Analysis and Optimization of a Special Type of Dielectric Loaded Resonant Cavity for Mobile Communication Filters

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1 328 Analysis and Optimization of a Special Type of Dielectic Loaded Resonant Cavity fo Mobile Communication Filtes Haold S. Showes, Banmali S. Rawat *, Syam S. Challa Depatment of Electical and Biomedical Engineeing Univesity of Nevada, Reno, NV 89557, U.S.A. Tel: ; Fax: ; awat@ee.un.edu (Invited Pape) Abstact- In this pape a new type of dielectic loaded cavity fo mobile communication filte application has been analyzed. An optimization method fo suppoting the dielectic inside the cavity has been discussed and analyzed using Modefinde softwae pogam and Finite Element analysis softwae known as High Fequency Stuctue Simulato (HFSS). Results have been compaed with an expeimental esonato with some ageement. The main eason fo the diffeences between expeimental and theoetical esults is also discussed. Index Tems- dielectic loaded, filte, losses, mobile communication, optimization, esonant cavity I. INTRODUCTION The dielectic esonatos have become an integal pat of pesent day communication systems paticulaly fo filte applications. The dielectic mateials used in these esonatos ae geneally alumina, titanium oxide o ceamics. The dielectic esonato filte has the advantage of being smalle in size than a esonant cavity opeating at the same fequency. The dielectic is geneally shielded by a metal enclosue to educe losses. Enegy is coupled to the esonato by a coaxial feed line to the enclosue. Attaching a looped wie in shunt to the coaxial cable may incease coupling to the esonato. The distance fom the input /output feed loops to the dielectic can be adjusted fo optimum pefomance. It is also common fo seveal esonatos to be coupled togethe within the same filte. The main focus of this pape is a dielectic esonato which consists of a volume of dielectic within a metal cavity. The pefomance of this type of esonato diffes fom simple dielectic esonatos in that the electomagnetic fields ae substantially affected by both the dielectic esonance and the shielding cavity esonance [1]. In this analysis a paticula type of esonato filte geomety is optimized to educe cost and weight. This optimization method includes vaying the adius of a cylindical void though the cente of the dielectic and subjecting to the hypothetical stuctue to numeical fequency esponse simulation. Also, the height of the esonato is adjusted and analyzed. Numeic solutions ae geneated fom Mode Finde softwae pogam and Finite Element analysis softwae known as High Fequency Stuctue Simulato (HFSS). II. BASIC CONCEPT OF DIELECTRIC RESONATOR AND ANALYSIS A cylindical esonato can be made to esonate at a specific fequency to be used as a bandpass filte. The design involves the solution of diffeential equations of vaying ode. The mode of popagation is elated to the ode of the associated diffeential equations. In the dielectic esonato used fo filte applications, the cavity is loaded with a dielectic mateial. A consideable eduction in size of the esonato can be achieved by selecting a highe dielectic constant mateial. Cohn has shown that a TiO 2 dielectic esonato filte has a volume 3 to 5 pecent of that of a waveguide filte having an equivalent esponse [2]. The only disadvantage of the dielectic loaded cavity is the dielectic losses. The electic and magnetic fields inside

2 329 these cavities ae confined to be in o nea the dielectic. Howeve, if the distance between the dielectic and the cavity walls is quite small compaed to fee space wavelength, the adiation to the walls is negligible [2]. The unloaded Q of the cavity is given by 1 Q u (1) tanδ whee δ is the loss tangent of the dielectic, which ae typically between.6 to.5. The loss tangent educes the unloaded Q of the cavity fom the value achieved without the dielectic esonato. Tempeatue vaiation also changes the dielectic constant of the mateial in the ange of 2 ppm/ C to 1 ppm/ C, which in tun changes the esonant fequency of the esonato. Anothe impotant paamete of inteest in the filte design is the spuious esponse of the filte i.e. the sepaation between the modes which also depends on the filte geomety. Wang et al. have used theoetical analysis to ceate mode chats showing at what wavelengths diffeent modes would exist as a function of the esonato geomety [3]. It means that fo optimization of the esonato pefomance, the spuious esponse paamete is to be minimized. Fo analysis pupose, a pototype shielded paallel plate dielectic esonato in cylindical shape as shown in Fig. 1 was fabicated. The conducting metallic plates ae paallel to each othe on top and bottom of the cylindical esonato and nomal to the axis of the dielectic. The esonato may be shielded by a metal enclosue to educe adiation losses. Fig.1. Test dielectic esonato sliced along x-axis A computeized pogam known as Modefinde is usded fo detemining all possible modes of the esonato as a function of the geomety of the dielectic cylinde and fequency. The Modefinde pogam detemines values of x such that [4-5] ' ' ' ' Jm() x Km() yjm() x Jm() x Km() yjm() x + + x yk ( y) x yk ( y) m m 2 β 1 1 J m( x ) = kaam x y (2) whee 2 2 x= k a = a k β ; ρ1 ( ) 2 2 y = k 2a = k a ( 1) x ; ρ ( ) 2 2 βa = ka x ; m is an intege; J m is the Bessel s function of fist kind and m th ode; K is the modified Bessel s function of m the second kind and m th ode; pimes denote diffeentiation with espect to the agument of the function; a is the adius of the dielectic cylinde; k = k is the wave numbe of the dielectic; k is the fee space wave numbe; β is the popagation in the medium and is the dielectic constant of the mateial. If Eq. (2) is satisfied fo a cylinde of adius a and dielectic constant, Maxwell s equations have a non-tivial solution and wave pattens exist in and nea the stuctue. It is difficult to explicitly detemine the values of x that satisfy Eq. (2). Howeve, a method to detemine the value of x unde these conditions is to change x by a small incement and find the solution of the equation. The exact zeo of the function may not be detemined in using this pocess but a check can be made to show if thee has been a change of sign when the equation is solved. The

