Dielectric Bandstop Resonator Richard Filters Chan Kayip Submitted in accordance with the requirements for the degree of Doctor of Philosophy The University School of Electronic Leeds of and Electrical April Engineering 2011 The candidate confirms that the work submitted is his own and that has beengiven where reference has beenmade to the work of credit appropriate others. This copy has beensupplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement 1 Abstract Dielectric resonators have been widely employed in wireless and satellite commuloss low fashion large Q due to inherently them to their allowing nication systems in bandwidth filters. Recent has these resonators adopted progress and narrow The demanding low for specifications. volume and mass applications requiring dielecfilters bandpass using technology at present consists of an assortment of filters little but bandstop is there employing tric resonators published material on front filters frequencies the Bandstop desirable to at are suppress such resonators. end of wireless communication imperait is demands, future To systems. meet dielectric filters both in these the to tive reduce costs of volume and weight using resonators. This thesis presents compact mono-mode and dual-mode bandstop dielectric resonator structures. The former consists of a dielectric-loaded filter that offers a miniaturised ters requiring waveguide cavity fildielectric typical to resonator version cavity high unloaded Qs. The niono-mode filter described is ideal for Q lower specifications a resonator to replace common coaxial relaxed requiring filters. high For bandwidth, requiring applications resonator this resonator is im- A by line. dielectric to transmission coupling ring resonator a proved a coaxial dual-mode bandstop resonator is developed taking advantage of the geomnovel etry of a cylindrical puck within a single shielded cavity to create two degenerate modes with equal resonant frequency, effectively replacing two mono-mode cavities. Miniaturisation is achieved by sitting the dielectric puck at the base of the cavity and correct phase separation between the orthogonal modes is produced from a curved uniform transmission line. Abstract 11 The mode behaviour is observed in the physical realisations using a 3D FEM Advanced filtering solver. functions using prescribed reflection zeros is demon- dual-cavity, dual-mode bandstop the with simulation resonator where of a strated inter- and intra- cavity couplings are controlled. discussed in this thesis will provide cost-reduction highQ bandstop filters. requiring systems The miniaturisation techniques for microwave communication 111 Contents Acknowledgments vii List of Figures viii List of Tables xvii 1 1 Introduction 1.1 Applications of Microwave Filters .................. 1.2 Review of Dielectric Resonators ..... 1.2.1 Background 1.2.2 Dielectric Resonator Filters ..... ..... ...... 5 . ..... ........ ..... ..... 1.3 Scope of the Study ..... 3 6 ...... ..... ... ... ..... 17 ................ 18 1.4 Organisation of Thesis ........................ 2 Filter 20 Design 2.1 Introduction 8 ... ... 2.2 Types of Filters . ... ..... ... 2.3 Impedance Transformations ... .... ..... ..... ...... ....... . .. ........ ...... ..... . .... . ... 20 21 23 iv Contents 2.4 Lowpass to Bandstop 'Transformation 2.5 Transfer Functions 2.6 ................ 24 .......................... 2.5.1 Butterworth or Maximally Flat Approximation 2.5.2 Chebyshev Approximation 2.5.3 Inverse Chebyshev Response 2.5.4 Generalised Chebyshev Response Direct-Coupled 2.6.1 3 Dielectric Bandstop Filters Quality Factor Resonator . ..... ..... . .. ..... ... 29 .............. ... . ..... ......................... Quality Factor 3.3 Coupling to a transmission line 3.4 Configurations ... . ..... ..... . ..... 3.5.1 Cohn's Model ........ ... ....... HFSS Finite Element Model Compact .... Bandstop ....... ..... 43 . ..... 44 ...... ... ... 53 ................ . .......... . ..... Filter . .... TElos Rectangular Waveguide Resonator 46 50 .............. 3.5.3 ... ..... . .......... Mode-Matching Model ... ..... . .......... 3.5.2 Dielectric-Loaded 38 39 ............................. . ... 30 38 Filters .... 27 36 3.2 4.2 ...... 26 . .... Basic Properties of Dielectric Resonators 4.1 Introduction 25 .................. 3.1 3.5 Resonant Modes 4 23 55 59 . ....... .............. . ... 59 60 y Contents 4.3 Configuration 4.3.1 Single Resonator Design 4.4 FEM Simulations ...... 4.6 Fabrication of Filter 5 ...... . ..... ...... 91 ........... 94 Filter ... . ..... .... . ..... ..... 94 95 ........... 5.3 Configuration of Proposed Resonator ....... Single Cavity Design 88 . .. ..... ..... 5.2 Dual degenerate HEEII mode . ........ 5.4 74 . ............ Bandstop Resonator DR Bandstop 5.1 Introduction 69 ...... . .......... .... Coaxial Dielectric-Loaded Dual-Mode 66 ................... 4.5 4th Degree Chebyshev Design . ...... 4.7 64 Filter Proposed of ................... . ........ 96 102 ......................... 106 5.4.1 FEM Simulations for single cavity . ......... 5.4.2 113 Fabrication and measurements of dual-mode single cavity . 5.5 4th Degree inverse Chebyshev Design 5.5.1 5.7 Fabrication of filter 5.8 Direct-coupled .... ..... 117 ................ Inverse Chebyshev element values 5.6 HFSS optimisation . ... . .... ... . ..... ........... ... ... 127 .................. 6 Conclusions 6.1 Future Work 120 125 .......................... DR bandstop filter 118 137 ...... ..... ....... . ..... ... ... 139 Contents A Conferences References vi and Publications 141 142 Vii Acknowledgments Firstly I would like to thank Ian Hunter for his invaluable supervision and guid- ance throughout this work. Thanks also to Filtronic for funding this work. Many thanks to Terry Mosely and Nick Banting for the amount of time spent discussing the construction of the filters. I would also like to thank Richard Cameron for his comments in this thesis. A big thank you to my Mother and Father for making all this possible. viii List of Figures 1.1 RF front-end of a cellular radio base-station . ..... 1.2 ... 4 ... 4 Typical diplexer response ....................... 1.3 TEola resonant mode dielectric resonator ...... . .. ..... 1.4 E-field plots of shielded TEO,& mode dielectric resonator ... 1.5 Structure of 6.9 GHz DR filter .............. 1.7 Configuration of a TM016 mode DR filter . .... 1.8 Dual-mode configuration of a DR filter .... .9 . ... .... . ... . .... ... ..... 7 . .. ..... 1.6 TEola DR filter for cellular base-station application 6 ... 9 10 11 1.9 Tuning screw orientations for cross couplings in an elliptic function DR dual-mode filter .......... ........ ... ..... 11 1.10 Conductor-loaded dual-mode DR filter configuration ........ 12 1.11 Quadruple-mode DR filter configuration 13 . ....... ... ... 1.12 Configuration of a 6th degree mixed-mode elliptic function DR filter 14 1.13 Structure of 6th degree mixed-mode DR filter . ..... . ..... 1.14 Configuration of 41' order combined conductor and dielectric-loaded filter .................................. 14 15 ix List of Figures 1.15 Bandstop filter with DRs placed transversely along waveguide 1.16 Bandstop filter with DRs placed outside waveguide 16 .. 16 ........ 1.17 Microstrip DR bandstop filter with quarter-wavelength unit elements 17 2.1 Lowpass prototype ladder filter networks 21 .............. 2.2 Impedance inverter terminated in a load ........ 2.3 General Nth degree inverter coupled lowpass prototype inductors (b) capacitors .... ..... 2.4 Lowpass to bandstop transformation . . .... . .... (a) with . ... . .... ....... 22 ... . ..... 22 24 2.5 Bandstop transformation of an inductor and capacitor ....... 24 2.6 Frequency responseof butterworth lowpass filter for varying N .. 25 2.7 Frequency response of a Chebyshev lowpass filter 26 2.8 Frequency response of an inverse Chebyshev filter 2.9 Highpass prototype for inverse Chebyshev filter ... . ... 2.10 Frequency response of an elliptic lowpass filter ..... 2.11 N+2 multicoupled resonator circuit ...... . ... . .... ..... 28 ...... 29 ...... 29 ...... ... ... 2.12 4th degree N+2 coupling matrix with all possible cross-couplings. Core NxN matrix within double lines ..... ... ... ..... 2.13 Direct-coupled (4-2) bandstop filter : (a) coupling-routing (b) realisation with coaxial cavities ...... ..... Transmission bandwidth response displaying . ... ... ... ..... 31 diagram 35 ...... 2.14 Direct-coupled cul-de-sac (4-2) bandstop filter (a) : coupling-routing diagram (b) realisation with waveguide cavities .... ... ... 3.1 31 36 resonant frequency and 3 dB ..... ..... ... ... 42 List of Figures 3.2 X 43 Magnetic field coupling of a DR to rectangular waveguide ..... 3.3 Magnetic field coupling of a DR to microstrip line ........ 44 . 3.4 Three DR configurations: (a) rectangular resonator, (b) cylindrical resonator, L<D, 3.5 (c) and cylindrical resonator, L>D... 44 ... 45 Commonly used DR structure ..................... 3.6 Field plots of common DR modes ......... 3.7 Typical DR mode chart . .... ... ... . ..... ....... 47 48 ... . ..... 3.8 Mode chart of a DR in cavity as a function of aspect ratio 48 .... 3.9 Mode chart of a DR in cavity as a function of aspect ratio with improved spurious performance . ....... 49 ...... ..... 3.10 Classification of HE modes showing E-field component for (a) electric wall (b) magnetic wall ... . ..... ... ..... ..... 49 3.11 Cohn's second-order DR model showing a DR inside a magneticwall waveguide below cutoff ............ 51 . ... . .... 3.12 Improved model for a shielded DR .................. 51 3.13 Generalized multilayer cylindrical DR ....... 54 ... ... ... 3.14 Mesh with tetrahedral elements for maximum flexibility to approximate shape of 3D dielectric puck ....... ...... ..... 56 3.15 Finite element method analysis of dielectric puck with axial hole: (a) basic geometry, (b) view of mesh with 0.2A (c) view of mesh, mesh with 0.1A mesh ....... .... ... ... ..... ... 4.1 Field distribution of TE101rectangular cavity ..... ... 57 61 ... 4.2 Schematic of third-degree strip transmission line bandstop filter . 65 List of Figures xi 65 4.3 Schematic of third-degree cavity waveguide bandstop filter 4.4 Schematic of (a) Circular coaxial transmission line coupled to DR cavities (b) Cross-section of feasible realisation .... 66 ........... 4.5 Structure of TE10 mode dielectric bandstop resonator 66 . ..... 4.6 Frequency responseof air-filled square coaxial TEM line with circular centre conductor, D= 10 mm and r=4.68 mm . ..... 4.7 Details of TEIOamode dielectric bandstop resonator .... 69 . 70 .... 4.8 Electric field of TEloa mode DR: (a)Vector Lines (b)Magnitude 71 . 4.9 Magnetic field of TE106mode DR: (a)Vector Lines (b)Magnitude . 71 4.10 H-field plots of fundamental mode DR coupled to coaxial line: (a) Magnitude acrosstransverse plan (b) Vector view cut through middle (c) Magnitude cut through middle ...... 72 .. . ....... 4.11 Resonant frequency versus DR length for various coupling gaps .. 73 4.12 3 dB bandwidth versus coupling gaps for different DR lengths .. 73 4.13 Ladder network ............ 76 ...... .......... 4.14 Transforming resonators of equivalent Q (a) Reactance slope parameter (b) Transformation of capacitor to magnetically-coupled resonator ..... . ..... .... ...... 79 . .......... 4.15 Prototype circuit for 4th degree Chebyshev bandstop filter 4.16 Simulated results of prototype bandstop filter ..... 82 .... network for 4th degree Chebyshev ........ ..... ..... ..... . 82 4.17 Normalized reactance slope parameter against spacing of resonator from coaxial line ... ............. ..... ...... 83 List of Figures 4.18 3 dB bandwidth X11 in MHz MHz 2°d 11t 5.1 8.6 and resonator of = = Chebyshev design with fo = 1.85 GHz ... ... .......... 84 4.19 Resonant frequency against spacing of uncoupled dielectric side with sidewall 85 ............................. 4.20 Simulated resonant frequency against depth of tuning screw ... 85 4.21 HFSS simulated tuned 1st resonator, 3 dB bandwidth = 5.11 MHz fo GHz 1.8502 and = 86 ......................... 4.22 HFSS simulated tuned 2nd resonator, 3 dB bandwidth =9 MHz fo and = 1.8498 GHz .... ... ..... ..... ........ 4.23 Schematic of HFSS design of final filter .... 4.24 HFSS simulated response of filter to be fabricated 87 ...... ..... 86 87 ......... 4.25 HFSS simulated wideband response of filter to be fabricated ... 88 4.26 Practical resonator design 89 ...................... 4.27 Fabricated 4th degree Chebyshev Bandstop filter . ... ...... 4.28 Interior of fabricated 4th degree Chebyshev bandstop filter 4.29 Measured frequency response of Chebyshev bandstop filter .... . ... 89 90 90 4.30 Measured wideband frequency responseof Chebyshev bandstop filter 91 4.31 TNIo16dielectric-loaded bandstop resonator: (a) Schematic (b) Hfield plot in dielectric region .... . ..... ... ... ..... 4.32 Dimensions for experimental coaxial dielectric-loaded resonator, L 80mm, W= 40 mm, Ll = 10 mm, L2 9.57 = = mm . ... ... 4.33 Simulated transmission response for experimental resonator for various inner coaxial transmission line radii, r . ..... ..... 92 92 93 List of Figures 5.1 Field distributions plots ....... 5.2 Xiii (b) (a) H-field E-field dual HEEII plots mode of ... ... ..... ..... ... ..... ... 97 Diagram of dielectric puck in perfect conductor cavity ....... 5.3 Mode chart variation of H/h with frequency ......... . .. 5.4 Mode chart variation of h2/hl with frequency ..... ... 5.5 Mode chart variation of R/r with frequency ...... 96 ... 98 99 100 . ..... 5.6 Topologies for coupling of transmission line to dual-mode dielectric (a) puck: weakly coupled probes (b) probes for maximum coupling (c) side view ..... ............. ... ..... ... 100 5.7 Coupling, of right-angle transmission line to dual-mode dielectric (a) (b) top puck: side view ................... view 101 5.8 Coupling mechanism for dual-mode HEEII bandstop resonator: (a) top view (b) side view 5.9 102 ........................ Circuit model for coupling post 102 ................... 5.10 Structure of HEEII mode dielectric bandstop resonator: (a) Corner (b) Cross section (c) Top view view ... ...... ... ..... 5.11 Mode chart variation of ri/r with frequency . ..... ... ... 103 104 5.12 Coaxial transmission line with various centre conductor curvature radii (a) c= 40.25 mm, e= 63.2 mm (b) c= 29 mm, e= 68.1 mm (c) c= 19 mm, e= 72.77 mm . ..... . .... 5.13 Frequency response of coaxial transmission . .. ...... 104 line, outer and inner conductor diameters, 13.5 mm and 6 mm respectively, for various radii of inmost coaxial conductor wall curvatures .... ... 5.14 Details of HEE11 mode dielectric bandstop resonator . ... ... ... 106 107 List of Figures XIV 5.15 Field plots of single degenerate HEE11 mode coupled to transmis(b) (a) line: E-fields 11-fields in xy- and in sion xy- and xz-plane yz-plane 108 ................................ 5.16 Field plot of first higher order spurious mode, TEO,&: (a) Side view (b) Top view (c) . ..... ........... .. . ... ..... 109 5.17 Dielectric puck with removed ring section for improved spurious: (a) 3D view (b) Top view (c) Side view ...... ... ... ... 109 5.18 Diagram of orthogonal frequency tuning and coupling screws arrangement 110 ............................... 5.19 Frequency response for penetration 110 of cross-coupling screw .... 5.20 Frequency response for penetration of single resonant mode tuning 111 screw .................................. 5.21 Optimisation of coupling rod diameter 5.22 HFSS simulation of experimental ...... . ........ filter for fabrication . ...... ..... ............. 113 ....... 5.23 HFSS simulation of the spurious mode of the prototype fabrication 112 filter for 113 ...... 5.24 Fabricated single cavity of HEE11 dual-mode bandstop filter 114 ... 5.25 Measured frequency response of HEEII experimental bandstop filter 115 5.26 Measured Chebyshev responsewith tuning screws of HEEII single cavity bandstop filter . ..... . ......... ... ... ... 116 5.27 Inverse Chebyshev frequency responseof HEEII single cavity band116 stop filter . ..... ........ ............ . .... 5.28 Spurious frequency responseof HEEII single filter bandstop cavity 117 5.29 Matched inverse Chebyshev filter prototype 118 ....... .... . List of Figures xy 5.30 Circuit network of inverse Chebyshev elements ........... 118 5.31 Inverse Chebyshev bandstop filter prototype 118 ............ 5.32 4th degree circuit model inverse Chebyshev bandstop filter 120 .... 5.33 4th degree circuit model inverse Chebyshev bandstop filter 121 .... 5.34 Top view of HFSS simulation with variables for optimisation ... 122 5.35 Variation of resonant frequency with DR circular cavity height .. 122 5.36 Variation of 3 dB coupling bandwidth with coupling post to puck 123 spacing ................................. 5.37 Final HFSS simulated model for inverse Chebyshev bandstop filter 124 5.38 Frequency response of optimised HFSS design for inverse Cheby124 shev bandstop filter .......................... 5.39 Fabricated 4th degree inverse Chebyshev bandstop filter 125 ...... 5.40 Measured frequency response of inverse Chebyshev bandstop filter 126 5.41 Measured wideband frequency responseof inverse Chebyshevbandstop filter . ... ........ .......... 127 . ........ 5.42 Frequency response of direct-coupled (4-2) bandstop filter .... . 5.43 Coupling routing diagram of a direct-coupled (4-2) bandstop filter 129 129 5.44 Configuration of HEE1I dual mode direct-coupled (4-2) dielectric bandstop filter .... . ..... ....... . ..... . ..... 130 5.45 Variation of coupling coefficient with iris width of length 3 cm and thickness 2 cm ............................. 132 5.46 HFSS model of optimised direct-coupled HEEII dual-mode bandstop filter . ... ... ....... . .... ... ..... . ... 132 List of Figures Xvl 5.47 Simulated response of optimised direct-coupled bandstop filter HEEII dual-mode 133 ............................. 5.48 Coupling routing diagram of cul-de-sac direct-coupled (4-2) bandfilter stop . .... . ..... .... .... 134 . ........... 5.49 Frequency responseof cul-de-sac direct-coupled (4-2) bandstop filter134 5.50 HFSS model of optimised cul-de-sac HEEII dual-mode bandstop filter ........ . ..... .... .... ..... ..... .. 135 5.51 Simulated response of optimised cul-de-sac HEEII dual-mode band- stop filter . .... . ..... ..... ..... . ......... 136 xvii List of Tables 3.1 High-Q dielectric materials . ....... ... ... ........ 3.2 Computed and measured resonant frequencies of DRs . ... ... 40 55 banddielectric TE105 dimensions Typical 4.1 mode and performance of resonator stop .... . ... . .... . .... . .......... 69 isofive frequencies Qus first Simulated of 4.2 modes and of resonant lated dielectric rectangular cavity resonator ....... 4.3 First five resonant modes of prototype resonator .... 4.4 Filter specifications 71 ...... ... ... 74 74 .......................... 5.1 First five resonant modes of a dielectric puck . ..... ... . .. 96 5.2 Typical dimensions.and performance of HEEII dual-mode dielectric bandstop resonator ... .... . ..... ..... ... ... 106 5.3 First five modes in a dielectric puck in contact with base of cavity 109 Filter specification for 4th degree inverse Chebyshev bandstop filter 118 5.4 5.5 Requirements for resonant frequency and bandwidth for each mode 123 5.6 Filter specification for 4th degree direct-coupled bandstop filter .. 131 1 Chapter 1 Introduction With current trends in communication systems calling for lower manufacturing Qs, factors, higher high performance, resonating elements with quality costs and become a neccessity. These elements play a fundamental design in the of role filters as the resonator quality factor is proportional microwave becomes an important limiting to volume and factor. Typically, waveguide structures have been high Q high for their temperature stability and used bandallowing very narrow large frequency in domain, 900 MHz to 100 GHz. a widths The disadvantage is bulky and cumbersome filters are required that are expensive to produce and heavy. Microstrip excessively and stripline technology have been the main con- in bulky these removing waveguides in the majority stituents of microwave sys- tems and are used in the high frequency domain, 100 MHz to 30 GHz, to realise high bandwidth integration filters due to their low Q. Their small dimensions and ease of with microwave circuits are of great interest but their disadvantage is their low losses are usually compensated by active devices or superconducting technology. A miniaturisation technique providing a low-loss solution employs dielectric resDRs, as they allow a reduction in size inversely proportional to the onators, square root of the permittivity of the dielectric material used. In addition, the loss in a dielectric-loaded cavity with metallic shielding is dominated by the loss tangent owing to the dielectric material and minimally dependent on the outer 2 I Introduction loss. An dielectric improving losses is that this conare advantage with conductor losses due being to. more advanced materials produced, whereas metallic stantly have remained fairly constant with no signs of improvement, of superconductors. with the exception As a result, these resonators have the ability filters but better in terms of minimisation, are much waveguide as weight. This advantage can be seen in satellite communication inherently high-loss microstrip equivalent application. to function stability and systems where for DR disregarded technology a and stripline are In recent years, these low-loss DRs have led to the reali- lightweight small, reliable, of sation and stable microwave systems. In microwave filter technology, DRs have been preferred for their superior high Q, low loss and miniaturisation attributes. In recent years, motivation for more com- bulk for low demand have these increased ease of manufacture at cost pact and types of filters. For example, in wireless communications, a more cost-effective DR low-cost that can replace coaxial air-filled resonators with smaller, solution filters is a necessity. Further size-reduction techniques have been developed in the form of higher-order mode filters, [1]. These higher-order filters are mode design in and often rely on measured data to implement the recomplex more frequencies resonator and coupling coefficients that satisfy the equivalent quired With improved model. computer speeds, full-wave electromagnetic circuit field becomes increasingly software useful in simulating these 3D structures simulation reducing practical test times and enabling the filter designer to observe modalfield behaviour for different parameters. Although much work has been presented using DRs with bandpass filters, only a limited number of publications on bandstop filters employing DRs have been published and very little is known about dual-mode dielectric bandstop filters. Filters DRs coupled to microstrip line have been presented but require housing that with increase their volume, [2] and [3]. A triple mode hybrid reflection filter was also presented using two cubic dielectric resonators coupled together through a3 dB [4]. hybrid, The design requires complex tuning for each mode and quadrature is limited as it caters for filters of degree six and above. More conventionally, 3 1 Introduction Applications of Microwave Filters for lines DRs have been transmission to attenuacoupled waveguide mono-mode [5]. It but behaviour DR increases tion volume, each requires a cavity which also is the aim of this thesis to design bandstop filters using DRs making full use of their high Q and low loss to achieve miniaturisation techniques suitable for wire- less systems where the emphasis is on cost and not highly demanding low-loss dielecThe first for is to objective provide a solution a mono-mode performance. tric resonator bandstop filter providing a low-cost alternative to coaxial bandstop The second objective is to incorporate resonators. the hybrid dual-mode prop- dielectric resonators allowing the reduction in cavity number compared erty of to mono-mode resonators. The final objective is to propose an improvement for type to address shortcomings and demonstrate realisability resonator each functions. filtering This thesis provides an introduction vanced of ad- to size reduction for bandstop filters employing dielectric resonators that have potential for further filtering techniques and, therefore, only provides possibilities for the use of this implement fullly to advanced filter functions. structure 1.1 Applications Microwave of Filters Microwave filters are used to define wanted and unwanted frequency bands. They important role in terrestial, radio and satellite communications along with play an As communication radar systems. systems improve at a tremendous rate, the difficulty to meet filter specifications becomes more challenging. In a cellular base station, they perform important roles at different stages of the radio frequency, RF, front-end unit, figure 1.1. Typically, low loss is required in the passband high rejection of signals at the passband edges to give greater selectivity. with a This prevents a high level of cross-channel interference between the number of subscribers that share the spectrum available to them. A broad stopband and highly symmetrical frequency responseis usually preferred for bandpass filters, although asymmetrical designs be more adcan sometimes vantageous when distinguishing between two adjacent bands in the spectrum. 4 1 Introduction Ap)j)lirat on. ý of Alicro11(0'( Filtr .