in 95 independently by Campbell and Wagner. Their results were obtained rom earlier work on loaded transmission lines and classical theory o vibrating systems. Aterwards, two dierent ilter theories were developed, known as image parameter theory and insertion loss theory [-9], [-]. The image parameter method was developed in the 9s by Campbell, obel, and some others. This method involves speciication o the passband and stopband characteristics or a cascade o -port networks. The image viewpoint, used in this method is similar to the wave viewpoint used in the analysis o transmission lines. Hence, this method provides a link between practical ilters and ininite periodic structures [-]. Simple ilters can be designed without requiring a computer. However, sometimes impractical component values can be obtained using image parameter method [-]. This approximate technique was the only practical ilter design method untill computers become widespread. The insertion loss theory, also known as modern ilter theory, is ar more complex but accurate design technique. It owns its origin to the work o Cauer and Darlington who put orward a theory that involves a set o problems relating to modern network synthesis [-3]. This design method consists o two basic steps: determination o a transer unction that approximates required ilter speciication and synthesis o electrical circuit using requency response estimated by the previous transer unction. Although this method was very eicient, it had become widely used only since highspeed computers, used to make all necessary complex calculations, became widely available. Nowadays, lowpass prototype network with angular cuto requency o rad/s terminated by in -Ω impedances is normally used as a starting point in the design o microwave ilters. The inal design o lumped-element lowpass, bandpass, bandstop and highpass ilters can be obtained rom lowpass prototype using requency and impedance transormation. Modern ilter theory is expanded rom lumped-element (LC) resonators to distributed resonators, such as waveguide, coaxial and 4

18 microstrip/stripline. In the design o many distributed resonator ilters values o elements o lowpass prototype network are used to determine important transmission characteristic o ilters using ormula derived or each type o ilters [-5]. 5

19 .3. Microstrip Bandpass Filters According to their requency response, electronic ilters are categorised into our groups: lowpass, highpass, bandpass, and bandstop ilters. In wireless communications bandpass ilters are the most widely used. For the design o microstrip bandpass ilters, several various techniques exist and most o proposed novel ilters with advanced characteristics are based on these several structures [-]. Combline bandpass ilters consist o array o parallel resonators which are short circuited at one end with a loading capacitor at the other end [-4]. These are very compact ilters with the length o resonators equal to λ g 8 at undamental passband requency and spurious response centered at about 4. Combline ilters are widely implemented using coaxial resonators. The design o these ilters in microstrip includes optimisation and computer aided design tools [-5], [-6]. Interdigital ilters consist o parallel coupled quarter-wavelength lines which are short-circuited at one end and open-circuited at another end [-7]. Interdigital ilters have the irst spurious harmonic at 3. Coupling between interdigital lines is stronger then between comblines and gap between resonators can be larger, making interdigital ilters simpler to abricate or high requency and wide bandwidth applications, when dimensions o ilters are quite small [-8]. Accurate design o interdigital ilters in microstrip also involves optimization techniques, such as or example aggressive space mapping optimization [-9] or optimization that uses an accurate computer aided design method which is based on the identiication o direct and parasitic coupling o each resonator [-]. Parallel-coupled-line ilters, initially proposed or stripline [-], are the most popular microstrip ilters. They are composed o hal-wavelength resonators that are coupled to each other along hal o their ull length. For all types o microstrip ilters in which coupling is arranged by parallel coupled lines dierent phase velocities between even and odd mode in coupled-line region should be taken into account. Thus, or the design o microstrip parallel-coupled-line ilters, special design curves or optimization techniques are used [-], [-3]. Parallel-coupled-line ilters in which olded 6

20 resonators are used, are known as hairpin-line ilters [-4], [-5], in which halwavelength resonators have U-shaped orm. The introduction o this modiication substantially decreased the size o ilters. Miniaturized hairpin resonators [-6], in which arms o resonator are bent inside to orm coupled lines region, are requently used in the design o compact cross-coupled bandpass ilters [-7], [-8]. Miniaturized hairpin resonators have some similarity with square open-loop resonators [-9, -3], which are used to obtain capacitive and inductive coupling by only proximity coupling through ringing ields. This type o resonators can be used to build microstrip cascaded quadruplet and other types o cross-coupled bandpass ilters. Another type o resonators and ilters employed or compact size bandpass ilter are dual-mode patch and ring microstrip resonators [-3], [-3]. Both, open-loop and dual-mode resonators have been employed in the design o a huge variety o microstrip bandpass ilters. Due to the development o wireless communications and the appearance o new systems there is high demand in small size, low cost ilters with high perormance. Thereore, miniaturization o bandpass ilters with improvement o their characteristics is a big challenge in modern ilters design. This is achieved by improvement o conventional concepts and approaches, as well as by introduction o new topologies and designs. For example, size o parallel-coupled-line ilters can be reduced by bending coupled microstrip lines, while suppression o spurious harmonic [-33] or dual-band operation is achieved by the use o SIR [-34]. Implementation o bandstop generating spur-lines inside resonators can also result in size reduction and spurious harmonics suppression [-35]. For miniaturized hairpin resonator ilters, urther size reduction with rejection o spurious harmonic has been achieved by employing either interdigital capacitors embedded in resonators [-36], or sections with dierent characteristic impedances, i.e. SIR hairpin resonators [-37]. Implementation o SIR also can be used in the design o compact dual-band hairpin resonators ilters, with these resonators employed on top [- 38], as well as on both, top and ground layer [-39]. 7

21 .4. Aims and Objectives o this Thesis. The aims and objectives o this work are the development o compact, low cost, high perormance, microstrip ilters and diplexers or wireless applications. The irst aim o the work is the development o simple design procedure that can be used or design o compact, high selectivity bandpass ilters. As the irst objective, coupled pseudo-interdigital lines and resonators need to be analysed; approximate conditions o transmission zeros (Ts), the nature and range o coupling, and the eects o physical dimensions o resonators on both these characteristics are to be determined. The easibility to design pseudo-interdigital bandpass ilters using a procedure based on classical design approaches is then investigated, ollowed by an attempt to incorporate technological constraints and to achieve maximum possible improvement and miniaturization. Additionally, the possibility to design compact microstrip diplexer composed o developed ilters is investigated. Dierent diplexing techniques and circuits need to be studied to ind the most optimal way to combine bandpass ilters in diplexer in order to achieve small size and high perormance. The second aim o this work is to extend and apply developed design approach in order to design bandpass ilters with advanced perormance, such as dual-band bandpass ilters and bandpass ilters with improved stopband. At irst, a study o the various techniques available in literature is carried out in order to ind the ones most appropriate or implementation. Then the possibility to design compact dual-band ilter is investigated. Various approaches, used or the suppression o spurious harmonics and improvement o stopband, are investigated and then applied in the design o pseudointerdigital bandpass ilters with improved stopband. Finally, integration o the designed ilters and diplexers with patch antennas, as one o the applications o these circuits, is investigated. The purpose o such integration can be the suppression o spurious harmonics, the reduction o the number o elements in the RF ront end, size reduction, and improvement o perormance o subsystem. Singleband, multi-band, and wideband antennas can be used. 8

22 .5. Outline o the Thesis This thesis is organized into eight chapters. Chapter gives a brie introduction to electronic ilters in wireless applications and an overview o the main types o RF/microwave ilters and two main approaches in the design o ilters. It briely reviews key types o microstrip bandpass ilters and a ew approaches employed to achieve size reduction and improvement o perormance simultaneously. It also outlines the aims and objectives o this works. Chapter provides a review o the basic theory used in the design o ilters, presented in next chapters. It starts with description o main parameters o microstrip and coupled microstrip transmission lines. Then it presents analysis and physical properties o quarter- and hal-wavelength microstrip transmission-line resonators. Coupling o resonators, analysed using RLC resonant circuits, is presented at the end o this chapter. Chapter 3 ocuses on the analysis o coupled microstrip pseudo-interdigital lines and resonators. Approximate T conditions o coupled lines are derived. These conditions describe requencies at which transmission through coupled lines is zero, i.e. coupling between coupled pseudo-interdigital lines is zero as well. Coupling between pseudointerdigital resonators and dependence o the coupling coeicient and transmissionzero requencies on the main dimensions o resonators are investigated. Chapter 4 is devoted to the development o compact pseudo-interdigital bandpass ilters. Design o these ilters is based on the second order microstrip parallel-coupled transmission-line-resonator ilter designed using image parameter method, applied directly to coupled microstrip lines. Parallel-coupled transmission-line-resonator ilter has been transormed into hairpin bandpass ilter and subsequently into pseudointerdigital bandpass ilter. This is very compact bandpass ilter with high selectivity improved by Ts occurred below and above the passband. Chapter 5 presents the designs o dual-band bandpass ilters and bandpass ilters with improved stopband. Quarter-wavelength SIR are implemented in both kinds o ilters to 9

23 control the irst spurious harmonic o ilters. An SIR with an impedance ratio bigger than one is used in dual-band bandpass ilter designed to shit second harmonic closer to the undamental passband, whereas SIR with impedance ratio smaller than one are used to extend the stopband o ilter by pushing the second harmonic to the higher requencies. Further improvement o stopband is achieved by generating bandstops at harmonic requencies. Two types o circuits are used or this: spur-lines and opencircuited stubs connected in cascade with ilter, and deected ground structures (DGS), etched in ground plane under the eeding line o bandpass ilter. Suppression o the second and third harmonics using this approach is demonstrated. Chapter 6 illustrates application o bandpass ilters in designs o compact microstrip diplexers. Two dierent approaches o combining ilters in diplexers are used: Y-junction and modiied common-transormer diplexer. Degradation o the passband o the low requency channel is observed when the Y-junction is used. The use o the common-transormer diplexing technique provides a very compact solution with minimal degradation o passbands o both ilters. Compact diplexers designed using this technique, composed o single-band and dual-band bandpass ilters, are presented. Chapter 7 demonstrates the application o bandpass ilters and diplexers in integrated antenna ilters and antenna diplexers. The integration o inset-ed rectangular patch antenna with single-band bandpass ilter with extended stopband is proposed to suppress the irst and the second spurious harmonics o the antenna. A dual-band antenna is integrated with a dual-band ilter in order to improve selectivity and bandwidth o the antenna. Diplexers are integrated with dual- and multiband antennas to reduce component count in dual-band systems. Such integration is needed or the separation o high and low bands o antennas. Finally, chapter 8 concludes the thesis with a summary and oers recommendations or uture work.

24 .6. Reerences [-] R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave ilters or communication systems : undamentals, design, and applications. Hoboken, New Jersey: John Wiley & Sons, 7 [-] J. G. Hong and M. J. Lancaster, Microstrip Filters or R/Microwave Applications, New York: John Wiley & Sons, [-3] I. C. Hunter, Theory and design o microwave ilters. London: Institution o Electrical Engineers, [-4] M. Makimoto, S. Yamashita, Microwave resonators and ilters or wireless communication:theory, design and application. New-York: Springer, [-5] G.L. Matthaei, L. Young and E.M.T. Jones, Microwave ilters, impedancematching networks, and coupling structures, Dedham, MA: Arthec House 964 [-6] F. Ellinger, Radio Frequency Integrated Circuits and Technologies, Berlin: Springer, 7 [-7] Q. Gu, RF System Design o Transceivers or Wireless Communications. New- York: Springer, 5 [-8] M. N. S. Swamy and K.-L. Du, Wireless Communication Systems: From RF Subsystems to 4G Enabling Technologies, New York: Cambridge University Press, [-9] G. C. Temes and S. K. Mitra, Modern ilter theory and design, New York: Wiley-Interscience, 973 [-] D. E. Johnson, Introduction to ilter theory, New Jersey: Prentice Hall, 976 [-] D. M. Pozar, Microwave engineering. 3 rd edition, New York: John Wiley & Sons, 4 [-] C. W. Sayre, Complete wireless design. New York: McGraw-Hill,. [-3] M. E. Van Valkenburg, Introduction to Modern Network Synthesi, New York: John Wiley & Sons, 96 [-4] G. L. Matthaei, "Comb-line band-pass ilters o narrow or moderate bandwidth," Microwave J., vol. 6, pp. 8-9, August 963 [-5] H. Oraizi and N. Azadi-Tinat, "A Novel Method or the Design and Optimization o Microstrip Multi-section Bandpass Combline Filters," 36 th

25 European Microwave Conerence, Manchester, UK, September 6, pp.7- [-6] A. D. Vincze, "Practical Design Approach to Microstrip Combline-Type Filters," IEEE Trans. on Microwave Theory and Tech., vol., no., pp. 7-8, December 974 [-7] G. L. Matthaei, "Interdigital Band-Pass Filters," IRE Trans. on Microwave Theory and Tech., vol., no.6, pp , November 96 [-8] R. Levy, R. V. Snyder, and G. Matthaei, "Design o microwave ilters," IEEE Trans. on Microwave Theory and Tech., vol.5, no.3, pp , March [-9] J. W. Bandler, R. M. Biernacki, C. Shao Hua, and H. Ya Fei, "Design optimization o interdigital ilters using aggressive space mapping and decomposition," IEEE Trans. on Microwave Theory and Tech., vol.45, no.5, pp , May 997 [-] C. Saboureau, S. Bila, D. Baillargeat, S. Verdeyme, and P. Guillon, "Accurate computer aided design o interdigital ilters applying a coupling identiication method," MTT-S, Int. Microwave Symp. Dig., vol.3, pp.89-9, [-] S. B. Cohn, "Parallel-Coupled Transmission-Line-Resonator Filters," IRE Trans. on Microwave Theory and Tech., vol. 6, no., pp. 3-3, April 958 [-] H. Oraizi, M. Moradian, and K. Hirasawa, "Optimum design o parallel coupled-line ilters," 9 th Int. Con. on Communications Systems, September 4, pp [-3] R. A. Dell-Imagine, "A Parallel Coupled Microstrip Filter Design Procedure," MTT-S, Int. Microwave Symp. Dig.,vol.7, no., pp. 9-3, May 97 [-4] E. G. Cristal and S. Frankel, "Hairpin-Line and Hybrid Hairpin-Line/Hal-Wave Parallel-Coupled-Line Filters," IEEE Trans. on Microwave Theory and Tech., vol., no., pp , November 97 [-5] U. H. Gysel, "New Theory and Design or Hairpin-Line Filters," IEEE Trans. on Microwave Theory and Tech., vol., no. 5, pp , May 974 [-6] M. Sagawa, K. Takahashi, and M. Makimoto, "Miniaturized hairpin resonator ilters and their application to receiver ront-end MICs," IEEE Trans. on Microwave Theory and Tech.s, vol. 37, no., pp , December 989 [-7] K. Jen-Tsai, M. Ming-Jyh, and L. Ping-Han, "A microstrip elliptic unction ilter with compact miniaturized hairpin resonators," IEEE Microwave and Guided Wave Lett., vol., no.3, pp.94-95, March

26 [-8] D. Yingjie, P. Gardner, P. S. Hall, H. Ghaouri-Shiraz, and. Jiaeng, "Multiple-coupled microstrip hairpin-resonator ilter," IEEE Microwave and Wireless Components Lett., vol.3, no., pp , December 3 [-9] J. S. Hong and M. J. Lancaster, "Couplings o microstrip square open-loop resonators or cross-coupled planar microwave ilters," IEEE Trans. on Microwave Theory and Tech., vol. 44, no., pp. 99-9, November 996 [-3] J. S. Hong and M. J. Lancaster, "Theory and experiment o novel microstrip slow-wave open-loop resonator ilters," IEEE Trans. on Microwave Theory and Tech.s, vol.45, no., pp , December 997 [-3] J. A. Curtis and S. J. Fiedziuszko, "Miniature dual mode microstrip ilters," MTT-S, Int. Microwave Symp. Dig., vol., pp , July 99 [-3] H. Yabuki, M. Sagawa, M. Matsuo, and M. Makimoto, "Stripline dual-mode ring resonators and their application to microwave devices," IEEE Trans. on Microwave Theory and Tech., vol.44, no.5, pp.73-79, May 996 [-33] W. Shih-Ming, C. Chun-Hsiang, H. Ming-Yu, and C. Chi-Yang, "Miniaturized spurious passband suppression microstrip ilter using meandered parallel coupled lines," IEEE Trans. o Microwave Theory and Tech., vol.53, no., pp , February 5 [-34] S. Sheng and. Lei, "Compact dual-band microstrip bandpass ilter without external eeds," IEEE Microwave and Wireless Comp. Lett., vol.5, no., pp , October 5 [-35] W. Yu-hen, W. Chia-An, and L. Kun-Ying, "Miniaturized Paralleled-Coupled Microstrip Bandpass Filters with Spur-Line or Multi-Spurious Suppression," Asia-Paciic Microwave Con., Bangkok, Thailand, 7 [-36]. Jiwen and F. henghe, "Microstrip Interdigital Hairpin Resonator With an Optimal Physical Length," IEEE Microwave and Wireless Comp. Lett., vol.6, no., pp , December 6 [-37] L. Sheng-Yuan and T. Chih-Ming, "New cross-coupled ilter design using improved hairpin resonators," IEEE Trans. on Microwave Theory and Tech., vol.48, no., pp.48-49, December [-38] C. Qing-Xin and C. Fu-Chang, "A Compact Dual-Band Bandpass Filter Using Meandering Stepped Impedance Resonators," IEEE Microwave and Wireless Comp. Lett., vol.8, no.5, pp.3-3, May 8 3

27 [-39] W. Bian, L. Chang-hong, L. Qi, and Q. Pei-yuan, "Novel Dual-Band Filter Incorporating Deected SIR and Microstrip SIR," IEEE Microwave and Wireless Comp. Lett., vol.8, no.6, pp , June 8 4

28 . MICROSTRIP TRANSMISSION LINES AND RESONATORS.. Introduction Microstrip ilters are one the most popular realizations o planar microwave ilters. Proposed in 95 s as one o the planar transmission lines [-], microstrip become very attractive technology or building passive circuits and microwave integrated circuits (MIC) in 96 s with the advent o 99-percent pure alumina. Nowadays, many novel microstrip and other planar ilters with advanced iltering characteristics are developed using novel materials and abrication technologies such as HTS, liquid crystal polymers (LCP), LTCC, MMIC, and microelectromechanic systems (MEMS) [-]. These ilters as well as advanced ilters built using conventional Alumina or Duroid substrates are designed using novel CAD tools. Coupled microstrip lines are employed in the design o bandpass ilters based on interdigital, parallel coupled and combline structures. Using these lines stronger coupling between resonators can be achieved. This is very important in the design o bandpass ilters [-3], which are in general composed o a number o coupled resonators, tuned at a given center requency o the passband [-4]. For the design o bandpass ilters with wider bandwidths, stronger coupling between resonators is required. In this chapter background theory or the design o microstrip bandpass ilters based on the implementation o coupled lines is presented. Sections. and.3 present brie analysis and main characteristics o microstrip lines and coupled microstrip lines respectively. The structure and physical properties o open-circuited λ g and shortcircuited λ g 4 microstrip resonators, where λ g is a guided wavelength, are described in section.4. These resonators are most requently used in the design o microstrip bandpass ilters. Analysis o coupled resonator circuits is presented in section.5. 5

29 .. Microstrip Lines Microstrip is the most popular planar transmission structure used in MIC. Planar transmission structure is the one in which the characteristics o the circuit elements, built using this structure, can be determined by the dimensions in a single plane. This is the main requirement or a transmission line to be used in MIC. Microstrip can be abricated using photolithographic processes. Open coniguration makes it easily integrated with other discrete lumped passive and active microwave devices. Microstrip transmission lines consist o a conductor printed on top o thin, grounded dielectric substrate, as it is shown in Figure - (a). The width o the conductor w, thickness o the substrate h, and relative permittivity ε r are the main important parameters. Thickness o the top metallic line t is much less important and oten can be neglected. This is because the thickness t is about - µ m and ew electric ield lines, shown in Figure - (b), start on the side planes o the top metallic line. As thickness t increases, the ield distribution changes as more electric ield lines start on the side planes o the top line and this aects the characteristic impedance and the eective dielectric constant ε e o microstrip. From the synthesis ormulas or microstrip, which consider the thickness t [-5], it can be derived that or a microstrip witht h. 5, ε r, and w h., the eect o thickness t on and ε e is approximately about % [-5]. Figure -: Microstrip transmission line: (a) geometry; (b) electric and magnetic ield lines. Due to the abrupt dielectric interace between the air and the substrate, microstrip lines do not support pure transverse electromagnetic (TEM) propagation mode. The 6