3 33 value of x that satisfies the Eq. (2) is an eigen value of Maxwell s equation applied to the cylindical dielectic esonato. Once the eigen value is detemined fo a given a and k, a o k may be inceased by a small incement and anothe coesponding eigen value may be detemined. Thus a plot can be obtained fo eigen values x as a function of a fo a constant k o vice-vesa. If paallel conducting plates ae placed at z = and z = h, the component of the magnetic field nomal to the plates becomes zeo at the bounday of the plates and a standing wave in z-diection is fomed. The esonance of the paallel plate dielectic esonato fo a paticula mode mn is obtained at [4] 2 a xmnp = ( ka) pπ (3) h whee p = 1, 2,3,... and the values of x ae detemined fo given values of a, p, h, and as a function of k and ae plotted on the same plot as those fo x satisfying Eq. (2). The intesection of these two plots occus at x and k. Thus fo a given geomety, the mnp value of k can be detemined. This k is elated to esonance fequency by f = ck /2π. At the same time in ode to keep y fom becoming imaginay, the maximum value of x is obtained fom xmax = ka 1 (4) It is useful to daw a plot of Eq. (4) on the same gaph as the intesections of Eqs (2) and (3). III. FABRICATION OF THE TEST RESONATOR Fo futhe analysis and veification of computed esults a pototype esonato has been fabicated. The shield is Nickel-coated Aluminum. The cavity is cylindical with adius a = 61 mm and height h = 58 mm. Inside the 2 cavity is a dielectic cylinde of adius a = 21.5 mm and height 58 mm. The dielectic constant = 38. The input and output pots ae located opposite to each othe and midway up the wall of the shield. A 3 mm length of coppe wie is bent into a semi-cicle loop and connected to one of the input pots. The loop extends into the cavity and the fee end of the wie is diected back to the cavity wall and makes contact with it. Pot 1 is diffeent in that the coupling wie is Nickel having a length of 45 mm and does not loop back to make contact with cavity wall. Instead, the wie is bent downwad at 45 angle and makes contact with the cavity floo. IV. RESUTLTS AND DISCUSSION The Modefinde pogam unning on Matlab has been used to poduce fequency and eigen value gaphs fo = 38,5,1 fo diffeent modes. These esults ae shown in Figs.2, 3 and 4, espectively. These gaphs also contain the supeimposed plots of Eq. (3) as a function of p fo the same esonato. Fom Fig. 2, the intesection of mode TM 1 and p = 1 line is obtained at f = GHz. Fig.2 Modefinde output fo = 58 mm, = 21.5 mm, = 38. h a

4 331 esonato should be placed in the top o bottom plates of the shielding stuctue to cause the most effective petubation to the electic field. At the same time a TM mode esonato should have tuning scews placed in the walls of the shield. It is obseved that the esonant fequency of a given mode deceases as the dielectic constant inceases. Fig.3 Modefinde output fo = 58 mm, = 21.5 mm, = 5 h a Fig.4. Modefinde output fo = 58 mm, = 21.5 mm, = 1 h a Seveal modes have been plotted on the same gaph to get an idea of the popagating modes even though the esonant fequencies may have aleady been detemined expeimentally. By doing this the ode whee the modes appea in elation to fequency can be easily seen. The knowledge of the popagating modes helps in detemining the location of the input coupling stuctues in the field and tuning devices. Fo example, a esonato opeating in TE mode would use coupling stuctues that have some length paallel to the axis of the esonato, thus intecepting moe of the electic field than a stuctue pependicula to the axis of the esonato. Also, tuning scews fo TE mode Fo the fabicated esonato with a= 21.5 mm, h= 58 mm, = 1 and a shield adius of 63 mm we ae able to get good spuious esponse and elatively low esonant fequency as shown in Fig.4. The Modefinde2 pogam is also used to plot the eigen values of Eqs. (2) and (3) as a function of adius of the dielectic fo given values of mn,, ph,, and fequency. In Fig. 5 Modefinde2 is used to obtain the adius of a esonato of height 58 mm, = 38 and opeating fequency at 45 MHz. Fig. 6 is a close view of Fig. 5 wheein the dielectic adius is seen to be mm. Theoetical pediction of the esonant fequency fo this esonato as shown in Fig. 7 is about 1.41 GHz. A close view of Fig. 7 is shown in Fig.8 showing the pedicted esonance fequency at 1.41 GHz. Fig.3 Pedicted Radius of Dielectic fo Expeimental Resonato using Modefinde2 Fig. 5. Pedicted adius of dielectic cylinde fo expeimental esonato