ý Antenna TX Filter Up-Converter BTX Power Amplifier RX Filter Down-Converter - 00 RX Low Noise Amplifier TX/RX Figure Diplexer 1.1: RF front-end of a cellular radio base-station This is the case for diplexers where a highly asymmetrical attenuation specifica- tion is needed as more rejection is required from each filter over the passband of the other filter, figure 1.2. Tx. Rx" S,, Frequency Figure 1.2: Typical diplexer response Bandstop filters have been widely used in many microwave circuits and systems [6], [7]. important In particular, narrowband reject, or notch, filters have become more in most microwave communications there are as systems and radar interferences signals and unwanted at air interfaces. more Systems that utilise the spectrum with interleaving spectra require notch filters to avoid interference between two operators if they are too close. For example, in the Advanced Mobile Phone System/Global System for Mobile communications extremely narrowband filters often require resonators factors Q with unloaded AMPS/GSM, these in excess of 25 000. To realise such filters, cavity structures measuring 9x9x 9 cm. at 2 GHz. are usually required per resonator leading to physically large devices. Microwave filters with both a compact size and high Q are desired. The 5 1 Introduction Review of Dielectric Resonators level dielectric bandstop filters be to a resonator provide would suitable proposed band, the on receive when transmitting, of rejection diplexer and amplifiers at communication 1.2 Review of Dielectric between the and vice versa system front-end units. Resonators Low-loss DRs or superconductor filters are capable of high Qs and although the latter may produce Qs in the order of 100 000, DRs do have the potential attain Qs exceeding 20 000. They are considerably to smaller than the size of a hollow resonant cavity operating at the same frequency, provided the dielectric is the of material of an order much greater than unity. constant DRs are com- in as short, solid shaped pucks and such a geometry, the common resonant monly denoted TEola is figure be 1.3. dipole, which may observed as mode a magnetic The electric field lines are concentric circles along the azimuthal axis and for DRs dielectric constant approaching 40, the typical stored electric energy with relative for TEoia mode is greater than 95% and over 60% for magnetic energy within the distributed The is remaining energy puck. into the surroundings, rapidly decaying from the Ceramics resonator surface. away used in constructing DR filters typi- dielectric have constants in the range 20 to 90, thus, DR filters gain a huge cally to compared advantage similar waveguide or coaxial filters when operating. size In addition, although planar filters are more convenient to fabricate and, consebulky in the majority replace can waveguides quently, of microwave systems, their low Q, only up to 500, limits them to moderate performance and cannot be used in demanding communication system applications. DR filters are then useful to fill the gap between waveguide and stripline technologies high the accomodating Qs needed and also a system integrability approaching that of planar resonators. Furthermore, they offer versatility and are adaptable to various microwave structures and coupling configurations. Unfortunately, the disadvantage of DRs is although their geometrical forms may be simple, an exact solution for Maxwell become more difficult to obtain than for hollow metal cavities. This is equations 6 I Introduction Review of Dielectric Resonators for fields from DRs in in the shielded metal cavities, which, uniform even more so isolated resonators become distorted due to the presence of metal boundaries, figure 1.4. However, boundary approximations are possible and simple resonant frequency equations may be derived. For example, the resonant frequency for an isolated TE01 mode dielectric cylindrical resonator is fo-34(2+3.45) a 1.1) Er 1 dielectric height is in in is the the the constant radius mm. mm a and Er where of the resonator. This formula has an accuracy of 2% for 0.5 < a/1 <2 and 30 < Er <50. For a resonator with radius 18.5 mm and height 23 inin, its resonant frequency in free space is 1.18 GHz. When the dielectric is placed in the centre of a shielded cavity with square sides 60 mm and height 50 mm, the resonant frequency increases to 1.3 GHz. z 1.2.1 - Y .X Figure E-field H-field 1.3: TE016 resonant mode dielectric resonator Background The propagation of guided electromagnetic waves in dielectric first was media days leading in the DR of to the microwaves early the where studied prominence of functioned dielectric [8]. The term objects as microwave unmetalised resonators, 7 1 Introduction ZL Review of Dielectric Resonators yýlý LX x Figure 1.4: E-field plots of shielded TE1A mode dielectric resonator dielectric resonator was coined in 1939 but the theoretical work reported failed to first interest DRs 1960s. the until early were rediscovered and generate significant [9], [10]. in designs. Unfortunately, terms of mode and resonator analysed dielectric constant materials at the time had poor temperature stability highcausing frequency in in As shifts spite of microwave systems. a consequence, unwanted their high- Q factor and small size, DRs were not considered suitable for microwave In the mid-1960s, theoretical work with experimental systems. evaluation of ru- tile ceramics that had an isotropic dielectric constant in the order of 10(1 was for the DR was developed along with and a perfect magnetic wall model studied formula for between the coupling approximate coefficient adjacent resonators, an [11]. A bandpass DR filter was also presented by placing TEols mode dielectric in TEO, [12]. As before, the coaxially a cutoff resonators circular waveguide, rod temperature problem of poor stability continuing velopinent of practical applications. the first temperature-stable Raytheon, by veloped [13]. was present preventing the de- The breakthrough 1970s in the when came and low-loss barium tetratitanate Bell laboratories reported ceramics were de- a modified material leading to improved performance, one the afore-mentioned to [14]. These results led to the first realisations of DRs as microwave components but these materials in for supply and were short not marketable were commercial purposes. Murata Manufacturing Company provided the first commercial DRs (Zr, Sa)TiO4 using that offered adjustable compositions allowing temperature ceramics coefficients to [15]. +10 between This and ppm/°C, -12 vary allowed the desired small control- 8 I Introduction lable temperature Review of Dielectric Resonators coefficients over the useful operational temperature range. It filters, from developed DR this in that the point onwards rapidly microwave was [16,17,18,19]. Furthermore, filters dual-mode filter technologies, new such as function [20], filters developed, to techniques response were along with and elliptic improve the spurious response, [21,22,23]. To accomodate these improvements, full-wave involving implemodels and were modeling analytical methods rigorous [24,25,26]. mented, 1.2.2 Dielectric Resonator DR filters play an important Filters role in mobile and satellite communications. A typi- filter dielectric DR inside consists of a number cavities of resonators, mounted cal in Probes a metallic enclosure are or an evanescent-mode machined waveguide. input the to couple and output electromagnetic energy and irises are typically used for inter-cavity resonator coupling. DR filters used in microwave systems can used be divided into two configurations: individual enclosure or a metallic individual DRs that are loaded coaxially in resonators mounted in a planar configuration. The first practical DR filter was reported in 1975 and a schematic of the 6.9 GHz filter is shown in figure 1.5, [15]. The mono-mode filter with all resonators operating in the TE016mode provides low loss and small volume. A planar layout offers many advantages over an in-line configuration although they are larger in size. These advantages include layout flexible DR structure, simple a supports and easier tuning mechanisms for mass production, therefore, these are widely used in base stations for mobile [27]. A major problem with DR filters is the proximity of communication systems, For instance, in a filter operating under TEola mode, the ratio of modes. spurious this fundamental resonant frequency to the first spurious HE11smode resonance is 1.3:1, although this may be improved to 1.5:1 by inserting a hole in the centre of the DR. Inter-resonator coupling is magnetic and controlled through irises since a greater proportion of magnetic than electric energy leaks from DRs. A typical 9 1 Introduction 'Adjusting Review of Dielectric Resonator. Screw for Q, Fine tuning screw for f, Tuning screw for the coupling Higher mode and neighbouring O 1.5: Structure of 6.9 GHz DR filter, [15] Figure TE0m DR filter for cellular base station applications is pictured in figure 1.6. In this configuration, non-adjacent couplings can be used to realise more advanced filter features. such as elliptic Quadruplet responses. function or asyInilletri(al be basic building blocks to generate symmetric triplet sections can regarded as and for TE transmission zeros mode cavities. or asymmetric J PI- ý" Figure An alternative is Cfir 1.6: TE0Ia DR filter for cellular base-station application, structure consists of grounded dielectric This filter has a simpler structure TMoi mode. s single [281 rods operating in the compared to the previous 10 1 Introduction structure Reviewof DielectricResonators dielectric irises the are needed as since no other electrically. rods are coupled to each A compact DR filter may be constructed by placing these high- Q dielectric rods coaxially in a TMOIS circular cutoff waveguide as shown in figure 1.7. SRM connector Tuning screw TM., cutoff circular waveguide Figure 1.7: Configuration Dielectric rod resonator Resonator support [29] TMolb Dß, filter, mode of a Even with a dielectric constant of 45, a typical 900 MHz resonator occupies a 8x8x5 of cavity size cm which is still relatively become factor. techniques a major size-reduction large. As a consequence, Higher-order modes are usu- however, have the as spurious modes, property considered certain modes ally to generate multiple modes for a given structure. The HElla mode is such a dual-mode for D/L, diameter-length, operation and ratios certain mode allowing frequency its falls TE01a below the puck resonant that cylindrical mode. a of of The dual HElla dual-degenerate mode in cylindrical DRs was first reported by Fiedziusko in 1982, [30], as shown in figure 1.8. In this configuration, only half the number of physical cavities is needed, offering smaller volume and DRs are in the Low-loss, in axially centre of each circular mounted cavity evanescence. is to mounting required assure good electrical and thermal performance. stable Coupling between modes within a single cavity is achieved via a mode-coupling location an angular with of 45° with respect to orthogonal tuning screws. screw Intercavity coupling is provided by coupling slots in the form of cruciform irises situated throughout the filter such that both resonances are able to couple to in adjacent cavities. Elliptic each other function responses can also be produced by cross couplings between non-adjacent cavitites and the signs of these couplings by determined the orientations of the tuning screws to are each other. relative 11 1 Introduction N( cif u' of J), 1 (ir it R( , otlalovs The theory used for an empty cavity dual-mode filter based on a coupling screw design can also be applied here to determine the required couplings as shown in figure 1.9. [31]. Connectors %"1C\ ý'Th Iris Slots 4ý\ Dielectric Resonator (TYP) Units cm Figure Although 3.29 Dia x 10.16 long [30] DR filter, of a 1.8: Dual-mode configuration is achieved, unfortunately good size-reduction the fundamental mode for this cylindrical the HEiib mode is not resonator and a straight 2: 1 reduction in size is not possible for the same Q. These bandpass filter devices are commonly used in mobile and satellite communications applications due to their low loss Subsequently, this work has and small size compared to single-mode realisations. [33]. been [18], improved [32], by Zaki, Gendraud, Kobayashi, upon since and Output , ? Coupling Screws n Output Polarization is rotated 90° for p n-(4m-2) m= 1,2,3TE. Mode (1) (Polarization lll(Input A1 For Square Waveguide TE, (2) i Polarization Figure 1.9: During screw orientations DR dual-mode filter, [31] A planar modification Mode for cross couplings in an elliptic function was reported by positioning the DR on the base of the 12 1 Introductioli with cavity conducting the DR with conductors discs placed on top of each resonator, at both ends, tangential bottom top both the and at for this structure theoretically. Review of Dielectric of the DR. This allowed A typical dual-mode these metallic Figure E fields are diminished a simple model to be used variations conductors as shown in figure 1.10. Devices of this in the metal conductor It is no surpise that exploiting greater size reduction. coaxial filter but, unfortunately on top of the DR caused frequency 1.10: Conductor-loaded Electrically. drifts due as high power was applied. dual-mode DR filter configuration, multiple Q and Q1A this type of 6300 of achieved a resonator half the volume of an equivalent type can occupy to frequency By loading using the TM110 mode to analyse the resonant frequency 6.5 x 6.5 x 6.5 cm cavity in MHz 900 a at placing electric, [34]. Resonators [34] degenerate resonant modes will give the optimum geometry for a triple-mode he a sphere but this is not ideal for bulk would resonator manufacture. To com- dielectric be cube may a used although spurious modes become a detripromise. here. An example of this is a triple-mode TE0I6 DR filter factor inental operating [35], 2: GHz, 1 in 2 offering a reduction size over conventional TEO, & filters. at A quadruple-mode DR filter has also been realised and a2 GHz compact filfor WCDMA communication systems has beeil reported as shown in ter suitable figure 1.11, [36]. 13 1 Introduction Tuning groove Metal cavity Review of Dielectric Resonators Quad mode dielectric resonator port Loop probe Figure 1.11: Quadruple-mode DR filter configuration, [36] Although multimode DR filters have many advantages, they also have a major drawback in having inferior additional out-of-band spurious characteristics. lowpass filter is needed to eliminate increases the size, insertion loss, complexity Usually, an the unwanted modes but this filter. the and cost of Significant filters, been into improving has DR the especially put spurious response of efforts dual-mode filters. For example, both the TE018 mode and HE116 mode filters have free but by limited into them performance a mixed-mode spurious combining very DR filter, spurious performance can be improved. An example uses TEolb monodual-mode HElla DRs filter in function to as shown produce an elliptic mode and figure 1.12, [22]. A lateral offset between the axes of the TEola and HElla mode because the magnetic field at the cavity centre provides greater coupling cavities is maximum for HE116 mode and minimum for TElla mode respectively. Unfortunately, an in-line configuration is seen as too cumbersome due to the latbetween dispositions dual-mode the two cavitites the accomodating eral single and A is, therefore, much simpler to implement as planar configuration resonators. [23]. figure 1.13, The in frequencies spurious shown of the two types of resonators MHz 500 to free produce a offset spurious are window, however, since the filter essentially operates under single-mode operation, the dual degenerate modes are that dual-modes the is used adding further complexity. only such one of split 14 I Introduction h'f rir ur of Do It ý lI I J?'r. tiuiiulor., Single Iris (Msv) Single Iris (M Figure f22] 1.12: Configuration Dielectric Resonator 12) of a 6`t' degree mixed-mode elliptic function DR filter, Toi HE, ri 2 ---. -Iris Iris l Iris 3 0 X HE,, M12 f M23 001 Iris Iris 2u In Mc JO.. TEo, Figure O M. LA .-. mm" 'J HE,, L-3 TEo, 1.13: Structure of 6h degree mixed-mode DR filter, [23] Another technique to improve spurious performance is to combine different types together. resonators of One such resonator is produced on the basis that if the DR in a dual-mode filter is replaced by a perfect electric conductor, significant miniaturisation can be achieved, since the relative dielectric constant of the res- infinity. approaches now onator The dielectric-loaded Q higher have resonators than conductor-loaded resonators, therefore, low loss is also achievable along with 15 I Introduction Review of Dielectric Resonators impressive spurious performance due to conductor-loaded resonators. Another advantage is these resonators both operate in HE,, dual-mode so that inter-cavity couplings are simple to realise using cruciform irises. A 1.55 GHz filter is shown in figure 1.14 where spurious modes are suppressed to below dB up to 2.8 -40 GHz, [37]. Dielectric Loaded Cavities Figure 1.14: Configuration filter. [37] Conductor Loaded Cavities Dielectric Loaded Cavities of 4th order combined conductor and dielectric-loaded The first waveguide Bandstop filter was proposed by Okaya and Barash, [9], by placing rutile crystals inside the main waveguide to operate under TE016 mode. Colin also reported a design configuration of a waveguide bandstop filter using Ti02 resonators as shown in figure 1.15. However, problems with these earlier designs included too niuch perturbation waveguide to the placement of the DRs within due the of waveguide modes the main guide producing a poor match in the passband. Futhermore, unwanted non-adjacent and inter-resonator couplings were unavoidable as there was no isolation between these resonators. Chung-li Ren noted the problems of the aforementioned filters, [38], and solved them by positioning the DRs outside the main waveguide. In this configuration the resonators were isolated in their own metal enclosure coupled to the main waveguide through small apertures on the waveguide walls as shown in figure 1.16. The couplings between the waveguide and resonators could now be controlled via apertures and there was now scope for independent tuning for each DR. In all the above configurations, the placement of the resonators is seen to be in especially providing cumbersome supports for each cylindrical waveguides are used as the propagation Also, as puck. medium, a 3/4 wavelength separation is 16 1 Introductimi -Rectangular Review of Dielectric Resonators Waveguide OO0b ýa Dielectric Resonator 0aa1o a Waveguide -Rectangular Figure 1.15: Bandstop filter with DRs placed transversely along waveguide, [38] Y 1 b 3/41,80 I-- a=2b (a) Hx Coupling L 3/4 Xea a=2b (b) HZCoupling Figure F a x 1aT-0 ii ý-b-4 'Y 1.16: Bandstop filter with DRs placed outside waveguide, [38] between between fringing field to each resonator avoid excessive needed coupling For leading degradation in to in the topologies. the a resonators response above TEMPIlines, such as coaxial or microstrip, needed producing more compact structures only 1/4 wavelength separations are [26]. figure 1.17, in shown These designs have shown how cumbersome the fabrication process can be to provide the frequency, coupling and phase separation between each resonator. correct resonant It is, therefore, not surprising that there has been very few bandstop filter designs involving higher order modes where the coupling scheine involves a large number for independent tuning elements control of each degenerate modes. intra-cavity of 17 1 Introduction and inter-cavity Scope of the Study To date, a triple mode hybrid reflection mode was coupling. described but involves coupling bandpass resonator cavities to a3 dB quadrature hybrid, thus, it is not strictly a pure dielectric bandstop resonator. To realise a dual-eiode design, along with correct control of resonant frequencies and couplings within the cavity, the separation between the tap points of the main transmission line must also be accurate and the finite dimensions of these tap elements will provide some measure of unwanted coupling between them. lý. (:....,... Figure 1.17: Microstrip TT-:, ýý:.. M---- DR bandstop filter with quarter-wavelength unit ele- ments 1.3 Scope of the Study DR filters have been of considerable interests recently but have only evolved bandpass filters. around There is little published material on DR bandstop fil- ters, thus, the proposal for this work was to develop and realise practical bandstop filters using high permittivity dielectric materials to miniaturise conventional air- bandstop in filters. resonators microwave cavity Note that the development of filter is Chebythe this thesis, prototypes therefore, out of scope of novel classical Chebyshev inverse approximations shev, and direct-coupled design The for the process. majority used of the research work centred around the configurations factors in the physical realisations using 3D HFSS simulations. been has incorporated design mode using dielectric-loaded knowledge, To the author's previously uides. lines forming transmission bandstop to filter. a coupled Firstly, a mono- rectangular only cylindrical were waveg- been have pucks In using the properties 18 1 Introduction dielectric-loaded of a Organisation of Thesis waveguide resonator, an advantage is seen in the spurious dielectric Using isolated to rectangular as compared an resonator. performance DRs also provide ease of manufacturing compared to cylindrical for lower costs mass manufacturing. viding resonators pro- The design is much simpler as these leaving grounded cavity resonators are against only a coupling walls, waveguide face to the transmission line and an open face for tuning. The result is no complex design is required for the dimensions of the cavity. A Chebyshev filter was de- SZ 50 line. The to each resonator coupled with a second structure coaxial signed filter has DR dual-mode knowledge, to the never which again, author's uses a been published before. By exploiting the dual degenerate modes, miniaturisation is achieved through producing two modes in a single cavity as opposed to monodesigns. its The is in two this coupled-cavity versatility novelty of structure modes for DR filter novel configurations. as a practical Measured results produced an inverse Chebyshev response. To achieve coupling into both modes, a right-angle designed line was and the resonators were magnetically coaxial coupled through fixing small coaxial probes to metal posts in the base of the cavity. A number design including HFSS in filters both the simulations were performed use of of of the eigenmode solver and parametric analysis to achieve the required dimensions for fabrication. The final section leverages the dual-mode bandstop resonator in direct-coupled novel configurations, lations demonstrating including a cul-de-sac form, with EM simu- only a quarter wavelength transmission line is required to directly couple the source and load resonators to create miniaturised dielectric bandstop filters. resonator 1.4 Organisation Thesis of Firstly, this chapter has identified the benefits of DRs and how, only in recent times, they have become popular in the microwave industry due to the availability of temperature-stable materials. Advantages over bulky waveguide and coaxial have been discussed. The benefits in using higher-order modes includstructures I Introduction 19 Organisation of Thesis ing recent DR filter designs has also been described and this allows a substantial filters. in volumes of cavity reduction In Chapter 2, a review is presented of filter designs stating the stages from the initial prototype to the transformed circuit model. Also included is an advanced technique using a coupling matrix synthesis design direct-coupled to polynomials to generate generalised Chebyshev bandstop filters. Note that physical realisa- tions are not discussed here. Chapter 3 reviews the properties of DRs and how they are designedusing a variety Couplings from to simple models more rigorous numerical models. of methods between these DRs and different transmission lines is also discussed. Chapter 4 covers the design of a TEloa mode compact DR bandstop filter. First, is dielectric-loading before the waveguide analysed concept of a rectangular is introduced and the effects on its Q factor are considered. A bandstop filter is designed based on the Chebyshev characteristic. Simulated and measured results for a 4th degree bandstop filter are shown with shortcomings in the fabrication discussed. At the end of this chapter a novel wideband dielectric-loaded coaxial introduced. is resonator In Chapter 5, a novel HEE11 dual-mode dielectric bandstop resonator is analysed faced developed is in discussions the experimental cavity an with problems and on design process. A dual-cavity 4th degreebandstop filter is designedand measured. The direct-coupled bandstop resonator is discussed showing how the dual-mode bandstop resonator compliments the synthesised coupling matrices for the original forms. and cul-de-sac Lastly, Chapter 6 summarises the fundamental aspects of this thesis, along with advantages and shortcomings for both filters. Improvements are also discussed. 