Design of Slotline Ring Resonator 報告人：施冠州 日 期： 2003/02/27

大綱 簡介 設計原理 設計步驟 結論 參考資料

簡介 Slotline configuration [4][7]

FIELD DISTRIBUTION IN CROSS-SECTION VIEW [7]

設計原理 Circuit configuration of the slotline ring resonator with different coupling schemes[1,2,8] Slotline ring

The frequencies of the slotline ring resonator are determined by 2πR ＝ nλg [1,2] R is the mean radius of the slotline ring λ g is the slotline guide wavelength n is the mode number

The resonant frequency of a ring with a mean radius R can be calculated by ε eff is the effcetive dielectric constant c is the speed of light

參數介紹 (Harmonica) G ： Gap width Z0 (Z 0 ) ： Transmission line impedance F ： Analysis frequency ER(ε r ) ： Relative dielectric constant H ： Substrate thickness HL ： Distance between bottom of substrate and ground HU ： Cover height above substrate A ： Width between sidewalls

Harmonica Microwave office For synthesis of slot line transmission lines, the parameters Z0, H, HU, HL, A, F and ER must be entered prior to clicking the Synthesis button. The width, G, will be computed. T/G < 0.02 (T is the total conductor thickness) ε r must be ≦ 20 the parameters G, H, F and ER must be entered to clicking the button. The impedance, Z0, will be computed or enter the parameters Z0, H, F and ER to clicking the button. The width, G, will be computed.

w ： Gap width Z 0 ： Transmission line impedance F ： Analysis frequency ε r ： Relative dielectric constant h ： Substrate thickness λ 0 ： free-space wavelength λ g ： slot mode wavelength

The equations for design are from [3]~[5] 9.8 ≦ ε r ≦ 20.0 high dielectric constants (1)0.02 ≦ w/h ≦ 0.2 (2)0.2 ≦ w/h ≦ 1.0 (3)0.01 ≦ h/λ 0 ≦ 0.25/(ε r –1.0) ≦ ε r ≦ 9.8 intermediate dielectric constants (1) ≦ w/ λ 0 ≦ (2) ≦ w/ λ 0 ≦ 1.0 (3)0.006 ≦ h/λ 0 ≦ ≦ ε r ≦ 3.8 lower dielectric constants (1) ≦ w/ λ 0 ≦ (2) ≦ w/ λ 0 ≦ 1.0 (3)0.006 ≦ h/λ 0 ≦ 0.06

3.8 ≦ εr ≦ 9.8, ≦ w/ λ 0 ≦ 0.075

The expressions obtained by curve fitting the numerical results.

approximations for slot line [6] [7]

設計步驟 substrate – h (thickness), ε r (dielectric constant) film thickness resonant f (Hz) coupling methods (cpw,slot,microstrip……) Z 0 (  ) → w (line width) → ε eff → R By eq. or microwave office or harmonic. By equation

範例 G-10 ： h =15 00μm, ε r =4.6 film thickness = 100 μm resonant f = 2G Hz coupling methods → CPW Z 0 = 50  → CPW ： w=1500μm, g=410μm Z 0 = 85  → slotline ： G=530μm, ε eff = , R=17259μm. coupling gap=546μm

The CPW-fed Slotline Ring Configuration Slotline ringCoupling gap CPW

結論 The slot transmission line has a simple planar geometry that is compatible with microwave integrated circuit. Various coupling methods were devised for different applications. The slotline annular ring element with the advantages of good performance and ease of adding series and shunt components. Slotline types of annular ring elements have been developed as circuit components for the resonator, filter, latching phase shifters and hybrid coupler.

參考資料 [1] Chien-Hsun Ho; Lu Fan; Kai Chang,” Slotline annular ring elements and their applications to resonator, filter and coupler design”, Microwave Theory and Techniques, IEEE Transactions on, Volume: 41 Issue: 9, Sep 1993 Page(s): 1648 –1650. [2] Navarro, J.A.; Lu Fan; Kai Chang,” The coplanar waveguide-fed electronically tunable slotline ring resonator”, Microwave Symposium Digest, 1992., IEEE MTT-S International, 1-5 Jun 1992 Page(s): vol.2. [3] Brian C. Wadell,'Transmission Line Design Handbook",1991 ARTECH HOUSE,INC.page(s):156~161. [4] Garg, R.; Gupta, K.C.,” Expressions for Wavelength and Impedance of a Slotline (Letters)”, Microwave Theory and Techniques, IEEE Transactions on, Volume: 24 Issue: 8, Aug 1976 Page(s): 532 –532. [5] Janaswamy, R.; Schaubert, D.H.,” Characteristic Impedance of a Wide Slotline on Low-Permittivity Substrates (Short Paper)”, Microwave Theory and Techniques, IEEE Transactions on, Volume: 34 Issue: 8, Aug 1986 Page(s): 900 –902.

[6] Cohn, S.B.,” Slot Line on a Dielectric Substrate”, Microwave Theory and Techniques, IEEE Transactions on, Volume: 17 Issue: 10, Oct 1969 Page(s): 768 –778. [7] Cohn, S.B.,” Slot Line - An Alternative Transmission Medium for Integrated Circuits”, Microwave Symposium Digest, 1967 G-MTT International, Volume: 68 Issue: 1, May 1968,Page(s): 104 –109. [8] Kai Chang,"MICROWAVE RING CIRCUITS and ANTENNAS",1996 by John Wiley & Sons, Inc.