5 332 Fig.8. Close view of Fig. 7 Fig. 6 Close view of Fig.5, adius of dielectic pedicted to be mm. The actual esonant fequency was detemined expeimentally using a HP 8753D netwok analyze. Fig. 9 shows the S 21 esponse of the esonato fo a fequency sweep fom 1 MHz to 1.5 GHz. This esult shows that the esonant fequency of the dominant mode of the filte is 486 MHz. This is a facto of 3 below the esonant fequency pedicted by Modefinde. Fig.7. Pedicted esonant fequency of expeimental esonato using Modefinde Fig. 9 Dominant mode esonant fequency fo expeimental esonato (S 21 ) The eason that the actual measued fequency is lowe compaed to theoetically pedicted value may be the shielding effect. The shielding foces the maximum electic and magnetic fields to be conf ined insi de the diel ecti c as sho wn in Figs. 1 and 11, espectively.

6 333 Fig. 1 Dense electic field in and nea the dielectic Fig..12. S 21 Fequency esponse as simulated using HFSS The HFSS simulated and expeimental fequency esponses used fo detemining Q- facto ae shown in Fig. 13 and 14, espectively. It is evident fom these figues that this esonato has elatively low Q- facto as 133 fom HFSS simulation and 88.4 expeimentally. The eason fo low Q-facto is patially due to esonato being opeated in TM mode. A lage potion of the electic field popagates along the length of the esonato causing high cuents and theefoe losses in the dielectic mateial. Fig.11 Dense magnetic field in and nea the dielectic Fig. 12 shows the S 21 paamete o tansmission though the esonato as analyzed by HFSS. It shows the dominant mode esonance at about 45 MHz and the second esonance at about 9 MHz. We have aleady seen in Fig. 9 that the fist esonance occus at 486 MHz and the second esonance takes place at about 847 MHz. This is faily good ageement and the mino diffeence may be due to (i) somewhat diffeent value of the dielectic constant of the pactical esonato than the value 38 consideed in the model (ii) not quite homogeneous and pefect natue of the dielectic mateial and (iii) input/output pots in the model ae not same as in the actual filte. This fequency esponse of TM 1 mode can also be used fo Q-facto detemination of the esonato. Fig.13. S 21 Tansmission as simulated by HFSS with Q = 133. Anothe dawback of this design is that the dielectic has a lage volume making the cost of the esonato high. It is also noticed that in the pototype esonato assembly thee is no mounting fo dielectic. The dielectic is simply set aside the shield and has no fastening at all. Theefoe the fo making a good esonato it is impotant that the volume of the dielectic should be educed while peseving the excellent compactness of the esonato and the dielectic should be secuely mounted to the shielding.

7 334 [2 ] S.B. Cohn, Micowave Bandpass Filtes Containing High- Q Dielectic Resonatos, IEEE Tans on Micowave Theoy and Techniques, Vol. 16, No. 4, pp , Apil [3] C. Wang et al., Dielectic Combline Resonatos and Filtes, IEEE Tans on Micowave Theoy and Techniques, Vol. 46, No. 12, pp ?, Decembe [4] D. Kajfez, P. Guillon, Dielctic Resonatos, Atech House, Dedham, MA, Fig. 14 Expeimental detemination of Q-facto, with Q = 88 at f = 486 MHz. [5] D. Kajfez, Basic Pinciples Give Undestanding of Dielectic Waveguides and Resonatos, Micowave Systems News, Vol. 13, pp , May 1983 One main advantage of this esonato is its compactness. It is due to lage amount of magnetic flux passing though the dielectic. In this case, vey little tansvese magnetic field lies in the cente of the dielectic as shown in Fig. 11. The cost of the filte can be educed by emoving the dielectic potions that ae not cost effective. Theefoe the expeimental designs ae dawn in which dielectic has been emoved fom the cente of the esonato. Thus by gadually inceasing the amount of the dielectic to be emoved and ecoding the fequency and Q-facto, an optimum thickness of the dielectic may be obtained. V. CONCLUSION A dielectic loaded esonant cavity has been analyzed using mode finde method and HFSS. Expeimental cavity measuements have been compaed with the analytical esults and a close ageement has been obtained with HFSS values. An optimization method fo cavity dimensions has also been suggested. This pocess is helpful in the design of dielectic loaded cavity filte fo mobile communication. RFERENCES [1] Haold S. Showes III, Analysis and Measuement of Dielectic Loaded Resonant Cavity Using High Fequency Stuctue Simulato, MS Thesis, Univesity of Nevada, Reno, USA, August 21.