20 2 Chapter Filter 2.1 Design Introduction Microwave filters are important to extract the desired frequency spectrum from a theoThis describes basic and signals. concepts chapter, wide variety of electrical [39]. Generally, filters RF design their and considerations, ries of microwave and has a brick-wall transfer response with instantaneous transition filter ideal an due delay to in impractical but is the this bands and constant group passband finite-order limitations lossy of practical To realise the filter function filters. for a lowpass prototype transfer the and reflection polynomials required, be established. It is seen later that a lowpass prototype must be translated can to bandpass or bandstop response as required and the synthesis of a highpass, a lead to the implementation circuit will eventual physical prototype in transmis- design line, filters. The procedure waveguide, printed circuit or other media sion the required transfer function, follows from the required specifications outlining degree of filter and location, if required, of transmission zeros to form loss, return the ideal characteristics filter the of polynomials. first introduced to calculate these polynomials The recursive technique was for symmetrical and asymmetri- [40]. The into be then translated polynomials a prototype may performance, cal through [41], the either circuit synthesis, network or the direct coupling matrix [42]. An advantage of the latter is the be transapproach, coupling matrix may 21 2 Filter Design Types of Filters formed to suit the physical couplings required in the physical implementation, [43] and [44]. This is the case for dual-mode designs where the matrix can be form The the then to may necessary coupling paths. prototype network arranged be realised by a physical resonator using 3D electromagnetic, EM, simulations as dimensions for filter. Tuning to the the achieve correct methods are guide entire a for discrepencies implemented to between the simulated and compensate any also fabricated designs taking into account manufacturing behind The theory errors. found be in is these techniques but the this thesis out of of scope may of much [45]. 2.2 Types of Filters Filters can be classified as one of lowpass, highpass, bandpass or bandstop, [46]. The first is a filter permitting low frequencies and rejecting frequencies higher than the rated cutoff frequency and the highpass performs the opposite function. Bandpass and bandstop combine lowpass and highpass filters to select interested bandwidths lumped-element rad/s, w=1. The lowpass prototype and reject others. operating in a1 In addition, is defined as a two-port SZsystem with angular cutoff frequency of 1 it is passive and reciprocal. These responses can be by ladder the synthesis of networks, of which the simplest is Cauer's analysed form consisting of series inductors and shunt capacitors as shown in figure 2.1. S, ------------- g S: 9H 1g4 N-ý N odd 1!2 N even 9N., - 14 rn Figure 2.1: Lowpass prototype ladder filter networks An alternative transformation technique, [47], compliments inverters with reactive 22 2 Filter Design Types of Filters lowpass ladder in a network where the inverters are coupled with series elements inductors or shunt capacitors, figure 2.3. This process provides a good approxibandwidths for depending 20% narrow upto on the physical realisation. mation An inverter, shown in figure 2.2, is a frequency independent two-port network between load impedance, input impedance, Zen the the relationship and where ZL, is defined by K2 Zin = ZL (2.1) ZL F ZIN Figure 2.2: Impedance inverter terminated in a load in (a) in (b) Figure 2.3: General Nth degree inverter coupled lowpass prototype with (a) inductors (b) capacitors 23 2 Filter Design 2.3 Impedance Impedance Transformations Transformations For impedance transformation, the 11 impedance of the prototype is converted to an impedance level of Zo by scaling all the reactive elements in the filter by ZOusing the following transformations L -ý ZOL C (2.2) Zö K -+ZOK 2.4 Lowpass to Bandstop Transformation Bandstop configuration allows power to pass through the resonator at frequencies but is resonance power absorbed from the coupled line at resonance inoutside impedance the effective of the resonator leading to more reflections. The creasing transformation from the lowpass prototype to a bandstop filter with arbitrary frequency bandwidth and centre can be performed where the transmission zeros for lowpass the infinity prototype is mapped to wo. The response is shown in at figure 2.4 and the transformation is set out below. w -+ -1 ö- ) (2.3) where, wo = (w1w2)1/2 (2.4) bandwidth factor, the scaling and a is given by, a= wo wo _ Ow w2 - wl band the w2 and are wl edge frequencies. when (2.5) 2 Filter 24 Design Transfer 152112 Functions 152112 Co, w, Co -1 Co Figure 2.4: Lowpass to bandstop transformation Applying this transformation leads to the transformation of elements as shown in figure 2.5. L, _aL wo L C, _ aLo ,: = C 1 1 aCwa 41- HH -f C, =aC Wo Figure 2.5: Bandstop transformation of an inductor and capacitor 2.5 Transfer Functions The transfer function of a two-port network can be written as: 1S21(jW)12 1 °1+ c2F 2 ri (w) (2.6) 'a is F(w) e ripple constant, where represents a filtering or characteristic function frequency is For the transfer function in equation 2.6, the variable. a w and insertion loss response of the filter can be solved using: LA(w) = 10109 1 dB ý921(jW)12 (2.7) 2 Filter 25 Design Since ISll(jw)12 + IS21(jw)12 =1 Transfer Functions for a lossless, passive two-port network, the filter loss is the of return 2.5.1 Butterworth (2.8) IS21(jw)12)dB LR(w) = lOlog(1- or Maximally Flat Approximation filter. low ideal is butterworth the to The pass response simplest approximation an The response is flat at d. c. and rolls off to 3 dB at w=1 before flattening out figure in 2.6. infinity shown as at again IS121 =2 =4 6 0 we G) Figure 2.6: Frequency response of butterworth lowpass filter for varying N The transfer function describing this response is given by: IS21(jw)12 =1 1 +. W2N . (2.9) loss insertion is the and LA(w) = 10log(1 + w2N) dB degree of the network. N is the where (2.10) 26 2 Filter Design rnnsfer Design formulae for both lowpass prototypes Functions for a general Nth degree with in- (b) (a) by inductors figures 2.3 in and or capacitors, shown verters separated for G,., below. the given are element values, respectively, G, = L,. or C,. =2 sin l Kr, 2.5.2 Chebyshev A better approximation is one containing r+l =1 )7r (2r 2N (2.11) (r = 1, N) ..., (r = 1, N..., (2.12) 1) Approximation than the maximally flat to the ideal transfer function a rippled response in the passband region. Chebyshev approximation a The response of is shown in figure 2.7 and the insertion loss at the defined by is level ripple (2.13) LA = 10log(1 +w2TN(w)) 1 IS.,I2 WO (! ) Figure 2.7: Frequency response of a Chebyshev lowpass filter An expression for the transfer function of this response is given by IS (jW) 12=1 21 1+ ý2TN(w) (2.14) Thznsfer Functions 27 2 Filter Design defined is in as level, the the and passband the e, ripple controls ripple where e_ (10LR/10 (2.15) 1)-1/2 - Chebyshev Nth is TN the polynomial and e<1 order where is a real constant. These polynomials are defined in terms of a real variable w as TN (c) cos[N = (2.16) cos-'(w)] the below be to in terms of either Element values, of rj, are given applied and can Nth degree lowpass prototypes asfor the butterworth design. Kn, n+i = [712+ sin 2(r7r/N)] 77 r=1, ..., N-1 (2.17) is impedance inverters. KR, the the of R+l where [(2r 1)ir L, =2 sin l 2N 77 r = 1, ..., N (2.18) where 1 rý = sinh 2.5.3 Inverse Chebyshev sinh-1 (2.19) Response This approximation is the inverse of the normal Chebyshev in that it is maximally flat in the passband but is equiripple in the stopband as shown in figure 2.8. This function is used in applications where a non-infinite stopband attenuation is tolerated and a symmetrical stopband can be achieved by controlling the ripples in the stopband using zeros in a low pass transfer function. 2 Filter Transfer Functions 28 Design 12 IS12 1 .2 HS2 -a Figure 2.8: Frequency response of an inverse Chebyshev filter The transfer function is defined as IS21(jW)12=11 1-F (2.20) ý2T2 (1/W) and LA 1 20 1og (2.21) A highpass prototype is shown in figure 2.9, [41], and the element values are calculated using Cr 217sin[(2r - 1)7r/2N] ( (2r 1)ir , B,. = Cr cos L 2N Kr, r+l =1 (2.22) (2.23) (2.24) 29 °LFilter Design Transfer Functions to is Figure 2.9: Highpass prototype for inverse Chebyshev filter 2.5.4 Generalised Chebyshev It is possible to realise a polynomial adjacent cross couplings. Response function using extra resonators with non- The response of elliptic filters has rippled approxima- tions in both the amplitude of the passband and stopband regions. This provides filter to selective attenuation more slopes as of equal compared any other much degree. The frequency response is as shown in figure 2.10 with finite-frequency transmission zeros present in the stopband. is.X 1 Minimum Attenuation Attenuation Floor VIW Figure 2.10: Frequency response of an elliptic lowpass filter a disadvantage of this response is transmission zeros are prescribed frequencies. Thus, basic Chebyshev the at certain polynomial is considered too filter for designs. The advanced generalised Chebyshev transfer response simple Unfortunately, for a lowpass prototype is, IS21(. 7w)12-11+ FN(w) for +1 < < <w< with -1 -1 +1 e2FN(w) (2.25) 30 2 Filter Design for FN(Wr) r=1,..., and Direct-Coupled Bandstop Filters N frequency is the transmission the of rth zero. w, where The cross couplings can be made in an inverter-coupled inductive, or positive, capacitive, negative, couplings add transmission zeros or Adding transmission ther to real response. poles increase selectivity. can network where additional zeros in the frequency doman The design for such a filter can be approached through the addition of cross-couplings to a Chebyshev prototype, performing an analysis and optimisation program to achieve the response. This technique is suitable for basic structures but for more complex designs requiring asymmetric or multiple further is technique transmission a zeros, of required. pairs 2.6 Direct-Coupled Bandstop Filters In conventional Chebyshev bandstop filter designs, each resonant element is couA/4 to a main transmission line. An advanced approach of multiples odd at pled between the transmission line and resonant cavcouplings of number can reduce ities dramatically, therefore, wideband performance is potentially better. Since the resonant frequencies are tuned within the stopband, the main signal need input through the travel and output only tap points, bypassing direct-coupled high handling to give power and minimum resonators insertion loss. The technique stems from generating transfer polynomials for the solving and filter function as described in [40] following the Darlington synthesis procedure the [31] around coupling matrix model, and revolves and [42]. This can be applied to the asymmetric case and to singly and doubly terminated That is, networks. filter networks for any type of filter function including: the method produces 1. Even and odd degree 2. Prescribed transmission zeros 3. Asymmetric or symmetric characteristics 31 2 Filter Design 4. Singly or doubly terminated Direct-Coupled Bandstop Filters networks An example of the 4th degreeN+2 coupling matrix with all possible cross-couplings is shown in figures 2.11 and 2.12, [45]. The core 4x4 matrix describes the adjabetween resonators and the whole matrix is symmetrical around couplings cent the diagonal axis. From this matrix it is possible to calculate the element values in the circuit network using equations described in [47]. Ms. Mss Ms. c x Ms. 1 MIL ýM M, w M,.,, Figure 2.11: N+2 multicoupled resonator circuit Si S Mss Msl 1 Ms, 2 3 4 L 234L MS2 MS3 MS4 MsL Mil M11 MI3 MIL ,4 MS2 M12 MS3 MIS M23 M33 Al34 M3L MS4 Mu M24 A M M4L MsL '", M4L 1v M22 1v! M24 23 2L 34 A2L M3L L Figure 2.12: 4th degree N+2 coupling matrix Core NxN matrix within double lines M LL with all possible cross-couplings. To generate the exact solution for the filter element values given a set of initial three essential steps are required: parameters, 32 2 Filter Design Direct-Coupled Bandstop Filters 1. Network synthesis 2. Generation of coupling matrix for Nth degree network 3. Reduction of matrix to represent realisable coupling elements The network synthesis begins from first considering a losslesstwo-port network degree Nth functions defining transfer the two the and reflection as ratio of and [45], polynomials, F(s)/ER' Sll(s) _ P(S) S21(s) E(s) (2.26) - cE(s) from for is is 2.19 the equiripple general passband equation e and CR unity where for functions canonical where all transmission zeros are prescribed casesexcept frequencies is finite ei given as, and at ER E -2- (2.27) 1 To develop the bandstop characteristic, the reflection and transfer coefficients and become, to exchanged are constants P(s)/c S11(s) _ S21(s) E(s) F(s) (2.28) _ -RE(s) The shared common denominator of both functions preserve the unitary condition for a passive losslessnetwork, 5112+S 212 =1 (2.29) In effect, with respect to a Chebyshev characteristic, the original equiripple return loss is now transformed to the transfer response and the minimum rejection level 33 2 Filter Design Direct-Coupled Bandstop Filters As the degree for top and is now equivalent to the original return loss level. bottom of S21 are now equal, the synthesized network is now canonical, thus, the S11 function is the transfer of original polynomial new numerator and can realise less figure is transmission this prescribed or of equal zeros provided any number than the Nth degree. Note that e1 =1 degree. To form the polynomials for the number of zeros less than the for a bandstop filter, P(s)/e and F(s)/eR are in the process to calculate the polynomials exchanged for a lowpass prototype, [40]. described below in as outlined For a losslessnetwork, 1 S21M' -1 1 (1+icN(w)) (w) e2CN2 "t- (2.30) (1_jCN()) ER CR where Fw CN ýwý _ 7 To generate the polynomials and location of transmission zeros, the recursive technique is performed on the derived equation 2.31 for the general Chebyshev through mathematical techniques described in [45]. characteristic 1 CN (W) 2 [(w nn i - 1/Wn) + (1 - 1/wn 1n=1(1 -ý JIN- L/W- O1 - Zw -W/Wn) (2.31) 11 2(w2 1)1/and w' wn are the prescribed transmission zeros. These must = where be symmetrical about the imaginary axis of the s-plane for F(w) and P(w) to be purely real and the number of zeros must be of order no greater than N-2 to implement the physical filter. The polynomial, CN(w), is of Nth degree and the be infinity. The recursive technique is performed zeros must placed at remaining from n=1 to the Nth degree to yield the polynomials for F(w). PN(W) may now J 34 2 Filter Design be derived as the denominator Direct-CoupledBandstopFilters of CN(W)4 wJ PN(w) = IIn 1 11wn L (2.32) The next polynomial E(w) is more complex and requires the Hurwitz polynomial have they in that the that are negative so all roots real parts s-plane condition hand left imaginary The the the located side of on axis. complex polynomial now p(w)/e - jF(w)/ER is formed and the roots are found positioned alternately and is bottom top The the the a root of and of w plane. conjugate symmetrically on by j and E(w) may now be obtained. The coupling through multiplying taken from finding be the synthesised now admittance parameters, y21(s) may matrix for for As two-port an even short-circuit network. a an example, and y21(s), load SZ impedances, 1 and source network with (F(S)/ER) Y21n(s) Y21(S) = _ yd(S) ml(S) y22n(s) 1122(8) - yV(s) (2.33) _ ni(s) (2.34) mi(s) where ml(s) = Re(eo+po)+ ni(s) = jIm(eo jIm(el +pl)s+Re(e2+p2)s2 +po) + Re(el + pl)s + jlm(e2 + +p2)82 + ... N, i=0,1,2,3,..., the P(s)/e pi, are E(s) and complex e; coefficients and and reof The coupling matrix is synthesised with spectively. one noticeable exception since S21(s)is now fully canonical, the direct source-load coupling NISL is calculated from, 35 2 Filter Design jMSL = Y21(8) yd(s) Direct-Coupled Bandstop Filters ni(s) (2.35) __ ml(s) For the noncanonical case where the number of transmission zeros is less than the Nth degree, PN = 0, and from the equations above, yd(s) = 1. Together with the properties that the leading coefficient F(s) is unity for Chebyshev characteristics, for e1 noncanonical designs, therefore, MSL = 1. This provides the along with direct-coupled property where the source and load coupled inverter have the same line. impedance be \/4 transmission and can modelled as a characteristic uniform Note that for the fully canonical case, MSL will have a value slightly below unity finite the return loss at infinite providing frequency. The synthesis technique by finding the residues and eigenvalues of the admittance functions to proceeds construct the coupling matrix. form using similarity This coupling matrix is then reduced to folded transforms, such that it represents the coupling network of the physical filter. An example of a symmetric 414degree bandstop filter in folded form is shown in figure 2.13 demonstrating the signal path is directly coupled, MSL. SL Coaxial (a) Figure 2.13: Direct coupled (4-2) bandstop diagram (b) realisation with coaxial cavities (b) filter, [48]: (a) coupling-routing For a doubly terminated network between source and load impedances and if the less is than the Nth degree, then cul-de-sac configuration zeros reflection order of a by formed be adding two unity impedance 45° phase lengths at either end may 36 2 Filter Design of the network. Direct-Coupled Bandstop Filters This represents multiplying the F(s) and P(s) polynomials by j that only introduces a 90° phase change without changing the overall transfer A the typical configuration response of network. and reflection filter is illustrated for the bandstop in figure 2.14 and clearly shows the core quartet of resonators for for diagonal the removing need cross-couplings, even in a square formation asymmetric characteristics. As for the original direct-coupled form, MSL is unity for the number of reflection zeros less than the Nth degree meaning only a A/4 transmission line is required between the input and output. The form is defined by the last resonator in each of the two chains having no output coupling, hence the name for this form. SL M -º a s` -º MssýMAL t -0----------2143 1® O Mýj (a) M, ® " Mý" O (b) Figure 2.14: Direct coupled (4-2) bandstop filter, diagram (b) realisation with waveguide cavities These two configurations [48]: (a) coupling-routing demonstrate that only a A/4 length of uniform trans- form line is to bandstop This filter. needed a multi-resonator asserts the mission lengths transmission between reduced of phase advantage resonator to transmisline tap the points removing need to tune these phase lengths and reduce sion transmission line dispersion. In addition, matrix operations can be applied to the topology and performance of the simulated circuit. reconfigure 2.6.1 Quality Factor Practical filters have components with finite resistance producing loss in the sysloss be This can accounted for by the Q of the filter. In Chebyshev prototem. Nth degree bandpass for filter of centre frequency, fo, an types, and bandwidth 2 Filter if, 37 Design Direct-Coupled Bandstop Filters the unloaded Q is given by Qu 4.343foN _ fILE gr (2.36) r=1 IL is insertion loss is the the value of the rth element of midband and gr where the lowpass prototype. External losses are also evident due to coupling fields from input probes to the filter and is attributed to an external quality factor, QL. The loaded quality factor, QL relates any external and internal lossesand is design It for is bandpass filter bandstop important parameter structures. and an defined as ,L QU+Q (2.37ý ext U$Y UNNERSIT`( LEEDS 38 Chapter 3 Dielectric 3.1 Resonator Basic Properties Resonators are important Filters Dielectric of Resonators filtering, in components microwave systems acting as frequency selection in oscilloscopes, amplifiers and tuners. At resonance, stored fields leading to maximum energy stormagnetic energies and are equal electric difference fields. Since internal by the is to resonator reactance proportional age between electric and magnetic energy storage, the input impedance at the resoA is dielectric boundaries frequency free-space purely real. can object with nant due in internal to modes various reflections of electromagnetic resonate dielectric high the constant material/air at boundary. waves The dimensions of a DR fundamental dielectric in for the the the of one wavelength order material are on As Ad =aE,., mode of resonance. the dielectric, where Ad is the wavelength associated with A is the wavelength in freespace and dielectric is the relative er dimensions become the A to resonator as Er smaller when compared constant, increases. Since the dimensions of an air-filled cavity are of the order of A, a DR has much smaller dimensions than the cavity resonator. During the previous decade, many advances in dielectric materials have led to the successfulcombinations of high Qs, high dielectric constant and small temdrift in for materials suitable use at microwave frequencies. High Q perature dielectric with constants ranging from 20 to 90 are now commercially materials 39 3 Dielectric Resonator Filters from various manufacturers. available Quality Factor At microwave frequencies, the classical dis- increases dielectric loss dielectric that the theory with of materials states persion frequency, f, whilst er remains unchanged, [49]. Therefore, the product of Q and f can be used to classify the fundamental properties for each dielectric material. Table 3.1 lists the characteristics of dielectric materials currently available. These have highbut Q high dielectric also good values and constants materials not only temperature stability. By adjusting proportions in the mathe of compounds for the linear expansion of the ceramic, perfect temperature terial and allowing The is temperature possible. compensation dielectric the material, of frequency the resonant coefficient of r,, combines three independent factors that include temperature cofficient of the dielectric, Te, thermal expansion of the material, aL, the thermal of expansion environment and in which the resonator is mounted. Resonant frequency shifts due to intrinsic material parameters are related by the in below, the temperature coefficients equation above Te Tfý-2 -aL (3.1) To advance the technology of these materials, the properties of the material must be measured accurately. Hakki and Coleman provided a method to measure the loss tangent of the dielectric, [51], which was later improved upon by Kobayashi [52]. Katoh The technique involved measuring the greater with accuracy, and dielectric dielectric properties of a microwave both ends by two parallel conducting plates. rod resonator short circuited at This allowed the advancement of new materials. 3.2 Quality Factor Practical filters have components of finite resistance that produce a degradation in performance. The effects of this resistance can be related directly to the Q 3 Dielectric Resonator Materials Quality 40 Filters I E_ 0 7`C (DDm) r, (GHz) .f 7 10 10 MgTiO3-CaTiO3 Ba(NIg,Ta)03 Ba(NIg,Ta)03 21 25 25 8000 16000 35000 0 3 4 Ba(Sn, Mg, Ta)03 25 20000 0 10 0 0 0 5 2 0 2 +5 -5 15 0 +460 +910 +1700 10 12 10 11 6 7 6 5 2 1 Ba(Mg, Ta)03-Ba(Zn, Ta)03 Ba(Zn, Nb)03-Ba(Zn, Ta)03 Ba(Zr, Zn,Ta)03 (Ca,Sr,Ba)Zr03 BaO-Ti02-W03 (Zr, Sa)Ti04 Ba2Ti9O20 Sr(Zn, Nb)03-SrTiO3 BaO-Sm203-5TiO2 BaO-PbO-Nd2O3-TiO2 Ti02 CaTiO3 SRTi03 15000 27 14000 30 10000 30 4000 30 8800 37 7000 38 8000 40 43 5000 77 4000 90 5000 104 40000(Qf) 180 70000(Qf) 304 33000(Qf) Factor - Table 3.1: High- Q dielectric materials, [50] factor. The definition of the Q factor is given by, in resonator energy stored in resonator energy stored 27r Q_W = energy dissipated energy dissipated per cycle (3.2) In figure dimensionless Q is loss in the providing order a of merit of circuit. where be the energy must resonator, coupled into the resonator with either to excite To into input/output take the coupling. electric account of effects magnetic or factor the loading, of a structure can be broken down into different factors, quality Qv,, Q, Q, Qe The first the QL. Q, loaded the external the unloaded and namely for internal lossesand the external Q accounts for external Qv, accounts unloaded losses when the resonator is part of an external circuit. The loaded Q is the into account the loading effects of any external circuits on factor taking quality itself includes both internal and external losses. This figure and the resonator however, Q. Qe In be easily, be measured and can cavity only extrapolated. may dielectric medium, conductor loss the and radiation can contribute resonators, Q. These losses be individually dielectric If the can the unloaded to classified. 