30 necessity o the longitude component o electric and magnetic ields can be proved using Maxwell s equations. Figure - (b) illustrates electric and magnetic ields distributions at transverse cross-sectional plane. The analysis methods used to determine the microstrip characteristic impedance and propagation constant can be divided in two groups, quasi-static analysis methods and ull wave analysis methods [-6]. Full wave analysis methods consider a hybrid mode o propagation and provide more analytically complex and rigorous solutions. These methods show that the characteristic impedance and phase velocity o the microstrip have dispersive nature, i.e. change with requency. Quasi-static methods consider microstrip to have pure TEM mode o propagation. Transmission characteristics are ound rom two electrostatic capacitances: C a - capacitance per unit length o microstrip line with dielectric replaced by air, and C - capacitance per unit length o microstrip line with dielectric substrate. These methods provide quite accurate results or the requency up to a ew gigahertzes. The eective dielectric constant deined as C c e = ε = (.) C v a p where c is a ree space velocity o electromagnetic waves and v p is a phase velocity. Eective dielectric constant has a range o [-5] ( ε r +) εe ε r (.) The eective dielectric constant is introduced in quasi-static analysis. It represents the permittivity o homogeneous medium that replaces dielectric substrate and the air in original microstrip structure. The phase constant β and the characteristic impedance o microstrip line can be also written in terms o the distributed capacitances: C ω C β = β = (.3) Ca c C a 7

31 = (.4) ( cc C ) a Where ω is an angular requency and β is a ree space phase constant. The approximate synthesis and analysis ormulas or microstrip can be ound in [-6]. In modern CAD tools, such as Agilent ADS package, more accurate models presented by Hammerstad and Jensen [-7] are used. 8

32 .3. Coupled Microstrip Lines Two microstrip lines placed in close proximity and parallel to each other orm coupled microstrip lines. These lines are the basic building elements o directional couplers and ilters. There is continuous coupling between electromagnetic ields o the lines. The ield distribution o the coupled microstrip lines is shown in Figure -. Figure -: Field distribution o coupled microstrip lines: (a) odd mode; (b) even mode. Coupled lines support two modes o propagations. Even mode exists when charges on both lines are o the same sign, odd mode when the sign is opposite. Each o these modes o propagation has dierent characteristics o transmission line, namely even and odd mode characteristic impedances e and o, and even and odd mode phase velocities v pe and v po. Even and odd mode characteristic impedances o microstrip coupled lines depends on the dielectric constant ε r and normalised dimension s h and w h, where s is a width o slot o coupled microstrip lines, w is a width o lines and h is a thickness o substrate. The characteristic impedances o coupled lines with dierent s h and ε r can be ound using equations presented in [-8]. Figure -3 illustrates even (black solid line) and odd (black dashed line) mode characteristic impedances, which were obtained using ADS Linecalc, o coupled microstrip lines with slot width s =. 3 mm, h =. 787 mm andε =.. It can be seen rom this igure that even mode impedance is higher than odd mode and the absolute discrepancy between them increases with the decrease o the width o the lines. Also rom impedance curves or coupled lines with dierent r s h, presented in [-8] can be seen that with increase 9

33 o slot width s even and odd mode impedances are approaching the curve or characteristic impedance o single microstrip line, shown with a grey solid line in Figure -3, even mode impedance s curve is moving down and odd mode impedance curve is moving up. It is obvious considering that with the increase o slot width the strength o coupling decreases and two microstrip lines become more and more decoupled. The approximation widely used in the design o coupled-line directional e o couplers [-9] is shown in Figure -3 with a grey dashed line. This approximation is not good or tight coupling. Another approximation, shown as a black dotted line in Figure -3 and that will be used in the analysis presented in next chapter is: ( + ) (.5) e o Approximation (.5) also holds better or more loosed coupling, i.e. or coupled lines with wider slot width s. Figure -3: Characteristic impedances: even mode (black solid); odd mode (black dashed); single line (grey solid); arithmetic average (black dotted); geometric average(grey dashed). The eective dielectric constants o coupled microstrip lines are not equal. The evenmode eective dielectric constant is higher than the odd mode s one because or the

34 odd mode the density o electric ield lines in the air is higher than or the even mode, i.e. or odd mode relatively more electric ield is concentrated in the air compared to even mode. The curves o modelled even and odd mode requency dependent eective dielectric constant or RT-Duroid 587 ( ε =. 35 and h =. 787 mm) are given in [- r ]. Even and odd mode electrical lengths o coupled lines calculated using Eq. (.6) are also dierent due to dierent eective dielectric constantε e. πl = ε e (.6) c θ However or pure TEM coupled lines, such as or example a stripline, the phase velocity o both modes o propagation is the same and the even and odd mode electrical lengths are equal. Approximation θ e = θ o = θ is oten used in the analysis o coupled microstrip lines. The dierence in characteristics o modes o propagation can be easily seen in the analysis o coupled lines in terms o distributed capacitances which are shown in the Figure -4.The distributed capacitances are equal: o C e = C + C + C' (.7) p p ga C = C + C + C + C (.8) gd Figure -4: Distributed capacitances: (a) odd mode; (b) even mode. In (.7) and (.8) C p is the parallel plate capacitance between strip and the ground plane, C is the ringe capacitance o the outer edge which is equal to the ringe capacitance o single microstrip line, C' is the modiied ringe capacitance o single

35 line due to presence o other line, ield across the gap in air region, C ga is the capacitance o odd mode or the ringing C gd is equivalent to C ga but in the dielectric region. The analytical and empirical ormulas or these capacitances, obtained rom dimension s h and w h, and ε r were presented in [-]. The characteristic impedance and phase constant o each mode can be ound using ormulas given or single microstrip line (.3-.4), with even and odd mode capacitances o coupled line with dielectric present and with dielectric replaced by air should be used. To design the coupled microstrip line i.e. to ind the dimension or speciied even and odd mode impedances the procedure presented in [-] can be used. For synthesis and analysis o microstrip coupled lines in this research, we have been suing Agilent ADS Linecalc tool in which ormulas by Kirschning and Jansen [-] are used. The equivalent circuit o two coupled transmission lines is shown in Figure -5 [-3]. TheC, C, L and L are sel-capacitances and sel-inductances o lines and Lm and C m are mutual inductance and mutual capacitance respectively. I microstrip lines are the same size, then their sel-inductances and sel-capacitances are equal and their capacitive (electric) and inductive (magnetic) coupling coeicients are: k k C C = (.9) m m C = C C C L L = (.) m m L = L L L Figure -5: Equivalent circuit o coupled transmission lines.

36 In terms o even and odd mode capacitances inductive and capacitive coupling coeicients can be expressed as [-4]: k k L C C = C L = L m m C = C C = C o o a o a o C + C C + C e e a e a e (.) (.) where Ce and Co are even and odd mode capacitances which can be ound using a a (.7-.8), Ce and C o are even and odd mode capacitances or microstrip coupled lines with substrate replaced by air. Although Eq. (.-.) give good representation o electric and magnetic coupling coeicients in terms o even and odd mode capacitances, the expressions or these coupling coeicients as unctions o physical dimensions o coupled lines are more useul or general understanding o physical properties o microstrip coupled lines. Such empirical expressions were presented in [-5]: [ ( A s h B w h) ] [ ( A s h B w h) ] k C.55 exp + = (.3) =.55 exp + (.4) k L Where A and B are unctions o relative permittivity ε r, A and B are unctions o relative permeability µ r : A A 4 ε + r ( ε ) = + ln B ( ε ) ε r 4 µ + r = r + r ( µ ) = + ln B ( ) µ r µ r = r (.5) + From Eq. (.3-.5) it can be seen that electric coupling is stronger or substrate materials with lower dielectric constant because the electric ield is much conined in the substrate closer to microstrip line with higher dielectric constant. It is clear that or microstrip transmission line magnetic coupling is larger than electric coupling due to physical properties o the substrate. Figure -6 illustrates electric and magnetic coupling coeicients as a unction o width o the slot or ixed width o the lines, 3

37 calculated using (.3-.5). The electric coupling o coupled microstrip lines or substrate with dielectric constant ε =. is also included in Figure -6 to r demonstrate the dierence in electric coupling coeicients or dierent substrates. Figure -6: Coupling coeicients o coupled microstrip lines. The exponential increase o the coupling coeicient with a decrease o the slot width is due to the exponential decaying nature o the ringing ields. Electric and magnetic coupling coeicients calculated using Eq. (.3-.5) or substrate with h =. 8mm and ixed slot between coupled lines s =. 3 mm are shown in Figure -7. Figure -7: Coupling coeicients o coupled microstrip lines with ixed slot width. the coupling coeicients are decreasing with an increase in the width o microstrip line because the ringing ield is stronger or narrow microstrip lines. 4

38 .4. Microstrip Transmission Line Resonators. Microstrip resonators in the orm o terminated transmission line are one o three big groups o distributed microstrip resonators used in the design o ilters. Other two groups o distributed resonators are microstrip ring and patch resonators. Microstrip ring resonators are used or the design o dual-mode ilters [-6], [-7], whereas patch resonators are mostly used in application where high power handling capability is required [-8], [-9]. While in general the microstrip resonator can be any structure that can contain at least one oscillating electromagnetic ield, a section o microstrip transmission line bounded with two relective boundaries in the orm o open or short circuit becomes microwave resonator at some particular requencies. Other types o transmission line, such as coaxial line, stripline and hollow waveguide are also used to build microwave resonators. The input impedance and admittance o lossless open-circuited microstrip line is: in = j cot βl = j cotθ (.6) Y in = jy tan βl = jy tanθ (.7) Where, Y and θ are characteristic impedance, admittance, and electrical length o the line. From (.6) it can be seen that input impedance o open-circuited line is zero when θ = ( n ) π, where n =,,3..., or at the requencies at which the physical length o the line l is an odd multiple o quarter wavelength or l = n ) λ 4. ( g Thereore in the vicinity o these requencies open-circuited line is equivalent to the series resonant circuit, or which the resonant condition is =. Similarly it can be seen rom (.7) that open-circuited line is equivalent to parallel resonant circuit in the vicinity o requencies at which the physical length o the line is a multiple o a hal wavelength long, i.e. when θ = nπ, as the resonance condition o parallel resonant circuit is Y =. Microstrip λ open-circuited line resonators are basic building in g in blocks o ilter []. bandpass ilters based on the original parallel coupled line bandpass 5

39 By analogy with the open-circuited line, the behaviour o lossless short-circuited line as a resonator can be seen rom ormulae or input impedance and admittance. in = tan βl = tanθ (.8) Y in = jy cot βl = jy cotθ (.9) From (.8-.9) the short-circuited line behave as a parallel resonant circuit at requencies when the length o the line is close to an odd multiple o quarter wavelengths and as series resonator at requencies when the length o the line is a multiple o hal wavelengths. Microstrip λ g 4 short-circuited line resonators are used in the design o interdigital bandpass ilters [-]. Detailed analysis and comparison o these lines with losses and the comparison with resonant circuits is presented in [-9], [-]. The ormulae or values o lumped elements o parallel resonator equivalent to λ g open-circuited line are: R = α l π C = ω = (.) ω C L The values o lumped elements o parallel resonator equivalent to λ g 4 short-circuited line are: R = α l π C = 4ω = (.) ω C L In (.-.) α is the attenuation o microstrip line and ω is the resonant requency or each o the equivalent resonators. For distributed transmission line resonators, the distribution o electric and magnetic ields at resonance is very important as it can depict the nature o ields o coupled resonators. The voltage distribution or both resonators at the resonant requency is shown in Figure -8. The y-axe on this igure is the exited end o the line, while l is the end o the line, open-circuited (a), and short circuited (b). Solid lines show the 6

40 distribution at the undamental resonance requency o resonators, dashed lines at the irst spurious resonance requency. Figure -8: Voltage distribution: (a) λg open-circuited line; (b) λg 4 line; n= (solid), n= (dashed). short-circuited Every resonator is characterised by its Q actor, which is used as measure o losses in resonant circuit and is deined as: ( average energy stored in the resonant circuit) ω Q u = (.) energy loss per second in the rsonant circuit As resonant circuit does not exist by itsel, it is always coupled to external circuitry, due to which the unloaded Q actor given in (.) becomes smaller and is called the loaded Q actor. Loaded Q actor is considered as an average energy stored in resonant circuit over total energy loss per second and can be expressed as: Q L = + (.3) Q Q e u Where Q e is external quality actor, which is the ratio o the average energy stored in resonator to the energy loss per second in the external circuit. For microstrip transmission line, the unloaded Q actor can be expressed as [-3]: Q u α = = β Q c + Q d + Q r (.4) 7

41 WhereQ, Q, and c d Qr are Q actors describing conductor, dielectric and radiation losses respectively. The dependence o the total Q actor o microstrip resonators on the characteristic impedance o the line is quite complex and depends also on the other parameters o the microstrip, such as the thickness and dielectric constant o the substrate. In general, the Q actor increases with an increase o characteristic impedance, till it reaches its maximum or the resonators made o the microstrip line with characteristic impedance 8-9 Ohms. With urther increase o impedance Q actor s value is alling with about twice the rate as it was increasing beore. the curves o the unloaded Q actors as a unction o characteristic impedance o resonators made on the dierent thickness Alumina and Duroid substrates can be ound in [-3]. The unloaded Q actor can be ound using ormulae or the transmission type measurements [-4]: Q u Q = L S Q L = (.5) Where and are 3-dB requencies, is a resonant requency and S is a transmission coeicient in db. Figure -9 illustrates the unloaded Q actor o opencircuited microstrip λg transmission line resonator built using microstrip line with h =.78mm andε =.. Q actor is shown in terms o characteristic impedances o r microstrip line. It has been extracted using EM simulations and calculated using Eq. (.5). Figure -9: Unloaded Q actor o microstrip open-circuited λ g resonator 8

42 .5. Coupled Resonators. Coupling is a transer o power rom one circuit to another. Coupled resonators are very important or ilter design. In the development o coupled resonator ilters, the same general technique is used despite the physical structure o resonator. Coupling between two coupled resonators, whether synchronously or asynchronously tuned, is characterised by two eigen requencies that can be indentiied by experiment or ull wave EM simulation. Extraction o coupling coeicients or electric, magnetic, and mixed coupling o synchronously and asynchronously tuned resonators rom critical requencies was presented in [-5], [-6]. The coupling coeicient o coupled microwave resonators can be deined as a ratio o coupled energy to stored energy: k = ε E εe E dv dv ε E + dv (.6) µ H µ H H dv dv µ H dv The E and H are vectors o electric and magnetic ields o resonators as it is shown in Figure -. Fields are determined at resonance and volume integrals are over whole eective region with permittivity ε and permeability µ. The resonators and can have dierent resonance requencies. The irst term is eqn. represents the electric coupling and the second term the magnetic one. The coupling coeicient can have positive or negative sign due to the dot multiplication o ields space vectors. Negative coupling reduces the storage energy o the uncoupled resonator, Figure -: General coupled microwave resonators. 9

43 The circuits are coupled together i they have a common impedance, which can be a resistance, capacitance, or inductance [-7]. The common capacitance produces electric coupling, whereas inductance produces magnetic coupling. Mixed coupling is a combination o both. Figure - illustrates equivalent lumped-element circuit models or magnetic coupling (a) and electric coupling (b). Figure -: Coupled resonators: (a) magnetic coupling; (b) electric coupling. Where C and L are sel-capacitance and sel-inductance o resonators, and M and C m represent mutual inductance and capacitance. For the circuit on Figure - (a) we have: V = I = I + jωmi + jωmi (.7) Where jω MI is the voltage induced due to current in the second circuit. In the case o synchronously tuned resonators both circuits are identical and the sel-impedance o the circuit is = = R + j( ωl ) (.8) ω C with R = R = R, L = L = L, and C = C = C. We can deine coupling coeicient as k = M L = M L L and rom (.8) we can get the equations or currents in both circuits: I = V ( + k ) = jω kl V ( + ω k ) ω L I (.9) L 3

44 At the resonance requency ω = LC currents in the both circuits are: I = V ( R + k L ) = jω kl V ( R + ω k ) R ω I (.3) L As the coupling coeicient becomes smaller the I increases continually, whereas I initially increases and then alls ater reaching its maximum value when k = R ( ω L) = Q, where Q = ω L R is a quality actor o resonator. I = V R At requency near ω we can introduce new variable d ω = ω ω, the reactance o the resonator circuits can be expressed with high accuracy as: ( ω ω ω ω) Ldω ωl ω C) = ω L (.3) ( As it assumed in [-8] and the currents in resonators are: I = V ( R + jldω) ( R + jldω) + ω k L = jω klv I (.3) ( R + jldω) + ω k L The maxima and minima or currents can be ound by dierentiating and equating to zero the moduli o currents using d ω as a variable. Three values or the requencies o the maxima and minima o the current I are: [ ] ω d ω = and dω = ± ( kq) (.33) Q I in (.33) kq > there are three real roots and d ω = is a minimum and other two roots are maxima. This is a tight coupling case and resonators are said to be overcoupled. Tight coupling produces two resonances in both circuits and as k increases, resonance peaks move outwards and the trough in the middle deepens. 3

45 I kq = then all three roots coincide and dω = second resonator I = deines the maximum current in the V R. This is critical coupling case. I both resonators have the same resonance requency but dierent quality actor then critical coupling is k = Q Q I in kq < there is only one real root that deines the maximum. This is loose coupling and in this case circuits are virtually independent and the current in the second resonator is smaller than I V R. = Figure - illustrates the current I in coupled resonator circuit with coupling. The variations in current o the primary circuit is similar. k = Q critical Figure -: Current in the coupled resonator circuit. The coupling coeicient or the coupled circuit depicted in Figure - (b) is equal to k = C C C (.34) m Alternative orm o two magnetically coupled synchronously tuned resonators with symmetry plane is shown in Figure -3 [-6]. I the symmetry plane T-T in this igure is replaced by a short-circuit (or an electric wall) the new single resonant circuit will have a resonant requency h = π ( L L )C m (.35) 3

46 where L m represents mutual inductance. The resonant requency increases because the coupling reduces the stored lux in the single resonator circuit when short circuit is inserted instead o the symmetry plane. Figure -3: Magnetically coupled synchronously tuned resonators When the symmetry plane is replaced by an open-circuit (or by a magnetic wall) the resonant requency o single resonator will be: l = π ( L + L )C m (.36) In this case coupling increases the stored lux and the resonant requency is lower than the resonant requency o single uncoupled resonator. Using Eq. (.36) and (.38) general ormula or coupling coeicient in terms o resonant requencies o two modes can be derived [-6]: h h l l k = (.37) + Eq. (.37) can be used or synchronously tuned resonators with magnetic, electric and mixed coupling. Eq. (.37) cannot be used when =, i.e. when resonators are h l critically or loosely coupled, as in this case according to Eq. (.3) k = Lm L =, but as it has been shown above coupled resonators have single resonance mode when k = Q (critical coupling) and when k < Q (loose coupling). 33

47 .6. Reerences [-] H. Howe, "Microwave Integrated Circuits: An Historical Perspective," IEEE Trans. on Microwave Theory and Tech.,vol.3, no.9, pp , September 984 [-] J. G. Hong and M. J. Lancaster, Microstrip Filters or R/Microwave Applications, New York: John Wiley & Sons, [-3] A. Ikuo, "Meaning o resonator's coupling coeicient in bandpass ilter design," Electronics and Communications in Japan (Part II: Electronics), vol. 89, no.6 pp. -7, 6 [-4] M. Dishal, "Alignment and Adjustment o Synchronously Tuned Multiple- Resonant-Circuit Filters," Proceedings o the IRE, vol.39, no., pp , November 95 [-5] T. Edwards, Foundations or microstrip circuit design. nd edition, Chichester, U.K.: John Wiley & Sons, 99 [-6] K.C. Gupta, R. Garg, I.J. Bahl and P. Bhartia Microstrip Lines and Slotlines. nd edition. Boston: Artech House, 996. [-7] E. Hammerstad and O. Jensen, "Accurate Models or Microstrip Computer- Aided Design," MTT-S, Int. Microwave Symp. Dig., vol.8, no., pp , May 98 [-8] T. G. Bryant and J. A. Weiss, "Parameters o Microstrip Transmission Lines and o Coupled Pairs o Microstrip Lines," IEEE Trans. on Microwave Theory and Tech., vol.6, no., pp. - 7, December 968 [-9] R. E. Collin, Foundations or microwave engineering, nd edition, New York: McGraw-Hill, 99. [-] M. Kirschning and R. H. Jansen, "Accurate Wide-Range Design Equations or the Frequency-Dependent Characteristic o Parallel Coupled Microstrip Lines," IEEE Trans. on Microwave Theory and Tech., vol.3, no., pp. 83-9, January 984 [-] R. Garg and I. J. Bahl, "Characteristics o Coupled Microstriplines," IEEE Trans. on Microwave Theory and Tech., vol.7, no.7, pp. 7-75, July

