Chebyshev Microwave Filter Design by Using Dielectric Combline Resonators ABSTRACT Microwave filters are important in the design of modern communications systems, military applications and the satellite communication systems. In this decade the rapid growth of mobile communication has catalyzed an increasing demand for a high performance microwave filters []. Cellular communication base-stations demanded low loss high power-handling filters with small physical size, capable of being manufactured in tens of thousands at a reasonable cost. These demands led to advances in coaxial resonators and dielectric loaded resonators. Dielectric combline resonators combine the merits of conventional combline and dielectric loaded resonator. They are based on quarter-wave length long coaxial structures. By replacing the metallic inner with a high permittivity dielectric inner rod of a conventional combline resonator, it can achieve higher unloaded Q without increasing the volume of the resonator. This resonator will fill the gap between waveguide and stripline technologies [], []. This work will investigate and model the tuning characteristics of individual dielectric combline resonators, a way of achieving very low external Q and also the nature of the coupling between adjacent and non-adjacent resonators. Finally 3 rd Chebyshev and Elliptic function microwave filter by using dielectric combline resonators for GSM 8 mobile communication base stations will be designed.
I. INTRODUCTION Microwave Cavity Filter A microwave cavity filter can be treated as a two-port network. Such a network is used to control a frequency response by allowing transmission at frequencies within the passband and attenuation in the stopband of the filter. It is normally realized by cascading a series of resonators which all have the same resonance frequency. Combline Resonators A conventional combline resonator (see Fig.) has an inner metal rod and a rectangular or cylindrical enclosure. Such resonators are low cost, have a wide tuning range and an excellent spurious free performance [], [], [3]; however, the draw back of the conventional combline resonators is their relatively high loss, due to the low unloaded Q (e.g. 5) of the resonator compared to dielectric combline resonators. Metal / Dielectric Inner Post λ 4 r L Figure- Schematic of a Quarter-Wave Resonator A dielectric combline resonator (see Fig-) is formed by replacing the metallic inner with a high permittivity dielectric inner rod, it can achieve high unloaded Q of up to, because the magnetic filed is continuous at the boundary of the dielectric and no current is introduced in the dielectric rod []. Quarter-Wave Length Resonator
Basic Principle of Dielectric Combline Resonator The precondition of replacing the inner metal by a dielectric is that the dielectric must behave like a metal in terms of the electric field pattern within the cavity. It means that there must be no (or very little) static electric field within the dielectric. The electric flux density D within the dielectric of permittivity r is defined as: D = r = E () E The electric flux density D of free space is defined as: D = () E The boundary condition (see Fig-) states that the perpendicular component of electric flux density D is the same on either side of the boundary if the boundary carries no free charge. D = D (3) Figure- Interface between Two Materials E D D E = (4) = = r r Hence E inside the dielectric is reduced by the factor of r, it means that E (5) r The dielectric will behave like a perfect conducing metal ifr approaches to infinity. The dielectric combline resonator is based on this principle. r 3
Quality Factors Quality factor is used to measure the loss of a resonator circuit. Low loss implies a higher Q. It can be defined as: Q = ω average energy stored average energy loss/second Q factor can be also defined in terms of resonance frequency f and bandwidth f of the resonator circuit, which is stated below f Q = (6) f A high Q factor results in a steep roll-off and narrow bandwidth of the resonator (see Fig-3) Transmitted Power in db 3 db f f Frequency Figure-3 Graph of Quality Factor General Theory of Coupling A general technique for designing coupled resonator filters is based on coupling coefficients of inter-coupled resonators and the external Q factors of the input and output resonators [] The external Q is characterized the external coupling between a microwave resonator and the external circuit, which is shown as Q ea and Qeb in Fig-4. 4