3 Dielectric Resonator 41 Filters Quality Factor high DR is from is the the the enclosure, and of physically remote walls constant the electric and magnetic fields of a given resonant mode will be confined in and fields forming These the the of will material vicinity a resonant structure. around freespace distance to the to values negligible within a small relative attenuate Q As losses become the a result, radiation unloaded minimal and wavelength. determined filter by loss is dielectric the tangent the the primarily material of of DR filter. is loss The the for dielectric to tangent material construct a used defined by o' tanb= WEper dielectric is is the the constant, ever a conductivity where frequency. is the radian w Note that (3.3) of the medium and Q is inversely proportional to fractional bandwidth allowing DR filters with high- Q to have narrow bandwidths. If all the is losses the inside DR the of resonant energy mode stored occur no and electric due to external fields, the unloaded Q is tan S (3.4) Dielectric losses then become dominant and largely dependent on Q. For all DRs, losses external will always occur due to some form of radiation or practical dissipation in a surrounding metal shield. These losses will reduce Q., however, increase Q. energy stored will external For a permittivity greater than 100 or higher, these effects are negligible and equation 3.4 becomes a good approximation for the unloaded Q of a DR. The benefit of this is that an unloaded Q of 50 000 in be a reasonable volume, of which, would be impossible for metallic obtained can filters. waveguide For a resonator in bandpass, or bandstop configuration, with resistive matched load impedances, loaded the and quality factor can be obtained from measource dB bandwidth of the S21,or S11 3 the suring as shown below, Quality Factor 42 3 Dielectric Resonator Filters f0 QL = (3.5) tf3dB S21, frequency the Of3dB dB bandwidth fo is is 3 the the of resonant and where A 3.1. figure is in typical transmission S11, response shown response. or 0 M -3 b N N 0 a. u E Iw F to Frequency Figure 3.1: Transmission responsedisplaying resonant frequency and 3 dB bandwidth The external Q can then be obtained from QL and the insertion loss of the frequency by the at resonant solving, resonator ýQw QL Qe - S21 f0) or QL e= (3.6) s11(f0)) S21 is S11 the transmission fo, the and reflection resonance, at coefficient where for a bandpass and bandstop resonator respectively. The unloaded Q can then be found from, QL Qu =1- or S21(.fo) (Qe QL =1- Sii (fo) I (3.7) For accurate measurements,the coupling should be weak such that any influence from the loss of the feedline structure has negligible impact on extrapolation of Q. The definitions three above the unloaded can be related by 43 3 Dielectric Resonator Filters Coupling to a transmission line 11_1 Qu QL (3 8) Qe Thus, the Qv of a resonator can be measured. 3.3 Coupling to a transmission line An advantage of DRs is the ease with which they can couple to common transA DR lines. be in typical TEola transversely the operating can mode mission inserted into a rectangular waveguide and by coupling to the magnetic field, a filter formed is figure bandstop in 3.2. Coupling the to magnetic as shown simple field in the waveguide can be adjusted by rotating the resonator or moving the In the the line the towards side of waveguide. applications, microstrip resonator Rectangular tic Field TE,,, Dielectric Resonator Figure 3.2: Magnetic field coupling of a DR to rectangular waveguide forms bandstop DR figure in filter 3.3. magnetically couples and a same as shown This is the simplest way to incorporate a DR into a microwave network. In this by is lateral the adjusted coupling movement of the resonator from the micase, A low-loss line. low dielectric be support with crostrip may material constant the increase to which resonator the Q. In order to prevent losses would raise used due to radiation, the entire device is enclosed in a metallic box, often aluminium. The resonant frequency may be calculated using equations from [53] and may be increased through perturbing the magnetic field via a tuning screw, or metal the down in frequency resonator or shifted above by moving the resonator plate, Configurations 44 3 Dielectric Resonator Filters howis 10% A tuning typical from possible, the plane. range of ground away Q degrading be temperature of taken to performance or avoid must ever, care DR. in by the to the close proximity moving metal plates the resonator M S Figure 3.4 3.3: Magnetic field coupling of a DR to microstrip line Configurations DRs are the basic building blocks in DR filters. Fields inside a resonator store frequency the resonant where equal storage of electric and magnetic energy at is An DRs cavities advantage of over corresponding wall metal energy occurs. it fields inside be the to the whereas, perturb shaped they can evanescent cavity, Typically, hollow inserting to impossible is cavity without shape a extra materials. DRs have a disc form that can be modified to include notches, chamfers and holes in and multiple-order modes spurious to control inter-modal issues of address couplings. devices, these perturbations Three conventional may for DR a shapes figure in 3.4 the theoretically the and among geometries, explored shown are L<D, is considered the most advantageous as a resonator shape, cylindrical filter structures. in element c T L bý (s) (b) ODI (c) DR Three (a) 3.4: configurations: Figure rectangular resonator, (b) cylindrical L<D, and (c) cylindrical resonator, L>D resonator, 45 3 Dielectric Resonator Filters Configurations At microwave frequencies, any physical entity can be used to realise a resonator, boundary the shape, size and whereby, conditions applied will determine the internal electric and magnetic fields. The most common type of DR. structure is the cylindrical suspended DR structure as shown in figure 3.5. A 'Shielding is used losses from to prevent radiation enclosure an as aluminium and copper. and typical metals used include If the walls of the outer conductor are moved closer to the resonator, the resonant frequency of the TEola mode is increased due to the cavity perturbation theory. This theory states that when a metal wall of a is inward, frequency if decreases the stored the moved cavity resonant resonant displaced field is the predominantly of energy electric. Otherwise, if the majority fields frequency displaced is the increases the case magnetic, are resonant as of here for the TEolb mode resonator. The relative dielectric constant is typically between 20 to 80 and the DR is remote from conductive walls, usually about twice the largest dimension of the DR. This is important as any current induced by field the the metallic surface external of the resonator may incur serious on frequency the effects on resonant and also reduce the high intrinsic adverse Q of the resonator. Conducting "Enclosure , a, co z Lr 1 fa 1 alil Figure 3.5: Commonly used DR structure, [28] Since most of the electromagnetic energy is stored within the dielectric at the frequency, frequency this largely is resonant controlled by the dimensions and dielectic constant of the dielectric material itself. By assuming that the lateral DR behaves ideal the as of an magnetic boundary, the resonant frequency surface be approximately calculated field may patterns and since it is now assumedthere is zero tangential magnetic component on the curved surface of the DR. In all filter configurations, preventing Q degradation requires dielectric the mounting 46 8 Dielectric ResonatorFilters resonator 3.5 ResonantModes on special supports. Resonant Modes Similar to conventional metal wall cavities, an infinite number of operating modes DRs boundary be in excited satisfying conditions. exist and may These modes (TE), distinct known into three transverse be electric groups as classified may (TM), Each hybrid (HE) of and electromagnetic modes. transverse magnetic has families three an infinite variety of individual these individual suit will modes applications. modes, thus, particular Plots of the field distributions [54]. figure 3.6, For in L<D, a puck where shown are modes for these the lowest frequency has TEola distribution. field is the mode which a circular electric resonant mode The magnetic field is strongest on the axis of the puck and maintains a magnitude distance The field the outside puck. to a sufficient resembles that of an axial magis commonly used. For L>D, dipole this mode and netic the fundamental mode is the TMola mode which has an equivalent magnetic dipole moment transverse interest is The the HEI, s in which both the electric and of the other mode to axis. direction. field the azimuthal over vary magnetic has distinct This dual-mode configuration advantages over single-modes offering better performance, smaller fundamental [55]. less filters, TE than TM classical weight or mode size and Comprehensivestudies of modes in DRs have produced mode charts for the cylindrical system and a few examples are illustrated in, [56], [57], [58], [16] and [59]. design important tools for filters and other applications. A These charts are [28]. is in figure 3.7, shown chart typical mode The most commonly used mode in a DR is the TEolb mode in a cylindrical resin TE116 the mode a rectangular resonator since the former has the onator, or for frequency, certain diameter/length, D/L, ratios, and is therelowest resonant , fundamental the mode. The HElla degenerate hybrid mode fore, classified as smaller of the volume advantage and weight, half the number of cavities, offers Resonant Modes 47 3 Dielectric Resonator Filters 08 (0,15) . TEE, TT 0 @1 "o T"T T"T T 1T' T1 v T_r HE,,, EH, a .r T T 03 l' .1 T"r T"T r r 111 T TIr T {ý. týýýJ ii Tý 1% Vrý. hilt I T"T r "r ýI Tr=2 1 T HE,, Figure 3.6: Field plots of common DR modes, [54] devices. This is to single-mode possible since each resonator when compared independent in is DR two A drawback the and orthogonal of modes. resonates proximity of resonant modes to each other and in order to make the DR useful for practical applications, a goal in resonator design is to separate the resonant frequency of the operating mode as far as possible from higher frequency modes. little to exhibit shown Side walls were effect when placed at a distance greater DR, however, diameter the the have the of the aspect can than a ratio of puck improving in the spurious In TEola performance. effect mode operation, positive diameter, height H/D, the for both over 0.4 is of of around recommended a choice 3 Dielectric Resonator 48 Filters Resonant Modes iss--------------'_"_ -qri$ I Figure optimum M. i- fnetlwd for % ao Q. o,w .,, waq ayüidn ---"Motif r 3.7: Typical DR mode chart, [28] Q and minimal interference of spurious modes. A chart depicting this is shown, figure 3.8. [24]. By introducing a hole at, the centre of the DR, the spu- between the fundamental separation rious TEol s mode and higher-order modes be Figure improved. 3.9 shows how the spurious characteristics are improved can function diameter, of as a ring [17]. This property can be used to improve the spurious performance of dielectric loaded filters. ýZ ri U Er = 36 Er =1 , , 2 D/A=I. 5 ýn 5' L/13.0 » h: --TE02 V 2 HE 12 HE13 C C C ýý TMOI 5 HEIL TEOI 1 1 1.5 2 2.5 d// (Diameter Figure 3 DR/Length 3.5 4 4.5 of DR) [24] 3.8: Mode chart of a DR in cavity as a function of aspect ratio, Even for a radially symmetrical anode such as the TE01 which only has three , 3 Dielectric Resonator 49 Filters 3r - ýrý ý rT-r Resonant rT Er, 36, Er2=1 d/l=3.5 ddD ý2 Modes TE02 D/d = 1.5 L/l-3.0 5 HE13 L T U C U C U HE12 TMO1 2 U. C A C 0 H .. S HE11 TEOI -. 1 0 .1 .2 d, /d (Diameter .3 .4 of Ring/Diameter .5 of DR) .6 Figure 3.9: Mode chart of a DR in cavity as a function of aspect ratio with improved spurious performance, [17] components of the electromagnetic various simplifying field, rigorous analysis is still a problem and assumptions are required. The situation is more complex for higher order modes that are generally hybrid, usually degenerate, and have all six components of the electromagnetic field. To identify and distinguish the hybrid modes with strong axial magnetic or electric fields, Kobayashi proposed a naming convention using EH and HE notations, [58], respectively. A modern classification system proposed by Zaki, [59], is more simple and defines HEE,,,,, and HEH7,,,, with the first two letters indicating the symmetry wall, z=0, a hybrid mode and the third letter, E or H, if is an electric or magnetic wall, respectively, as shown in figure 3.10. The first subscript, n, indicates order of angular variation of the fields and the second subscript. in, is the order of the resonant mode. This system is used in the study of the hybrid modes for the proposed dual-mode resonator. Z=o Z=o (a) (b) Figure 3.10: Classification of HE modes showing E-field component for (a) electric wall (b) magnetic wall 50 3 Dielectric Resonator Filters 3.5.1 Resonant Modes Cohn's Model An accurate prediction of the resonant frequency is possible only when all boundary perturbations are taken into account in the theoretical A preferred practical approach intensive. orously complex and mathematically is rigand analysis is to find solutions for the DR in simple ways to produce results close to actual At high the of surface regions of permittivity, values. PEC, conductor, or short-circuit a perfect electric the boundary behaves like boundary when observed from the air to dielectric regions. The reflection coefficient of a plane wave normally incident at the dielectric to air boundary is given by, rho-? 1 = +7 770 -1 N+ er +1 (3.9) impedance the dielectric, are waveand rj of 71o air and respectively, and where boundary, The from dielectric 1. » to air, can now be approxiwhen observed er hypothetical by a mated perfect magnetic conductor, PMC, on which the normal field the of electric and tangential components components of the magnetic field boundary. This internal the in total the concauses at reflections resulting vanish finement of energy in the high permittivity hypothetical be as a explained can object. To a first approximation, a DR perfect magnetic conductor, PMC, waveguide field distribution the therefore, cavity, be calculated analytically. onator can and resonant frequencies for such a resThe magnetic wall waveguide below cutoff dielectric in the middle is as shown in figure 3.11. resonator situated a with In reality, electromagnetic fields leak out of the resonator and eventually decay This leaking be described by a mode subscript S and the may exponentially. is model modified to account for this by removing two lateral wall magnetic Thus, the the effects of the top and bottom covers resonator. of walls magnetic dielectric the and support or substrate are factored in to improve the puck of figure in the 3.12. model as A simple mathematical model of shown of accuracy below is introduced waveguide cutoff in which a second-order model a magnetic 3 Dielectric Resonator 51 Filters Resonant Modes 3.11: Cohn's second-order DR model showing a DR inside a magneticbelow cutoff wall waveguide Figure of a cylindrical DR is used, [11] and [60]. This model reduces to Cohn's standard model when the two plates are moved to infinity, L1 = Do and L2 = oc with air occupying spaces on each side of the dielectric, 6,1 =1 and Ere = 1. Thus, an isolated resonator in free space is assumed. Both the TE016 and HEI1 modes of DR be can a solved using the modified Cohn's model. for the TE016 mode is approximately accuracy A calculated frequency 6%, [61]. fz PEC, Enclosure r Figure 3.12: Improved model for a shielded DR The EM field within each region can be expressed as Hz = (Aeryz + Be-rynz)J0(knp)) (3.10) 52 3 Dielectric Resonator Filters HP --P P (Ae')"pz- Be-"pz)Ji (kPP)) tt"(AeYPz E4,_J Resonant Modes +Be_ Pz)Jl(kpp)) (3.11) (3.12) P fixed index. is The is the the region mode radial propagation constant of where p by the PMC wall at p=a, and for TE016mode to be solved, (3.13) kPa = Xoi = 2.4048 HE118 be for to the mode solved and (3.14) kpa = X11= 3.832 The separation constants are Q2 = -rye = köe,. 2- 71 12 - (Xa 1) 2-k,. (Xa l) 2 (X-') 2 (3.15) aI (3.16) 1 (3.17) kj r2 Using the properties of the perfect electric wall, PEC, at the top, where z= L1+L+L2, and bottom enclosure plates, where z=0, and applying the boundary dielectric the Ll at surface, z= conditions and z= Ll + L. This ensures the tangential components of the electric and magnetic fields are continuous at the interface. Solving the field equations, the following can be obtained. 01 01 ßL = tan-1 = tan-1 L'L2 +2+ (cotiviLi) (3.18) (coth2L2) 17r, 1=0,1,2,3, (3.19) """ (3.20) 3 Dielectric Resonator 53 Filters Resonant Modes For generality, the added angle 17rgives all possible resonance conditions. When 1=0, the mode is the lowest fundamental mode TE016or TElla with the desired 6 than smaller constant, propation where nonintegral signifies a number, radial for lowest As 1=0 desired the the shown, mode, of radial propagation unity. field in DR less half the than variation a wavelength within undergoes a constant, the resonator length, L, due to the end effects of the air-filled region. This model by improved further the leading the to removing of calculations circular wall was frequency [62] [61]. to 1-2%, an accuracy within and resonant 3.5.2 Mode-Matching Model A simple DR model is helpful during the initial stages of the analysis or design lacks but design. In the for accuracy needed modern microwave circuit process housing is to configurations, resonator a metal-wall necessary cavity or actual the Q. Due field degradation in electromagnetic of radiation of resulting prevent to recent progress in computer technology and computer aided design, CAD, tools for microwave engineering, many EM simulation software and methods have been developed and can be used to compute the exact resonant frequency and field patterns for a DR. The model described previously was modified leading to for formulae frequency distribution field resonant and accurate electromagnetic in the structure through mode matching method, [63] and [53]. The radial mode matching method is used to analyse any cylindrical DR configu[64] described in using a general multilayer configuration with adjustable ration as layers in both longitudinal material of number and radial directions as shown in figure 3.13. The resonator structure is partitioned by boundaries. appropriate terminated into a succession of waveguides Region ii of the resonator is filled with a dielectric material with relative permittivity, e, t and loss tangent, tan6; j. The layers and material properties of can be assigned individually number to the resonator structure. The top and bottom according planes of the structure can be PEC, electric conductor, perfect or perfect magnetic conductor, PMC. either 54 3 Dielectric Resonator Filters Resonant Modes The variations of the TE and TM fields of the modes contributing to resonance are first expressed in each radial region and are matched at each interface to establish the continuity of the fields tangential to a discountinuity of the medium. To simplify the analysis, the normal mode fields are decomposed into two orthogonal These TE, Ez the 0, and TM, modes, where are solutions. modes, of where sets = z H, = 0. Finally, the orthogonality property of the modes is applied providing z linear infinite These set of equations. are then rearranged and truncated to an form a matrix whose determinant will be zero at the resonant frequencies of the field The field be the to then coefficients of each mode can obtain solved cavity. distribution and unloaded Q. Z bN- er Pr b" bý I1Nz /N. Cr gr 2Ns 2N: Er gr Er12 Er22 Er tr I. 12 Rr 22 9, Cr Er 21 Er I b 1 T Rr 11 11 "O Fr 21 NrN: NrN. N, 2 N.2 PEC or PMC Nr1 Nrl P NnJ Figure 3.13: Generalized multilayer cylindrical DR, [64] In advanced models, additional factors such as dielectric supports and tuning into taken The are account. resonant frequency of the DR in these mechanisms be can calculated using the mode matching method with accuconfigurations Recently available electromagnetic 1%. better than racies simulation programs improvements in the calculations of relatively complex strucadditional enable tures. Using such programs, the resonator housing, tuning and coupling elements be precisely modelled obtaining accurate results taking into account practical can design. An the additional advantage is the electromagnetic field disaspects of 55 9 Dielectric Resonator Filters Resonant Modes Table 3.2 be dissipated power, easily. tribution, etc. can visualised and plotted Cohn's frequencies both DRs by the simple computed of several resonant presents model and rigorous mode matching method. Mode 6, DR Radius (mm) DR Length (mm) L1, L2 (mm) Cohn's Model MM Method Measured (MHz) TEol TEol HE,, HE,, 36.2 3.015 4.16 3.411 7419 7941 7940 [61] 36.2 37.6 38.2 3.995 8.00 6.80 2.14 6.90 5.60 4.43 inf inf 7159 4373 5152 7758 4210 4980 7790 [61] 4196 [30] 4994 [30] Table 3.2: Computed and measured resonant frequencies of DRs, [65] This method is one of the most efficient and precise methods for DR analysis and design but for complex three-dimensional designs, 3D, with non homogeneous is is time there to this a vary a number of consuming need where method media, dynamically. parameters 3.5.3 HFSS Finite Element Model The finite element method, FEM, is used to solve Maxwell's equations in the three-dimensional from transfinite the this, arbitrary structure of and, volume be determine field to the two-dimensional can used method solution to element input and output ports, [66]. This method has been successfully used to analyse dielectric-loaded cavity resonators using one-dimensional FEM and is economical for dielectrics extended along the length of the cavity, [67]. 2D and 3D FEM have been applied to evaluate and design high quality TM and hybrid DR modes and full 3D for is the for of a analysis structure shown need greater accuracy of a [68]. Resonant frequencies for TE devices, and TM modes of axisymasymmetric dielectric been containing common have structures resonators calculated metric in different environments with tuning screws, [69]. HFSS is a software simulation package that uses the generality strength of FEM to analyse arbitrary, complex voluminous or planar 3D closed device with var- Dielectric Resonator Filters Resonant 56 Modes ious levels of resolution in the problem space. This allows the user to address large in based problem spaces efficiently problems on the adaptive mesh minute refinement method. The inner materials must be homogeneous and linear but dielectric losses. The be possess and or metallic studied structure anisotropic can is generally closed by perfect magnetic and electrical conditions or excited by The lines or waveguides. obvious advantage is the ability to visutransmission be include fields thus, the to modes. the resonant structure of may modified alise This fields tool in the true the approximates problem space modes. or suppress by discretizing the field domain into basic elements that are roughly 1/10 of a guide wavelength. The finite elements are contactual domains, in 1D line triangular elements as such 3D in problems. elements volume their flexibility form the simplest and of in 2D domains and tetrahedral The advantage for these simple elements is to subdivide any arbitrary geometry, figure 3.11. Components of elements of field tangential to edges stored at vertices explicitly of field tangential to faces and normal to edges of elements explicitly stored at midpoints of edges Components '-" Value of interior point vector field interpolated from nodal values Figure 3.14: Mesh with tetrahedral eleiiieirts fur tiiaxiiºiiiºii imate shape of 3D dielectric puck flexibility to approx- The solution is found by summing the magnitude of t lie fields or potentials at junction each of elements. It computes the eigenmodes at each port by using by the user and the S-parameters, for the structure, modes chosen of the number by to tolerance the within a set user. The finite-element, mesh is calculated are desired the number of passes a tolerance is achieved. Once a until over refined frequency, is the at one created raine mesh can be used to sweep a range mesh frequencies impedances the and are calculated at each port for eac11 of proximate An adaptive pass is run at the frequency S-parameters. set of of interest to create frequency sweep is finite-element mesh and a performed acrosss the interested a Adaptive be passes range. can run at the end frequencies to check the spectral 57 Filters Resonator 3 Dielectric Resonant Modes the mesh. of validity HFSS has different frequency domain solvers. For a driven problem, an external is applied at a physical access port and a matrix energy source of is built and inverted to find the solution at each frequency of interest, of which the scatterA sourceless problem can also be solved using an ing parameters are calculated. defined with short circuited planes. The solutions to the solver eigcnnlode solver from derived stationary are field configurations and formulate cutoff frequencies for frequenconstants waveguide structures propagation and resonant natural and Qs field For dielectric in and of plots resonators. a situated resonator puck cies, frequency between produce can mode one charts of variations resonant a cavity, the of resonator. variable any and The mesh algorithm topologies boundary density and in the vicinity becomes high, coefficients depicted allows it to predict in that thus, area. in figure 3.15(b). This time is required. accuracy and computational (e) the energy of the solution, is very sensitive finer subdivisions The resolution to elements of 0.2. E in figure 3.15(b). tive mesh, a convergence of a singularity requires for particular density mesh the value of the functional figure in 3.15(c) as shown aceiiu"acy longer computational the required for better to the accuracy as for he the greater varied of mesh can where the elements The compromise E 0.1. in comparison are for greater resolution is a Also, to ensure the accuracy of each adap- value is required that also has a compromise between time. (b) (a Finite 3.15: element method analysis of dielectric Figure hole: with axial puck (a) basic geometry, (h) view of mesh with 0.2A mesh, (c) view of mesh with 0.1A mesh 3 Dielectric Resonator 58 Filters Resonant Modes There are some drawbacks to HFSS, notably performing a frequency sweep with dependent frequency. frequency Eigenmodes on are calculated at each eigenmodes but to in HFSS, the the according propagation mode numconstant ordered and bering may become erroneous towards a higher frequency. For example, eigen- 2 in low frequency is 1 remain will shown and order mode at until an extra mode in the structure that has a frequency less than eigenmode 2. This new mode will be labelled Furthermore, 2. and will as eigenmode replace now impedances are. HFSS in lines These impedance defined the unless ports. are on not calculated the lines difference points connecting of maximum voltage at each port and are for Only for defined different impedance lines mode. each one set all the of are are frequencies in a sweep and must be defined in the same order as the corresponding When during lines impedance the modes are switched a switch, are no modes. longer valid at each frequency and no impedances will be calculated. factor is time as the simulation tion a Computa- must subdivide the whole volume, thus, more solutions are required at each node in the mesh. The material properties [70], in HFSS, [71], dielectric have been design filters, DR resonators and of of latter, a combination For the analysed. of the accuracy of HFSS and rigorous inter-resonator has couplings of produced slotted-DR filters without tunanalysis ing. Unfortunately, a frequency shift of 0.2% between simulated and measured that HFSS is although shows promisingly responses accurate in 3D simulations, for dielectric-loaded cavity resonators, tuning must be present to compensate for imperfections. practical With regards to this, sensitivity simulations should be to the understand efifect of physical tolerances on the response of the performed device. 