48 [-] S. Akhtarzad, T. R. Rowbotham, and P. B. Johns, "The Design o Coupled Microstrip Lines," IEEE Trans. on Microwave Theory and Tech., vol.3, no.6, pp , Jun 975 [-3] M. K. Krage and G. I. Haddad, "Characteristics o Coupled Microstrip Transmission Lines-I: Coupled-Mode Formulation o Inhomogeneous Lines," IEEE Trans. on Microwave Theory and Tech., vol.8, no.4, pp. 7-, April 97 [-4] M. K. Krage and G. I. Haddad, "Characteristics o Coupled Microstrip Transmission Lines-II: Evaluation o Coupled-Line Parameters," IEEE Transactions on Microwave Theory and Techniques, vol.8, no.4, pp. -8, Apr 97 [-5] S. Kal, D. Bhattacharya, and N. B. Chakraborti, "Empirical Relations or Capacitive and Inductive Coupling Coeicients o Coupled Microstrip Lines," IEEE Tran. on Microwave Theory and Tech., vol.9, no.4, pp , April 98 [-6] M. Guglielmi and G. Gatti, "Experimental Investigation o Dual-Mode Microstrip Ring Resonators," th European Microwave Conerence, Budapest, Hungary, September 99, pp.9-96 [-7] I. Wol, "Microstrip bandpass ilter using degenerate modes o a microstrip ring resonator," Electronics Letters, vol.8, no., pp.3-33, June 97 [-8] H. Jia-Sheng and M. J. Lancaster, "Microstrip triangular patch resonator ilters," MTT-S, Int. Microwave Symp. Dig., vol., pp , June [-9] R. R. Mansour, B. Jolley, Y. Shen, F. S. Thomson, and V. Dokas, "On the power handling capability o high temperature superconductive ilters," IEEE Trans. on Microwave Theory and Tech.,vol.44, no.7, pp.3-338, July 996 [-] S. B. Cohn, "Parallel-Coupled Transmission-Line-Resonator Filters," IRE Trans. on Microwave Theory and Tech., vol. 6, no., pp. 3-3, April 958 [-] G. L. Matthaei, "Interdigital Band-Pass Filters," IRE Trans. on Microwave Theory and Tech., vol., no.6, pp , November 96 [-] D. M. Pozar, Microwave engineering. 3 rd edition, New York: John Wiley & Sons, 4 [-3] E. Belohoubek and E. Denlinger, "Loss Considerations or Microstrip Resonators (Short Papers)," IEEE Trans. on Microwave Theory and Tech., vol.3, no.6, pp. 5-56, June

49 [-4] D. Kajez, "Q actor measurements, analog and digital," [Online], Available: [-5] J. S. Hong, "Couplings o asynchronously tuned coupled microwave resonators," Proc. Inst. Elect. Eng. Microw., Antennas, Propag. vol.47, no. 5, pp , October [-6] J. S. Hong and M. J. Lancaster, "Couplings o microstrip square open-loop resonators or cross-coupled planar microwave ilters," IEEE Trans. on Microwave Theory and Tech., vol. 44, no., pp. 99-9, November 996 [-7] B. I. Bleaney, and Bleaney, B., Electricity and Magnetism, vol., 3 rd edition, Oxord: Oxord University Press, 976 [-8] W. J. Duin, Electricity and magnetism, 3 rd edition, London: McGraw-Hill, 98 36

50 3. ANALYSIS OF PSEUDO-INTERDIGITAL LINES AND RESONATORS 3.. Introduction Pseudo-interdigital resonators proposed in [3-] and used in the design o bandpass ilter, are modiied interdigital resonators with grounding replaced by interconnection o λ g 4 resonators in pairs. These resonators can also be treated as intertwined hairpin resonators [3-], which are olded open-circuited λg resonators. Pseudo-interdigital resonators are used in the design o bandpass ilters and they have advantages over both interdigital and hairpin resonators. Compared to interdigital resonators and ilters, the pseudo-interdigital ilters are cheaper to manuacture as grounding through the holes in substrate is not required. The main advantage over hairpin bandpass ilters is that pseudo-interdigital bandpass ilters have transmission zeros (Ts) ( S = ) at inite requencies below and above the passband. This considerably improves the skirt selectivity and can be used in the design o small size and low cost bandpass ilters with high selectivity. The main disadvantage o these ilters is that due to the complex nature o coupling between the resonators, the simple design procedure or these ilters does not exist and the EM simulators and solvers are used or inal tuning and optimization o the ilters. In this chapter, the analysis o coupled pseudo-interdigital lines and resonators is presented. In section 3., coupled lines and resonators are analyzed in order to derive the approximate T conditions and requencies. These conditions o coupled lines are derived using impedance matrices and method proposed by Swanson or modelling multiple coupled microstrip lines [3-3]. In order to obtain simple equation describing T conditions, some assumptions and approximations relevant or coupled thin, i.e. high impedance microstrip lines are used. The dependence o T requencies on physical dimensions o resonators and eeding lines is investigated using EM simulators. Section 3.3 presents the analysis o coupling between pseudo-interdigital resonators, carried out using EM simulators in order to obtain the dependence o coupling coeicient on physical dimensions o coupled pseudo-interdigital resonators. 37

51 3.. Analysis o Transmission ero Conditions o Coupled Pseudo- Interdigital Lines and Resonators. A pair o pseudo-interdigital resonators proposed in [3-] is a key element structure o pseudo-interdigital ilter. Figure 3- (a) illustrates the pseudo-interdigital resonators which can be considered as a pair o intertwined conventional hairpin resonators, which are shown in Figure 3- (b). Conventional hairpin resonators are coupled through proximity coupling by slot s. Pseudo-interdigital resonators are coupled through spacing s, s, and s 3, which is equal to s i resonators have the same length L and height H. Proximity coupling due to slot g is very small and will be neglected in urther analysis. Figure 3-: Layouts o coupled resonators: (a) pseudo-interdigital resonators; (b) hairpin resonators. It can be seen rom the symmetry o the coupled pseudo-interdigital resonators that the nature o coupling by the slots s is equivalent to the coupling by slot s 3 and both are dierent rom coupling by slot s. Coupled microstrip lines can have zero transmission ( S = ) at some particular requencies. These are requencies at which lines are completely decoupled, i.e. coupling coeicient is equal to zero. These requencies can be controlled by termination o coupled lines [3-4] and by the length o coupled region [3-5]. 38

52 Comparative analysis o these two coupled resonators should be started with the analysis o coupled lines, when ports and in Figure 3- are connected to 5 Ω lines. As will be shown in next sections, the type o coupling determines the appearance o Ts at inite requencies, requencies at which the coupled lines are completely decoupled. The simulated transmission coeicients or coupled hairpin and pseudo-interdigital lines are shown in Figure 3-. The dimensions o these resonators are given in Table 3-. Slot (mm) Line (mm) s.3 w.3 s.3 L 3 s.3 3 H.5 g.3 Table 3-: Dimensions o coupled resonators. Lines are simulated using EM Sonnet [3-6] or RT Duroid 588 substrate with thickness h =. 787 mm and dielectric constantε =.. r Figure 3-: Simulated S or coupled pseudo-interdigital lines (solid) and hairpin lines (dashed). 39

53 As it can be seen rom Figure 3-, both structures have Ts around 5 and GHz, 5.45 and.8 GHz or coupled hairpin lines and 5.5 and.5 GHz or coupled pseudointerdigital lines. As it will be shown in the next section, Ts appeared at these requencies are due to coupling through separation s. Coupled pseudo-interdigital lines have additional Ts at.7 GHz, 3.5 GHz, 6.5 and 7.9 GHz, which can be attributed to coupling through slots s and s 3. 4

54 3... Transmission ero Conditions o Parallel-Coupled Lines To obtain the T conditions both coupling will be analyzed. For the sake o simplicity the hairpin resonators were unbent and the coupling by slots s and s can be represented using parallel-coupled lines as shown in Figure 3-3. Figure 3-3: Coupling o lines: (a) slot s coupling; (b) slot s coupling. The structure shown in Figure 3-3 (a) consists o a section o parallel-coupled lines with length L, used in the design o parallel-coupled transmission-line-resonator bandpass ilters [3-7]. It can be analyzed using the representation o coupled lines as a 4-port network with speciied termination conditions I = I, as shown in Figure = Figure 3-4: Conventional parallel-coupled lines. The impedance matrix o this 4-port network has been derived in [3-8] and the expressions or its entries in terms o even and odd mode characteristic impedances and electrical lengths e, o, θ e, and θ o are: i = = = 33 = 44 = j ( e cotθe + o cotθo ) (3.) n = = = 34 = 43 = j ( e cotθe o cotθo ) (3.) 4

55 t = 3 = 3 = 4 = 4 = j ( e cscθe o cscθo ) (3.3) = 4 = 4 = 3 = 3 = j ( e cscθe + o cscθo ) (3.4) Using these expressions and the termination conditions I = I, impedance 4 = matrix [ '] or -port network can be derived. Ports and o this network are connected to ports and 3 o 4-port network representing coupled lines. V = V ' ' ' ' I I = i I i I (3.5) Transmission coeicient S can be calculated rom -port impedance matrix using conversion ormula [3-9]: S ' = ' ' ' ' ( + )( + ) (3.6) ' From (3.6) the T condition is, or = = cscθ = cscθ (3.7) e e o o The numerical solution o Eq.(3.6) calculated in Matlab or coupled lines with dimension given in Table 3-, is shown in Figure 3-5. The calculated S coincides with S coeicient obtained by simulation o coupled lines using Agilent ADS. From comparison o Figures 3- and 3-5 it can be seen that Ts or both coupled hairpin lines and coupled lines analyzed above, appear at the same requencies. 4

56 Figure 3-5: Calculated S or conventional microstrip parallel-coupled lines. Coupled lines shown in Figure 3-3(b) are analyzed in the similar way and can be treated as asymmetrically terminated coupled lines, as it is shown in Figure 3-6, and can be considered as an analogy to asymmetrically terminated interdigital lines analyzed in [3-]. Parallel-coupled lines asymmetrically terminated by open-circuited stub are also used in the design o microstrip extracted pole bandpass ilters [3-], [3-].As it can be seen rom this igure, ports and o -ports network are connected to ports and o general 4-ports network representing coupled lines, and open-circuited stub is connected to port 4. Figure 3-6: Asymmetrically terminated parallel-coupled lines. The physical length o open-circuited stub is equal to the length o coupled lines. Both these lengths are equal to L and equal to quarter-wavelength at.5 GHz, which is the undamental resonant requency o the considered microstrip line resonator. The microstrip line, with length L connected to port o the 4-port network to orm the structure shown in Figure 3-3 (b), is removed and is not considered to simpliy the 43

57 analysis o structure shown in Figure 3-6. This will not aect the occurrence and requencies o Ts. The input impedance o the open-circuited stub is equal: j in = = jx c cotθ (3.8) Termination conditions or a 4-ports network are I = (3.9) 3 V = (3.) 4 I 4 Iin = in Using these conditions the system o 4 linear equations with 6 unknowns can be reduced to the system o linear equations with 4 unknowns, in order to obtain impedance matrix or -port network: t t i n V I [ ] + + I i in i in = ' = (3.) V I t I n i i + in i + in Combining Eq. (3.6) with expressions or entries o -port impedance matrix taken rom Eq. (3.) transmission coeicient S can be calculated: S = ( ni + nin t )( i + in ) ( + )( + ) ) ( + )( + ) i i in t ( ) ( + ) i i in n i n in t (3.) Figure 3-7 depicts S in db calculated or structure with dimensions given in Table 3-. Calculation results coincide with results o simulations which is done using ADS schematic simulation o microstrip transmission lines. Three Ts at. GHz, 3.6 GHz and 8.46 GHz are observed. Two irst Ts are the most important or us as one o 44

58 them is below and another is above the undamental resonant requency o resonators and both will aect the out-o-band perormance o bandpass ilter. The T condition is: ' t = n = (3.3) + i in Using ormulas or impedance matrix entries o general a 4-port network o coupled lines (3.)-(3.4) in the Eq. (3.3) T condition in terms o even and odd mode characteristic impedances o coupled lines, electric lengths o coupled lines, characteristic impedance o open-circuited stub, and electric length o open-circuited stub can be derived: ( cotθ cotθ ) = ( ) cotθ e e o o e o (3.4) Figure 3-7: Calculated S or asymmetrically terminated coupled lines. Eq. (3.4) is complex to analyse; thereore some approximation will be used. The irst approximation, which is equivalent to placing a dielectric sheet made rom the substrate material on top the conducting strip [3-3], is the equality o propagation constant or even and odd modes β e = β o = β, which means the equality o even and odd mode electrical lengths o coupled lines θ θ = θ. With the application o this approximation T condition will be: e = o 45

59 θ ( ) (3.5) cot = e + o The requency o two irst Ts are shited rom. GH to.6ghz and rom 3.6 GHz to 3.73 GHz respectively as a result o the usage o this approximation. From Eq. (3.5), it can be seen that T requencies can be tuned by adjusting the impedance. The general rule or this tuning obtained rom the calculation results is that or low values o, the irst two Ts are located urther rom each other and with an increase o the irst two Ts are shiting towards each other. Thus, or = 5 Ω, Ts occur at.84 GHz and 3.99 GHz, or = Ω they occur at.9 GHz and 3.73 GHz, and or = 8 Ω, the irst two Ts occur at.3 GHz and 3.5 GHz. Figure 3-7 illustrates the calculated S or =35. 7 Ω which is the characteristic impedance o the microstrip line with w =. 3 mm. The width o each o the coupled microstrip lines and the width o the slot between them is also.3 mm. For these coupled microstrip lines, another approximation, which has been justiied above in the previous chapter, can be used: ( + ) (3.6) e o Thus, the simpliied T condition, which is the special case o Eq. (3.5) when Eq. (3.6) holds, can be derived as: cot θ (3.7) This T condition will be simpliied to ( ) 4 θ = n where n =,,3... This π simpliication will result in a shit o T requencies rom. to.5 GHz and rom 3.6 to 3.74 GHz. At.5 GHz, the electrical length is θ = 45 o and at 3.74 GHz θ = 35 o.thus, with good approximation the Ts appear at the requencies at which the electrical length o coupled lines and open-circuited stub is equal to ( ) 4 θ = n. π 46

60 3... Transmission ero Conditions o Coupled Pseudo-Interdigital Lines and Resonators In this section, analysis o coupled pseudo-interdigital lines and resonators will be presented. It has been carried out in order to derive the T conditions and will ollow the analysis presented in [3-4], [3-5]. The method or modelling several coupled microstrip lines, proposed by Swanson [3-3], is used. In order to apply this method, the -port circuit, representing coupled pseudo-interdigital lines, which is shown in Figure 3-8 (a), should be transormed into 8-port circuit, as it is shown in Figure 3-8 (b). Figure 3-8: Coupled pseudo-interdigital lines: (a) -port circuit; (b) 8-port circuit; (c) 8-port model. The general 8 8 impedance matrix or the structure shown in Figure 3-8 (b), composed as is described in [3-3] and is equal to: 47

61 = ' ' '' '' ' ' ' ' '' '' ' ' ' ' ' ' ' ' ' ' ' ' '' '' ' ' ' ' '' '' ' ' I I I I I I I I V V V V V V V V s s n n n s s s n n s n n s s s n n s n s s s n n n s s n n s n s s s n n n s n s s s n n n s s (3.8) In Eq. (3.8) two impedance matrix's entries o single unit element, i.e. o single lossless microstrip line with length θ will be calculated or long lines and short lines: cotθ j s = (3.9) cscθ j s = (3.) In Eq. (3.8) the terms s, s, ' s and ' s are calculated using (3.9) and (3.) or long and short lines respectively, n,, ' n, ', '' n and '' are calculated using (3.) and (3.3). n and are entries o the impedance matrix o two adjacent coupled lines. Impedances ' n and ' are impedance matrix entries or nonadjacent coupled lines, such as line connecting ports and coupled to the line connecting ports 5 and 6 o the circuit shown in Figure 3-8 (b). Impedances '' n and '' are used or line connecting ports and coupled to line connecting ports 7 and 8. The only termination condition o this model is: 5 4 = = I I (3.) Using this terminal condition and (3.8) we will have system o 8 linear equations and 4 unknowns. Thus it is not possible to derive the impedance matrix or -port circuit, shown in Figure 3-8 (a), as it has been done in previous sections. Thereore, some assumptions will be made to get the approximate solution. First the length o short lines connecting port to 6 and port 3 to 7 is assumed to be negligible and pseudointerdigital lines can be presented as it is shown in Figure 3-8 (c). This results in

62 49 additional termination conditions: 6 V V =, 7 3 V V =, 6 I I = and 7 3 I I =. Thus, now there will be unknown and 8 8 impedance matrix can be transormed to impedance matrix o -port network. Another assumption, which has already been made, is that the width o lines w and width o slots s are equal or all pairs o coupled lines, which means that pairs o adjacent coupled lines have the same even and odd mode impedances and eective dielectric constants. We also assume that the coupling or nonadjacent line can be neglected. Thus, all entries in matrix (3.8) which describe coupling between nonadjacent lines will be equal to and new simpliied version o Eq. (3.8) will be: = I I I I I I V V V V V V V V i t n t i n n i t n n t i n n i t n n t i n n i t n t i (3.) Solving Eq. (3.) or voltages and currents at ports and 8 the entries o impedance matrix o -port network shown in Figure 3-8 (a) will be: ' ' 4 i t i n i n t i + = = (3.3) ' ' 4 4 i n t n t i = = (3.4) The comparison o simulated S with the one calculated using Eq. ( ) and (3.6) o the structure with dimensions given in Table 3- is shown in Figure 3-9. The even and odd impedances and eective dielectric constant o lines with these dimensions were obtained using ADS Linecalc: 3 = 79. e Ω, = o Ω, =.776 ee ε and.547 = eo ε.

63 Figure 3-9: Simulated (solid) and calculated (dashed) S o coupled pseudointerdigital lines. As it can be seen rom Figure 3-9, usage o ormulas ( ) provides good approximation, at least till 4.5 GHz. According to the calculations, two irst Ts appear at.54 and 3.6 GHz, which is very close to.7 and 3.5 GHz, obtained by simulation. ' ' The T condition is = and ater using (3.-3.4) in (3.4) becomes too = complex to analyse. Thereore, urther simpliication is required. First the equality o even and odd modes electrical lengths θ e = θ o = θ is assumed. With this assumption the T condition reduces to: + (3.5) 4 4 ( ) cot θ = ( + ) csc θ + ( ) θ e o e o e o cot From Eq. (3.5) the T requency can be manipulated by adjusting the even and odd mode characteristic impedances. These impedances depend on the physical dimensions o the coupled microstrip lines. Thus, tuning o T requencies can be done by adjusting the dimensions o coupled microstrip line. The easiest approach to such tuning is to change the width o the slot between lines o ixed width or by changing the width o the coupled lines with the ixed width o slot. Table 3- contains calculated T requencies or coupled microstrip lines with dierent dimensions. It can be seen rom this table that both T requencies are shiting to lower values with increase o the slot s width between lines when the width o lines is ixed. When the width o slot is 5

64 ixed T requencies are shiting to lower requencies with an increase o the width o the lines. Thus, it can be seen that T requencies can be controlled by the dierence between even and odd mode impedances. This also can be assumed rom Eq. (3.5). With the increase o the dierence between the even and odd mode impedances, the T requencies are shiting to the higher values. s (mm) w (mm) e (Ω) o (Ω) T (GHz) T (GHz) Table 3-: T requencies or coupled microstrip lines with dierent size Looking at the values o even and odd modes characteristic impedances in Table 3- or thin microstrip lines with thin slot between them, it can be said that: ( ) >> ( ) + (3.6) e o e o Using this simpliication the T condition can be reduced to: cos θ (3.7) 4 Eq. (3.7) can be considered as a special case or Eq. (3.5) that can be applied when condition in Eq. (3.6) is true. Figure 3- illustrates the comparison o calculated coeicient A = cos θ 4 in db with simulated transmission coeicient S. 5

65 Figure 3-: Simulated (solid) S o coupled pseudo-interdigital lines and calculated (dashed) coeicient describing T condition. As it can be seen rom this igure, Eq.(3.7) provides good approximation or Ts, caused by the coupling due to slot separations s and s 3 o the resonators shown in Figure 3- (a). Thereore, it will be correct to assume that the combination o coupling by slot s with the coupling by slot s 3, changes the approximate requencies o Ts rom ones described by (3.7) to the ones described by (3.7). The T requencies o simulated S are at.7 GHz, 3.5 GHz, 5.66 GHz and 8. GHz, whereas these requencies calculated using (3.7) are.6 GHz, 3.4 GHz, 6.48 GHz and 8. GHz. These are requencies at which the electrical lengths o single microstrip lines are equal to 6º, º, 4º and 3º respectively, which are all solutions o Eq. (3.7). The Ts o simulated lines at 5.3 GHz and.5 GHz, are not given by Eq. (3.7). They can be ound with good approximation using Eq. (3.7), because, as it has been noted beore, they appear due to coupling by slot s or by coupling depicted on Figure 3.3 (a). As a result o analysis carried out in these sections, the T requencies o coupled pseudo-interdigital lines can be approximately obtained using Eq. (3.7) and Eq. (3.7). These approximate conditions depend solely on the physical length o coupled lines, but as it has been shown in the analysis o coupled lines, the maximum degree o coupling between two parallel-coupled lines occurs when the coupling length is λ / 4 g 5