Figure-4 Block Diagram of Microwave Filter The coupling coefficient kij of coupled microwave resonators can be defined on the basis of the ratio of coupled energy to stored energy. It can be defined mathematically, k = E E E dv dv E + dv µ H µ H dv H dv µ H dv Electric Coupling Magnetic Coupling The interaction of the coupled resonator is mathematically described by the dot operation of their space vector fields, which allows the coupling to have either positive or negative sign. A positive sign would imply that the coupling enhances the stored energy of uncoupled resonators, whereas a negative sign would indicate a reduction. Therefore, the electric and magnetic coupling could either have same effect if they have the same sign, or have the opposite effect if their signs are opposite. [] All fields are determined at resonance 5
General Theory of Two Coupled Resonators The magnitude of the coupling coefficient defines the separation d of the two resonance peaks (see Fig-5). Normally the stronger coupling, the wider separation d of the two resonance peaks and deeper the trough in the middle. [] Figure-5 Resonant Response of Coupled Resonator Structure The coupling coefficient can be defined in terms of f and f, see Eq.7 k f f = (7) f + f f is the lower resonance frequency and f is the higher resonance frequency. Loss Tangent and Skin Depth Loss Tangent The loss tangent, tan δ, is used to determine whether conduction current or displacement current is more significant (see Fig-6). According to Ampere s Law, Conduction current density D H = J = σ E + jωe (8) t J c = σe and displacement current density = jωe. J d 6
Figure-6 Characteristics of Loss Tangent Loss tangent is defined as: Skin Depth tan δ = J j c d The amplitude of the electric field, E, in a metal, diminishes by a factor of /e, after travelling a distance of one skin depth (see Fig.4). The skin depth of a conductor is defined as: = σ ω (9) δ s = = = () α ωµσ π fµσ where α = ω = πf µ = µ µ r attenuation constant As seen in Eq (), when σ, δ that means most current in a good conductor occurs in an extremely thin region near the surface. s Figure-7 Characteristics of Material Skin Depth 7
In copper, aluminium and silver, the skin depth at various frequencies is shown in Table-. Frequency δ s in Copper δ s in Silver δ s in Aluminium 3 GHz.48 µ m.4 µ m.83 µ m Table- Skin Depth of Copper and Aluminium VS frequency Dielectric Materials Dielectric materials are continuing to play a very crucial role in microwave communication systems. These materials are key in the realisation of low-loss, temperature-stable resonators and filters for satellite and mobile equipment. At microwave frequencies, according to the classical dispersion theory 4, the dielectric constant r is unchanged, and the dielectric loss increases with frequency f. Therefore the product Q f can be used to describe these basic properties of each dielectric material. Some common used materials are shown in Table-. Materials r Q f (GHz) τ f ppm / ο C Descriptions MgTiO3 CaTiO 3 55, + ~ - Class I ceramic [3] capacitor material Ba ( Sn, Mg, Ta) O 5, +5 ~ -5 Extremely high Q [4] 3 Application at frequencies higher than GHz Ba ( Zn, Ta) O 3 68, +5 ~ -5 Extremely high Q [5] 3 Application at frequencies higher than GHz Ba ( Zr, Sn, Ta) O 3, +5 ~ -5 High Q [6] 3 Good temperature stability ( Zr, Sn) TiO 38 5, +5 ~ -5 High Q [7] 4 Ref Copper Silver 7 σ = 5.8 7 σ = 6.3 σ = 3.77 3 Aluminium (99.99%) 4 Reference [9] 7 8
Good temperature stability Ba Ti9O 4 3, + ~ + High K and high Q resonator material BaO PbO Nd O3 TiO 9 5, + ~ - Widely used at lower frequencies around GHz [8] [7] Table- Current Dielectric Materials II. METHODS The CST Modelling Package can be used to model an extremely wide range of electromagnetic components. Two solvers of this modelling package are mainly used in this work, these are Eigen Mode Solver and Frequency Domain Solver. Eigen mode solve were used to find the appropriate external Q factor and Frequency Domain Solver were used to find the appropriate coupling coefficient. III. CHEBYSHEV FILTER DESIGN Introduction Cellular radio has provided a significant driver for filter technology. This has resulted in various innovations in filter technology for base-stations. The global systems for mobile communications GSM-9 and GSM-8 are used in most part of the world: Europe, Middle East, Africa and Asia. More detailed descriptions of these two solver can be found in Appendix 9