59 Chapter 4 Dielectric-Loaded 4.1 Compact Bandstop Filter Introduction Proposing the use of dielectric loading within waveguide sections is not uncom- [50], [72] the filters in as size and of resonant sections and other components mon, dramatically are reduced. However, energy is now strictly confined to metallized Q by least the the ratio of 1/ values are reduced at and sides losses. Since resonances are fully supported within that of a conductor-loaded exceeds performance is because energy is not in substantial E,.neglecting metal the dielectric region, high Q or cavity metal resonator. This contact with metal except on enclosure filter A bandstop by realised means of rectangular walls. dielectric-loaded res- inner to the rod of a coaxial transmission line with square outer coupled onators described. Commonly, is coaxial resonators are normally realised for conductor base station filters but conventional waveguide components are used as they offer lower loss. The existence of a dielectric-loaded waveguide allows for near perfect For hollow example, walls. when a magnetic waveguide is transversely cut, the but in the high radiate ends presence open of a Cr medium, the open ends approximate a near perfect magnetic wall and will not radiate, although a small leaky fields of are present. Maximum reduction is obtained by the percentage loading the of rectangular waveguide resonator cavities and although complete Q. values are smaller, calculated values are acceptable for base station mobile 4 Dielectric-Loaded Compact Bandstop Filter applications. 60 TE10b Rectangular Waveguide Resonator This physical arrangement allows a simplicity design where rectangular dielectric-loaded line. to the coaxial coupled cavities in the mechanical resonators are fitted into prescribed The narrow rectangular resonators allow for inter-resonator spacings of A/4 offering further miniaturisation. For example, dielectric resonators waveguide and pucks, when coupled to a transconventional [3]. [73] 3A/4 line, flexibility The design require spacings, and adds mission in that the resonators may be positioned at any distance along the transmission line for adjustable phase lengths. Also, the cavities may be easily machined to in- dielectric different shaped resonators, metal-loaded or completely unloaded clude Initial designs have focused dielectric narrowband slabs of permiton resonators. tivity, 44, exciting the TE10 mode at 2 GHz. Preliminary bandwidths dB 3 coupling produced data have simulation in the region of 25 MHz for a 4th degree filter. Possible applications for this device include UNITS base stations and other communication applications where rejection of signals is necessary. The advan- tages of this filter are that more complex designs can be carried out based upon this simple structure, i. e. layering coaxial lines and resonators on top of each forming multiple other instances of bandstop behaviour over a broad frequency layout similar to end-coupled bandpass filters. The physical structure range with also allows ease of positioning of tuning screws for both input coupling and res- frequency is which neccessary to ensure the response meets the required onant In designs, fabrication all practical specifications. tolerances can make the mea- different to the response simulated response, thus, some form of tuning is sured required. 4.2 TEios Rectangular Waveguide Resonator The design for the TElos dielectric-loaded rectangular resonator begins by finding the dimensions for the required resonant frequency. The rectangular waveguide is a hollow-pipe waveguide where an air-filled, or dielectric, region of width, a, height, b, and length, l extend indefinitely in the axial, z, direction and is enclosed 61 Dielectric-Loaded Compact Bandstop Filter TE106 Rectangular Waveguide Resonator by conducting boundaries on four sides. In this one-conductor guiding structure, TEM, wave exists since no axial field components no transverse electromagnetic, for TE TM do and modes propagate through this waveguide. which unlike exist, The TE10 is the dominant mode in this waveguide for a>b propagating it is the lowest cutoff in this rectangular structure, since figure 4.1. By shorting the two ends of a segment of waveguide, a rectangular cavity resonator is formed with two groups of resonant modes, TEmnp and TMmnp, and these correspond to TEmn first in The TMmn propagation modes open-ended waveguides, respectively. and two subscripts, m and n, follow from TEmn and TMmn modes, representing the directions. the along x and cycles y changing the along z axis. cycles changing fundamental mode for b<a<l The TE101 mode corresponds to the lowest [74], field the of which solutions are, Ev = -2 Hý The third subscript, p, denotes A wµa sin (äx ) Aa (äx) sin 1 _ Hz = -j2A cos Ca sin cos sin (7Z) (4.1) (äz) (4.2) (7Z) (4.3) Ey=Ez=Hy=O (4.4) u /I b ,ýZ1 x 4- a -* Figure 4.1: Field distribution of TElol rectangular cavity In such cavity resonators, the resonant frequency for be TE101 may cavity a 62 4 Dielectric-Loaded Compact Randstop Filter TE10b Rectangular Waveguide Resonator [75], from, calculated fmnp = 21rc 2+ (Plr)2 (-. µr r -) \aJZ+ (4.5) The rectangular waveguide should be designedto operate at a considerably higher frequency than the cutoff frequency which is given as [m1r'2 ý-(nlr)2]'/2 b(4.6) -a1 light dielectric for in is typical the of aspect velocity medium a v a and where free in by 2b is space, w,, given a= ratio of we =ä (m2 + 4n2)112 (4.7) The reason for this design factor concerns the group velocity of the waveguide, by v9, given 1/z 2 A9=dý=vf1-(w°)1 (4.8) As shown, as vg approaches zero, w approaches w, and 0 tends to zero leading to phase distortions as the signal frequency approaches too close to the cutoff frequency. The guide wavelength for a TEIG waveguide is defined as 2ic IN9 ==Q Ao [1 - (wc/w)2]1/2 (4.9) free is A0 the space wavelength, ,ß is the propagation constant and w, is where For frequency. the E field to be zero at z=0 the cutoff to form a and z=l TEloi mode cavity resonator, l must be one half-guide wavelength and knowing frequency of a mode in a rectangular waveguide, this length is given as the cutoff 63 4 Dielectric-Loaded Compact Bandstop Filter TE10b Rectangular Waveguide Resonator xO 12 (4.10) 2[1 - (o/2a)2]1/2 /w)2]1/2 2[1 - (wý\O frequency be from to the resonant calculated which allows C fo_ To c(a _ 2+ 12)1/2 (4.11) 2al Q determine losses finite in the the The effects of unloaded of the conducting walls determine EE be by forming integral to This calculated a volume of can resonator. dividing dissipated in by due it the to the currents energy and the stored energy [76]. be The factor the the estimated quality of resonator, resonancemay walls of from, [(m)2 b Q-=X ý0 + abc (a)2] {(m)2 (2)2 + 4 J } [(4)2 + ac{(d)2ýc)2+ +bc + (n)2,2 (4.12) 222 nl2 ý/ \l 54 (P)2] +[()2+ `b/ [G; +ab(E)2 ) 2+ (n)2] following the leads to This result for the unloaded Q for a TElol mode cavity, Aabl Q"lol =S2ä U-7+ 3/2 (a+ 2b) +a (l + 2b) (4.13) free space wavelength to the is the A/b of ratio skin depth of the conductor where frequency. To find the Q, lossy losses dielectric overall the in the resonant any at for be found from equation 3.4 and the total loss is accounted and must medium from, be calculated may 64 Q Dielectric-Loaded Compact Bandstop Filter (_1 Qioi =+ Qu1o1 Configuration of Proposed Filter 1 -' Qu (4.14) The design equations above have produced initial dimensions based on a dielectric waveguide resonator with short-circuited ends to approximate the TElol mode, however, the resonator used in this filter has open-circuited ends to allow coupling to the transmission line to produce the required attenuation transfer response. These open ends allow a small leakage of magnetic fields outside the dielectric boundary. Although the resonator length was designed to be l= a9/2, such that there was a half cycle in the z-direction, for classification correctness the dielectric-loaded defined is the TEloa as mode mode. The subscript, S, denotes 2l/a9 in the z-axis to account for the leaky fields, how<1 ratio noninteger a from this section are still applicable in the design of the initial calculations ever, dimensions of the TElob mode dielectric-loaded resonator. 4.3 Configuration Proposed of Filter The proposed filter follows the classical design of bandstop filters with a planar topology consisting of a main transmission line capacitively coupled to inductive [73]. figure 4.2, The shown as same design can also be realised using a stubs series of waveguide resonator cavities positioned periodically along a waveguide transmission line, figure 4.3. The principal objective is to load the waveguide high dielectric with cavities e,. resonator material to reduce the volume of the form dielectric-loaded to segments resonant resonators coupled to a transmission line. From circuit theory, these segments must be spaced at odd multiples of a to cover a relatively narrow bandwidth at the centre frequency. wavelength quarter As reported previously, [73], a disadvantage with the waveguide transmission line is a minimum resonator separation of 3A/4 is required to reduce interaction effects if the resonators are wide with respect to the transmission line. This increasesthe length of the transmission line but by using rectangular DRs, only A/4 separa- 4 Dielectric-Loaded Compact Bandstop 65 Filter Configuration of Proposed Filter (2n-1))L v, Figure 4.2: Schematic of third-degree strip transmission line Bandstop filter Figure 4.3: Schematic of third-degree cavity wavegi ide haixlstop filter tions would be needed reducing the length of the line leading to miniaturisation. is possible but physical realisation would be For the TE106 DRs, a inicrostrip complex and weak couplings between the resonators and transmission line would be problematic, even for narrowband designs. Also, shielding is needed to confine the fields leading to a larger volme. A coaxial line would be more advantageous for is high power, allows ease of coupling and a uniform it suitable as section offers advanced configurations discussed later. resonator, coaxial conductor, rather than circular, cross- dielectric-loaded broadband the such as An air-filled coaxial line with a square outer is chosen as the square shape compliments the DR for waveguide coupling purposes. If a conventional circular outer rectangular fabricated the lid used, was conductor would be positioned in the middle of the figure 4.4. line, in will which the cause transmission spurious effects cross-section In addition, portions of the outer circular coaxial conductor must be removed to enable a coupling window to the rectangular resonator. Removing this section 4 Dielectric-Loaded Compact Bandstop discontinuity a will cause Filter 66 of Proposed Filter Configuration in the coaxial transmission line at the coupling points. Thus, a square outer conductor was more suitable. ýý, jý (a) ' (b) (a) DR Circular Schematic line to transmission 4.4: Figure of coupled coaxial Cross-section of feasible realisation (b) cavities The resonator structure is shown in figure 4.5 with the length of each rectangular long. A/2 resonator The dielectric is metallised on the four longer faces using between inside the direct of sides placed a and contact cavity with plating silver line from These distance the displaced DR resonators were at a the and walls. tangential DR face that the the was such narrow rectangular of and positioned direction the of the coaxial line. to propagation Meal Line Coaxial Tuning Screw, Plating vIcicciric Slab Figure 4.3.1 Aluminium Enclosure 4.5: Structure of TEI0e mode dielectric bandstop resonator Single Resonator Design from dielectric was made material The a coiiipouiid a permittivity of 44. They were manufactured of CaTiO3-NdAlO3 and have with a measured Q. f product of 41 Compact Bandstop d Dielectric-Loaded 67 Filter of Proposed Filter Configuration had GHz, be They 21 000 2 a stable also available. aQ of would 000, therefore, at for dimensions Initially, in isolation. 1 the a temperature coefficient of ppiu/°C frequency TElob in the of mode with a resonant operating waveguide rectangular 2 GHz were calculated. To utilise the dominant mode, the width of the rectangular DR, a, was taken to be at least greater than A/2. Taking into account the dielectric loading of the waveguide, the effective wavelength, Aej j, is calculated from, 8 108 c=3x f 2x10 Aeff=_ 15 e,. 44 22.6 mm = (4.15) However, this length should be kept near the minimum allowable value to ensure dominant the only mode propagates in the interested frequency range, there- fore, higher-order modes are avoided. Thus, a was reduced to 14.1 mm and the height, b, was taken as approximately half the value of a, therefore, b=7.1 The length, 1, of the resonator was then found by substituting mm. these values into 4.11 to give, equation l = [l a - (iref f/2a)2]1/2 0.0226 18.8 mm = 2[1 - (0.0226/0.0282)2]1/2 (4.16) Using the above dimensions, the Q for this resonator was calculated, first by Q imperfect the ideal the of cavity with and conducting an walls calculating dielectric material with zero intrinsic loss. Taking into account that silver plating GHz, 2 was used, at a_1.479 b and substituting x 105 `/7 104581 _ (4.17) into equation 4.13, Qloi = 2586 (4.18) 4 Dielectric-Loaded Compact Bandstop Filter Hence, as tans 68 Configuration of Proposed Filter = 0.000048, Quloi 1 1+1 (Q. 101 Qu (4.19) 2302 Thus, a large unloaded Q. for a compact resonator is produced allowing the delosses for that to should a narrowband response compensating any achieve signer irregularities to a system, coupling surface occur such as and other perturba- line between line A/4 The transmision was a coaxial enabling separations tions. line. This enforces the objective to achieve miniaturito the coupled resonators lines in to 3A/4 transmission avoid separations are needed waveguide sation since fordesign To line, inter-resonator the the couplings. empirical coaxial unwanted line inner for with conductor square conductor coaxial outer and round a mula is, 770 Zo = In [(1.0787D/r)] 21r Fcr (4.20) free-space, impedance D is is is the the the wave of and rho square r side of where inner A the diameter of conductor. system impedance of 50 SZand a dimenthe defined to give r=4.68 mm and a simulated response as 10 D= was mm sion The coaxial transmission line achieved greater than 20 dB 4.6. figure in shown GHz bandwidth loss GHz, 2 frequency a2 thus, over at an operation of return line for design the was suitable transmission the and these dimensions were used for the physical realisation. Details of the typical dimensions and physical performance for the resonator with coaxial connectors are shown in figure 4.7 and The the tuning screw has also been included, however, for 4.1. of position table in preliminary HFSS simulations. it omitted was simplicity, 4 Dielectric-Loaded Compact Bandstop 69 Filter FEM Simulations 0 0 -5 -5 -10 -10 -15 -15 -20 -20 CO -25 -25 in -30 -30 -35 -35 -40 -40 -45 -45 -50 -50 -55 -SS 1.5 2 Frequency GHz 3 2.5 co 4.6: Frequency response of air-filled square coaxial TEM line with circular centre conductor. D= 10 mm and r=4.68 inin Figure Typical Dimensions 14.1nini a b 7.1 min 1= 18.1mm al = 30 mm bi = 45.1 mm b2 = 47.1 min b3 =5min Table 4.1: Typical Typical Performance 11 45mm d1 = 1.3 mm d2 =4. lmm T = 1.7 mm 2.61 mm s D 10 mm 4.68 mm r dimensions foý=1.85GHz Er44 Q, 1=2200 First spurious frequency 2.5 GHz and performance of TE10 dielectric mode Band- stop resonator 4.4 FEM Simulations Electromagnetic field simulation the interaction of electromagnetic has proved to be a useful tool for predicting fields in microwave filter designs. By using the eigenmode solver of HFSS, FEM simulations of a TE106 mode rectangular DR with the calculated dimensions, produced field plots as shown in figures 4.8 fields The 4.9. shown clearly represent those of a TElol mode rectangular and half-wave there are as variations resonator direction and no variations in they and z both in the E the x of component direction. The tangential electric field 4 Dielectric-Loaded Compact Bandstop FEM Simulations 70 Filter C' --. r -------------- Lx .............. b, -º - b, ..- b -- 1ý 1 ........ I_-. y ý.. ................ Figure 4.7: Details of TEloa mode dielectric bandstopresonator vanishes at x=0 and x=1 long. half is the wavelength guide confirming one has field is E the the zero at end walls and Thus, one maximum at the centre of favourably how figures fields The the store electric also show modal the cavity. disperse boundary to its is walls whereas magnetic allowed energy within energy interface. five The first frequencies the the natural modes beyond air-dielectric of in broad 4.2 first table the shown showing and a advantage of were simulated MHz 885 fundamental the frequency. at above response spurious between the transmission line and the rectangular DR was dominant coupling The Dielectric-Loaded Compact Bandstop ýý Filter 71 FEM Simulations v (a) Figure =o (b) 4.8: Electric field of TE10a mode DR: (a)Vector Lines (h)Magnitude ý. ý, `ýI p I (U) 1.9: Magnetic field of TE10 mode DR: (a)Vector Lines (b)Magnitude Figure Table (b) Mode Resonant Frequency GH, Q TEIG, 2.0024 2554.1 TE102 TEo11 TE201 TM 110 2.8847 3.3937 3.415 3.5533 3628.5 2457.6 2879.1 3050.1 4.2: Simulated dielectric rectangular resonant frequencies cavity resonator and Qs of first, five triodes of isolated has been it that TE10 the DR already shown since readily stores mode magnetic but fields to leak. Simulations for the field allows magnetic energy electric plots of line to resonator couplings are shown in figure To transmission achieve the -1.10. the rectangular DRs were orientated coupling. maximum such that the magnetic fields from both the resonator and transmission line were not orthogonal. When the rectangular DR was coupled to the coaxial line, the resonant frequency 4 Dielectric-Loaded Compact Bandstop Filter 72 FEM Simulations a fl.. (a) P k == (b) (c) Figure 4.10: H-field plots of fundamental mode DR coupled to coaxial line: (a) Magnitude across transverse plan (b) Vector view cut through middle (c) Magnitude cut through middle decreased in frequency from 2 GHz to 1.85 GHz. This was expected as the couby dominated fields has inverse inductance magnetic relationship was and an pling The fast frequency. FEI\i is advantage as apparent of using an now solver with be performed to observe the relationships can simulations between physical di- found It the frequency. the that resonator and of required resonant was tnensious frequency of the rectangular the resonant DRs was determined by their lengths dependence distance Figure line. the 4.11 to the on coupling minimal coaxial with frequencies DR for different the length resonant simulated against values shows ranging of coupling spacing bandwidth was simulated ranging from 1= from s=0.5 mm to 10.5 min. to find the coupling 12.8 inin to 18.8 uim, figure The 3 dB coupling needed for different 4.12. The simulation for shorter DR. lengths, greater coupling bandwidth DR lengths showed that can he attained, however, the for this is the unloaded Q vVott1d compromise The first five modes and their resonant frectuencies for the experimental resonator 4.3. The in table mode classification has reverted back to shown are classical Filter Bandstop Compact 4 Dielectric-Loaded FEM Simulations 73 1.9 1.88 1.86 N 0 1.84 u c 1.82 LL 1.8 1.78 1.76' 2 .r.. -.. y........ length for DR frequency Resonant various coupling gaps versus Figure 4.11: 2: 21 N I Z 0 C to Co m1 V M n 0.5 1.5 2.5 4.5 5.5 3.5 Coupling Gap mm 6.5 7.5 8.5 DR lengths bandwidth dB for different 3 4.12: coupling versus Figure gaps distinguish between to variations modes with wavelength waveguide rectangular The is direction. the first spurious resonance significant observation in the z bandwidth MHz 650 spurious-free of approximately above the has maintained a these resonators are superior to conventional and confirms mode fundamental DR resonators where poor spurious performance often gives rise to more complex 4 Dielectric-Loaded Compact Bandstop Filter Mode No. 1 2 3 4 5 74 4th Degree Chebyshev Design Name Resonant Frequency GHz 1.850 TElol 2.494 TE102 3.336 TEoll 3.356 TE201 3.363 TE103 Table 4.3: First five resonant modes of prototype resonator designs, [77]. 4th Degree Chebyshev 4.5 Design inverter-coupled designed using was a shunt capacitor, A Chebyshev prototype from (b). follows figure design 2.3 The that the network, network to synthesise [39]. The specifications of the filter were assumed to have a centre frequency of bandwidth. MHz loss dB 3 insertion 40 than GHz greater at 1.85 and a stopband GHz, At in 1.85 the sepa4.4. table The complete specifications were as shown line to resonator tap points were calculated to transmission between the rations be a quarter wavelength long to avoid unwanted inter-resonator coupling. E Filter Specifications Centre frequency 1.85 GHz Passbandbandwidth d.c. - 1.844GHz, 1.861GHz - 2.5 GHz Passband return loss (La) 20 dB Stopbandbandwidth 3 MHz Stopband insertion loss (LA) System Impedance > 40 dB 1c Table 4.4: Filter specifications filter the degree needed to meet the requirements was calculated from, The of [39], N LA+Lß+6 201oglo[S + (S2 - 1)1/2] 3.68 (4.21) 75 4 Dielectric-Loaded Compact Bandstop Filter 4th Degree Chebyshev Design S, defined is N is the the required order and selectivity, ratio of passband as where 4th degree therefore, a network was required and the ripple level, e, to stopband, following for from lowpass the equation a prototype, was calculated (10LR110 1)-1/2 0.1005 6_ = Hence [sinh_1(1, 77= sinh (4.22) (4.23) e)] = 0.8201 Using, Cr =2 sin 77 Kr, r+l (2r2N )'ý (4.24) L 712 + sin2(rir/N)]1/2 (4.25) = 7) giving Cl = C4 = 0.9332 (4.26) C2 = C3 = 2.253 (4.27) K12 = K34 = 1.3204 (4.28) K23 = 1.5769 (4.29) For unity admittance inverters, a technique is used to scale the nodal admittance force ladder for to inverters the network a to have the same value. A matrix is figure in ladder 4.13 with N+2 shown network typical nodes. 