66 i.e. when θ = π / [3-6]. Thereore, in order to achieve maximum coupling, the length o coupled lines should be ixed and dependence o T requencies in the other physical dimensions o coupled pseudo-interdigital lines should be investigated using electromagnetic (EM) simulators. In order to compare the eects o the couplings through slots s and s on the requency o Ts, the structure shown in Figure 3-8 (a) was simulated with the condition that s + s mm. The total length o hairpin line corresponds to the length = o resonators with undamental resonance at.5 GHz. The simulated requencies o the irst and the second Ts ( T and T ) changing with respect to coupling space s are shown in Figure 3-. Figure 3-: Simulated T requencies. As it can be seen rom Figure 3-, both Ts occur symmetrically, with good approximation, with respect to the resonant requency o resonators. This also can be derived rom (3.7). Ts occur at requencies shiting towards the undamental resonance requency with increasing s, i.e. with decreasing coupling through spacing s and increasing coupling through spacing s. When s >. mm, Ts do not occur, as coupling becomes equivalent to coupling o hairpin lines used in the design o conventional hairpin bandpass ilter. 53

67 It should be noted that Eq. (3.7) and Figure 3- provide the inormation about Ts or coupled pseudo-interdigital lines, which can be modelled as 8-port network consisting o coupled lines as it is shown in Figure 3-8 (b). As it was discussed in the previous chapter, transmission line resonators consist o a section o transmission line bounded rom both ends either by open-circuited or short-circuited termination. Thereore, in the design o bandpass ilters, pseudo-interdigital resonators coupled to the eeding lines are used. The two most popular eeding approaches are the eeding through parallel-coupled lines and tapped-lines eeding [3-7]. As one o the aims o this work is to design compact ilters, eeding through parallel-coupled lines will be used. It has been observed during simulations that the replacement o 5 Ω eeding line at ports and 8 o structure shown in Figure 3-8 (b) by eeding through additional parallel-coupled lines causes the change o T requencies. This result is obvious, as now resonators with eeding lines should be modelled as ports network consisting o 6 coupled lines, and using the same procedure as above impedance matrix should be used. In this case simple expression or T conditions, analogous to Eq. (3-7) has not been obtained. Thereore, EM simulations are used to determine the dependence o T requencies on the physical dimensions o coupled resonators and eeding line. First o all, similarly to Eq. (3.7) the electrical length o coupled lines, assuming that all lines are o equal length, is the main parameter that aects T requencies. This parameter will not be changed as the length o resonators controls the resonance requency, i.e. center requency o ilter. The second parameter that aects the location o Ts is the type o eeding o coupled resonators. It has been observed that the stronger the eeding the bigger the gap between the irst and the second T requencies T and T respectively. Thus, the gap between resonance requency and the requency o T above and below resonance requency, is increasing as well. The biggest gap is given by (3.7) or the strongest eeding through simple straight connection o 5 Ω line to pseudo-interdigital resonators, as it shown in Figure 3-8 (a). Table 3-3 contains T requencies or coupled pseudo-interdigital resonators with undamental resonance requency.5 GHz. Feeding by parallel-coupled line with three 54

68 dierent slots width s is included to demonstrate the rate o change o T requencies. All values in table are in GHz. Type o eeding T T T T T Strait connection o 5 Ω line Coupled line eeding ( s =. mm) Coupled line eeding ( s =. 3 mm) Coupled line eeding ( s =. 6 mm) Gap eeding ( s =. 3 mm) Table 3-3: T requencies or dierent eeding o coupled pseudo-interdigital resonators. For the weakest eeding through the serial gap, the Ts are very close to low and high resonance peaks o coupled resonators, which occur at.5 and.69 GHz. The eeding o coupled resonators plays crucial role in the design o bandpass ilter and the width o slot s is adjusted very careully in order to obtain required ilters' perormance. Thereore, the possibility to tune the requency o Ts by adjusting the width o eeding slots is very limited. The third parameter aecting requency and occurrence o Ts is the width o slots s and s between dierent arms o coupled pseudo-interdigital resonators. As it has been reported beore, Ts below and above resonant requency occur due to coupling by slot s and in situation when s s + is ixed, the Ts do not occur or small s, i.e. when coupling o conventional hairpin resonators prevails. As it shown in Figure 3-, or s >. mm, i.e. or s <. 8 mm Ts do not occur. Figure 3- illustrates the extracted T requencies or s + s mm and or s + s mm or coupled = = resonators with eeding through parallel-coupled line with s =. 3 mm. These both curves are similar to the one shown in Figure 3-. They can be used in the design o bandpass ilters to predict the requencies o Ts below and above the passband. 55

69 Figure 3-: Simulated T requencies: s + s mm (black); s + s mm (grey). = = From Figure 3- it can be seen that Ts do not occur when s >. 7 mm or the case when s + s = mm, and when s >. mm or the case when s + s = mm. The dependence o T requencies on s and s is very important because these dimensions will be used to control coupling coeicient between resonators and, as a consequence, to control the bandwidth o bandpass ilters. 56

70 3.3. Coupling o Pseudo-Interdigital Resonators The comparative investigation o coupling o pseudo-interdigital resonators and hairpin resonators was presented in [3-8]. As it was mentioned above, the coupling o pseudointerdigital and hairpin resonators is a proximity coupling through the ringe ields. Coupling o pseudo-interdigital resonators with very good approximation can be considered as a combination o proximity couplings due to slots s, s, and s 3, as it is shown in Figure 3-3 (a). I resonators have the same dimensions L and H then the widths o slots s and s 3 are equal. In order to determine the contribution o couplings due to each o these slots, structures shown in Figure 3-3 have been investigated using the EM simulator. Figure 3-3: Coupled λ g resonators: (a) Pseudo-interdigital; (b) Hairpin; (c) Coupled through slot s ; (d) Coupled through slots s and s 3 ; (e) Coupled through slots s and s. All microstrip resonators used in this investigation are λ g open-circuited resonators with undamental resonance at.5 GHz and width equal.3 mm. All coupling slots, except s 3 in Figure 3-3 (d) and s 3 in Figure 3-3 (e) were chosen to be.3 mm. The eeding o resonators is arranged through short parallel-coupling with 5 Ω eeding 57

71 lines. The dielectric constant o the substrate used in the simulation is ε =. and the thickness is h =. 787 mm. The width o the slot s o coupled resonators shown in Figure 3-3 (d) was chosen to be.4 mm. This is the minimum width o slot s at which coupled hairpin resonators, shown in Figure 3-3 (b), are critically coupled, i.e. simulated S o coupled resonators have only one peak at resonant requency, and the contribution to total coupling by separation spacing s can be neglected. This value has been ound by simulating coupled resonators shown in Figure 3-3 (b). Similarly, by simulating the coupled resonators shown in Figure 3-3 (c), it has been ound that when the width o slot reaches s =. 8 mm resonators become critically coupled. Thereore, the width o slot s 3 o the structure shown in Figure 3-3 (e) was chosen to be.8 mm and contribution to total coupling by separation spacing s 3 can be neglected. The physical length o coupled lines is.4 mm or resonators shown in Figure 3- (a-c), mm or resonators shown in Figure 3- (d), and.8 mm or resonators shown in Figure 3-3 (e). This dierence occurred due to the condition that all resonators should have the same electrical length and the length o coupled lines is chosen to be as long as possible, approaching 9º. r Simulated S o all resonators shown in Figure 3-3 are shown in Figure 3-4. Figure 3-4: Simulated S o resonators: Pseudo-interdigital (black dotted); Hairpin (black solid); Coupled through Slot s (grey solid); Coupled through slots s and s 3 (black dashed); Coupled through slots s and s (grey dotted). 58

72 At irst, it can be seen that all coupled resonators which contribute to total coupling by the separation spacing s or s 3 i.e. all coupled resonators except conventional coupled hairpin resonators, have Ts at inite requencies higher and lower resonant peaks. The T conditions o lines coupled as it is shown in Figure 3-3 (a) and (c) have been approximately derived in sections 3.. and 3.. respectively. It also can be seen that the coupling coeicients, which can be ound using ormula derived in [9], are dierent or all structures. The coupling coeicient can be calculated using ollowing Eq. (.37) to obtain the coupling coeicient rom the requencies o high and low resonant peaks h and l. Eq. (3.7) can be used only in case when >, i.e. simulated coupled resonator have two resonance modes. h l Eq. (.37) is used to obtain the coupling coeicient o synchronously tuned resonators, i.e. resonators with equal resonant requencies. Stronger coupling occurs when resonant peaks occur urther rom each other and thereore the strongest coupling is between resonators coupled through slots s and s 3 Figure 3-3 (d). or the coupled resonators shown in The simulated and calculated coupling coeicients o structures shown in Figure 3-3, as a unction o the length o coupled lines, are shown in Figure

73 Figure 3-5: Simulated and calculated coupling coeicient as a unction o θ : Pseudo-interdigital (black dotted); Hairpin (black solid); Coupled through slot s (grey solid); Coupled through slots s and s 3 (black dashed). The coupling coeicient o resonators coupled in the way shown in Figure 3-3 (e) or all lengthsθ is equal to k e Q, i.e. k. 9 as the Q actor o these resonators is e equal to 7 and resonators are critically coupled. The ollowing approximate assumptions can be made rom Figure 3-5. First, the coupling coeicient k d o resonators coupled through slots s and s 3, as it is shown in Figure 3-3 (d), is approximately twice the coupling coeicient kc o resonators coupled by separation spacing s only, which is shown in Figure 3-3 (c), i.e. k k d c. This assumption is based on the identical physical nature o coupling through slots s and s 3, and a combination o couplings by slots s and s 3 can be considered as a sum o coupling caused by each o these slots separately. The second assumption is that couplings due to slots s and s are opposite in sign and cancel each other and the combination o both couplings has a very small value, as it has been observed or resonators shown in Figure 3-3 (e) which are critically or even loosely coupled, i.e. k e k k. 9. The coupling coeicient k a o pseudointerdigital resonators, shown in Figure 3.3(a), can be approximately considered as: 6

74 k a = k (3.8) + k3 k where the subscript o the coupling coeicient corresponds to the subscript o the separation slots. It should be noted that these assumptions are approximate because although all resonators shown in Figure 3.3 are equal in length, the length o the coupled line region is dierent or each pair o coupled resonators. Thus, coupling coeicient k d, is about. to.3 smaller than kc and the dierence between coupling o pseudo-interdigital resonators k a and coupling due to slots s and s 3 minus coupling due to slot s, i.e. k k is about.4 to.5. d b 6

75 3.4. Summary In this chapter analysis o coupled pseudo-interdigital lines and resonators is presented. In section 3. the lines and resonators are analyzed in order to ind out the dependence o T requencies on physical dimensions o the resonators and lines. Using impedance matrices and some approximations or coupled microstrip lines, it has been ound that, with an approximation o about 7%, the requencies at which pseudo-interdigital lines and resonators are completely decoupled, depend mainly on the length o coupled lines. The EM simulations have been used to investigate the eect o other parameters, such as the width o coupling slots between resonators, and between resonators and eeding lines, on T requencies. In section 3.3 the coupling between pseudo-interdigital resonators is analyzed. EM simulators and Eq. (3.8) have been used to investigate the coupling nature and to ind the eect o width o slots between resonators arms on coupling coeicient. Other dimensions do not have much inluence on coupling between resonators. It has been ound that coupling due to the separation o slots s and s 3 is opposite in sign to the coupling due to separation slot s. Using this act, wide range in couplings can be achieved by manipulating the width o these slots. 6

76 3.5. Reerences [3-] J. S. Hong and M. J. Lancaster, "Development o new microstrip pseudointerdigital bandpass ilters," IEEE Microwave and Guided Wave Lett., vol. 5, no. 8, pp. 6-63, August 995 [3-] E. G. Cristal and S. Frankel, "Hairpin-Line and Hybrid Hairpin-Line/Hal-Wave Parallel-Coupled-Line Filters," IEEE Trans. on Microwave Theory and Tech., vol., no., pp , November 97 [3-3] D. G. Swanson, Jr., "A novel method or modeling coupling between several microstrip lines in MIC's and MMIC's," IEEE Trans. on Microwave Theory and Tech., vol. 39, no. 6, pp , June 99 [3-4] T. Chih-Ming, L. Sheng-Yuan, and L. Hong-Ming, "Transmission-line ilters with capacitively loaded coupled lines," IEEE Trans. on Microwave Theory and Tech., vol. 5, no. 5, pp , May 3 [3-5] D. Gao Le,. Xiu Yin, C. Chi Hou, X. Quan, and X. Ming Yao, "An Investigation o Open- and Short-Ended Resonators and Their Applications to Bandpass Filters," IEEE Trans. on Microwave Theory and Tech., vol. 57, no.9 pp. 3-, September 9 [3-6] Sonnet EM Suite, Sonnet Sotware Inc., Liverpool, NY. [3-7] S. B. Cohn, "Parallel-Coupled Transmission-Line-Resonator Filters," IRE Trans. on Microwave Theory and Tech., vol. 6, no., pp. 3-3, April 958 [3-8] G. I. ysman and A. K. Johnson, "Coupled Transmission Line Networks in an Inhomogeneous Dielectric Medium," IEEE Tran. on Microwave Theory and Tech., vol.69, no., pp , May 969 [3-9] D. M. Pozar, Microwave engineering. 3 rd edition, New York: John Wiley & Sons, 4 [3-] S. Sheng and. Lei, "Wideband microstrip bandpass ilters with asymmetrically-loaded interdigital coupled lines," Int. Con. on Microwave and Millimeter Wave Tech., Nanjing, China, April 8, pp.-3 [3-] S. J. Hedges and R. G. Humphreys, "An Extracted Pole Microstrip Elliptic Function Filter using High Temperature Superconductors," 4 th European Microwave Conerence, Cannes, France, September 994 pp

77 [3-] J. G. Hong and M. J. Lancaster, Microstrip Filters or R/Microwave Applications, New York: John Wiley & Sons, [3-3] M. Horno and F. Medina, "Multilayer Planar Structures or High-Directivity Directional Coupler Design," IEEE Trans. on Microwave Theory and Tech., vol.86, no., pp , June 986 [3-4] W. Wen, J. S. Fu, L. Yilong, and X. Yong hong, "A compact bandpass ilter using olded lambda/4 coupled-line resonators," Int. Con. on Microwave and Millimeter Wave Tech., Nagoya, Japan, October 4. [3-5] T. Chih-Ming, L. Sheng-Yuan, C. Chia-Cheng, and T. Chin-Chuan, "A olded coupled-line structure and its application to ilter and diplexer design," IEEE MTT-S, Int. Microwave Symp. Dig., vol.3, pp.97-93, June [3-6] T. Edwards, Foundations or microstrip circuit design. nd edition, Chichester, U.K.: John Wiley & Sons, 99 [3-7] J. S. Wong, "Microstrip Tapped-Line Filter Design," IEEE Trans. on Microwave Theory and Tech., vol.7, no., pp. 44-5, January 979 [3-8] J. S. Hong and M. J. Lancaster, "Investigation o microstrip pseudo-interdigital bandpass ilters using a ull-wave electromagnetic simulator," Int. J. Microwave and Millimeter-Wave Computer-Aided Engineering, vol. 7, pp.3-4, May 997 [3-9] J. S. Hong and M. J. Lancaster, "Couplings o microstrip square open-loop resonators or cross-coupled planar microwave ilters," IEEE Trans. on Microwave Theory and Tech., vol.44, no., pp.99-9, November

78 4. COMPACT PSEUDO-INTERDIGITAL BANDPASS FILTERS 4.. Introduction A pair o pseudo-interdigital resonators, investigated in the previous chapter, has two transmission zeros, appearing below and above undamental resonance requency due to the nature o coupling. This, together with very compact size, makes these resonators very attractive or the design o compact bandpass ilters with improved skirt selectivity. One o the designs consists o three pairs o pseudo-interdigital resonators, together with the concept o development o these resonators rom interdigital resonators, was proposed in [4-]. The main challenge in design o pseudo-interdigital ilters is determine the dimensions o the resonators rom the required bandwidth and central passband requency. This can be done by cut-and-try method using modern EM simulators. A more constructive approach, which will be described urther in this chapter, is based on the image parameter method (IPM) applied to distributed structures [4-]. This approach proposes application o IPM directly to distributed microwave structure without consideration o the lumped prototype. This is a more lexible design procedure in which technological constraints can be easily incorporated. As this method solely relies on the accuracy o modelling o distributed structures, EM simulators are used or modelling, as well as or the inal tuning and optimization o ilters obtained using IPM. In this chapter, the development o compact microstrip bandpass ilter that consists o one pair o pseudo-interdigital resonators is presented. This design approach is based on the image parameter design o parallel-coupled transmission-line-resonator bandpass ilters. Bandpass characteristics o image impedance o parallel-coupled microstrip lines are described in the section 4.. Section 4.3 presents the image parameter design o second order parallel-coupled transmission-line-resonator bandpass ilter using procedures described in [4-3], [4-4]. This is technology-driven procedure, and thereore the width o microstrip resonators has been chosen to be equal to. mm, which is the smallest width o the line realizable with available manuacturing 65

79 acilities. In section 4.4 design o hairpin bandpass ilter, which is a modiication o ilter designed in previous section is presented. In this ilter the parallel-coupled resonators are bent to orm U-shaped hairpin resonators. This is an intermediate step in the design o pseudo-interdigital bandpass ilter, in which two intertwined hairpin resonators are used. Section 4.5 presents the design o compact pseudo-interdigital bandpass ilter. The results rom investigations the dependence o coupling coeicient and transmission-zero requencies o coupled pseudo-interdigital resonators on the physical dimensions, discussed in previous chapter, were used to design the bandpass ilter o required bandwidth with good skirt selectivity, improved by transmission zeros occurred at inite requencies below and above the passband o the ilter. 66

80 4.. Image Impedance o Coupled Microstrip Lines The impedance matrix o two coupled microstrip lines with ports and 4 opencircuited, as shown in Figure 4- (a) has been used in the previous chapter to derive the condition o transmission zeros that occur due to the physical nature o coupling. Figure 4-: (a) Coupled microstrip lines; (b) two port network terminated in its image impedance. With approximation θ θ = θ, and using Eq. (3-)-(3-4), the impedance matrix o e = o coupled lines presented as -port network, as is shown in Figure 4- (b), is equal to: [ ] ( e + o ) cotθ ( e o ) cscθ ( ) cscθ ( + ) cotθ = j (4-) e o e o The electrical length θ in (4-) can be replaced by arithmetic or geometric mean o even and odd mode lengths in order to ind the electrical length o microstrip coupled lines. The bandpass perormance o coupled lines can be derived using the concept o image impedances. Image impedance i, shown in Figure 4- (b), is an input impedance at 67

81 port when port is terminated with i and visa versa. I both ports o -port network are terminated with their image impedances, they are matched. The image impedance o coupled microstrip lines can be ound using ormulas (4-) to obtain image impedances o general two-port network rom its impedance matrix [4-4]. It is clear that or symmetrical network image impedances are equal. i = det[ ] det[ ] i = (4-) By applying Eq. (4-) and (4-) the image impedance o a section o coupled microstrip line is: e + o e o i = i = det[ ] = (4-3) sin ( θ ) Figure 4- illustrates the real and imaginary parts o the image impedance o coupled lines, given by (4-3). It is calculated or even mode impedance Ω and odd e = mode impedance.3 Ω. The electrical length o coupled lines is calculated o = using the arithmetic mean o even-odd mode eective dielectric constant, rom 6º to º. Image impedance is normalized to ( ) impedance at θ = π, which is the value o image e o Figure 4-: Normalized image impedance o coupled lines. 68

82 The coupled-line section has an image passband when the image impedance is real and rom Eq. (4-3) this condition can be derived as: sin ( ) o o e e θ 4 + (4-4) As sine is a periodic unction, there is ininite number o sets o solutions o (4-4). Each o them is symmetrical with respect to ( ) θ = n π, which corresponds to the length o the coupled lines equal to odd multiples o quarter wavelength. For the undamental passband two boundary values o θ are: e e θ = + sin π, θ < (4-5) o o θ = π (4-6) θ For the image impedance shown in Figure 4- relative image passband width is: θ 75.6 o andθ 4.4 o, and the w I θ θ 4 = e e = sin + π π o o (4-7) As it can be seen rom Eq. (4-7), the relative image passband width depends only on the ratio o even to odd mode impedances. Thereore any relative passband width can be achieved by properly deining even and odd mode impedances o coupled lines, and only practical realization o these lines limits the passband width to some maximally achieved value, which varies or dierent substrates o microstrip. 69