Chebyshev Filter Specification Parameters Specifications Number of Filter Orders n = 3 Centre Frequency f c = 87 MHz Bandwidth Cut-off frequency f b =5MHz (4%) f c = 5MHz Passband Ripple α =. Stopband Attenuation α s db Table-3 Chebyshev Filter Specifications Required Parameter Values for the Specification A small Matlab program is utilised to find the appropriate external Q and coupling coefficient. These values were found (see Table-4). Pass Band Ripple S (db) N=3 Q ext kc kc.db -6.373 54.49.478.478 Table-4 Required Parameter Value for the Set of Specification Full Chebyshev Filter Design Procedure can be found in Appendix
IV. CST SIMULATION ANALYSIS Activity : Find an appropriate external Q factor Figure-8 (a).87 GHz Dielectric Combline Resonator Configurations Figure-5 (b) Schematic of the Resonator Parameter Description Dimension(mm) L Length of the cavity 45 H Height of the cavity 65 W Width of the cavity 45 R Radius of the dielectric rod 5. C Length of the extended wire 35 d Length of the tuning probe 4 h Height of the dielectric rod 57.7 Table-8 Dimension Table of.87ghz DCR
For this set of Chebyshev filter specification, it is required a low external Q for the input (see Table-4), a.87ghz dielectric combline resonator has been designed with a piece of wire is attached at the end of the input coaxial cable(see Fig-8 b) to achieve lower external Q and stronger coupling at input. The dimensions of the resonator can be found in Table-8. At the required external Q value 54.49, the frequency response of the resonator is shown in Figure-9. Figure-9 Frequency Response of Single Resonator As seen in Fig-6, the resonance frequency is shifted around 7MHz (.4%) compared to the designed resonance frequency.87ghz. It is mainly due to the input coaxial cable and the piece of extension wire, which may cause extra capacitance in the two port system. Simulation Result is obtained from JDM Solver of CST(see Appendix )
V. REFERENCES [] High-Q dielectric combline resonator with wide spurious free performance Shen, G.; Budimir, D.; Microwave and Optoelectronics Conference, 3. IMOC 3. Proceedings of the 3 SBMO/IEEE MTT-S International Volume, -3 Sept. 3 Page(s):49-4 vol. [] Dielectric combline resonators and filters Chi Wang; Zaki, K.A.; Atia, A.E.; Dolan, T.G.; Microwave Theory and Techniques, IEEE Transactions on Volume 46, Issue, Part, Dec. 998 Page(s):5 56 [3] Microwave Dielectric Materials K.Wakino, M. Katsube, H. Tamura, T. Nishikawa, and Y. Ishikawa, IEE Four Joint Conv. Rec., 977, Paper 35 [4] High-Q dielectric resonator material for millimetre-wave frequency H. Tamura, D. A. Sagala, and K.Wakino, Proc. 3rd U.S.-Japan Seminar Dielectric Piezoelectric Ceram., 986, pp.69-7 [5] Ba(Zn,Ta)O3 ceramic with low dielectric loss S. Kawashima, M.Nishida, I. Ueda, and H.Ouchi J.Amer.Ceram. Soc., vol.66,pp.4-43, 983. [6] Improved high-q dielectric resonator with complex perovskite strcture H. Tamura, T.Konoike, and K.Wakino J.Amer.Ceram. Soc., vol.67,pp.c-59-6, 984. [7] Microwave characteristics of (Zr,Sn)TiO4 and BaO-PbO-NdO3-TiO K.Wakino, K.Minai, and H. Tamura J.Amer.Ceram. Soc., vol.67,pp.78-8, 984. [8] A new BaO-TiO compound with temperature-stable high permittivity and low microwave loss H.M. O Bryan, Jr., J. Thomoson, Jr., and J. K. Plourde, J.Amer.Ceram. Soc., vol.57, pp.45-453, 974 [9] Far infrared dielectric dispersion in BaTiO3, SrTiO3, and TiO W.G.Spitzer, R. C. Miller, D. A. Kleinman, and L.E. Howarth, Phys. Rev., vol.6, pp. 7-7, 96. [] Filter technologies for wireless base stations Mansour, R.R.; Microwave Magazine, IEEE Volume 5, Issue, Mar 4 Page(s):68-74 Digital Object Identifier.9/MMW.4.84945 [] Microwave Engineering David M Pozar [] Microstrip Filters For RF/Microwave Applications Jia-sheng Hong/M.J.Lancaster 3