4Dielectric-Loaded 4th Degree Chebyshev Design 76 Compact Bandstop Filter 11 In Figure 4.13: Ladder network for ladder is, the network matrix The general admittance Yoo -Yoi 0 -Yoi Yll -Y12 00 -Y12 0 Y22 0 -Yr_l, [Y, -Yr-l, r Yrr Yr, r Yr, r+l r+l N -YN-1, -YN-1, N YNN -YN, N+1 -YN, YN+1, N+1 N+1 internal the the rth row and using column required constants, By multiplying each be terminal the characterscaled negligible can with effect on admittances nodal Note is it that input to the the not possible and output network. scale istics of loads be N+1 transformers the 0 as respectively, must at source and nodes, and independently. The inverters may be constructed from a scaled appropriately line discontinuities from transmission isolated length the with no of and single for improved response. Consider the nodal admittance matrix for the resonators design, d Dielectric-Loaded Compact Bandstop Clp [Y] _ 77 Filter 4th Degree Chebyshev Design -jK12 C2p -jK12 0 -0: 23 00 0 -3K23 ß! 3p -3K34 The scaling is performed through multiplying each row and column by a constant factor, A and B respectively. In this case, appropriate scaling is performed on the first and last nodes, therefore, the technique was also performed on the first in the last matrix. columns and 4A Clp [Y} _ '. B -jIC12 00 I{i -j 2 0 0 A2Clp [Y] ýB -jABK12 0 0 C2P -j K23 0 -jABK12 B2C2p -jB2IC23 0 .. A t-- A K23 -j C3P E--B 0 B IC34 -j A CO -jK34 0 0 K23 -jB2 0 B2C3p -jABK34 -jABK34 A2C4p Scaling the middle two rows and columns, the following equations are obtained 4.30 from 4.31, for A B, the and equations values and constants, and are found that satisfy the condition for unity inverters. The constant, A, was used to load impedances in for the the the correct and source circuit scale simulations impedance. K23B2 = 1, B=0.7963 (4.30) K12AB = 1, A=0.9511 (4.31) 4 Dielectric-Loaded Compact Bandstop Filter 78 4th Degree Chebyshev Design The new element values with unit inverters were then calculated Cl = C4 = 0.8441 (4.32) C2 = C3 = 1.4287 (4.33) K12=K23=K34=1 (4.34) These element values have been calculated for a broadband lowpass prototype. For this particular design, the TEloa filter is coupled to the transmission through magnetic coupling and is narrowband, approximately line 5%, therefore, the lowpass prototype was modified by the reactance slope parameter method. The determines the the parameter slope reactance with rate of of change reactance frequency. A steep gradient expresses a fast changing reactance when varying the frequency, which corresponds to a high-Q resonator. A comparison of two having frequency, figure the ff, 4.14(a). in is same resonant shown resonators A high Q resonator equates to a steeper reactance slope. The reactance slope is tool to the a useful relate resonance properties of any circuit parameter lumped circuit. a simple to Any dual types of resonator with the same reactance frequency response. For a series resonant circuit, demonstrates a similar slope definition of the reactance slope parameter, x, can be written as, [57], the general Iwo x2 dw (4.35) By forcing the impedance inverters to be fixed at unity to allow a broader out-ofband bandpass response, it is necessary to use a decoupled structure to control between line transmission and resonator. Although the DR should, the coupling be modelled as an open circuit stub of length \/2, calculated elements strictly, 79 ¢ Dielectric-Loaded Compact Bandstop Filter 4th Degree Chebyshev Design for a magnetic coupled resonator is used in the circuit inductive between the transmission coupling model to simulate the line and DR. The two circuits in figure 4.14(b) are now considered. CT ZA-. o--ý I---I11 1 ZB--º (a) (b) 4.14: Transforming (b) Transformation rameter Figure resonators of equivalent Q (a) Reactance slope paof capacitor to magnetically-coupled resönator For two circuits to have the same Q value, it is required that their reactance slope ZA is input be impedance to a lowpass to bandstop transformed an equal. should 2.3, using equation which may be expressed as capacitor aw ZA(iw) = C, r wo Wo-w) (4.36) ZB is the input impedance of the magnetically-coupled transmission line resbe can expressed as onator, which ZB(p) = Lip +1 C+ 1/L2p Lip + L2p (4.37) + CL1L2p3 1+ CL2 p2 (4.38) Hence ZB(jw) [w(Li + L2) - w3CL1L21 1- w2CL2 4)39 . ,ý Dielectric-Loaded Compact Bandstop 80 Filter 4th Degree Chebyshev Design Equation (4.35) states the reactance slope of the resonator can be found by differentiating the reactance expression of such a resonator, thus dZdw w) - (4.40) ,ro+ W2UJO and dZA(jw) dw 2a (4.41) = uCrwo Also, dZý w) lw=wo LL LL2 2 2Li = ia (4.42) At resonance,ZB = 0, thus Wo Substituting (4.43) CL iaL2 (4.43) into (4.42) and equating with (4.41) yields equation (4.44) = wöCLi C, WO The value of C can be chosen for physical realisabilty L2 Ll and are found and (4.43) equations through solving and (4.44) simultaneously. From (4.43) Li+L2 L1L2 (4.44) and (4.45) from and 2C =w (4.45) 4 Dielectric-Loaded Compact Bandstop Filter Ll + L2 L1L2 81 4th Degree Chebyshev Design a woCTL1= woC (4.46) Hence Ll, C 0 w3C (4.47) and L2r _2 The bandwidth be 3 pF in a11 scaling factor is a= Li, (4.48) woCLir -1 fo/Of, system, the transformed and choosing all the capacitors to element values are calculated from (4.47) and (4.48) equations L11 = L14 = 8.80 nH (4.49) L12 = L13 = 6.76 nH (4.50) L21 = L24 = 3.43 nH (4.51) L22 = L23 = 3.88 nH (4.52) The final prototype circuit is shown in figure 4.15 with all unit elements a quarter long at the centre frequency and have wavelength characteristic impedance of 50 Q. A circuit simulation produced a frequency repsonse of the ideal 4th degree filter, figure bandstop 4.16. Chebyshev Compact Bandstop 4 Dielectric-Loaded Filter 82 lath Degree Chebyshev Design 11 10 4.15: Prototype circuit for 4th degree Chebyshev baudstop filter Figure 0 0 -10 -10 -20 20 -30 30 -40 -40 -50 -50 -60 -60 -70 -70 -80 '-80 1.88 Co 1.83 1.84 1.85 Frequency GHz Figure 4.16: Simulated results of prototype bandstop filter 1.86 1.87 N Cl) x 109 Chebyshev degree for 4th network In order to realise the dielectric filter, a technique was used to equate equivalent normalized reactance slope parameters of individual between the cirresonators EM1 simulated models, commonly used to design microstrip cuit and bandstop filters, [78]. The required coupling between each resonator to the transmission line was dependent on the spacing deterinined by finding the normalized reactance frone following the parameter slope expression, Xi Zo fo (4.53) 20 fags /Zo is the normalized reactance slope parameter x; where of a resonator coupled 83 4 Dielectric-Loaded Compact Bandstop Filter 4th Degree Chebyshev Design to the coaxial line, fo is the centre frequency and f3dB is the 3 dB bandwidth of Parametric the coupling resonator. simulations were used to produce frequency for between dielectric-loaded line the transmission spacings various and responses The from extracted resonator. normalized parameters reactance slope rectangular these frequency responseswere taken from which the desired coupling gap was interpolated from figure 4.17. 600 550 500 450 400 350 300 250 200 150 100' 0.5 1 1.5 2 2.5 3 3.5 S mm 4 4.5 5 1 5.5 Figure 4.17: Normalized reactance slope parameter against spacing of resonator from coaxial line know the physical parameters that control the frequency and to important is It bandwidth for each resonator independently. The coupling bandwidth was dedistance between by the DR the termined and coaxial transmission line and the frequency was at first determined by the space between the end wall and resonant the that resonator of end could accomodate a tuning screw. Following the open frequency determined by the depth of the tuning screw. was the resonant this, FEM solvers is simulations can be performed to observe variaAn advantage with to the dimensions in obtain optimised parameters tions needed. A limiting factor these simualations is determined by computing power, thus, of the in accuracy best, only provide, at optimum solutions. As the filter was these simulations for the first two simulations only resonators for optimisation were symmetrical, 4 Dielectric-Loaded Compact Bandstop Filter th Degree Chebyshev Design 4 84 figure 4.18. required, -10 -20 -30 co -40CO -50-60-70-80 1.848 1st Resonator 2nd Resonator 1.8485 1.849 1.8495 1.85 1.8505 Frequency GHz 1.851 1.8515 1.852 x 109 Figure 4.18: 3 dB bandwidth of 15t = 5.1 I\iHz and 2°d = 8.6 I\'1Hz resonator in Cliebyshev design with fo = 1.85 GHz The relationship between the resonant frequency and spacing between the uncoupled side of the resonator and wall of cavity is shown in figure 4.19. Fields in this region may be modelled as a series inductance, thus, a tuning screw inserted here will effectively increase the resonant frequency. The end cavity wall must, therefore. he at a greater distance from the open face of the rectangular resonator such that the resonant frequency is lower than centre frequency in order to tune frequency. A plot of resonant frequency against tuning screw the to correct up depth is shown in figure 4.20. The next step was to optimise the dimensions of the dielectric resonator and the tuning screw such that the simulated response curve closely matched the ideal As the of circuit model. response shown from figure 4.21 and figure 4.22, a close approximation between the circuit for individual achieved model response and 3D model response was first and second resonators. between each resonator, initally The length of separations calculated from A/4, provided an asymmetrical response and was corrected through final The 91°. an optimised separation of filter was simulated in HFSS meeting the specifications filter bandstop the as of 4th Degree Chebyshev Design 85 Bandstop Filter Compact Dielectric-Loaded 4 N S 0 C C m lL 1.5 2 2.5 3 T mm 3.5 4 4.5 5 dielectric frequency Resonant 4.19: side against spacing of uncoupled Figure with sidewall 1.86 1.855 1.85 1.845 1y 1.84 1.835 1.83 1.8251.82L 1.815 0 2468 10 W mm 12 14 Figure 4.20: Simulated resonant frequency against depth of tuning screw figure 4.23. in shown filter the simulated was final with optimised tuning screws as shown The practical dB bandwidth the 4.24 simulation showed a3 figure and in GHz. The input 1.85 and output frequency of MHz 10.9 at centre of couplings were also optimised to low loss in out-of-band performance and a1 mm gap was the optimised achieve inner the between coaxial conductor and the outer cavity walls. distance Q Dielectric-Loaded Compact Bandstop Filter 86 4111Degree Chebyshev Design 0 3 -10 -5 -20 -10 -30 -15 -40` 1.82 -20 Co U, 1.83 1.84 1.85 Frequency GHz 1.86 1.87 Figure 4.21: HFSS simulated tuned Ist resonator, 3 dB bandwidth fo GHz 1.8502 and = 0 -. N MHz 5.11 = 0 -5 -5 -10 -10 co Co -15 -15 -20 -20 -25' 1.82 -25 1.83 1.84 1.85 Frequency GHz 1.86 1.87 Figure 4.22: HFSS simulated tuned 2nd resonator, 3 dB bandwidth GHz fo 1.8498 = and =9 MHz A wideband response was also simulated for and the location of the next spurious 2.49 GHz, thus, leaving a 640 NlHz spurious free window as at situated was mode figure 4.25. Compared in to DR filters, this spurious free band was quite shown Compact Randstop 4 Dielectric-Goaded Figure Filier 87 ;th llryir Figure 3 -10 -10 -20 -20 -30 -30 Co v -40 -40 -50 -50 -60 -60 -70 -70 -80 1.82 igin 4.23: Schematic of HFSS design of final filter 0 U, by.+lu r I)e r (li 1.83 1.84 1.85 Frequency GHz 1.86 1.87 r4 U) -80 4.24: HFSS simulated response of filter to be fabricated DR filter typical designs high considering require modifications spurious-free performance. to improve their 4 Dielectric-Loaded Compact Bandstop Filter 88 0 0 -10 -10 -20 -20 -30 -30 -40 -40 -50 -50 -60 -60 -70 -70 -80 Figure 4.6 of Filter Fabrzcatiou 1.5 1.75 2 2.25 Frequency GHz 2.5 2.75 -80 3 4.25: HFSS simulated wideband response of filter to be fabricated Fabrication Filter of It was essential the filter was precisely machined since any discrepancy could cause fixed frequency To at the shifts and couplings. unwanted ensure resonators were the required coupling distances from the transmission line. two fabrication tech- height implemented figure in Since 4.26. the niques were as shown cross-sectional line designed the to be smaller than the height of the rectangular coaxial was of in the indent into base lid the the an was sections machined resonator, of and vicinity between the transmission line and DR. This ridge prevented the dielec- tric resonator from shifting too close to the coaxial line, therefore, maintaining its coupling bandwidth. In addition, small aluminium plates were machined and fabricated The the in rectangular resonators secured position using small screws. filter is illustrated in figure 4.27 with brass tuning screws. A picture of the interior filter is the also provided as shown in figure 4.28. of The measured response is shown in figure 4.29 with 3 dB bandwidth of 19.6 MHz frequency 1.8501 GHz. At 40 dB, the stopbaind bandwidth centre at a MHz be 3 to which achieved the required specifications. sured was mea- However, a low Q 4 Dielectric-Loaded Compact Bandstop Filter 89 Fabrication of Filter Lid duminium 3ody DF Coupling Edge Figure 4.26: Practical resonator design 'i; ºý- 'ý ý°ý'ý ,rýyi 9 Figure IQ 11 nupngniýinipu 12 , 13 14 15 r'ahricated 1.27: 4"' ('Ii(-by 1i'v tºal(Iktop lilt(+r ci('grve . This was largely clue to the poor silver nietallisation 216 measured. was of only dielectric between resonator and air gaps the rectangular apparent were also of the cavities they were placed in leading to poor dielectric and slabs the electrical To improve the Q, improved inetallisat. ion techniques are required grounding. hybrid than rather a nietallisatioii Nickel spattering as using a sticking such coni- ¢ Dielectric-Loaded Compact Bandstop Filter 90 Fabrication (uý uuiý 12 of Filter 5 Figure 1.28: interior of fabricated 4`h degree Clieb shev ban(Istep filter It may also be feasible to solder the DR into its resonator before silver. poiin(l he thus, grounding proper will obtained. space, 0 0 -10 -10 -20- -20 Co -30 -40- -40 -so -50 -60 1.82 1.83 1.84 1.85 Frequency GHz 1.86 1.87 N -60 1.88 x 10° Figure 4.29: Measured frequency response of Cliebysliev bandstop filter The spurious performance of the filter is also examined. The TE, 02 mode was leaving GHz 2.41 a spurious-free range of 59() MHz as shown in figat observed Thus. a favourable spurious-free range is 4.30. ure achieved without the need for 5I.. vw x - Compact Bandstop 4 Dielectric-Loaded 91 Filter Coaxial Dielectric-Loaded Bandstop Resonator DR in filters. The filter demonimprovements required as commonly physical handstop high-Q dielectric-loaded a compact using the of rectprinciple strated high Q the unloaded allows and miniaturisation over coaxial waveguides angular designs. or cavity 0 -10 -10 -20 -20 to fV -30 -30 -40 -40 -50 1.9 2 2.1 2.2 Frequency GHz 2.3 2.4 2.5 -50 x 109 1.30: Measured widebaud frequency response of Chef) sliev Figure filter 4.7 1.8 Coaxial Although Dielectric-Loaded the TE106 dielectric-loaded Bandstop rectangular l)aiidstop Resonator handstop rctioiºýitor is sliital)le bandwidth, for narrow applications requiring greater handfor designs requiring between the space resonator and transmission line provides the coupling widths, bandwidth. It is possible to intersect the rectangular maximum on limitation a line improve to but it is difficult to insert the the coaxial coupling with resonator line through the rectangular resonator at the optinnnn position for niaxicoaxial A better option would be to use dielectric pucks to take advantage niurn coupling. An field broadband handstop experimental pattern. novel resonator of their radial figure 4.31 with the H-field plot of the dielectric ring displaying the in is shown fundamental Tl'toia mode. The structure comprises a coaxial transmission line 4 Dielectric-Loaded Compact Bandstop to a cylindrical coupled Filter 92 Coaxial Dielectric-Loaded Bandstop Resonator dielectric ring resonator replacing the rectangular res- The DR had the same material properties as for TE106 mode resonator onator. hole height. inner dimensions 13 5 9 of radius, mm, and radius, mm, mm, and the same coaxial transmission line, with outer diameter 10 mm and inner diamdimensions fundamental These 4.68 was mm, also used. allowed a eter resonant frequency of 1.85 GHz. Dielectric ring Iresonator -\ ,, Coaxia (a) (b) Figure 4.31: TMoia dielectric-loaded field plot in dielectric region (a) Schematic (b) H- Bandstop resonator: --L L, --L, -- WI Yý ýx _Z Figure 4.32: Dimensions for experimental coaxial dielectric-loaded W= 40 L, L2 80mm. 9.57 10 inm, mm nun, = = Due to the discontinuity resonator, L at the dielectric resonator intersection, the TEA1 proper- ties of the coaxial transmission line become distorted and is affected by dielectric loading. HFSS simulations can optimise the dimensions of the coaxial line to discontinuity these the problems such as matching address prove the selectivity of the rejection skirts. segments and also im- This is shown in figure 4.33 where bandwidth coupling of 200 MHz is possible for a smaller inner conductor radius line DR transmission to junction. An eignciunode solver calculated the unthe at loaded Q of this structure to be 2670. The coupling bandwidth is superior to the 4 Dielectric-Loaded Compact Bandstop 93 Filter Coaxial Dielectric-Loaded Bandstop Resonator -10 -20- C, 4 Co -30- -40 -50 -60 Figure 4.33: r=1.34 mm r= 1.84 mm 2.34 mm 1.5 1.6 1.7 1.8 1.9 Frequency GHz 2 Simulated inner coaxial various 2.1 2.2 for experimental transmission response line radii, r transmission resonator for TE, ()b dielectric-loaded rectangular resonator where only 18 MHz is possible for 0.5 nim spacing, figure 4.12, thus, TM016 mode coaxial dieletric-loaded Bandstop TEio the can easily replace previous resonators mode resonators for applications that require the removal of a high band of undesired spurious components, such as harmonics, parasitic effects and intermodulation These are required in transmitter become important distortion paths in communication devices for future communication through a system. satellites and also will systems as the frequency increasingly becomes for the congested requiring need spectrum widehand interference suppression in front end of communication Q resonators will also provide miniaturisation for filter design. commercial objective systems. Using these high and reduce costs, a paramount 94 Chapter 5 Dual-Mode 5.1 DR Bandstop Filter Introduction A novel dual-mode DR bandstop filter is described in this chapter offering a high weight less Q, better performance, small volume and compared to conventional filters TETM-mode and cavity air-filled filters. These benefits are due to the dimensions of the filter reduced by a factor of 1/ E,. and the high Q. prop- Although dielectric to materials metallic compared an empty enclosure. erty of dual-mode DRs are commonly used in bandpass filters, there has been very little in bandstop DR bandstop the only mono-mode and material sector published been investigated, [5]. It is the aim of this chapter to present the have structures dual-mode bandstop resonator compared to a mono of a advantages -mode strucflexibity its to realise advanced filter functions. One distinct drawback ture and for such a structure is the complexity highlighted throughout in the realisation process and these are from FEM simulations to fabrication. The DR structure dielectric below in puck situated cavity a a waveguide cutoff coupled to considers line through coupling elements. The fundamental resonance is the transmission a dual-degenerate HEE11 mode and FEM simulations have been used to generate field patterns for this resonator and perform frequency response simulations aiding in the design of the filter. Bandstop filters are necessary in rejecting unwanted interference. When low and cost, size, weight and simplicity signals are required, 95 5 Dual-Mode DR Bandstop Filter Dual degenerate HEE11 mode high frequencies filters DRs design targets meet the at can cost using of such large Qs. filter The for is their superior new structure well suited rejecting with frequencies carrier of a communications unwanted system. Although design itself is incredibly the may seem process arduous, struction the con- robust using to posts as opposed magnetic coupling wires, where vibration coupling metal impact in a mobile environment can distort the frequency behaviour. and The main transmission line is isolated from the DRs, thus, reducing impact of unwanted interference from stray coupling fields that were a problem seen in open transmisThis designs. isolation line and miniature sion coaxial coupling tap points allows the resonators to be spaced a/4 apart, unlike in open-transmission 3X/4 spacings are obligatory where distortion 5.2 to avoid transmission line structures line, inter-resonator, of the signal. Dual degenerate HEE11 mode To understand the properties of the hybrid mode HEE1I dielectric resonator, the be An FEM initial must modes studied. eigenmode solver calculated the resonant first five resonant modes for a dielectric puck of height 23 mm, radius 18.5 mm dielectric For 44, 5.1. HFSS table permittivity of accurate simulation results, and the puck was enclosedwithin a loo mm3 airbox and perfect magnetic layer, PAIL, boundaries were introduced on the airbox as absorbing conditions for the open The free TEola in space. mode is the fundamental for the specified dielectric puck different for but diameter length to aspect ratios of puck of the dielectric puck, the HEEII mode can be the fundamental mode in shielded cavities. The fields for a single degenerate polarisation of HEEII, have been generated figure 5.1. The orthogonal polarisation has identical field plots but are normal to the plots shown. Coupling between these two polarisations may be controlled by introducing a suitable perturbation either internally in the puck, [35] and [71], located in 45° the surroundings, at angle with respect to the direction of each or Tuning have screws generally been used but recent advances have excitation. 5 Dual-Mode DR Bandstop 96 Filter Configuration of Proposed Resonator Mode No. Name Resonant Frequency GHz 1 2 3 4 5 TEoia HEE11 HEH TNlo16 HEE21 1.178 1.342 1.649 1.740 1.771 Table 5.1: First five resonant modes of dielectric a puck included metallising the exterior of dielectric shapes, [79]. -_ Jam'.; I- -: - ¶: iIII - _- :ýý V ý+ (7/ ;4i; p$t \'; 4, (a) Figure (b) 5.1: Field distributions of HEED 1 dual mode (a) E-field Plots (b) H-field plots 5.3 Configuration of Proposed Resonator In the design of a microwave Bandstop resonator, anode charts are essential to unbehaviour the derstand of the resonant frequency in the proposed DR structure in design the prerequisites of bandstop filters. A cylindrical dielectric which are in is the common configuration a cavity puck suspended for a DR }nit, unfortu- fundamental in the a structure such nately, mode is the TESa mode, figure 5.2. A FEM simulation is produced to understand the frequency behaviour of the di- 5 Dual-Mode DR Bandstop 97 Filter Configuration of Proposed Resonator faces between in the the of the a cavity respective when spacings electric modes top and bottom cavity walls relative to the dieletric figure 5.3. The dielectric puck used was as before and placed in an air-filled, box with perfect conducting cavity H= With 63 nim. consideration by a relatively supported puck surfaces, are varied, walls of widths, to realisation, 2W = 65 mm and height, the dielectric puck would be low dielectric constant support but as its effect is in- for its to the the mode chart compared resonator, effect was removed significant In the range H/h simulations. < 1.2, with the top and bottom height but the cavity as node the dielectric surfaces, TM0I is the fundamental increases equally in both z-directions, fundamental the comes mode. walls close to this mode rapidly increases and TEO, be- A slight increase in H/h from unity causes a dramatic change in modes HEE11, HEE21 and TM0, as their axial E-fields are for from boundaries. fields As further, H/h the increases the conductor removed final distributions. into their stabilizes mode each For the specified dielectric puck for h/2r HEE11 0.35, this first the ratio, mode aspect remained spurious = with for between various equal spacings structure upper and lower cavity walls and the dielectric puck. Av A7 "--- r -- Top View Side Ea View Eo h E, Er hH h2 --º x Figure Although 5.2: Diagram of dielectric puck in perfect conductor cavity a dielectric puck with different r/h HEEii force aspect ratio could to be the fundamental mode, to preserve the dimensions of the puck, an alternative lower is the to puck to the cavity floor reducing h2 =0 whilst hl = 20 min method kept constant. This increases the frequency 32.5 R= below TM01 mm are of and 5 Dual-Mode DR Bandstop Filter 98 Configuration of Proposed Resonator 1.7r5 1 N i UU U 7 Q U- 25 LL 1g TEO, --$. - HEE11 HEH, t TMO, o., -ý- a i i. t HEE21 i"V i. V H/b ýLL. Figure 5.3: Mode chart variation of H/h with frequency, h2/h1 < 0.8 and leaves the resonant frequency of HEEII relatively unchanged as becomes first TEO, fundamental figure the 5.4. mode and spurious mode, the new The disadvantage of this is that Q. will decrease due to the interaction between dielectric but face by lowering both the the bottom puck and cavity wall of the further is height the the of volume reduction cavity, gained and reduces and puck foundation dielectric for Thus, for is support. a solid mechanical a stability need provided. The conductor sidewalls must be at a distance from the dielectric puck such that dielectric losses the fields in the conconcentrated at are region and resulting the ductor walls are minimised, however, the sidewalls must also be near enough for miniaturisation to be effective. A mode chart showing the effect of conductor DR R/r in the that 1.3, frequency the the < shows range on of the sidewalls by due the to their affected vastly conductor walls are near proximity to modes figure 5.5. For R/r 1.5, frequency dielectric the for HEEII > puck, resonant the mode varies constantly with conductor walls indicating the fields are concen- fields the puck and only weak evanescent trated within exist in the vicinity of the conductor walls. bandstop configurations, each resonator is located at an odd mulIn conventional 99 5 Dual-Mode DR Bandstop Filter Configuration of Proposed Resonator .8 .7 .6 N x' .4 - Cl m 7p IL .3 .2 6- i .1 1 - HEEII H E -ir- HEH11 TMot 9 -ýis E 0 0.2 0.4 0.6 HEE21 0.8 h1h, Figure 5.4: Mode chart variation of h2/hl with frequency tiple of a quarter-wavelength line transmission travelling in one direction. along a For the dual-mode configuration, the conventional design produces two physical by A/4 figure but (a), 5.6 the experimental coupling probes offset with topogies , fields are not focused on the surface of the puck and resulting coupling coupling be too poor for filtering applications. The height of the coubandwidths would be that they the may raised such extend over upper surface of the probes pling however, this would cause increased spuriincreased for coupling surface, puck both between bandwidths The be increased probes. coupling may coupling ous input the couplings perpindicular to each other such that the probe by placing figure (b), but the A/4 separation between the to 5.6 the puck, faces are normal be difficult would resonant probes to realise at the transmission line and extra higher loss within the cavity. The solution was to bend lengths cause would probe line 90° face lateral the around transmission of the puck, figure 5.7. This is the input and output ports required for canonical dual-mode DR bandto similar [18], and allows minimum length coupling probes to directly filters, excite pass dual for in mode A maximum coupling a orthogonal square cavity. small each is this the nature of the transmission line curve would cause with disadvantage a in the transmission response, however, FENI discontinuity simulations can slight DR Bandstop 5 Dual-Mode 100 