83 4.3. Design o Parallel-Coupled Microstrip Bandpass Filter Using Image Parameter The parallel-coupled transmission-line-resonator ilter proposed in [4-5] is still one o the most popular microstrip transmission line ilters used or the design o narrow and moderate bandwidth ilters. The implementation o this ilter is very cheap as it does not require such assembly operations as via holes or bond wire connections. The design procedure or this ilter is well known and ormulas, used to determine the even and odd impedances o coupled lines rom the bandwidth o the ilter and values o elements o used prototype, give good results or ractional bandwidth (FBW) up to about 3%. For wider bandwidth, the synthesis ormulas give less accuracy and the coupling between the two lines o the irst and last sections o coupled lines is so tight that it becomes unpractical or realization. One o the methods proposed to improve the bandwidth is to replace the end-coupled line sections by quarter-wavelength transormers [4-6]. The design o microstrip parallel-coupled transmission-line-resonator ilters using the image parameter proposed in [4-3] can be used or the development o moderate and wideband bandpass ilters avoiding the abrication problems o the conventional design approach. The image parameter method can be applied directly to coupled microstrip lines without any consideration o lumped prototype. The design procedure proposed in [4-3], [4-4] is applied urther to design a second order parallel-coupled transmissionline-resonator bandpass ilter with FBW 5% and the central requency 3.8 GHz. The development o this ilter is the irst step in the design o very compact pseudointerdigital bandpass ilter. The order o the designed ilter is two because the proposed pseudo-interdigital ilter consists o a pair o pseudo-interdigital resonators and the selectivity o second order parallel coupled bandpass ilter will be improved by the introduction o transmission zeros, as will be shown in section 4.5. The image parameter method can be considered as technology driven and can be used to design bandpass ilters with wide passbands that can be realized with manuacturing limits in abrication o narrow lines and tight gaps. In order to design the super compact pseudo-interdigital bandpass ilter, the width o coupled line has been chosen to be 7

84 . mm, which or a substrate with dielectric constant ε =. and thickness h =.78 mm will have characteristic impedance o 5.5 Ω. Thereore, the ilter speciications = 3. 8 GHz, FBW equal to 5%, N = will have additional starting r parameter - width o the coupled lines w =. mm and the substrate with parameters given above. From Eq. (4-7) the ratio o even to odd mode impedances rom known relative image passband width w I can be ound as: e o πwi + sin 4 = πwi cos 4 (4-8) As at θ and θ the image impedance is zero, then FBW o the ilter should be always smaller than the relative image passband and can be expressed as: FBW = δ (4-9) w I where δ is a margin actor, which is bigger than one. Using (4-8) and taking the relative image passband to be 3%, and a margin actor o., the even to odd mode impedance ratio will. 6. ADS Linecalc was used to ind the width o the e o slot between two coupled. mm wide microstrip lines, such that even to odd mode impedance ratio will be equal to.6. Ater a ew iteration it has been ound that coupled microstrip lines with slot width equal to.6 mm, have even mode impedance e = 86.3 Ω and odd mode impedance o = 3. 8 impedance ratio is equal to.63. Ω and even to odd mode The next step is to ind the length o coupled line section, which should correspond to electrical length o 9º at the center requency or, in other words, to be equal to a quarter o wavelength at this requency. As the ormula or wavelength or microstrip lines includes eective dielectric constant, and microstrip coupled lines have two modes o propagation with dierent dielectric constants, the arithmetic or geometric 7

85 mean o these two constants should be used to ind the approximate wavelength. For our coupled line arithmetic and geometric means are almost equal and the arithmetic mean will be used in urther calculations. λg c l = lo = 4 4 ( ε + ε ee eo ) l o (4-) where lo denotes the equivalent length o microstrip open end and can be ound using an approximate expression o extension length o single microstrip line [4-7]: l o ε e +.3 w =.4h ε e.58 w h +.6 h +.83 (4.) Using Eq. (4-)-(4-) the length will be l 5 mm. This length has been tuned and it was ound that 4.8 mm long parallel-coupled lines can be used to design a ilter with passband centered at about 3.84 GHz. The last step is to add the impedance transormers to the end-coupled sections. The impedance o transormer is ound using ormula: = (4-) T Im where is 5 Ω and equal to: Im is maximum image impedance at the mid-band requency Im ( ) = (4-3) e o The length o impedance transormer is ound using Eq.(4-)-(4-) with eective dielectric constant o transormer s. The impedance o transormer is 44.6 Ω, with corresponding width o the line equal to.86 mm and the length to 3.4 mm. The layout o designed second order parallel-coupled microstrip bandpass ilter with impedance transormers is shown in Figure

86 Figure 4-3: Layout o parallel-coupled bandpass ilter with impedance transormers. The simulated S-parameters o designed ilter simulated using ADS Momentum are shown in Figure 4-3 (a). Filter has.7 db insertion loss and 5 db return loss. Figure 4-4 (b) shows the simulated S-parameters o ilter without impedance transormer. Figure 4-4: Simulated S-parameters o edge-coupled ilter: (a) with impedance transormer; (b) without impedance transormer. It can be seen rom Figure 4-4 (b) that ilter without impedance transormer is not optimized and has larger insertion loss and smaller return loss. The FBW o the ilter without transormer is about.8% and in order to achieve 5% bandwidth, the gap between all coupled lines should be decreased rom.6 mm to.5 mm. By doing this, a bigger even to odd mode impedance ratio will be achieved. Thereore, the simple rule, or the image parameter design o coupled-lines ilter, which also can be obtained rom Eq. (4-7), is to increase the even to odd mode impedance ratio in order to increase the bandwidth o the ilter. This is achieved only by decreasing the gap between the coupled lines or, in the other words, by increasing the coupling between the resonators. 73

87 4.4. Design o Hairpin Microstrip Bandpass Filter The hairpin bandpass ilter introduced in [4-8] is a modiication o the conventional parallel-coupled bandpass ilter with resonators bent to orm U-shaped resonators that look like a hairpin. Analysis and design o these ilters are based on the sparse induction matrix assumption, as in the original paper, or the sparse capacitance matrix, as it was presented in [4-9]. Both these approaches provide satisactory approximation or the design o hairpin ilters with open circuited eeding line with FBW up to - 5%. The conventional design approaches o hairpin ilters have inherited the limit in the realization o a wide bandwidth ilter due to a very small width o slot between the eeding lines and the edge resonators. In this section, the hairpin bandpass ilter will be designed as a modiication o ilter presented in previous section in order to design compact technology-driven ilter. As second order bandpass ilter has poor out-o-band insertion loss the design presented here will be used as an intermediary step in the design o pseudo-interdigital bandpass ilter in which out-o-band rejection will be improved by the appearance o the transmission zeros at inite requencies above and below the passband. The irst step is the extraction o the coupling coeicient o resonators o parallelcoupled bandpass ilter designed above. As this ilter consists o two identical coupled λ / resonators with eeding through coupled lines and has no inite requency g attenuation poles, the synthesized network o this ilter can always be described by three constants: center requency, coupling coeicients K r( r+) between resonators r and ( + ) r, and the decrement o resonator r or Q actor Qr = d r [4-]. The unloaded Q actors o hairpin and simple λ / resonators can be ound using simulations and equation (.5). The Q actor o straight line resonators used in the design o edge-coupled ilters is 7, whereas the Q actor o hairpin resonators, that will be used later, is 3. This small decrease in the unloaded Q actor is caused by additional radiation losses due to additional discontinuities. g 74

88 The coupling coeicient o coupled resonators o parallel-coupled ilter is ound using Eq. (.37) and simulating the structure shown in Figure 4-3 with impedance transormer and eeding through coupled line replaced by end-coupled eeding. Using low and high resonance requencies and Eq. (.37) the coupling coeicient is ound to be equal to.37. The layout o hairpin bandpass ilter is shown in Figure 4-5. The length o the resonator is λ g or L λ g 4, the width o the slot s is ound rom the design curve in order to obtain the coupling coeicient equal to the coupling o resonator in the parallelcoupled ilter. The length o connecting line L c also called arm separation in most practical realizations is about ive dielectric thicknesses [4-]. From one side, the arm separation should be increased in order to minimise sel-coupling o both arms o the resonators, which is happening because voltages at opposite ends o the hairpin resonator are in antiphase. But the arm separation cannot be made as big as possible because in this case the length o coupled lines will be short and in order to achieve the same coupling the slot, s should be very small. Thus, a good compromise should be ound. Figure 4-5: Layout o hairpin bandpass ilter. The length o the connecting line has been chosen to be. mm, or six times the width o resonators line as it will keep the length o coupled lines almost equal to the length in the edge coupled ilter. Using the design curve, shown in Figure 4-6, we can get the 75

89 width o slot s between the resonators. This design curve was obtained by the ull wave EM simulation o a pair o coupled hairpin resonators to extract the coupling coeicient against the width s o the gap between coupled lines. From this curve it is ound that when the slot width is.4 mm the coupling between hairpin resonators is equal to.33. This slot width can be used as a starting value or our design in order to obtain coupling between hairpin resonators equal to coupling between parallel-coupled resonators used in the design o ilter described in section 4.3. The same slot width has been chosen as a starting value or the slot between eeding lines and resonators. Figure 4-6: Coupling coeicients o hairpin resonators. Hairpin ilter with L =4. 8 mm, L =. mm, and s =. 4 was simulated using ADS c Momentum. The simulated S-parameters are shown in Figure 4-7. The ilter has central requency 3.8 GHz, FBW 5 %, insertion loss. db and return loss 3.3 db. Figure 4-7: Simulated S-parameters o hairpin ilter. 76

90 4.5. Design o Compact Pseudo-Interdigital Microstrip Bandpass Filter the design o compact pseudo-interdigital bandpass ilter is based on the use o two intertwined hairpin resonators in the way they have coupling due to three parallel-coupled sections. The resonators proposed in [4-] and analysed in [4-] were called pseudo-interdigital resonators, as they are similar to interdigital resonators with grounding replaced by interconnections o λ g 4 resonators. The currents distribution o these resonators at resonance is similar to the current distribution o interdigital resonators. The layout o compact bandpass ilter designed using a pair o pseudo-interdigital resonators is shown in Figure 4-8. The main design parameters are the length L, width o the line w, and widths o slots s, s, and s. As it was discussed in the previous chapter, coupling due to separation s is equivalent to coupling or resonators in hairpin bandpass ilter and opposite in sign to the coupling due to separations s. Slot width s controls the coupling to eeding lines. In design o conventional parallel-coupled and hairpin bandpass ilters small s is the main problem in the development o moderate and wideband ilters. The length is L λ g 4, the same as in the hairpin ilter, the width w =. mm also has been chosen to be the same. Figure 4-8: Layout o pseudo-interdigital bandpass ilter. 77

91 To design the bandpass ilter with FBW=5%, all three slots widths described above should be determined. First the slot width s and s which control the coupling between resonators should be ound. The simplest option is to set s = s and to extract using EM simulation the coupling coeicient in terms o the slot width and to build design curve. Figure 4-9 illustrates the design curve or resonators with width o the line. mm and total length 3 mm. The total length o resonators is constant and the length o coupled lines section decreases due to the increase o length L c o interconnecting line, caused by the increase o slots width. Figure 4-9: Coupling coeicient o pseudo-interdigital resonators. From Figure 4-9 the width o slots can be ound, with which the closest to.37 coupling coeicient can be achieved. Due to manuacturing limitations multiples o.mm will be chosen irst as initial values or slot widths. The closest is.4 mm with which coupling coeicient.45 can be achieved. By analogy with parallel-coupled and hairpin bandpass ilters, eeding coupling slot s has been chosen to be the same as s and s. The simulated pseudo-interdigital ilter has.3 % FBW, db insertion loss and.8 db return loss in the passband. As the only way to increase bandwidth is to have stronger coupling between resonators, new bandpass ilter has been designed with a gap between coupled lines o resonators equal to.3 mm. With the same gap between eeding lines bandpass ilter has 4.7 % FBW,.68 db insertion loss and 7 db return loss in the passband. Further modiications in the original design have been made in order to decrease the total ilter size and to suppress spurious harmonic at, 78

92 that is done by reducing the length o the eeding coupled line. The layout o the developed ilter is shown in Figure 4-. Figure 4-: Layout o compact microstrip bandpass ilter ( w =. mm, s =. 3 mm, g =.3 mm). The S-parameters o presented ilter simulated using ADS Momentum are shown in Figure 4- by the dashed lines. Figure 4-: Simulated (dashed) and measured (solid) S-parameters o pseudointerdigital bandpass ilter: (a) S coeicients; (b) S coeicients The microstrip bandpass ilter was abricated on.76 mm thick Rogers RT/Duroid 588 ( ε =. ), and measured with Agilent PNA (E836A) network analyzer [4-3]. r A photograph o the abricated ilter is shown in Figure 4- and the measured S- parameters o ilter are shown in Figure 4- by the solid lines. 79

93 Figure 4-: Photograph o abricated bandpass ilter. From Figure 4-, it can be seen that the requency shit between simulated and measured S-parameters is minimal. An increase o insertion loss to.4 db and a decrease o return loss to db at the center requency is observed and is attributable to imperect manuacturing and additional losses caused by this. The decrease o measured S and S at requencies above 7 GHz is due to increased radiation losses which at high requencies are also attributable to manuacturing tolerances. The developed microstrip bandpass ilter has size o. x.7 mm at a center requency o 3.8 GHz, which is approximately.5λ. 4λ. The appearance o transmission zeros at 3.3 and 4.5 GHz improve the skirt selectivity o the ilter. Thus, the out-oband insertion loss attributable to the high order bandpass ilters is achieved with just two resonators. This eature o the proposed ilter, along with its size, which is very close to the width o 5 Ohms line, makes it very attractive or applications in the design o diplexers/multiplexer and antenna ilters. The irst spurious response o the g ilter is at 3, the same as the conventional interdigital bandpass ilter. Thus this ilter can be used or the design o bandpass ilter with improved stopband perormance. g Although, due to the complex nature o coupling o resonators, ull analysis o this structure is diicult, this ilter is easy to develop and the results are easily reproducible. The steps described above, the approximate dimensions o the ilter can be ound and the inal layout can be obtained using EM simulators. As the initial design o the edgecoupled ilter is technology-driven, it can be very quickly determined whether the required perormance o the ilter can be achieved with the existing manuacturing limits on width o microstrip lines and slots. For example, it has been ound that using 8

94 the same substrate and with the smallest width o line. mm and gap. mm compact pseudo-interdigital bandpass ilter with FBW up to 4-45 % can be developed. 8

95 4.6. Summary In this chapter design o compact microstrip pseudo-interdigital bandpass ilter is presented. Section 4. describes the image impedance o parallel-coupled microstrip lines and image passband limits. As it is derived in this section, the bandwidth o image passband depends solely on the ratio o even to odd mode impedances o the coupled microstrip lines. Section 4.3 presents the design o second-order parallel-coupled bandpass ilters using IPM. In order to implement the limits o manuacturing acilities and to achieve compactness in the inal design the width o the microstrip resonators is chosen to be. mm and the required even to odd mode impedances ratios is achieved by adjusting the width o the slot. In section 4.4 compact microstrip hairpin bandpass ilter is presented. This ilter is designed using the bandpass ilter presented in section 4.3 with parallel-coupled transmission-line resonators bent to orm U-shaped hairpin resonators. Section 4.5 presents design o compact pseudo-interdigital bandpass ilter which consists o a pair o coupled pseudo-interdigital resonators. This ilter has very compact size and skirt selectivity improved by the appearance o transmission zeros at inite requencies below and above the passband. 8

96 4.7. Reerences [4-] J. S. Hong and M. J. Lancaster, "Development o new microstrip pseudointerdigital bandpass ilters," IEEE Microwave and Guided Wave Lett., vol. 5, no. 8, pp. 6-63, August 995 [4-] M. Salerno, R. Sorrentino, and F. Giannini, "Image Parameter Design o Noncommensurate Distributed Structures: An Application to Microstrip Low- Pass Filters," IEEE Trans. on Microwave Theory and Tech., vol.34, no., pp , January 986 [4-3] G. Bianchi, R. Sorrentino, M. Salerno, and F. Alessandri, "Image Parameter Design o Parallel Coupled Microstrip Filters," 8 th European Microwave Conerence, Stockholm, Sweden, September 988, pp [4-4] G. Bianchi, R. Sorrentino, Electronic Filter Simulation & Design. New York: Mc Graw-Hill, 7 [4-5] S. B. Cohn, "Parallel-Coupled Transmission-Line-Resonator Filters," IRE Trans. on Microwave Theory and Tech., vol. 6, no., pp. 3-3, April 958 [4-6] P. A. Kirton and K. K. Pang, "Extending the Realizable Bandwidth o Edge- Coupled Stripline Filters," IEEE Tran. on Microwave Theory and Tech., vol. 5, no. 8, pp , August 977 [4-7] T. Edwards, Foundations or microstrip circuit design. nd edition, Chichester, U.K.: John Wiley & Sons, 99 [4-8] E. G. Cristal and S. Frankel, "Hairpin-Line and Hybrid Hairpin-Line/Hal-Wave Parallel-Coupled-Line Filters," IEEE Trans. on Microwave Theory and Tech., vol., no., pp , November 97 [4-9] U. H. Gysel, "New Theory and Design or Hairpin-Line Filters," IEEE Trans. on Microwave Theory and Tech., vol., no. 5, pp , May 974 [4-] M. Dishal, "Alignment and Adjustment o Synchronously Tuned Multiple- Resonant-Circuit Filters," Proceedings o the IRE, vol.39, no., pp , November 95 [4-] T. H. Lee, Planar microwave engineering : a practical guide to theory, measurement, and circuits. Cambridge, U.K.: Cambridge Univ. Press, 4 [4-] J. S. Hong and M. J. Lancaster, "Investigation o microstrip pseudo-interdigital bandpass ilters using a ull-wave electromagnetic simulator," Int. J. Microwave 83

97 and Millimeter-Wave Computer-Aided Engineering, vol. 7, pp.3-4, May 997 [4-3] D. ayniyev, D. Budimir, and G. ouganelis, "Super Compact Microstrip Pseudo Interdigital Bandpass Filters," th Int. Symp. on Microwave and Optical Tech., Monte Porzio Catone, Italy, 7- Dec 7 84

98 5. PSEUDO-INTERDIGITAL STEPPED IMPEDANCE BANDPASS FILTERS 5.. Introduction Stepped impedance resonators (SIR) are widely used in the design o modern microstrip bandpass ilters. The irst reported application o SIR was in design o coaxial bandpass ilters [5-], in which SIR were employed to achieve compact size without degradation o the Q actor. Nowadays SIR are used where control over the requency o the irst spurious response is required. The distinguishing eature o SIR is the possibility to shit spurious resonance requencies by adjusting the impedance ratio R. Thus, on the one hand, SIR are used to tune the second harmonic o bandpass ilters to generate two passbands in the design o dual-band bandpass ilters [5-], [5-3]. On the other hand, SIR are employed to push the irst spurious passband to higher requencies to achieve wide stopband o bandpass ilters [5-4], [5-5]. The improvement o the stopband perormance o bandpass ilters can also be achieved by the implementation o elements with bandstop perormance. These can be the elements realized on top o the microstrip, such as spur-line, and elements realized in the ground plane, such as the deected ground structures (DGS). These elements are employed to generate stopbands which are tuned to the harmonic requency o the bandpass ilters. This chapter presents designs o advanced pseudo-interdigital bandpass ilters. The key modiication in bandpass ilter presented in the previous chapter is the implementation o SIR. The description o the undamental characteristics o SIR is given in section 5.. Section 5.3 presents the design o compact dual-band SIR pseudo-interdigital bandpass ilters. In this ilter, SIR are used to shit the spurious passband rom 3 to.7. The designs o single-band bandpass ilters with improved stopband are presented in section 5.4. In all bandpass ilters, discussed in this section, SIR are employed to shit the irst spurious harmonic rom 3 to 3.6. Section 5.4 is divided into two parts. In the irst one, the bandstop perormance o spur-line and the opencircuited stub are discussed and the design o the pseudo-interdigital SIR bandpass ilter with stopband improved by the inclusion o these two elements is presented. In the second part, DGS structures are analysed and the designs o bandpass ilters with stopband improved using DGS spirals are presented. 85

99 5.. Description o Stepped Impedance Resonators Stepped impedance resonator is a TEM or quasi-tem mode transmission line resonator that consists o two or more than two lines with a dierent characteristic impedance [5-6]. The two most popular SIR are short-circuited λ g 4 and open-circuited λ g resonators that are shown in Figure 5-. As it can be seen rom this igure, the quarterwavelength SIR consists o the short-ended line with characteristic impedance and electrical length θ connected to open-ended line with characteristic impedance and electrical length θ. This structure can be considered as a undamental element o SIR and hal-wavelength resonators consist o two such elements connected to each other by short-circuited ends with the grounding replaced by this connection. Figure 5-: Stepped impedance resonators: (a) quarter-wavelength type; (b) halwavelength type. The input admittance o λ g 4 SIR, shown in Figure 5- (a) is equal to: Y tanθ tanθ Y Y in + = jy (5.) Y tanθ Y tanθ As it was discussed in chapter, short-circuited λ g 4 resonator behaves like a parallel resonant circuit. The parallel resonance condition Y = o quarter-wavelength SIR will be: in 86