Filter Configuration of Proposed Resonator 1 1 1 .7 1 .6 Ni S 0 >1 U C .4 - 7ý .3 u -i .2 - TEO, .1 HEE11 1 HEH11 -*- TM01 0 HEE21 0 R/r Figure 5.5: Mode chart variation of R/r frequency with dimensions for frequency the the optimum response. optimise X/4 X/4 Transmission LInc Coupling Probes DR Xý xt Vf y (a) (b) (c) 5.6: Topologies for coupling of transmission line to dual-mode dielectric (c) (a) (b) for side view weakly coupled probes probes maximum coupling puck: Figure A waveguide transmission line is commonly coupled to a DR situated in a cav- ity using irises but require 3A/4 separations to avoid transmission line spurious inter-resonator dispersion. line increases transmission couplings which resonator volume and A coaxial transmission lar inner conductor, line with square outer conducter and circu- as described from the TE106 filter in the previous chapter, The be ideal. benefits physical are it offers a uniform cross-section, when would diinto through be a curve, and coupling elements may shaped rigidly supported inner the to coaxial conductor. rect contact A coupling mechanism to isolate the i Dual-Mode DR Bandstop 101 Filter Configuration of Proposed Resonator ýý Transmission Line Coupling Probes DR DR ýx y.. (a) (b) 5.7: Coupling of right-angle (b) (a) top view side view puck: Figure degenerate mode excitations transmission line to dual-mode dielectric and provide controllable coupling is required. The design of the coaxial probe can also be isolated from the transmission line such that dielectric loading is insignificant and no physical changes in the main traiisIn the past, input and line are required to achieve acceptable rejection. mission output coupling elements to DRs have consisted of simple electric or magneticfield dipoles using wire probes or loops to excite the correct mode, [26]. The disadvantage with these elements is that in filter structures, wires may vibrate Although is the thus, cavity, within a more robust coupling structure considered. electric coupling pins would be more simple as only one end is fixed to the coaxial line, the dielectric-air boundary of a dielectric puck allows more magnetic energy to couple out. Thus. it was beneficial to make use of magnetic coupling to niaximise the coupling bandwidth available. The coupling mechansim was designed base tapped to the to of the cavity probe a metal post and grounded as a coaxial figure 5.8. in as shown A tuning element was also needed to correct any imperfections design. therefore, coupling screws were also introduced in the realised to time the capacitive A figure 5.9. in the for is the probe. circuit model element of coupling model shown This is equivalent to a resonant circuit such that as the tuning screw approaches the inductive post, the capacitance increases, effectively reducing the resonance from the the transmission allowing more post coupling of line to the dielectric 5 Dual-Mode DR Bandstop 102 Filter Single Cavity De. sigri Inductive Coupling Element Coaxial Transmission Line -º X/4 ýx ,ý y ýa) fib) 5.8: Coupling mechanism for dual-mode HEE11 Bandstop resonator: (a) top view (b) side view Figure Non-resonant S/C Stub Figure 5.9: Circuit model for coupling post To aid with the positioning puck. introduced was Tuning Screw in the puck. hole floor, the the a centre of puck on cavity The filial proposed HEE» bandstop structure is figure 5.10. in shown 5.4 Single Cavity Design The dimensions for a single cavity dual-mode resonator were calculated based on the same properties of the dielectric puck in the previous section with an additional circular hole along the axis of the puck. This modification for positional was purposes to align the puck at the centre of the cavity but to ensure the spuriThis figure 5.11. was unaffected, a mode chart was produced, ous performance insignificant there was showed variation in resonant frequency against increasing hole diameter for both HEE11 and TEoj modes, thus, the spurious-free bandwidth MHz It 250 is interesting was conserved. of to note that for operation of TEo1 improve hole in increases TMo1 will a spurious performance since mode, mode frequency due to removal of the axial electric fields of the TM0I mode. 103 5 Dual-Mode DR Bandstop Filter Single Cavity Tuning Screws Design Aluminium Enclosure Metal Coaxial Line cý Dielectric Puck 2 LX y. (a) Y L-. x ýbý 1c) Figure 5.10: Structure of HEEi1 mode dielectric Bandstop resonator: (a) Corner (c) Cross Top (b) section view view For ease of design, the sidewalls of the cavity were fixed to accoinodate the righttransmission coaxial angle line. In the design for this particular 27, 37 diameter diameter. mm, providing a suitable cavity = of dielectric puck a factor greater than 1.5 of 2R = 65 mm was suitable to minimise the effect of conductor losses. A prescribed cavity height spacing of It, = 20 min gave a resonant frequency of 1.07 GHz for the HEE>> mode, figure 5.4. One should ii<ºte that this frequency was simulated there is minimal for a puck in a box-shaped change in frequency cavity when a cavity but future corner simulations is curved shows inwards to frequency line This the transmission bend. to was used calculate the accornodate length of transmission line separation between the two modes as A/4 =7 cm. The line needed to be large enough to accomodate the coaxial transmission coaxial dimensions from the A 4.20. were and equation calculated square outer probe 13.5 111111 inner defined 6.35 width of and conductor round of inne were conductor thick between conductor innn a1 wall outer coaxial conductor and cavity with sides. 5 Dual-Mode DR Bandstop 104 Filter Single Cavity Design 1.6 1.5 1.4 N S HEEll ý- 1.3 S TEO, Ui TM01 1.2 HEE21 1.1 0 0.04 0.08 0.12 rilr 0.16 0.2 0.24 5.11: Mode chart variation of r1/r with frequency Figure t (a) (b) (c) Coaxial line transmission 5.12: with various centre conductor curvature Figure (a) c= 40.25 inin, e= 63.2 min (b) c= 29 iiini, U= 68.1 iiini (c) C= 19 iiiiii, radii 72.77 min e= The complexity in the design of this structure is now shown as the total length transmission line separation, including the right-angle inter-mode of bend, must their respective cavity sidewalls. tap the the of points coupling at centre position by length line determining be transmission the to undergo of controlled This can the right-angle transformation. Ideally, the transmission line is straight but devi- into a curve causes a discontinuity at which point, the pure TEN1 from this ating down into components of electric and magnetic fields along the axis breaks mode It bend causes changes in the electromagbend. that the was reported the of inversely proportional to the radius of the curvature, [80], therefore, a fields netic 5 Dual-Mode DR Bandstop 105 Filter Single Cavity Design transmission line of maximum curvature radius is desired to limit the sharpness bend. To the conform with the symmetry of of the dielectric puck and cavity, the maximum radius must be directly proportional to the radius of the puck at the sidewalls. Figure 5.12 shows a possible range of curve radii for this structure with each corresponding to a different separation between the degenerate modes at the centre of the coaxial conductor. In order to conserve the properties of the puck inside the cavity, the designer may increase the radius of the transmission line, 40.25 mm, to fulfill the A/4 separation and keep the maximum curvature of the bend, however, this would increase the volume of the structure. option is to decrease the radius in the transmission The second line and introduce straight line sections to preserve the 1 mm cavity wall between the cavity sidewall and outer coaxial conductor, figure 5.12 (c). FEM simulations filled coaxial transmission line with aluminium for a practical air- SMAs at each end conductors and frequency responses for various inmost coaxial conductor curvatures. produced Results show there is little variation in the transmission line response of differ- ent radii curves producing a range of separation values around the required A/4, figure 5.13. Although there is poor isolation at high frequencies above 2 GHz, loss better than 20 dB in the region of operation, 1 GHz, is achieved and return the second option was used to minimise volume. Dimensions for the tuning element must also be considered to provide the correct bandwidth coupling to the DR puck. Coupling probes of miminum size were ideal to avoid impedance loading of the transmission line and unwanted spurious in effects the cavity at the coupling tap points. The well-known coaxial impedance line equation was used to calculate the initial diameters for the circular coaxial These points. were initially configured to be 1.3 mm and 3 mm for the coupling inner and outer conductor, repectively. An introductory rod length between the inner conductor and tuning post was 10.8 mm and the post diameter was coaxial 3 mm. Based on the above discussions, the typical dimensions for a single cavity dual-mode HEEII bandstop filter are shown in table 5.2. 5 Dual-Mode DR Bandstop 106 Filter Single Cavity Design -10 2cm 2.45cm 2.9cm 3.35cm -12 -14 -16 -18 -20 -22 -24 -26 -28 -4n VÖ.5 2.5 2 1.5 Frequency GHz 1 3 line. transmission inner Frequency 5.13: of coaxial and response outer Figure diameters, 13.5 inm and 6 mm respectively, for various radii of inmost conductor curvatures wall conductor coaxial Typical Performance Typical Dimensions h=23 in" r=18.5min 6.5 mm n 65 inin c= 52.5 min R= 57 mm 25 min H l= hi G= = 14 13.5 g=6.35 Table min min min 5.2: Typical h= 18.5 min 12= 10.8 mm 13=3 Inns l4 = 1.5 nun f0= 1.07 GHz F,. = 1.1 Q= 9000 First spurious frequency 1.35 GHz 15 = 1.3 min d, =1.3min d2 = 4.1 Inns 71.7 e= el = 19 min min q1=1min dimensions haii(lstop resonator 5.4.1 FEM Simulations and performance of HEE1I dual-ino d' dielectric for single cavity behind the proposed dual-anode l)andstop filter. it is useful ideas the To confirm the behaviour of the fields of the proposed resonator cavity using to understand The fields in excite posts radial coupling the FEM magnetic simulations. 3D dual-modes. The field plots for a single HEE11 degenerate anode two orthogonal E-field is maximum near the centre of the top surface, and at the radial show 5 Dual-Mode DR Bandstop 107 Filter Single Cavity 4W Design R ý-Gý ------------- h, iy 14 1h `JI ZLý X 91 e, o 1,d, 1 #15 -, Figure 5.14: Details of HEE11 anode dielectric bandstop resonator the circumference of the bottom puck. The H-field is concentrated through the centre of the transverse plane towards the cavity base, figure 5.15. There is greater fields dissecting the ti-axis than in the axial direction of the puck the variation of which indicates that, in a fixed cavity, Er and the diameter of the puck have more frequency the than the puck height. resonant effect on The eigenmode solver was used to simulate the resonant frequencies of the first five bandstop DR the modes of resonator, table 5.3, with dimensions from table 5.2. For the structure described, HEEii is the fundamental mode but the resonant frequency increased from 1.07 GHz to 1.11 GHz caused by the interaction between the coupling posts. The Q,, of the fundamental bottom 8100 the as mode was face of the puck was now in direct contact with the cavity. The spurious response for DRs is generally poor and the first spurious TE0ý16 MHz 247 mode occurred at 5 Dual-Mode DR Bandstop Filter 108 Single Cavity Uesiyn yt YL. x i ol ;!;:: -- , =W ,4-ý --- Zý ZL X (a) (b) Figure 5.15: Field plots of single degenerate HEE1I mode coupled to transmission (b) H-fields in xy- and vz-plane in E-fields (a) line: xy- and xz-plane fundamental frequency. However, the axial path varies with the TM10» the above frequency hole increase the this thus, a centre would of spurious mode, spurious by improve It is to the the response removing possible portions spurious of mode. [81]. The fields E-fields for the spurious TE1116 spurious of modes exist, where puck figure By 5.16. E-field in to terminate the removing sections paths, the are shown bandwidth will increase. An example is shown of the saine dielectric spurious-free figure design in 5.17. dimensions The the removed, with a ring small used puck 7 14 inner height 5 outer the are radius, radius, mm, nine, ring and of mm of below 5 the puck. This modification produced the top mm surface of at situated increase in the spurious bandwidth MHz 50 a without affecting the fundamental frequency. Figure 5.18 presents the tuning screw arrangement required for dual-mode cavity designs, [30]. The orthogonal modes are initially designs, the bandwidth uncoupled but for cross-coupled of this coupling may be controlled by placing a metallic the perturbed opposite screw edge of the cavity at 45° with respect to the two 5 Dual-Mode DR Bandstop 109 Filter Single Cavity Mode Resonant Frequency GHz HEE11 TEola TMola HEE21 HEH11 1.111 1.3578 1.483 1.562 1.7913 Design Table 5.3: First five modes in a dielectric puck in contact with base of cavity Z" rt- ILS x X (a) (b) Figure 5.16: Field plot of first higher order slniriouti iiiode, TEO»b: (a) Side view (b) Top view (c) (bi ui Figure 5.17: Dielectric puck with removed ring section for improved spurious: (a) 3D view (h) Top view (c) Side view polarization axis. 'Tuning disks may also be used as the larger surface area will tuning effect. more provide As most of the fields lie within be tuned to close proximity must screw variation the dielectric, to have a desired effect. This coupling can clearly be seen in figure 5.19 where a penetrating the two frequency modes together, splitting frequency for each orthogonal the them further anode may be controlled dialing screws opposite each coupling post on the xy-plane. apart. screw couples The resonant individually by placing Figure 5.20 shows the disk tuning a penetration of of with a silver circular disk of 5 nine radius and effect 1 mm thickness attached on the end on mode 1. As the disk moves from 6.5 min 5 Dual-Mode DR Bandstop 110 Filter Single Cavity Design frequency 14 the towards the to the resonant puck, of mode 1, min inside cavity fl, decreases by over 3 MHz, while the frequency of mode 2, f2, increases slightly by 1.5%. For greater tuning bandwidth for each mode, a large screw is ideal but care must taken not to hugely distort the frequency of the second othogonal frequency have but reduce the Q Metal tuning screws a greater effect on mode. of the resonator. To maintain the Q. dielectric screws may he used but have a Metallic to tuning capacity when compared metal screws. smaller in the experimental used screws were resonator structure. Input Coupling Elements Frequency Tuning" Screws Mode Coupling, Screw Figure XtY 5.18: Diagram of orthogonal frequency tuning and coupling screws ar- rangement 0 -5 -10 -15 M -20 -25 -30 -35 t=15 mm t=20mm t= 25 mm -40 -451.11 Figure 1.115 1.12 Frequency GHz 1.125 5.19: Frequency response for penetration The amount of bandwidth 1.13 of cross-ccoupling screw is controlled by the coupling rod length and the diatu- 5 Dual-Mode DR Bandstop 111 Filter Single Cavity Design 0 -10 -20 f2 -30 -40 N N f2f2f2 -50 {' f1 -60 f1 6.5 mm 9 mm 11.5 mm 14 mm -70 _an 1.114 Figure 1.118 Frequency GHz 1.116 5.20: Frequency response for penetration 1.12 1.122 of single resonant anode tuning screw between dual-eiode The isolation the input the achievable post. maximum of eter limited due to the right-angle directions of the coupling elements is separation This limits the the within coupling cavity. measure of spurious some producing handstop attenuation but this problem can he reduced by optimising the size of the coupling the resonator elements, structure, l min, the frequency bandwidth. in particular the coupling figure 5.21. For rod diameters response achieves acceptable As a result, rod diameters the coupling for 0.9 5.2, to mm a, coaxial table rod diameter outer conductor between attenuation be can varied 15 = 0.8 mum and over the handstop was optimised diameter in frone 1.3 min, of 21.1 =3 mm. The original A/4 transmission line separation for 1.07 GHz was changed to accoGHz. The separation between the increased frequency 1.11 the centre at modate from 7 cm to 6.94 cm with a2 cm radius bend in tap was reduced points two To line. accomodate this reduction in the bend, the cavity walls were the coaxial increased to 6.5.1 cm. HFSS simulations were used to adjust all these physical distance single and a cavity was resonator simulated with a coupling parameters between inductive the 5 min of post and the puck. All dimensions were opti- HFSS including in the size of the cavity, the post sizes, input and output mised 5 Dual-Mode DR Bandstop 112 Filter Single Cavity Design 0 -10 -20 N -30 -40 15= 0.6 mm 15= 0.8 mm 15=1mm -50 15=1.2mm -60 1.115 Figure 1.117 1.119 Frequency 5.21: Optimisation 1.121 GHz 1.123 1.125 of coupling rod diameter The frequency the phase separation changed. and was also response of couplings filter is shown in figure 5.22. The bend at one edge of the cavity to experimental line the right-angle caused a reduction coaxial accolnodate in the volume which. GHz. The frequency 1.119 increased the to simulation in turn, bandwidth produced a3 dB loss MHz 3.6 of of 0.18 dB. In addition, and a mid-band return in dual-mode resonators, if the external surroundings are uniform and svini lctrical, degenerate the frequencies of the modes can be identical leading to correct couHowever, in between two discontinuity the orthogonal modes. cases where a pling imperfection in the cavity, such as an occurs in the symmetry of the cavity or an being inserted, this would distort the orthogonality object external of the dual- behaviour Tuning their coupling slightly. affecting screws were introduced modes in the simulation to de-couple the modes. The wideband performance of the filter was observed and a higher order mode GHz 1.432 figure This in 5.23. as shown gave a spurious-free window of at occured higher is MHz than the eigemnode solution. In fact, this mode was the 313 which TM0, from observation of the field pattern of this mode at its resonant frequency. The TEO, mode was not apparent because the inductive insufficient electric coupling. coupling post provided 5 Dual-Mode DR Bandstop 113 Filter Single Cavity 0 0 -20 -10 -40 -20 N N 0, -60 -30 -80 -40 -Inc Figure "II 1.11 1.12 Frequency GHz _cn 1.13 1.14" 5.22: HFSS simulation of experimental filter for fabrication 0 0 -20 -10 -40 -20 N N 0) -60 -30 -80 -40 -100. 1.1 1.15 1.2 Figure 5.23: HFSS simulation fabrication 5.4.2 Design Fabrication 1.35 1.25 1.3 Frequency GHz 1.4 1.45 -50 1.5 of the spurious mode of the prototype and measurements dual-mode of filter for single cavity The resonator mounting had to be mechanically robust and simple to fabricate. For this prototype it was found that applying a thin layer between the glue of DR Bandstop 5 Dual-Mode 114 Filter Single Cavity A small pocket island was also raised base provided adequate rigidity. puck and in the machining of the cavity for positional to avoid unrepeatable and uncontrollable Design purposes. One should note that effects on the resonant frequency, this be due between to the the puck not adequate would presence of air gaps method To remove these unwanted effects, a solution may be provided by and cavity. the base of the puck and depositing a layer of solder on the base silver-plating of the aluminium cavity. Next the puck may be clamped to the base and the baked high temperature under structure whole to solder the puck to the cavity base. This realises a good mechanical support of the puck, providing frequency for the temperature high Q. The as well good over as electrical contact a stability filter is figure in 5.24. shown manufactured W ,. ! 'A" " .: eýp r Figure 1 5.24: Fabricated single cavity of HEEi1 dual-iiiod(' l)aiidstop filter The measured frequency response of the experimental handstop filter is shown in figure 5.25. In this first measurement, no tuning screws were used and a centre frequency of 1.131 GHz was produced along with a3 dB bandwidth of 4.59 AMHz. The filter produced an attenuation of 18.56 dB. This figure incorporated any losses and dielectric losses of the resonator and its surroundings. In conductor between the top plate of the filter the air gap particular, and the body also creates 5 Dual-Mode DR Bandstop 115 Filter Single Cavity Design line between the in the the loss, coaxial main cavity. and vicinity especially much The losses here are due to the formation of the 1 nim diameter holes between the halves, into two line the top that as machined one cavity are and transmission in A here the the bottom symmetry change will small create a enclosure. of and face flow the in the of the wall leading to loss. along discontinuity current 0 0 -5 -5 -10 v -10 15 -157N -20 -20 -25 -25 -30 1.12 1.13 Frequency GHz 1.125 30 1.14 1.135 x 10° Figure 5.25: Measured frequency response of HEE1 i experimental Tuning screws were used to produce thogonal width dual modes to create a peak attenuation MHZ, 2.74 of response with 4.3 MHz figure 5.26. 1% fractional GHz, 1.13 at figure For a rippled bandwidth 5.27. higher-order the next measured with spurious the maximum free passband attenuation Bandstop filter between of 25.05 dB with response, was produced The spurious with an inverse tli e or- 3 dB bandChehysllev a3 dB bandwidth performance of the filter of was 1.3689 GHz, figure 5.28. offering at mode a of 240 MHz. it these was apparent how versatile this structure was since asnlnnnresults, From functions be filter can realised through creating coupling paths between ber of intra- or inter-cavity modes. However, for more complex functions, such as the the phatie of the transmission line may be varied in the approximation, elliptic filters but direct-coupled for A/4, than changes phase much of tllVV smaller case 5 Dual-Mode DR Bandstop 116 Filter Single Cavity C 0 -10 -20 m N -20 -40 -30 -60 -40' 1.12 Design 1.125 1.13 1.135 Frequency GHz co v 04 N Co '-80 1.14 x 109 5.26: Measured Chebyshev response with tuning screws of HEE, I single filter bandstop cavity Figure D 0 -5 -5 -10 -10 co U) -15 -15v -20 -20 -25 -25 -30 -, an 1.12 1.125 1.13 Frequency GHz 1.135 7 N N 1.14" x 109 Figure 5.27: Inverse Chebyshev frequency response of HEED i single cavity handfilter stop line be may scaled up by odd multiples of A/4. In the HFSS simulatransmission tions this was easily implemented through changing the radius of the transmission line bend which enabled the dual-mode separation to shift away from A/4. By 5 Dual-Mode DR Bandstop 4 Ih Degree i,tiver, +e Clirbysli. cv Design 117 Filter C u. -10 C -20 - -20 -30 -30 -401.1 Figure -10 1.15 1.35 1.3 1.25 Frequency GHz 1.2 1.4 1.45 N Co -40 1.5 x 109 5.28: Spurious frequency response of HEEL I single cavity bandstop filter inter-cavity it is to possible create cavities, cascading cross-couplings to create between to cavities model complex coupling matrices where rejeccross-couplings be the to stopband of controlled on either side control selectivity. can tion zeros 5.5 4th Degree For applications inverse requiring Chebyshev higher bandwidth, Design a 4tß' degree filter was designed for design into the single cavity resonator. the consideration results taking design had bandwidth, narrow very single cavity it is possible to increase the bandwidth The therefore, by increasing the order of the stophand of the filter. to achieve a wide stopband, the inverse Chebyshev approximation In order was used as it flat to passband skirt produce an equiripple stophand maximally and steep a offers for a symmetrical response. The design follows from the transformation of a highpass matched inverse prototype, figure 5.29, to the ladder prototype network, figure 5.30, [41]. The network then translates to a symmetrical handstop filter formed from an inverter-coupled network with each inverter equivalent to a unit figure The 5.31. filter for the two cavity design are shown specifications element, 118 Filter Bandstop DR Dual-Mode 5 4th Degree inverse Chebyshev Design in table 5.4. In is Figure 5.29: Matched inverse Chebyshev filter prototype, [41] 93 91 ýn S: in S+ ti Figure 5.30: Circuit network of inverse Chebyshev elements, [41] C2 Figure 5.31: Inverse Chebyshev bandstop filter prototype, [82] Filter Specifications Centre frequency 1.15 GHz Passband bandwidth 24 MHz Return loss (Lß) 20 dB Stopband bandwidth Insertion loss (LA) 6 MHz 30 dB for Filter 4th degree inverse Chebyshev bandstop filter 5.4: Table specification 5.5.1 Inverse Chebyshev element values for design have been calculated from [41]. Specifications the The synthesis values degree Chebyshev 4th that filter, 4.21, required a produced equation were N> 30+20+6 >3 68 201oglo[4+ (42 - 1)1/21 (5.1) 119 5 Dual-ModeDR BandstopFilter 4th DegreeinverseChebyshev Design hence, a filter of degree 4 was required and a two cavity dual-mode structure was Next the bandwidth suitable. factor, be 191.7 to a, was calculated and scaling the element values were as follows, 1B1 Ap +p= ... 9r Cp + (5.2) LP The element values are derived from the following approximate frequency trans- formation to realise the frequency invariant reactance from figure 5.29. The transformation is based on the approximation that a lumped inductor or capacitor of frequency behave invariant to the will similar reactance equal vicinity of wl <w< w2 where wl w2. The immitance reactance in the of the rth element is from calculated 2a + Cos0, `4 - 4wo? I sin Or B for r=1,0 for r=2,0 for r=3,0 wo(2o _ - ) 8,. cos 4rßsin B, (5.3) r \5.4 = 7r/8, Al = L1 = 2.8185e x 10-8 H (5.5) A2 = L2 = 1.1658 x 10-8 H (5.6) A3 = L3 = 1.1635 x 10-8 H (5.7) 3ir/8, = = 57r/8, 120 Filter Bandstop DR Dual-Mode 5 HFSS optimisation forr=4,9=77r/8, (5.8) A4 = L4 = 2.8049 x 10-8 H The same 0 values were used to calculate the rest of the elements. Bl = 1.4644 x 1012,Cl = 6.8284 x 10-13 F (5.9) B2 = 6.0745 x 1011,C2 = 1.6462 x 10-12 F (5.10) B3 = 6.0867 x 1011,C3 = 1.6429 x 10-12 F (5.11) B4 = 1.4715 x 1012,C4 = 6.7957 x 10-13 F (5.12) figure The in 5.32. is SZ the circuit approxcircuit model shown In a1 system, Chebyshev is in inverse ideal the shown response imation was simulated and figure 5.33. 11.64nH 11.66nH 28.19nH /4 -i X/4 T 6.83pF T29.05n11 2./4 6.8pF 6.07pF 6.09pF Figure 5.32: 4th degree circuit model inverse Chebyshev bandstop filter 5.6 HFSS optimisation dielectric design the to the design using same puck, single cavity The was similar however, line, transmission the and coaxial cavity was modified elements coupling for FEAT waveguide cutoff cavity under conditions efficient to use a cylindrical This is useful as the symmetry of the structure and appropriate simulations. boundaries drathe to time electric-wall reduce or simulation allows magneticA top view of the structure allows the dimensions that were varied for matically. 5 Dual-Mode DR Bandstop 121 Filter HFSS optimisation 0 0 -10 -10 -20 -20 a -30 -30 -40 -40 -50 -50 -60 1.12 Figure 1.13 1.14 1.15 Frequency GHz 1.16 1.17 N -60 1.18 x 109 5.33: 4tß' cleorec' circuit IflU(1cl üivcrsc Clicl>y&licv i»U1(istO1)filz cl. in particular, Optimisation, for even heights in loth cavities, the tililing depth is depicted by from first last t, to t4, figure 5.34. the to increased resonant mode The coupling bandwidths SI = s4 and S2 = for each tuning element was adjusted with spacings S3. To aid the design. initial simulations were performed to find the o1)timmil cavity height for the resonant frequency to be slightly above centre frequency to allow figure frequency, down 5.35. to the required tuning resonant bandwidths. pling bandwidth a simulation For correct cou- of the tuning element spacing against coupling was produced to extract the required spacings, figure 5.36. The reactance slope parameter method, as used for the TE, w bandstop filter, was filter from however, the the to physical model, realise circuit eacli resonance used be individually treated not mode could due to spurious coupling betwe eIl the degenerate modes in each cavity. The optiniisatioii technique involved performing HFSS simulations to equate the frequency response and 3 dB l»andwidtli for each consecutive dual-resonator circuit from the prototype, figure 5.32, and required in 5.5. The table first shown step was to observe the middle two resonators results 5 Dual-Mode DR Bandstop 122 Filtrr HFSS optimisation d2 y,LX LL Ä Figure 5.34: Top view of HFSS simulation with variables for optimisation 1.17 x 10' 1.16 1.15 1.14 LL 1.13 1.12 1.11 26 Figure 28 30 34 32 Cavity Height mm 36 38 40 5.35: Variation of resonant frequency with DR circular cavity height from the circuit since their symmetrical bandwidth and isolation within their dimensions desired the cavity allowed physical respective of their tuning elements. 123 Filter Bandstop DR Dual-Mode 5 HFSS optimisation N I L V_ CC W m C O a (5 CC d Q m V c) 10 123456789 Coupling post spacing from puck mm Figure 5.36: Variation of 3 dB coupling bandwidth with coupling post to puck spacing Moving into the first cavity, it was now possible to tune the resonant frequency first to the the both for resonance mode such coupling modes and also adjust bandwidth. The the both same process was showed required coupling modes that )//4 last to the the the to was adjust step separations second cavity and applied to achieve a symmetrical response. Mode Centre Frequency GHz S21 3 dB bandwidth MHz 1 1.147 2.823 2 3 4 1.149 1.151 1.153 6.787 6.787 2.823 Table 5.5: Requirements for resonant frequency and bandwidth for each mode At a centre frequency of 1.15 GHz, the length of the separations was taken to be 6.52 cm long. Unfortunately, this separation was too short for the middle resthe two intersect, for fabrication therefore, to cavities causing purposes, a onators 6.7 to input two the taps. This was incorcm was chosen separate centre of value final HFSS 3D model, figure 5.37 and the optimised frequency into the porated figure in is 5.38. The produced out-of-band asymmetry is caused by the response 3% increase of the separation between the middle resonators. For future designs, 5 Dual-Mode DR Bandstop 124 Filter HFSS optimisation it is proposed that the cavity radii be decreased to accoinodate the separations required. Figure 5.37: Final HFSS simulated model for inverse Chebvsliev handstop filter 0 0 -10 -10 -20 -20 to v N -30 -30 -40 -40 -501.12 5.38: Frequency Bandstop filter Figure 1.13 1.14 1.15 Frequency GHz response of optimised 1.16 1.17 -50 1.18 HFSS design for inverse Clielwshev 5 Dual-Mode 5.7 DR Bandstop 125 Filter Fabrication Fabrication filter of Precise machining was used for the desired dimensions and the dielectric were mounted and positioned to the base of each cavity. from the tolerances optimisation sional impractical, was which through manual tuning. of filter pucks The required dinien- hundredth was a of a millimeter process therefore, the fabricated tolerances must be accounted for The enclosure was made from aluniiniuni in three parts with a body, lid and an aluminium and Was made rod fixed to the four coupling filter figure 5.39. fabricated in The is shown posts. 1 3 Figure 5.39: Fabricated 4th dicgi 'v inverse ('liebysliev ýý 1)alldstop filter Tuning was necessary for this filter and the measured response is shown in figfilter frequency GHz dB 1.164 band3 the 5.40 with offering of centre and a ure MHz. The 16.3 is of performance comparable to the simulated results but width frequency in due fabrication increase 1% to centre was observed a inadequate tuning screws providing insufficient tuning bandwidth. is it proposed that timing signs. tolerances and For futtre de- disks with wide surface area to the dielectric for be due Losses tuning to poor tuning screws and used greater were puck effect. between dielectric the the contact surface puck and the base of the cavity. poor of 5 Dual-Mode DR Bandstop 126 Filter Fabrication These can be improved by using silver screws and the interior be silver-plated ensuring conductor losses are miiiiniised. of filter of the cavity can The tuning mechanism losses loss it increased in Of introduced the as cavity. note, there conductor also is a reflection zero on the left side of the response caused by the shortening of the separation between the two middle resonators. The asymmetric behaviour is due to an occurrence of a susceptance in the transmission line. By changing the length of the line, this susceptance will be absorbed into the line producing the required symmetrical response. C 0 -10 -10 -20 -30 U) N to -40 -20 -50 -301.13 Figure 1.14 1.15 1.17 1.16 Frequency GHz 1.18 1.19 -An7 1.2 z 10° 5.40: Measured frequency response of inverse Cliehyshev 1)andstop filter This filter demonstrated a significant Bandstop design producing improvement in bandwidth 16.3 MHz 3 dB attenuation to 4.3 MHz for the single cavity filter. bandwidth over the first in contrast The wideband response showed the first TMwI, GHz in the 1"' degree DR filter giving 1.516 mode, occurring spurious at free This 5.41. 352 MIHz, figure window spurious of a spurious frequency has been driven down along with the fundamental frequency as the puck was moved towards the base of the cavity. Although adequate for narrowband communication DR Bandstop 5 Dual-Mode 127 Filter Direct-coupled DR bandstop filter 0 -10 m -20 0 -30 -40 -50 1.1 1.15 1.2 1.25 1.35 1.3 Frequency GHz 1.4 1.45 1.5 1.55 x 109 Figure 5.41: Measured wideband frequency response of inverse Chehysliev handfilter stop be improved this as shown earlier through spurious performance can systems. fields the A the the with of spurious modes. of puck sections associated removing dual-mode bandstop filter has been designed that offers the hybrid niode as the fundamental mode which is an advantage over mono-mode dielectric resonator bandstop filters as it offers two resonances in a single cavity. Miniaturisation has been shown by moving the dielectric puck to the base of the cavity, thus, nearly half the cavity has been removed and the filter structure exhibits an unloaded high Q of 9000. 5.8 Direct-coupled DR bandstop filter In this section the dual-mode bandstop configuration synthesis technique polynomials that as described generates in chapter a l)andstop is used to realise a network function 2. The beauty frone the regular of this technique formed matrix produces a folded configuration coupling lowpass is that the degree handstop 4tß' a of filter and the main transmission line is of uniform impedance and can lxs modelled 128 5 Dual-ModeDR BandstopFilter Direct-coupled DR Bandstop filter [48] from An inverter. specifying a symmetexample coupling matrix as a unity filter with 22 dB return loss and two reflection zeros at ±j2.0107 degree 4th rical to give an out-of-band return loss of 30 dB is shown confirming the input/output \/4 transmission is therefore, a uniform simple unity, coupling between the transmission line-to-resonator coupling points. lit= 0 1.5109 1.5109 0 0.9118 0 0.9118 0 00 0 line would suffice 0001 0 1.3363 -0.7985 -0.7985 0 00 0.9118 0 0 0.98118 0 1.5109 1.3363 0 0, 10001.5109 j For bandstop transfer functions where the reflection zeros are less than the filter degree, a second solution is provided by performing the synthesis technique on The dual the dual above. network is established coupling matrix provided the of by multiplying the reflection numerator polynomials by -1, in effect adding unity inverters at the input and output. The coupling matrix is produced below showing the removal of the negative M23 coupling, to give positive values for all couplings. This is a unique solution to cross-coupled designs and removes the need for electric for both solutions is shown frequency for The response coupling. negative probes in figure 5.42. 0 1.5109 0 0 0 1 1.5109 0 0.9118 0 0.9465 0 0 0.9118 0 0.7985 0 0 0 0 0.7985 0 0.9118 0 0 0.9465 0 0.98118 0 1.5109 1 0 0 0 1.5109 0 The coupling routing diagram for this matrix is shown in fi gure 5.43. The dual- 129 5 Dual-Mode DR Bandstop Filter Direct-coupled DR bandstop filter 0 0 -10 -10 -20 -20 -30 -30 -40 -40 -50 -50 -nn 1.12 _an 1.18" Co U) Figure 1.13 1.14 1.15 Frequency GHz 1.16 1.17 5.42: Frequency response of direct-coupled (4-2) bandstop filter described, is bandstop filter, dielectric to perfectly already suitable realise mode this coupling matrix. A diagram of the possible realisation depicts the coupling figure between 5.44. the cross-couplings each othogonal required, mode and paths One should note that for practical realisation the bottom dielectric puck is now fixed to the top of its respective cavity, thus, a low permittivity dielectric support is have filter The be to to the the specifications assumed mount required puck. will in table 5.6. * 11.5109 1.51091 0.9465 M..= 01 10.9118 0.91181 0.7985 Figure [45] 5.43: Coupling routing diagram of a direct-coupled (4-2) handstop filter. The dimensions of the cavity and coaxial line and dielectric puck were identical to those from the previous design. To convert between the ccoupling matrix bandwidth and coupling values for each coupling in the physical model, the coupling 5 Dual-Mode DR Bandstop 130 Filter Direct-coupled DR bandstop filter 4A 4ß 4 C' L- M.: -ý® M rlý yý_L x Bc Figure 5.44: Configuration bandstop filter direct-coupled dual HEE>> mode of (4-2) dielectric [47], from, is calculated coefficient Ow k",j = 111, j WO (5.13) k;; is Mij from the the the coupling matrix. coupling value coefficiant and where Intra-cavity couplings are now required from the coupling matrix and mode cou- disks tuning were used in the simulations. pling The coupling can be controlled by the physical dimensions of the disk such as the thickness and diameter but its position from the dielectric puck will cause the most variation. An eigenmode solver can easily compute the coupling coefficients within the dual-mode resonator [45], cavity using, 131 5 Dual-Mode DR Bandstop Filter Direct-coupled DR bandstop filter Filter Specifications Centre frequency 1.15 GHz Return loss (LR) 22 dB Stopband bandwidth 5 MHz Insertion loss (LA) 30 dB Reflection zeros out-of-band 30 dB lobe levels f j2.0107 Table 5.6: Filter specification for 4th degree direct-coupled bandstop filter f2-fl = (5.14) f2 be to irises inter-cavity placed couple modes of the the may coupligs, To realise Simulations for the between two the coupling coefficavities. polarisation same In figure the 5.45. to iris coupling order calculate performed, were an of cient [45] has been in The described DRs, the technique the used. resonant between frequenciesfe and f,,,, are calculated by using a perfect electric or magnetic symbetween find inter-cavity the iris to in the the coupling middle of metry plane frone found the is The well-known equation, coupling coefficient modes. fee - fmg k= f +f e2 (5.15) m2 from loading the irises shifting the rescaused effects This cross-coupling approach To increase frequency, frequency. below the the frequency centre resonant onant 30.5 height from bottom 37 to the top mm was mm and reduced cavity cavity the height was reduced to 28.37 mm. The optimisation process began by observdimensions the top such that each coupling element ing the cavity and adjusting for bandwidth. The lengths irises from the the correct calculated were produced figure 5.45 and for K12 = K34 = 0.00246, slot widths of 1.26 inm were required for irises of length 30 mm and thickness 20 mm. From these initial dimensions, it was possible to draw an initial model in HFSS and after lengthy fine tuning involving adjusting positions of tuning disks and heights of both cavities, the fifigures in 5.46 5.47 model and response simulation providing shown and are nal 5 Dual-Mode DR Bandstop 8 132 Filter Direct-coupled DR bandstop filter x10; 7 6 Y C5 Ü4 a C ä3 2 1 0 0.5 1 2 1.5 Iris Width mm 2.5 3 length iris 3 cm and with width of of coupling coefficient Figure 5.45: Variation thickness 2 cm Dielectric Puck Metal Coaxial Line Aluminium Tuning Hollow Cavities Screws Croce-Iris ý-' Z y--ý, X Figure 5.46: HFSS model of optimised direct-coupled filter stop HEE>> dual-mode band- ideal to the Thus, HEE1I dual-rnode bandstop the comparison good response. a demonstrates the principle of the coupling matrix synthesis apreadily resonator 133 5 Dual-Mode DR Bandstop Filter direct-coupled the to proach Direct-coupled DR bandstop filter bandstop filter. 1oF..... ... .:. _ ........... H....:.. ý..ý.. ;... :............:...... 1.1 ..................:..... .. ý........... I f. .. .40 12 1113 .... . ........... .......... ýý.. ý: N f.. y...:. ... .....:...........:.... 1'14 1.15 Frequency GHz ... 1.10 1.16 i-30 .:........... ........,. to note that the same structure form direct-coupled the of cul-de-sac matrix. m v N N . -60 1.18 1.17 Figure 5.47: Simulated response of optimised direct-coupled bandstop filter It is interesting 1-20 HEE1I dual-irrode may also be used to realise a Bandstop filter. By considering an example [48], and associated coupling paths, figure 5.48, the same couplings can he realised in the same structure, described above, for the original direct-coupled form, figure 5.44. This shows the flexibilty dual-mode the of novel bandstol) in their as mono-mode an resonators overhaul realised resonator requires resonator between direct-coupled the two structure coupling 0 1.5497 1.5497 0.5155 1ý1= forms, figures 2.13 and 2.11. 0 0 01 1.2902 0 1.28008 0 00 0 1.2902 -0.0503 0 0 0 0 0.9465 0 1 0 0 0 0.4222 0 0.4222 -0.2057 1.5497 0 1.5497 0 -1.0187 It is also clear that the cul-de-sac form brings an advantage for the dual-mode bandstop filter in that no M23 cross coupling is required. This ineans no anode 5 Dual-Mode DR Bandstop 134 Filter Direct-coupled DR bandstop Jilte? M=0.5155 M22= -0.0503 W=-1.0187 M= -0.2057 1.29Ul 5.48: Coupling Figure [48] filter. stopp routing diagram I. LUUö of cul-de-sac U. 4Lll direct-coupled (4-2) band- 0 0 -20 -20 -40 -a0 -60 -60 m y -80 L1.12 Figure 1.13 1.14 1.15 Frequency GHz 1.16 1.17 5.49: Frequency response of cul-de-sac direct-coupled -80 1.18 (4-2) bandstop filter filter disk bottom is in tuning the the cavity required of reducing the coupling design. The frequency ideal is the this response of of matrix shown in complexity figure 5.49 showing an asyn1n ctrical response. with centre frequency of 1.15 GHz bandwidth, MHz 5 and can he acquired and is perfectly realisable in the dual- bandstop dielectric filter. resonator mode optimisation Again, performing criteria as per the former symmetrical for the cul-de-sac configuration similar design and design, the HFSS simulation was performed with the final optimised structure figure in 5.50. Note for design, improve loss, that to this the the cavity shown as height was used to control the centre frequency of the higher resonant mode in disk for thus, tuning this degenerate anode and as no cavity. was required each stated, only one cross-coupling tuning disk in the whole structure was required. The frequency response for the HFSS design, figure 5.51, is comparable to the ideal 5 Dual-Mode DR Bandstop 135 Filter Direct-coupled DR bandstop filter dielectric bandstop dual-mode therefore, the resonator resonator novel response, is perfectly suitable to realise an asymmetrical cul-de-sac design. Dielectric Puck Metal Coaxial Line Aluminium Hollow Cavities Z Y. i j-. __/ x Tuning Screws 7', 7 ýI Eýy 1/ ZL __ x Figure filter yf ýyx -ý 5.50: HFSS model of optimised cul-de-sac HEE11 dual-niode Bandstop 5 Dual-Mode DR Bandstop Filter 136 Direct-coupled m v DR Bandstop filter m v N U) Frequency GHz Figure 5.51: Simulated response of optimised cul-de-sac HEE11 dual-mode bandfilter stop 137 Chapter 6 Conclusions This thesis describes mono- and dual-mode dielectric resonator bandstop filters offering compact and miniaturised solutions over convential coaxial cavity or filters are necessary in communication bandstop Bandstop resonators. waveguide systems, particularly with the ever-increasing congested radio spectrum, interfer- between transmitters ence high harmonics harmful power are and receivers and dielectric fundamental be The the concept revolves around suppressed. and must bandpass have filters but little been in These integrated is commonly resonator. known about their inclusion in bandstop filters. A dielectric-loaded rectangular waveguide resonator is developed from classical determine frequency Q for to the and unloaded resonant a cavity wavegequations It loading is dielectric, the through the dicavity apparent with uide resonator. by factor dielectric the the the of cavity permittivity reduce of a of mamensions terial. In addition, the material properties of dielectric allow them to achieve high Qs for comparable performance to cavity resonators, even after miniaturisation. By metallising the four longer faces of a rectangular dielectric resonator, a coinis pact resonator achieved and observation of the resonant modes indicate TEloa is the fundamental mode. To create the bandstop characteristic, the rectangular is resonator coupled to a coaxial transmission line achieving narrow bandwidths. It has been demonstrated that the compact resonator allows A/4 transmission line separations avoiding unwanted spurious inter-resonator coupling. An unloaded Q 138 6 Conclusions for less ideal miniaturisa2300 where applications stringent performance offers of dielectric filters for Spurious key is the are typically many aim. performance tion poor and require modification to the resonator structure. here allowed a spurious free bandwidth The technology shown MHz 650 allowing the ease of these resof Chebyshev A degree band4th broadband be in implemented to systems. onators but fabrication bandwidth designed techniques 1% filter poor achieving was stop have incurred losses in the final filter desgin, notably poor metallisation of the dielectric resonator. The drawback of this resonator is the narrowband coupling is unsuitable for applications requiring large bandwidths. This is the compromise for high Q materials where E-fields are mostly concentrated for fields external coupling. tric and only magnetic are allowed dieletric-loaded a novel coaxial developed. was resonator within the dielec- To counter this, Investigations of this dB bandwidths 3 Q 2670 have coupling and of oberved an unloaded resonator MHz 200 are achievable, therefore, multi-section of bandwidth designs can provide superior designs at higher frequencies. The second area of contribution is the novel dual-mode dielectric-loaded filter operating in the HEE11 mode. Due to symmetrical the typically allow onators bandstop geometries, these res- higher order dual degenerate hybrid modes to resonate half frequency the the therefore, the within only number of cavities cavity, same at The in to compared mono-mode resonant modes resonators. a cylinare required drical dielectric puck were observed and for an assumed aspect ratio dielectric HEE11 first in the the mode a suspended structure. was spurious puck size, forcing the puck to the base, the HEEII became the fundamental integration ease of in communication By mode allowing The drawback is to this unloaded systems. Q decreases due to metallic contact with one side of the puck but an unloaded Q The bandstop 9000 achieved. was still response was achieved through magnetic of coupling to coupling posts attached to a coaxial transmission line. An experimental cavity was designed highlighting complexities to bend the transmission line to produce the required coupling separations between the transmission line and orthogonal modes of the puck. Simulated and measured responses demonstrated 139 6 Conclusions Future Work the principle of the resonator and a 4th degree filter was designed. The response dB bandwidth 3 showed design from 4.3 MHz improved the cavity single was over to 16.3 MHz. The main drawback to this filter was the poor spurious performance, however, it was shown this could be improved by physically removing segments due DR The to to the the a gave rise rejection puck. measured zero response of length of transmission extra line separation between the middle two resonators but it is proposed future designs should reduce the radii of the cavity walls. The dual-mode dielectric bandstop resonator was perfectly suitable to realise direct-coupled bandstop filters. The benefits of this class of filter are the coubetween direct the source and technique coupling allows pling matrix synthesis load, bypassing the bandstop resonators. The coupling matrix demonstrated the length a/4 transmission implying a single of only source-load coupling was unity, line was required. A full FEM simulation for the novel dual-mode bandstop filter demonstrated the principle producing symmetrical rejection zeros on either side of the stopband for greater selectivity. The coupling matrix synthesized a secby dual-mode bandstop the same cul-de-sac configuration realised ond which was filter with an improvement in the structure where a cross-coupling element was not required compared to the former design. The principle was demonstrated in a FEM simulation showing the advantage over mono-mode cavity filters where the cavity positions must conform to the correct coupling paths. It has also been for that direct-coupled bandstop filthe technique using coupling matrix shown ters, advanced filter functions involving prescribed rejection zeros for symmetrical and asymmetrical responsesare easily realised by this novel filter. 6.1 Future Work The work presented in this thesis has proposed and developed the early development of miniaturised mono- and dual-mode bandstop filters employing dielectric resonators. The promising results from these designs should be carried forward to investigate their use in advanced filtering techniques. Foremost, it is imperative 140 6 Conclusions that future work includes the fabrication Future Work direct-coupled the of filters to confirm their concepts and compare against simulated reponses to adjust for any repetitive fabrication be Also, interesting it that errors may occur. would direct-coupled between the sults to compare re- bandstop filter and cul-de-sac form for the same difference in to the performance, appreciate specifications for example, when a (4-2) is in the the second cavity of not required cul-demode coupling screw The direct-coupled form. in resonators sac filters can consist of mono- dual- or higher order modes to create mixed mode bandstop filters to collectively improve the spurious performance. Lossy filter techniques should also be investigated for the dual-mode bandstop resonator as it allows the realisation of lossy filters with ideal lossless transmission and reflection response. This technique allows further miniaturisation be bandstop low Q dielectric would resonators required as only for ideal responses. For these 3D structures, FEM simulations can be time consuming, especially during the optimisation process where a huge number of iterations are required to tune the variables to the required response. Computer aided techniques that can be followed 3D should geometries such as readily optimise circuit elements with space-mapping optimization, pling matrix [83]. Also, a computer program to perform the cou- synthesis technique should be written to readily produce element filtering Chebyshev for functions filter syninvolving advanced generalised values thesis. 141 Appendix A Conferences Publications and R. Chan, I. C. Hunter, "Dielectric resonator bandstop filters, " Filtronic ing Symposium, September 2006 Engineer- 142 References (1J I. Hunter, L. Billonet, B. Jarry, and P. 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