100 tanθ tanθ = Y Y = = R z (5.) Eq. (5.) shows that the resonant condition o SIR is determined by θ, θ, and impedance ratio R. Compared to conventional uniorm impedance resonators (UIR), analysed in chapter, the resonance condition o which is solely determined by the electrical length, SIR have one more extra degree o reedom that can be used in uture designs. The total electrical length o resonator, given in Figure 5- (a) asθ T, or resonant condition (5.) is equal to: θ T ( R θ ) = θ (5.3) + θ = θ + tan tan Figure 5- illustrates the total electrical length o SIR in terms o θ or dierent impedance ratios R. Figure 5-: Relationship between total electrical length and θ or resonant condition given or dierent impedance ratios. 87

101 As it can be seen, the total electrical length o resonator has maximum value when R and minimum value when R. The condition or these maximum and minimum values has been derived as [5-]: θ = θ = tan R (5-4) The condition θ = θ is a special condition which gives the maximum and minimum length o SIR which can be expressed as [5-7]: R θ = = T T tan min θ max (5-5) R Eq. (5-5) provides minimum value or maximum value or θ T when R > and π < θ T < π. θ when R < and < θ T < π, and T < The distinct eature o SIR comparing with UIR is that the resonators' length can be controlled using the impedance ratio R. This can be used to design SIR which are shorter than their UIR counterparts resonating at the same undamental resonance requency. In bandpass ilter design, SIRs are employed to control the irst spurious passband o ilters. This is used to design bandpass ilters with extended stopband [5-8], as well as to design dual-band bandpass ilters [5-9]. The ratio o the irst spurious resonance requency to the undamental resonance requency o SIR is given by: S π = tan R (5-6) S π = tan R (5-7) where Eq. (5-6) is the ratio o the quarter-wavelength SIR, or which = S 3 when R =, and Eq. (5-7) is the ratio o the hal-wavelength SIR, or which = S 88

102 when R =. Figure 5-3 illustrates normalised spurious resonance requencies or both types o resonators. Figure 5-3: Relationship between normalized spurious resonance requency and impedance ratio. 89

103 5.3. Design o Compact Microstrip Dual-Band Pseudo-Interdigital Stepped Impedance Bandpass Filters The pseudo-interdigital bandpass ilter presented in the previous chapter has the irst spurious response at 3. The spurious response at has been suppressed to about - 5 db or the resonant peaks. As pseudo-interdigital resonators were developed rom interdigital resonators with grounding replaced by interconnection o two λ g 4 resonators [5-] with good approximation, the two arms o pseudo-interdigital resonators can be treated as two λ g 4 resonators with interconnected ends replaced by groundings. This approximation is also based on the ield pattern o resonators around the resonant requency. The ield patterns obtained rom simulated current distributions o resonators at resonant requency are shown in Figure 5-4. The current distributions o both the pseudo-interdigital and hairpin resonators were simulated using EM Sonnet. As it can be seen rom this igure, these resonators have dierent ield patterns. It is also clear that ield patterns o pseudo-interdigital resonators look similar to the ield patterns o conventional interdigital resonators with maximum current at the shortcircuited ends and maximum electric ield at the open-circuited ends o resonators. Thus, both arms o pseudo-interdigital resonators can be treated as λ g 4 shortcircuited resonators and Eq. (5-6) can be used in order to ind the approximate spurious resonance requency rom the impedance ratio R. Figure 5-4: Simulated current distributions: (a) pseudo-interdigital resonators; (b) hairpin resonators. 9

104 In the most microstrip dual-band ilters with SIR λ g type o SIR are used and the impedance ratio is adjusted to control the second passband using Eq. (5-7) [5-], [5-]. However, microstrip dual-band ilters with λg 4 type SIR have also been reported [5-], [5-3]. The layout o the proposed dual-band bandpass ilter is shown in Figure 5-5. The width o high impedance lines is.4 mm and.8 mm is the width o the low impedance lines. The bandpass ilter has been simulated or Rogers RO43 substrate with thickness.54 mm and dielectric constant Thus, the characteristic impedances o SIR are = 7.46Ω, and = 56.3Ω, and impedance ratio R =. 7. Using this data and Eq. (5-6), the calculated ratio o the irst spurious resonance requency to the undamental resonance requency is =. S 9. Figure 5-5: Layout o compact microstrip pseudo-interdigital SIR bandpass ilter. The width o slots between coupled lines is.3 mm and width o SIR lines has been chosen to satisy the requirements o design and to meet manuacturing limits. The size o the iler is mm or.3λ g. λg, where λg is a wavelength at.3 GHz. Taper lines have been used to minimise losses due to step impedance discontinuities. Feeding lines also have been adjusted to achieve maximum degree o coupling by keeping constant the width o the coupling slot, and to improve the second passband o the ilter. The ilter was simulated using ADS Momentum. The simulated S-parameters are shown in Figure 5-6 by dashed lines. 9

105 Figure 5-6: Simulated (dashed) and measured (solid) S-parameters o pseudointerdigital SIR dual-band bandpass ilter: (a) S coeicients; (b) S coeicients As it can be seen rom simulation results, the center requencies o the irst and the second passbands are.3 and 4.63 GHz respectively. The FBW o the irst passband is 33.3%. For the second passband, the bandwidth is 4%. Skirt selectivity o both passbands is improved by Ts at inite requencies, above and below the passband. The ratio o spurious resonance requency to undamental resonance requency extracted rom simulation is equal to.7. This is bigger than the calculated ratio o.9. One o the reasons o this discrepancy can be that SIR used in the design are just approximations o short-circuited λ g 4 type SIR. However, calculated S good approximation and can be used as a starting value or the ilter designs with subsequent tuning and optimisation. is a The microstrip bandpass ilter was abricated on.54 mm thick Rogers RO43 substrate ( ε = ) [5-4]. Figure 5-6 shows the measured S-parameters by the solid r lines. The response o the abricated ilter was measured with Agilent PNA (E836A) network analyzer. The measured center requency is GHz or the irst passband and 4.8 GHz or the second passband. The measured bandwidths o the irst and the second passbands are 3.3% and 7.3% respectively. It can be seen rom Figure 5-6 that there is slight 9

106 requency shit between the simulated and measured results. An increase o the insertion losses and a decrease o the return losses at both passband requencies are observed and are attributable to poor manuacturing and additional losses caused by this. The parasitic resonance peak measured at 3.3GHz can be due to increased parasitic coupling caused by inexact manuactured slots between the microstrip lines. This also can be a reason o increased losses and deteriorated bandwidth o the second passband. A photograph o the abricated ilter is shown in Figure 5-7. Figure 5-7: Photograph o the abricated bandpass ilter. 93

107 5.4. Design o SIR Bandpass Filters with Improved Stopband Perormance Bandpass Filters with Extended Stopband The implementation o SIR in the design o bandpass ilters is also used or the improvement o stopband perormance o single-band ilters. In this scenario, an impedance ratio R < is chosen and rom Eq. (5-6, 5-7) and the graph in Figure 5- < 3 the irst spurious resonance requency becomes higher than or λ g type resonators, and higher than 3 or λ g 4 type resonators respectively. Usually a minimum value o R is determined taking into account the manuacturing limits and degradation o insertion loss o ilters due to the additional losses caused by step discontinuities. To demonstrate the ability to extend the stopband o pseudo-interdigital bandpass ilter using SIR, a bandpass ilter with SIR and impedance ratio R =. 596 has been developed. This ilter will be used in the design o bandpass ilters with stopband perormance improved by the implementation o spur-line and DGS, which are presented in next sections. From Eq. (5-6) the irst spurious response o SIR should be at approximately An impedance ratio was realized using microstrip line with.4 mm and. mm width on the.867 mm thick substrate with ε =.. The layout o the designed ilter, with total size 6 4 mm, is shown in Figure 5-8. r Figure 5-8: Layout o compact microstrip pseudo-interdigital SIR bandpass ilter with extended stopband. The S-parameters o ilters simulated using ADS Momentum are shown in Figure 5-9. The center requency o the simulated ilter is.5 GHz, bandwidth.75 GHz and 3dB 94

108 FBW is 3%. The center requency o the irst spurious harmonic is 9.35 GHz or This value is very close to 3.78, calculated using Eq. (5-6). Spurious resonance at has been suppressed till -5 db. The appearance o TX zeros at.97 a 3.4 GHz provides good skirt selectivity o the irst passband. Although extension o the stopband to 3.75 is not a considerable improvement o stopband perormance, this ilter will be used as the initial building block or the bandpass ilters discussed in next sections. Figure 5-9: Simulated S-parameters o compact microstrip pseudo-interdigital SIR bandpass ilter with extended stopband. 95

109 5.4.. Analysis o Spur-line and Open-Circuited Stubs One o the ways to suppress the spurious passband in the design o bandpass ilter is an implementation o spur-line, which can be embedded into resonators [5-5], into the eeding line [5-6], and into both, resonators and eeding lines [5-7]. The spur-line section, introduced in the design o bandstop ilters in homogeneous propagation medium [5-8], is shown in Figure 5- (a). The spur-line section consists o a pair o coupled microstrip lines o length L, which is approximately a equal to quarter wavelength at stopband center requency. Figure 5-: Spur-line section: (a) Layout; (b) Terminal conditions. Spur-line section can be modelled as 4-port parallel-coupled transmission line network with terminal conditions, as it is shown in Figure 5- (b). The elements o the impedance matrix o this 4-port network are given in Eq. (3-) (3-4), and terminal conditions o spur-line section are: V A V = V = V B = V4 I A I + I = I B I 4 I = 3 = (5-8) wherev A, V B, I A, and I B are voltages and currents o -ports network that can be obtained rom the original 4-port network ater applying terminal conditions. Similarly with analysis presented in Chapter 3, -port network s impedance matrix can be derived rom the terminal conditions. This matrix is not very useul or our analysis; thereore transmission matrix o two-port network has been derived. 96

110 Transmission, or ABCD matrix, is a matrix used in analysis o microwave circuits, which consist o a cascade connection o two or more than two -port networks. ABCD matrix is deined in terms o voltages and currents o -port network: V A = I C B V D I (5-9) where V and I are voltage and current at port o network, and V and I are voltage and current at port respectively. The main eature o ABCD matrix, used or the analysis o microwave circuits, is that the ABCD matrix o cascade connection o two or more two-port networks is equal to multiplication o ABCD matrices o individual networks [5-9]. Transmission matrix o spur-line section has been derived as [5-]: V I A A cosθe = jy e sinθe j ( sinθ + tanθ cosθ ) e e cosθe o e o e o sinθ tanθ o e V I B B (5-) One o the decomposition o matrix (5-) is: V I A A cosθ = e j e sinθe jo tan jy e sinθe cosθe θo V I B B (5-) This decomposition corresponds to equivalent circuit that consist o transmission line with characteristic impedance e and electrical length θ e connected in series with short-circuited stub with characteristic impedance o and electrical length θ o, as shown in Figure 5-. As the short-circuited stub is connected in series, the sum o impedances o both lines should be used to ind the total input impedance. From Eq. (- 8) it can be seen that the impedance o short-circuited line becomes ininite when the electrical length o this line is π. Thereore, condition o bandstop caused by the 97

111 ininite impedance o short-circuited line is θ = π. Thus, the length o spur-line is equal to: v L = 4 po L (5-) where L is an eective length due to the gap G, which can be ound rom odd mode ringing capacitance using the ollowing ormula: v (5-3) ( 4π C ) po L = tan o o π Figure 5-: Equivalent circuit o spur-line. The even and odd mode characteristic impedances have a signiicant eect on the skirt selectivity o spur-line bandstop ilters [5-]. In our scenario, when the total width o spur-line section is equal to the width o the 5 Ω line, the general rule is to make the slot's width s as small as possible in order to achieve the best skirt selectivity, or in other words, the smallest 3dB bandwidth o the bandstop. In this case the insertion loss introduced by the spur-line section at the passband requency o the bandpass ilter is the smallest. The width o slot s =. 3 mm has been chosen, as it is small and easy to abricate. From the simulation results, it has been ound that the spur-line with a slot width.3 mm introduces.-.3 db insertion loss at requencies rom GHz to 3 GHz. 98

112 The bandstop ilters with open-circuited stubs are one o the most popular bandstop ilters. The exact design o these ilters or homogeneous medium is described in [8]. This design is based on the bandstop characteristics o the open-circuited stubs. Nowadays these properties are also used to improve the stopband perormance o bandpass ilters [5-]. The microstrip open-circuited stub is shown in Figure 5- (a). Its equivalent circuit is a shunt connected open-circuited stub, which is shown in Figure 5- (b). The shunt connected line has a stopband at requencies when its admittance is ininite. From Eq.(-7) the input admittance o the open-circuited line is ininite when the electrical length o the line is equal to ( ) π n or n=,,3 and the irst stopband requency corresponds to θ = π, i.e. when stub is a quarter wavelength long. Figure 5-: Microstrip open-circuited stub: (a) layout. (b) equivalent circuit. The characteristic impedance o the open-circuited stub has eect on the skirt selectivity o bandstop response, which aects the insertion loss in the out-o-band region. Using EM simulations it has been ound that high impedance open-circuited stubs have better bandstop skirt selectivity and smaller out-o-band insertion loss than low impedance stubs. 99

113 Bandpass Filters with Improved Stopband A bandpass ilter with improved stopband pseudo-interdigital SIR bandpass ilter, as discussed in section 5.3., has been designed with an impedance ratio R =. 66 and the irst spurious response at 3.6. This impedance ratio has been chosen to obtain a smaller insertion loss at the undamental passband o ilter. In the case when the impedance ratio is R <, a small impedance ratio R can be obtained only by the increase o the dierence between the impedances o the lines resonators. Big dierence between these impedances introduces more losses due to additional losses due to radiation on the impedance step. Thus the insertion loss o ilter increases as well.the center requency o bandpass ilter is.75 GHz with irst spurious harmonic rom 9.5 to GHz. To suppress this passband, a spur-line section has been embedded into eeding line and open-stub has been connected as shown in Figure 5-3. Figure 5-3: Layout o bandpass ilter with spur-line and open-circuited stubs. The spur-line sections and open-circuited stubs have been designed to have bandstop peaks at requencies rom 9.5 to GHz with approximately GHz between each other. The simulated S-parameters o spur-line section with open-circuited stub are shown in Figure 5-4. The bandstop requencies o open-circuited stub and spur-line section simulated separately are. and GHz. Ater the connection o the stub to spur-line, the bandstop requencies shited to.5 and.5 GHz respectively. As it can be seen rom Figure 5-5, the open-circuited stub integrated with spur-line section have a perormance o not optimised bandstop ilter with Ts at.5 and.5 GHz. Ater integration o spur-line section and open-circuited stub with bandpass ilter two additional T zeros occurred in the stopband o the ilter at.6 and.3 GHz [5-3]. The simulated S-parameters o pseudo-interdigital bandpass ilter with improved

114 stopband are shown in Figure 5-5. As a result o the integration with spur-line section embedded into eeding line and open-circuited stub, the stopband o bandpass ilter has been extended to about 5.5. Figure 5-4: Simulated S-parameters o spur-line section and open-circuited stub. Figure 5-5: Simulated S-parameters o compact microstrip pseudo-interdigital SIR bandpass ilter with improved stopband. The simulated transmission coeicient o bandpass ilter without spur-line and opencircuited stub is included in Figure 5-5 and noted as S '. The comparison o the transmission perormance o these two ilters clearly shows the eect o inclusion o spur-line section and open circuited stub on the stopband perormance o bandpass ilter.

115 Analysis o Deected Ground Structures The deected ground structures (DGS) is a common name o slots etched in the ground plane o microstrip and coplanar waveguide transmission lines. DGS can be treated as electromagnetic bandgap (EBG) structures as they orbid or allow the wave propagation at certain requency bands. EBG eects occur at some requency because any periodic slots or structures etched on the ground plane can disturb the ield distribution o guided electromagnetic waves. Although this eature o DGS has been used or suppression o harmonics in the design o power dividers [5-4], to improve eiciency o power ampliiers [5-5], and in the design o other RF ront-end applications, the most requently DGS structures are used in the design o lowpass ilters [5-6]. One o the most requently employed and the simplest or analysis DGS structures is a dumbbell-shaped slot (DSS), which is shown in Figure 5-6 (a). The simplest model o DSS, that excludes radiation, dielectric and conductor losses, is a parallel LC resonator [5-7]. The square slots o DSS etched on the ground plane are equivalent to inductance, and the narrow slot that connects two square slots is equivalent to capacitance. The square slots o DGS are equivalent to inductance because due to the presence o the narrow slot, the direct path or current propagation under metallic line o microstrip is broken. Thus, current is lowing along the edge o square slots and increased current density can be observed rom the EM simulations. Two square slots with current lowing along their edge become equivalent to loops with current. This current produces a magnetic ield and generates magnetic lux which is characterized by the inductance used to model DGS. The values o elements o equivalent circuit can be extracted rom the simulation results, which is or one DSS is equivalent to a one pole Butterworth type lowpass ilter. The series inductance can be calculated rom the prototype elements o Butterworth prototype, and the value o capacitance can be extracted rom the bandstop requency. The bandstop perormance o DSS will be used or the suppression o harmonics in the design o bandpass ilter with improved stopband.

116 The spiral shaped slots (SSS), shown in Figure 5-6 (b), is a DGS structure which also has been used in the design o lowpass and bandpass ilters. SSS is a modiication o DSS with square slots replaced by spiral shaped slots. For the same occupied areas, the attenuation poles o SSS occur at the lower requencies, compared to DSS. This can be used to reduce the size o the whole structure. The simplest proposed model o SSS consists o an inductor and a short-circuited stub, which represents the periodic requency response [5-8]. The characteristic impedance S and inductance L S also can be extracted rom elements values o irst order Butterworth prototype. For scenarios when the undamental and spurious stopbands o SSS are used equivalent circuit in which shorted stub with stepped impedances should be used to predict spurious requencies more accurately [5-9]. Figure 5-6: Structure and equivalent circuit o DGS: (a) dumbbell-shaped slot; (b) spiral shaped slot. To compare the bandstop perormance o DSS and SSS, there have been simulated using HFSS or substrate with ε =. and thickness.867 mm. The total sizes o r DSS and SSS are chosen to be equal with dimensions a =. 8 mm, b =. 6 mm, g = s = w =. mm, and width o 5 Ω line w =. 6 mm. The simulated S-parameters 3

117 are shown in Figure 5-7. The bandstop requencies o SSS and DSS are 8.9 GHz and 3. GHz respectively. It is clear that in order to achieve the same bandstop requency using DSS the size o square slots should be increased. This is one o the reasons why SSS have been chosen or the suppression o spurious harmonics o bandpass ilters. Another reason is that due to large total area o slots etched in the ground plane or DSS, the skirt selectivity o DSS is worse than the skirt selectivity o SSS. Thus, the insertion loss at the out-o-band requencies caused by the implementation o DSS type, the DGS is large than the insertion loss caused by SSS type DGS. Figure 5-7: Simulated S-parameters o SSS (black lines) and DSS (grey lines). 4

118 Compact Pseudo-Interdigital SIR Bandpass Filters with Improved Stopband using DGS The design o compact pseudo-interdigital bandpass ilters with improved stopband perormance is based on the addition o DGS structures etched under 5 Ω eeding lines at the input and output o ilters. Spiral shaped slots DGS have been used and adjusted to have a bandstop at the spurious harmonics requencies o bandpass ilters. This method, proposed in [5-6] also discusses the addition o spur-line section embedded into eeding lines to suppress more harmonics. In this section the design o bandpass ilters with suppression o harmonics using DGS only is presented. The irst step is the design o pseudo-interdigital bandpass ilter with extended stopband using procedure described in The bandpass ilter with a center requency.5 GHz, ractional bandwidth 38.% has been designed using Rogers RT/Duroid 588 substrate with dielectric constant ε =. and thickness h =.867 mm. The impedance ratio o SIR is equal to R =. 657 and the calculated spurious to undamental resonance requencies ratio is = 3. S 6. The ilter has been simulated using HFSS. The simulated requencies ratio is equal to = 3. S 5. To suppress the irst spurious harmonics rom 8.3 to 9. GHz, spiral shaped slots (SSS) etched below the eeding lines at input and output o ilter have been implemented. The dimensions o SSS are the same used in previous section, a =. 8 mm, b =. 6 r mm, g = s = w =. mm, with the stopband centered at 8.9 GHz. The layout o proposed ilter is shown in Figure 5-8, with the top layer conductors o ilter shown with black colour illed shapes and SSS etched on the ground layer shown with black lines. The size o the ilter is mm or.4λ g. 9λg where λ g is a wavelength at.5 GHz, which is the passband center requency o ilter. 5

119 Figure 5-8: Layout o bandpass ilter with one SSS. The S-parameters o the proposed ilter, simulated using Ansot HFSS are shown in Figure 5-9. From simulation results, it can be seen that the ilter has stopband with 5dB insertion loss till 3.4 GHz, which is For comparison with the stopband perormance o bandpass ilter without SSS, the simulated transmission coeicient o the ilter without SSS was included and is noted in Figure 5-9 as S '. It is clear rom this comparison that the addition o one SSS at the input and output o ilter caused the suppression o irst spurious harmonics to about db. The length o the ilter with one SSS was increased by 3.5 mm on each side. Figure 5-9: Simulated S-parameters o bandpass ilter with one SSS. 6

120 To investigate the possibility o a urther extension o the stopband o bandpass ilter using DGS, a ilter with two SSS etched below the eeding lines at the input and output has been designed. The layout o proposed ilter is shown in Figure 5-. The new ilter structure consists o bandpass ilter designed above with one more SSS etched below eeding line at the input and output and located between irst SSS and port connection. The second SSS has smaller size with dimensions, noted as in Figure 5-6 (b), a = b =. mm, g = s = w =., and width o 5 Ω line w =. 6 mm. The bandstop generated by small SSS is centered at.8 GHz. Figure 5- illustrates the simulated S-parameters o the two SSS located under 5 Ω microstrip line. It can be seen that this structure has two bandstop peaks, low requency peak generated by SSS o bigger size and high requency peak, generated by SSS o smaller size. Figure 5-: Layout o bandpass ilter with two SSS. Bandstop requencies o both spiral shaped slots are controlled by adjusting the length o etched spiral slots. I the width o etched slot and the width o separation between them is constant, lengthening o spiral slots can be achieved by increasing the total area o DGS. 7

121 Figure 5-: Simulated S-parameters o two SSS. The S-parameters o proposed bandpass ilter with two SSS etched under eeding lines were simulated using HFSS. Simulated S-parameters are shown in Figure 5-. It can be seen that 5dB insertion loss stopband o the ilter is extended to 6.5 GHz or to 6.6. For comparison S o ilter without DGS is included in Figure 5- and noted as S '. This comparison shows that the addition o the second small SSS caused the suppression o the second spurious harmonics o bandpass ilter to 5-3 db. The irst spurious harmonics was suppressed to 4 db by the use o SSS o bigger size. It also can be seen rom Figure 5- that the second resonant requency o small SSS, which resonates at.8 GHz, has shited to higher requency 3.4 GHz. This shit can occur due to additional coupling with bigger size SSS and stopband perormance o small SSS can be urther enhanced by the weak T o ilter at 3.5 GHz. The main drawback o the new ilter is that now the lengths o both etched spiral slots should be adjusted to achieve the best stopband rejection. The total length o ilter increased due to the addition o DGS by 6 mm on each side. The size o the ilter is mm or.46λg. 9λg where λg is a guided wavelength at the center requency o the undamental passband o ilter. 8

122 Figure 5-: Simulated S-parameters o bandpass ilter with two SSS. 9

123 5.5. Summary In this chapter pseudo-interdigital bandpass ilters with SIR are presented. The undamental characteristics o SIR are described in section 5.. Section 5.3 presents the design o compact dual-band bandpass ilter with passband centred at.3 and 4.6 GHz. In this ilter SIRs with impedance ratio R =. 7 have been used to shit spurious resonance requency to.7. The pseudo-interdigital bandpass ilters with improved stopband are presented in section 5.4. In all these ilters, SIRs with impedance ratio R =. 66 have been used to extend the stopband till 3.6. A urther improvement o the stopband has been investigated combining bandpass ilters with elements that introduce bandstops tuned to the harmonic requencies bandpass ilter. The design o band pass ilter with stopband extended to 5.5 using spur-lines and open-circuited stubs is presented. the spiral shaped slots etched in the ground plane under the eeding line on each side o bandpass ilters are employed to design ilters with stopbands to 5.36 and 6.6 or ilters with one and two slots respectively.

124 5.6. Reerences [5-] M. Makimoto and S. Yamashita, "Compact bandpass ilters using stepped impedance resonators," Proceedings o the IEEE, vol. 67, no., pp. 6-9, January 979 [5-] C. Qing-Xin and C. Fu-Chang, "A Compact Dual-Band Bandpass Filter Using Meandering Stepped Impedance Resonators," IEEE Microwave and Wireless Comp. Lett., vol. 8, no. 5, pp. 3-3, May 8 [5-3] K. Jen-Tsai, Y. Tsung-Hsun, and Y. Chun-Cheng, "Design o microstrip bandpass ilters with a dual-passband response," IEEE Trans. on Microwave Theory and Tech., vol. 53, no. 4, pp , April 5 [5-4] J. T. Kuo and E. Shih, "Microstrip stepped impedance resonator bandpass ilter with an extended optimal rejection bandwidth," IEEE Trans. on Microwave Theory and Tech.,, vol. 5, no. 5 pp , May 3 [5-5] L. Shih-Cheng, D. Pu-Hua, L. Yo-Shen, W. Chi-Hsueh, and C. Chun Hsiung, "Wide-stopband microstrip bandpass ilters using dissimilar quarter-wavelength stepped-impedance resonators," IEEE Trans. on Microwave Theory and Tech., vol. 54, no. 3, pp. -8, March 6 [5-6] M. Sagawa, M. Makimoto, and S. Yamashita, "Geometrical structures and undamental characteristics o microwave stepped-impedance resonators," IEEE Trans. on Microwave Theory and Tech,, vol. 45, no. 6, pp , July 997. [5-7] M. Makimoto, S. Yamashita, Microwave resonators and ilters or wireless communication:theory, design and application. New-York: Springer, [5-8] M. Makimoto and S. Yamashita, "Bandpass Filters Using Parallel Coupled Stripline Stepped Impedance Resonators," IEEE Trans. on Microwave Theory and Tech., vol. 8, no., pp , December 98. [5-9] A. A. A. Apriyana and P. hang Yue, "A dual-band BPF or concurrent dualband wireless transceiver," 5 th Con. Electronics Packaging Tech., Singapore December 3, pp [5-] J. S. Hong and M. J. Lancaster, "Development o new microstrip pseudointerdigital bandpass ilters," IEEE Microwave and Guided Wave Lett., vol. 5, no. 8, pp. 6-63, August 995

125 [5-]. Yue Ping and S. Mei, "Dual-Band Microstrip Bandpass Filter Using Stepped- Impedance Resonators With New Coupling Schemes," IEEE Trans. on Microwave Theory and Tech., vol. 54, no., pp , October 6. [5-] C. Yi-Ming, C. Sheng-Fuh, C. Chia-Chan, and C. Cheng-Yu, "A dual-band bandpass ilter by interleaving heterogeneous stepped-impedance resonators," 37 th European Microwave Con., Munich, Germany, October 7, pp [5-3] P. K. Singh, S. Basu, and W. Yeong-Her, "Miniature Dual-Band Filter Using Quarter Wavelength Stepped Impedance Resonators," IEEE Microwave and Wireless Comp. Lett., vol. 8, no., pp. 88-9, February 8. [5-4] D. ayniyev and D. Budimir, "Compact microstrip dual-band pseudointerdigital stepped impedance bandpass ilters or wireless applications," IEEE AP-S/URSI Int. Symp. Dig., Charleston, USA, June 9 [5-5] P. Hoi-Kai, H. Ka-Meng, T. Kam-Weng, and R. P. Martins, "A compact microstrip λg/4-sir interdigital bandpass ilter with extended stopband," IEEE MTT-S, Int. Microwave Symp. Dig., June 4, pp [5-6] K. Chul-Soo, K. Duck-Hwan, S. In-Sang, K. M. K. H. Leong, T. Itoh, and A. Dal, "A design o a ring bandpass ilters with wide rejection band using DGS and spur-line coupling structures," IEEE MTT-S, Int. Microwave Symp. Dig., June 5, pp [5-7] A. Griol, J. Marti, and L. Sempere, "Microstrip multistage coupled ring bandpass ilters using spur-line ilters or harmonic suppression," Electronics Letters, vol. 37, no. 9, pp , April [5-8] B. M. Schiman and G. L. Matthaei, "Exact Design o Band-Stop Microwave Filters," IEEE Trans. on Microwave Theory and Tech., vvol.63, no., pp , May 963 [5-9] D. M. Pozar, Microwave engineering. 3 rd edition, New York: John Wiley & Sons, 4 [5-] C. Nguyen and C. Hsieh, "Millimeter Wave Printed Circuit Spurline Filters," IEEE MTT-S, Int. Microwave Symp. Dig., vol.83, no., pp. 98-, May 983 [5-] Y.. Wang and M. L. Her, "Compact microstrip bandstop ilters using steppedimpedance resonator (sir) and spur-line sections," IEE Proceedings Microwaves, Antennas and Propagation, vol. 53, no. 5 pp , October 6.

126 [5-] I. N. Alvizuri Romani, A. J. M. Soares, and H. Abdalla, "Compact microstrip bandpass ilter with enhanced stopband perormances," IEEE Microwave and Optoelectronics Con., pp , October 7 [5-3] D. ayniyev and D. Budimir, "Compact microstrip pseudo-interdigital stepped impedance bandpass ilters with improved stopband perormance," IEEE Wireless and Microwave Technology Con., April 9 [5-4] W. Duk-Jae and L. Taek-Kyung, "Suppression o harmonics in Wilkinson power divider using dual-band rejection by asymmetric DGS," IEEE Trans. on Microwave Theory and Tech., vol. 53, no. 6, pp , June 5 [5-5] L. Jong-Sik, K. Ho-Sup, P. Jun-Seek, A. Dal, and N. Sangwook, "A power ampliier with eiciency improved using deected ground structure," IEEE Microwave and Wireless Comp. Lett., vol., no. 4, pp. 7-7, April [5-6] J. Dong-Jin and C. Kai, "Low-Pass Filter Design Through the Accurate Analysis o Electromagnetic-Bandgap Geometry on the Ground Plane," IEEE Trans. on Microwave Theory and Tech.,, vol. 57, no. 7, pp , July 9 [5-7] P. Jong-Im, K. Chul-Soo, K. Juno, P. Jun-Seok, Q. Yongxi, A. Dal, and T. Itoh, "Modeling o a photonic bandgap and its application or the low-pass ilter design," Asia-Paciic Microwave Con., Singapore, November 999, vol., pp [5-8] K. Chul-Soo, L. Jong-Sik, N. Sangwook, K. Kwang-Yong, and A. Dal, "Equivalent circuit modelling o spiral deected ground structure or microstrip line," Electronics Letters, vol. 38, no.9, pp. 9-, September. [5-9] K. Chul-Soo, L. Jong-Sik, N. Sangwook, K. Kwang-Yong, P. Jong-Im, K. Geun-Young, and A. Dal, "The equivalent circuit modeling o deected ground structure with spiral shape," IEEE MTT-S, Int. Microwave Symp. Dig., vol.3, June, pp.5-8 3

127 6. DESIGN OF COMPACT MICROSTRIP DIPLEXERS 6.. Introduction A diplexer is a three-port network which usually consists o two ilters connected in a special way in order to provide the passband and stopband characteristics o each ilter rom the common connection [6-]. Diplexers are two channel versions o multiplexers. These devices can be used to connect single antenna with several receivers or transmitters or to provide the coexistence o dierent wireless systems [6-] in multiservice and multiband communication systems. Diplexers and triplexers are needed in these systems to possess the capabilities o high compactness, light weight and high isolation. A low voltage standing-wave ratio should be displayed at the common ports o multiplexers, whereas high isolation should be maintained between each o the ilters. A multiplexer is called contiguous i the passband o adjacent channels cross-over is at the 3dB level. All other multiplexers have a guardband, channel that separates adjacent passbands. To design a multiplexer, component ilters should be connected in such a way that each ilter appears as an open circuit to each other ilter. For the design o diplexers only one open circuit condition should be satisied and this can be done using optimisation o the T- or Y-junction. For the design o triplexers with two open circuit conditions, or multiplexer with our channels, more complex matching circuits using rings and impedance transormers can be used [6-3], [6-4]. In this chapter, designs o compact microstrip diplexers using miniaturized pseudointerdigital bandpass ilters, developed in the previous chapters, are presented. Section 6. presents a diplexer designed using modiied Y-junction. In section 6.3, the design o a diplexer using common eeding techniques is presented. In both these diplexers, pseudo-interdigital bandpass ilters with uniorm impedance resonators are used. SIR dual-band bandpass ilters are employed in the design o three-port our-channel diplexer, presented in section

128 6.. Microstrip Diplexers using Y-Junction The design procedure or microstrip diplexer begins rom the design o two pseudointerdigital bandpass ilters as described in 4.5. The bandpass ilter with center requency at.44 GHz and FBW 4.7% was designed or the irst channel o diplexer. A bandpass ilter with a center requency at 3.5 GHz and FBW 4.9% was designed or the second channel o diplexer. The layout o ilters is the same as in Figure 4- and or the dielectric substrate with dielectric constant. and thickness.78 mm, the length o the irst and second ilter is 3.7 mm and 3.4 mm respectively. Figure 6- illustrates the S-parameters o both ilters simulated using ADS Momentum. Figure 6-: Simulated S-parameters o bandpass ilters: with passband centered at.44 GHz (black lines); with passband centered at 3.5 GHz (grey lines). From the simulation results the passband insertion loss o both ilters is.75 and the return loss is about 5 db. The irst ilter, with a center requency.44 GHz, has Ts at.97 and.87 GHz. The second ilter has Ts at.85 and 3.8 GHz. The passbands o ilters are approximately.36 GHz apart rom each other. Thereore, the designed diplexer should have a guardband or requency separation channel o the same size. 5

129 To build a diplexer, both designed ilters should be combined using some matching circuit. One port o this circuit should be matched at the center requency o ilter and the other port should be open-circuit. Thus, only one open condition is needed or diplexer design. For the design o diplexers the most popular option o combining circuits is the T-junction [6-5], [6-6], or one o its modiication- the Y-junction [6-7]. T-junction or Y-junction is combined with the branch lines which are optimised and should be designed to meet the condition o no relection at the center requency o one passband and total relection at the center requency o the other passband. Thus, or example the branch line that connects ilter to the junction should be adjusted to meet the open-circuit condition at the center requency o ilter. From the comparison o the simulated diplexer with T- and Y-junctions used to combine designed bandpass ilters, it has been ound that using the Y-junction introduces ewer losses than the T-junction. Thereore, the Y-junction was chosen or urther optimisation. Ater a ew optimisation steps, the Y-junction matching circuit has been chosen as it is shown in Figure 6-. The length o the 5Ω line connecting the low passband ilter is 5mm, the angle o slope o line connecting high passband ilter is 43.6º. The size o the diplexer is mm [6-8]. Figure 6-: Layout o microstrip diplexer with Y-junction. The simulated S-parameters o diplexer are shown in Figure 6-3. From simulation results it can be seen that the isolation between ports and 3 at the low channel is 5-3 db, at the high channel is 5- db. The passband perormance o the irst ilter is deteriorated and insertion loss has become.9 db and return loss 7dB. The width o the requency separation channel has increased.6 GHz due to the decrease o ractional bandwidth o the irst channel. The requencies o Ts o the irst ilter have 6

130 shited to.99 GHz and.74 GHz. The characteristics o the second channel ilter have not changed much and only the passband return loss is decreased by db. Figure 6-3: Simulated S-parameters o microstrip diplexer with Y-junction. 7

131 6.3. Miniaturised Microstrip Diplexers or Wireless Applications The main problem o the diplexer discussed above was the degradation o ilter's characteristics o one ilter due to the combination with another. The design o the matching network can be time consuming and demands a lot o optimisation iterations. Using other multiplexing techniques, such as transormers and circulators increases the total size o diplexer substantially. In order to decrease the degradation o the passband o low channel ilter and decrease the size o diplexer another diplexing technique is used. It is based on the common-transormer diplexer [6-9] which is common solution or diplexers based on combline or interdigital ilters. In these diplexers combline or interdigital ilters are coupled by means o the common transormer, as shown in Figure 6-4. Figure 6-4: Common-transormer diplexer with interdigital ilters. As microstrip bandpass pseudo-interdigital ilter has a lot in common with the microstrip interdigital bandpass ilter, coupling o the two pseudo-interdigital ilters using a common transormer has been studied. The eeding line o the pseudointerdigital ilter is much narrower than a 5 Ω line and the length o coupled eeding line is shorter than the length o arms o pseudo-interdigital resonator. Thereore, the common-transormer line was divided in two high impedance eeding line with dierent lengths. The width o slot between the eeding lines is ound using 8

132 optimisation. The application o common eeding reduces the total size o diplexer to mm or to.5λ g. 8λ g where λg is a wavelength at.7 GHz. The same diplexing technique was reported in the design o the diplexer using hairpin bandpass ilters [6-]. The layout o the proposed diplexer is shown in Figure 6-5. Figure 6-5: Layout o miniaturised microstrip diplexer. The most optimal width between the two eeding lines o the common transormer has been ound to be w =. 3 mm. For the design o diplexer, two bandpass ilters, analogues to the ones used in previous section, with center requencies.7 and 3.8 GHz are used. The simulated S-parameters o diplexer are shown in Figure 6-6 by the dashed lines. 9

133 Figure 6-6: Simulated (dashed) and measured (solid) S-parameters o miniaturized microstrip diplexer: (a) S coeicients; (b) S coeicients; (b) S 3 coeicients From simulated perormance o diplexer with common eeding, it can be seen that the passband characteristics o both channels o diplexer were not distorted much and that they are very similar to the passband characteristics o the ilter. Compared to microstrip diplexer with the Y-junction, the common eeding diplexer has passband o the second channel altered, but not much. Both channels have a passband return loss o about 3dB and insertion loss db or channel one and -.5 db or channel two. The Ts requencies o both ilters did not change and occurred at.3 and 3.9 GHz or channel one and 3.5 and 4.57 GHz or channel two. The isolation between ports two and three is db or both channels and the width o the guardband is.55 GHz. The miniaturized microstrip diplexer was abricated on.76 mm thick Rogers RT/Duroid 588 ( ε =. ). The response o the abricated diplexer was measured with Agilent r

134 PNA (E836A) network analyzer [6-]. The measured S-parameters o diplexer are shown in Figure 6-6 by solid lines. From Figure 6-6, the slight the requency shit between simulated and measured S- parameters is observed. Poor manuacturing and additional radiation losses caused by it is the reason o increased insertion losses and decreased return losses at both channels o diplexer. Parasitic peak in at 3.3 GHz in the out-o-band region o the second ilter is caused by the additional parasitic coupling between the two ilters. The deterioration o the bandwidth o the bandpass ilter o the second channel is also observed. This can be due to decreased coupling between resonators caused by roughness o milled slots between microstrip lines. A photograph o abricated diplexer is shown in Figure 6-7. Figure 6-7: Photograph o abricated miniaturized microstrip diplexer.

135 6.4. Microstrip Three-Port Four-Channel Diplexers In previous section, designs o the microstrip diplexer using single band bandpass ilters are presented. The possibility to use the same design procedure in order to develop the three-port our-channel diplexer using dual-band bandpass ilter will be investigated in this section. The simplest way to build such a diplexer is to use our single band bandpass ilters and connect them as shown in Figure 6-8 (a) [6-]. In this scenario, due to the unwanted interaction between ilters, the degradation o stopbands and passbands is possible. The size o such architecture is expected to be bigger than our times the size o ilter as matching circuit should also be designed. Figure 6-8 (b) illustrates the architecture o diplexer which will be designed in this section. The main advantage o this architecture over the one with our single band ilters is the size reduction. The implementation o this architecture with two dual-band bandstop ilters instead o the bandpass ilter was reported in [6-3]. Figure 6-8: Architecture o diplexer: (a) using our single band ilters; (b) using two dual-band ilters. Two dual-band pseudo-interdigital SIR bandpass ilters were designed using the procedure described in 5.3. The irst ilter was designed to have passbands centred at.65 and 4.65 GHz, the second ilter - at.5 and 6.9 GHz. Both ilters were designed with impedance ratio o SIR R =. 76. Thus the spurious to undamental passband requency ratio should be =. S 8. This ratio or the irst ilter, obtained rom simulation results, is equal to.8, and is equal to.76 or the second ilter. The diplexer was designed or a Rogers RT/Duroid 588 material with a substrate thickness

136 o.58 mm and a dielectric constant o.. The layout o diplexer is shown in Figure 6-9. Figure 6-9: Layout o three-port our-channels diplexer. A diplexer consists o two ilters with a layout analogous to the ilter shown in the Figure 5-5. Bandpass ilters are combined with eeding lines connected to a common eeding 5 Ω line. This combining technique can be considered as a modiication o the common-transormer diplexing, as it was discussed in the previous section. The diplexer is designed to take.65,.5, 4.65 and 6.9 GHz into port one and to separate.65 GHz and 4.65 GHz to port two and.5 GHz and 6.9 GHz to port 3. Figure 6- shows the simulated S-parameters o port to port 3 bandpass ilter. Figure 6-: Simulated S-parameters o port to port 3 bandpass ilter. The simulated S-parameters o diplexers are shown in Figure 6-. The simulation diplexer has very good transmission and relection characteristics on both channels o the irst passbands o dual-band ilters with minor distortions on the second passband o dual-band ilters [6-4]. The insertion losses o the.65 GHz and the 4.65 GHz 3

137 passbands o the irst channel are.6 db and.3 db respectively. For the second channels passbands insertion losses are.9 db and.9 db or the irst and second passbands respectively. The isolation between the channels is about db. The integration o two ilters caused the distortion o characteristics and appearance o additional peaks at about 3 and 6 GHz. Figure 6-: Simulated S-parameters o three-port our-channel diplexer. 4

138 6.5. Summary In this chapter, the application o pseudo-interdigital bandpass ilters in the design o compact microstrip diplexers is presented. Section 6. presents microstrip diplexer built using bandpass ilters with the passband centred at.44 GHz and 3.5 GHz. Optimized Y-junction is used to combine ilters and connect them to the common port. The isolation between the channels o about db is achieved, but deterioration o the irst channel is observed. The miniaturised microstrip diplexer with combining circuit based on common transormer is presented in section 6.3. Using this combination technique, a compact size and db isolation o channels o diplexer are achieved without substantial increase o insertion and return loss o both ilters. Section 6.4 presents the design o three-port our-channel diplexer in which two SIR dual-band ilters are combined using the same common transormer based technique. In this diplexer, our channels are separated in pairs to ports and 3. The isolation between channels is 5- db. 5

139 6.6. Reerences [6-] R. Levy, R. V. Snyder, and G. Matthaei, "Design o microwave ilters," IEEE Trans. on Microwave Theory and Tech., vol. 5, pp , March [6-] L. Ming-Iu and J. Shyh-Kang, "A microstrip three-port and our-channel multiplexer or WLAN and UWB coexistence," IEEE Trans. on Microwave Theory and Tech., vol. 53, no. pp , October 5 [6-3] D. Pu-Hua, L. Ming-Iu, J. Shyh-Kang, and C. Chun Hsiung, "Design o Matching Circuits or Microstrip Triplexers Based on Stepped-Impedance Resonators," IEEE Trans. on Microwave Theory and Tech., vol. 54, no., pp , December 6 [6-4] M. ewani and I. C. Hunter, "Design o Ring-Maniold Microwave Multiplexers," IEEE MTT-S, Int. Microwave Symp. Dig., June 6, pp.9- [6-5] A. F. Sheta, J. P. Coupez, G. Tanne, S. Toutain, and J. P. Blot, "Miniature microstrip stepped impedance resonator bandpass ilters and diplexers or mobile communications," IEEE MTT-S, Int. Microwave Symp. Dig., June 996, pp [6-6] L. Yo-Shen, C. Po-Ying, and L. Chun-Lin, "Compact parallel-coupled microstrip diplexers with good stopband rejection," Asia-Paciic Microwave Con., Singapore, December 9, pp.6-64 [6-7] G. Tudosie and R. Vahldieck, "An eicient design approach or planar microwave multiplexers," 34 th European Microwave Conerence, Amsterdam, Netherlands, October 4, pp. 9-3 [6-8] D. ayniyev, D. Budimir, and G. ouganelis, "Microstrip ilters and diplexers or WiMAX applications," IEEE AP-S/URSI Int. Symp. Dig., June 7, pp [6-9] J. D. Rhodes and R. Levy, "A Generalized Multiplexer Theory," IEEE Trans. on Microwave Theory and Tech., vol. 7, no., pp. 99-, February 979. [6-] W. Min-Hang, H. Cheng-Yuan, and S. Yan-Kuin, "A Hairpin Line Diplexer or Direct Sequence Ultra-Wideband Wireless Communications," IEEE Microwave and Wireless Comp. Lett., vol. 7, no. 7, pp. 59-5, July 7 6

140 [6-] D. ayniyev, D. Budimir, and G. ouganelis, "Miniaturized microstrip ilters and diplexers or wireless communication systems," Microwave and Optical Technology Lett., vol. 5, no., pp. 7-7, February 8 [6-] Y. Tae-Yeoul, W. Chunlei, P. epeda, C. T. Rodenbeck, M. R. Coutant, L. Ming-yi, and C. Kai, "A - to -GHz, low-cost, multirequency, and ullduplex phased-array antenna system," IEEE Trans. on Antennas and Propagation,, vol. 5, no. 5, pp , May [6-3] B. Strassner and K. Chang, "Wide-band low-loss high-isolation microstrip periodic-stub diplexer or multiple-requency applications," IEEE Trans. on Microwave Theory and Tech., vol. 49, no. pp. 88-8, October [6-4] D. ayniyev and D. Budimir, "Microstrip three-port 4-channel multiplexers using dual-band bandpass ilters or wireless applications," IEEE AP-S/URSI Int. Symp. Dig., July 8. 7

141 7. INTEGRATED ANTENNA FILTERS AND ANTENNA DIPLEXERS FOR WIRELESS APPLICATIONS 7.. Introduction Microstrip patch antennas, proposed in 95 s, consist o a radiating patch on one side o dielectric with a ground plane on the other side [7-]. These are low-proile, light weight antennas, which are used in a wide range o modern microwave systems, especially in aerospace and mobile applications. The main advantages o microstrip antennas are low cost o production and the possibility to integrate with microwave integrated circuits and to abricate eed and matching circuits simultaneously with antenna structure. Dual-requency and dual-polarization microstrip antennas can also be easily made [7-]. The main disadvantages o microstrip antennas are low gain, narrow bandwidth, and poor eiciency especially or antennas built using high dielectric substrate or easy integration with MIC RF ront-end circuitry. Although integration o patch antennas with ilters can be used to improve bandwidth and gain [7-3], the main purposes o such an integration is the reduction o size o the microwave ront-end [7-4], [7-5], suppression o higher order antenna s resonances [7-6] and the creation o wideband antennas with narrow band intererer rejection characteristics, or which band-stop ilters are used [7-7]. Dual-band patch antennas can be integrated with diplexers to reduce component count in dual-band wireless systems, in which diplexers are used to separate high and low bands o antennas [7-8], [7-9]. This chapter presents applications o ilters and diplexers discussed in previous chapters in integrated antenna ilters and antenna diplexers. The integration o inset-ed rectangular patch antenna with pseudo-interdigital bandpass iler is presented in section 7.. As a result o this integration, suppression o the irst and the second spurious harmonics o antenna has been achieved. Section 7.3 presents integration o multiband patch antenna with a diplexer. This integration was used to suppress the antenna s peaks that are out o the passbands o the diplexer s ilters and to separate physically bands o antenna. The integration o the dual-band multi-resonators microstrip-ed patch antenna with microstrip diplexer and ilter is presented in section 7.4. Improvement in perormance o the antenna and the physical separation o channels has been achieved as a result o integration. 8

142 7.. Integrated Antenna Filters with Harmonic Rejection A rectangular microstrip patch antenna is a basic coniguration o a microstrip antenna. The main disadvantages o this coniguration are narrow band and spurious harmonics. Suppression o spurious harmonics o antenna can be achieved by, or example, etching a U-slot in the antenna s patch [7-], or by designing special eeding technique using proximity coupling [7-]. The most obvious solution to the spurious harmonics problem is an integration o the antenna with a lowpass or bandpass ilter [7-4]. One o the main challenges o such an integration using a single layer microstrip is that or microstrip patch antennas the most preerable type o substrate is a thick substrate with a small dielectric constant. Using this substrate, better eiciency and larger bandwidth o the antenna can be achieved. For microstrip ilter, on the contrary, thin substrates with high dielectric constant are preerable as employment o this type o substrate reduces radiation losses and size o ilters. To address this issue composite substrates and multilayer solutions can be used [7-]. Another challenge is the size o the integrated antenna ilters. The necessity o using impedance matching in the eeding o antenna can increase the size o the circuit substantially [7-6]. The proposed integrated antenna-ilter is a good solution or both o these challenges as compact pseudo-interdigital bandpass ilter designed using low dielectric constant substrate will be used as a replacement o the impedance transormer employed as a eeding line o microstrip patch antenna. The layout o inset-ed microstrip patch antenna is shown in Figure 7-. The length o the patch is approximately equal to hal the wavelength. The width and length o antenna can be ound rom ormula [7-3]: W c ε + r =.5 c L = L ε e (7-) (7-) 9

143 where is resonance requency, L is length extension due to the ringing capacitance with a value that can be ound rom (7-3). For a.867 mm thick substrate with dielectric constant., and the resonance requency =. 4 GHz, using Eq. (7-) (7-3) the width is equal to 49. mm and the length 4.5 mm. As the width o the patch does not aect the resonance requency and aects only the gain o antenna, its value o 4 mm has been chosen in order to decrease the simulation time..4h L = ( ε +.3) W ( ε +.58) +.8 e e W h h +.64 (7.3) Figure 7-: Layout o microstrip inset-ed patch antenna. The length o inset distance X cannot be ound using some closed orm expression. It was reported that a shited cosine-squared unction describes the variation o the resonant input resistance with the eed location [7-4]. R in π = Acos n B ( X ) (7-4) 3

144 where X = X L and parameters A and B depend on the notch width S and the n geometry o the substrate. In order to obtain the initial approximate value o the X, parameters A and B given in [7-4] or the ε =. 4 substrate with the width o notch S equal twice the width o eeding line, were used. Ater a ew steps o tuning and iterations, the inal dimensions o the antenna were chosen to be L = 4. 7 mm, W = 4mm, S = 6 mm, X =. 8 mm, and the width o the 5 Ω eeding line r w =.6mm. From the simulation results, the undamental resonant requency o this antenna is.4 GHz, and the irst spurious response is at 4.64 GHz. For integration with the designed antenna pseudo-interdigital SIR bandpass ilter discussed in section 5.4. has been used. The impedance ratio R =. 6 has been chosen and the ilter is designed with a center requency at.7 GHz and with FBW = 3.5%. The irst spurious passband o ilter is centred at 8.3 GHz, thus the simulated the ratio o the irst spurious resonance requency to the undamental resonance requency is = 3. S 75, which is almost equal to the calculated value o The layout o the designed ilter is analogous to the one depicted in Figure 5-9, and the simulated perormance o the ilter is similar to the one shown in Figure 5-. As the next step, the eeding line o antenna has been replaced by the designed ilter. The layout o the integrated antenna ilter is shown in Figure 7-. The additional transition section consisting o microstrip taper and meander line sections is used to improver impedance matching [7-5]. Figure 7-: Layout o microstrip antenna ilter. 3

145 The integrated antenna ilter has been simulated using ADS Momentum and the simulated S coeicient o antenna-ilter is shown in Figure 7-3 by the solid line. The simulated S coeicient o the inset-ed patch antenna is shown in the same igure by the dashed line or comparison. Figure 7-3: Simulated S o inset-ed antenna (dashed) and antenna ilter (solid). As it can be seen rom Figure 7-3 the irst and the second harmonics o the inset-ed antenna were suppressed in the antenna ilter. The two peaks appearing in the antenna ilter s response at 7.85 and 8.4 GHz are due to the second passband o bandpass ilter. The simulated radiation patterns o both antenna and antenna ilter at undamental resonance are shown in Figure 7-4. It can be seen rom this igure that integration o antenna with ilter has not caused much alteration in radiation pattern but only decrease o gain rom maximum 6.8 db or antenna to 5.4 db or antenna ilter. 3

146 Figure 7-4: Simulated radiation patterns, E-plane (red) and H-plane (blue): (a) Patch antenna; (b) Integrated Antenna Filter. 33

147 7.3. Microstrip Antenna Diplexers or Wireless Communications The integration o microstrip antennas with ilters is used to suppress the spurious harmonics o antennas or to improve antenna s characteristics at the undamental resonance. The integration o microstrip antennas with diplexers can be used to reduce the number o components in wireless system [7-8] and to separate physically the signal rom the dierent antennas [7-9]. In this section, the integration o multiband antenna with diplexer or physical separation o antenna s bands is presented. The integrated antenna diplexers can be used in the design o wireless systems operating on multiple bands, such as or example WLAN IEEE 8. standard operating at GHz and GHz and WiMAX IEEE 8.6 standard, operating at.3-.7 GHz, GHz, and GHz. The layout o the proposed integrated antenna diplexer is shown in Figure 7-5. Figure 7-5: Layout o proposed microstrip antenna diplexer 34

148 The size o the whole subsystem is mm; it consists o a compact diplexer, constructed rom two ilters, and a patch antenna. The integration o the antenna with diplexer has been arranged by connecting the common port o the diplexer with the microstrip line eeding antenna. As both lines are 5 Ohms lines, no additional impedance matching was applied. The design speciications or the proposed antenna are, the dielectric material selected or the design is FR4 which has a dielectric constant o 4.4 and a height o substrate h =. 57 mm. The antenna is ed by a 5 Ω microstrip line. The main advantage o using a transmission line eeding is very easy to abricate and simple to match by controlling the inset position and relatively simple to model. The broadband characteristic o a microstrip patch antenna with dierent shapes has been conirmed by many published results and several designs o the broadband slots antenna has been reported [7-6], [7-7]. The T-slot has been applied on the patch antenna to let the current path travel longer than its usual way in order to achieve multiband perormance to be used in wireless applications. This is similar to the dual-band perormance o microstrip patch antennas with dual U-slot in which surace-current path has a dierent length or dierent resonance requencies. Thus, at.5 GHz surace current has a longer path and it has to go around T-slot. It has been ound that, by inserting the T-Slot to the patch and optimising width and length o slot, the required resonant requencies can be achieved. The proposed antenna has been simulated with commercially available package HFSS sotware which is based on the inite element method. The antenna was designed to operate in dual-band mode, mainly or the wireless applications standard.5 and 5. GHz. The simulated S o antenna is shown in Figure

149 Figure 7-6: Simulated S o proposed antenna. The microstrip diplexer is built using two compact pseudo-interdigital SIR bandpass ilters with extended stopband which were discussed in The ilters are combined using a common eeding technique based on the common-transormer diplexer. This combining method was discussed in 6.3. The ilters are designed or a.57 mm thick substrate withε = The impedance ratio o SIR in both ilters is.7 and the r calculated spurious to undamental requencies ratio is = 3. S 5. Both ilters have FBW = 3.4% and the irst ilter has a passband centred at.4ghz, the second has a passband centred at 5 GHz. The layout o ilters is similar to the one shown in Figure 5-9 and can be seen in Figure 7-5. The simulated S-parameters o the ilters are similar to the response shown in Figure 5-. Tthe simulated S-parameters o diplexer are shown in Figure

150 Figure 7-7: Simulated S-parameters o microstrip diplexer. It can be seen rom the simulation results that the diplexer has a channel isolation o about 5 db [7-8]. The insertion loss o each channel is almost the same as the insertion loss o bandpass ilter used in the corresponding channel, whereas the return loss in the passband is decreased to 5 db. The integrated antenna diplexer structure was simulated by the Agilent ADS electromagnetic simulator. The simulated S-parameters are presented in Figure

151 Figure 7-8: Simulated S-parameters o microstrip antenna diplexer. As a result o the integration o the antenna with the diplexer, the high requency band o antennas centered at 5. GHz is physically separated rom the low requency band o antenna centered at the.5 GHz. Unwanted spurious peaks o the antenna appearing at GHz and 3.9 GHz were suppressed by the diplexer. The total structure demonstrates good isolation o channels rom each other. 38

152 7.4. Integration o Microstrip Filters/Diplexers with Dual-band Multi- Resonator Microstrip-Fed Patch Antenna In the ollowing section, the integration o microstrip diplexers and ilters with dualband multi-resonators microstrip-ed patch antenna is presented. The integration with the diplexer is used to separate physically bands o antenna. The integration o antenna with dual-band ilters is employed in order to improve the bandwidth o the antenna. The procedure used to develop integrated antenna diplexer is the same as the one described in the previous section with dual-band monopole patch antenna used instead o multiband microstrip patch antenna. The layout o the proposed structure is shown in Figure 7-9. Figure 7-9: Layout o proposed antenna diplexer. 39

153 The multi-resonator microstrip-ed patch antenna proposed in [7-9] is used or a broadband dual-requency operation. The antenna consists o two resonators separated by a U-shaped slit. The lengths o resonators L and L are around a quarterwavelengths at the irst and second resonant requencies respectively. This antenna is the printed monopole antenna with eeding through proximity coupling. The operational principle o this antenna is equivalent to the operational principle o the conventional monopole antenna made o metallic wire or rod and which consists o one radiating arm. Very requently monopole antennas are used above a ull or partial ground plane and the relection rom this ground plane produces a virtual monopole below the ground. Thus, monopole antennas in this case can be evaluated in the same way as dipole antennas, which consist o two radiating arms with eed point at the center. The current distribution o these antennas is sinusoidal standing wave with current at the end o the radiating arms equal to zero and at the eeding point current is the maximum when dipole antenna is λ long and monopole antenna is λ 4 long. The radiation pattern o dipole antenna is slightly lattened torus and it is rotationally symmetric around the axe along which radiating arms are positioned. For monopole antenna above ground plane, radiation pattern is the upper hal o dipole antenna and the directivity o monopole antenna is twice o its dipole counterpart due to the power to the lower hal space relected to the upper space. One o the main reasons why the most popular size o dipole antenna is hal wavelength and or monopole antenna is a quarter wavelength respectively is that in this case the input impedance o antenna can be easily matched with a standard transmission line. Moreover, antenna o these sizes is a good trade-o between the directivity and size. The antenna shown in Figure 7-9 is ed by a 5 Ω transmission line printed on the opposite side o the substrate. The length o the eeding stub is tuned or impedance matching on both resonant requencies. The antenna was designed or Rogers RT 588 substrate with thickness.57 mm and dielectric constant.. The designed antenna was simulated with the commercially available package HFSS sotware which is based on the inite element method. The simulated return loss o antenna is shown in Figure 7-. 4

154 Figure 7-: Simulated return loss o multi-resonator patch antenna. The antenna was designed to resonate at the requencies.37 and 5.3 GHz. The bandwidth, or return loss <- db, o the irst band o antenna is 3.5% and or second band is.6%. The diplexer integrated with the antenna is equivalent to the diplexer used in the previous section, but designed or a substrate with dielectric constant.. The impedance ratio o the SIR o the bandpass ilters was chosen to be.5 with the ratio o spurious to undamental harmonic requencies calculated to be S 4. Such an impedance ratio was chosen to extend urther the stopband o the irst ilter in order to diminish interaction with the passband o the second channel. Filters were designed to have center requencies at.4 GHz and 5.3 GHz respectively. The S-parameters o the microstrip diplexer, simulated using EM Sonnet are shown in Figure 7-. The isolation between the bands is db or channel one and 5 db or channel two. The passband perormance o the second ilter was deteriorated by the losses introduced due to the big impedance step. To avoid this in uture designs, a smaller impedance step or SIR o the second, high requency band ilter, will be used. 4

155 Figure 7-: Simulated S-parameters o microstrip diplexer. The integrated antenna diplexer was simulated using HFSS and simulated S-parameters are shown in Figure 7-. Figure 7-: Simulated S-parameters o integrated antenna diplexer. As a result o the integration o antenna with diplexer, dierent bands o antenna were physically separated. The total structure demonstrates good isolation o channels rom 4

156 each other. An isolation o db was achieved or channel one and o 3 db or channel two [7-]. The integration o antennas with the bandpass ilter can also be used to improve the perormance o antenna [7-3]. The integration o dual-band antenna with the dual-band ilter was investigated in order to ind the eect and alteration o the perormance o antenna due to the integration with the ilter. The same multi-resonators microstrip-ed dual-band patch antenna, used or the integration with the diplexer, is employed or integration with the dual-band microstrip ilter. The dual-band bandpass ilter equivalent to the ilter discussed in section in 5.3 was designed or Rogers RT 588 substrate with thickness.57 mm and dielectric constant.. The passbands o ilter are centred at.45 and 5.55 GHz and FBW is equal to 3.4% or band one and 3% or band two. The impedance ratio o SIR o ilters was chosen to be equal to.4 with spurious to undamental resonance requencies ratio calculated to be equal =. S. This ratio extracted rom the simulation results is equal to.7. The perormance o the designed ilter is similar to the one depicted in Figure 5-6 with center requencies o bands shited to.45 and 5.55 GHz. The layout o the integrated dual-band antenna ilter is shown in Figure 7-3. The dual-band ilter was used to replace the microstrip eeding line [7-]. 43

157 Figure 7-3: Layout o integrated dual-band antenna ilter. The integrated dual-band antenna ilter was simulated with using Ansot HFSS package. The simulated return loss is shown in Figure