1. 微波電路期中報告 Southern Taiwan University Department of Electronic Engineering

2. Outline Abstract I. INTRODUCTION II. EXCITATION AND INTERCONNECTION OF RESONATORS III. RESONATORS IV. OPERATIONAL COMMENTS V. FILTERS AND CONCLUSIONS REFERENCES 1

3. Abstract (1/2) A structure consisting of dielectric-loaded feed lines (such as surface-wave lines similar to Goubau lines) and below-cutoff air-filled cavities can be used to form essentially L–C sections. The capacitance is due to electric-field coupling from the feed-line dielectric medium into the below-cutoff section. The inductance results from combining the inductors in the inductive tee equivalent circuit for such below-cutoff sections. Dielectric loading is used to shorten the guide wavelength at the input to the evanescent section, increasing the effective input inductance. The dielectrically loaded feed lines can comprise microstrip, coplanar waveguide (CPW), coplanar stripline (CPS), Goubau lines (surface-wave structures), waveguide, etc. The resulting resonant elements are usable at frequencies below 1 GHz, with small dimensions. If connected to the common ground plane, these L–C sections act as a transmission zero. 2

4. Abstract (2/2) If “floated,” i.e., connected in the “hot” line rather than to the ground plane, the sections form bandpass circuits (transmission poles). The air-filled below-cutoff sections (evanescent mode) are placed in a supporting low dielectric-constant medium (air, Teflon, or similar) with the open end in proximity to the dielectric portion of the feed line and are, thus, termed “suspended.” The individual L–C sections can be coupled together using microstrip, surface-wave line, CPW, CPS, finline, waveguide, or lumped elements. Such combinations can be chosen to implement Chebychev, Butterworth, quasi-elliptic, etc. responses. These applications will be covered at a later time. 3

5. I. INTRODUCTION 4 Fig. 3. Equivalent-circuit elements for both: (a) bandpass and (b) bandstop cases; values of capacitance C given from Table I, (4–4). Fig. 4. (a) Metallized wall and bottom below-cutoff cross section. (b) For a single-mode below cutoff, the equivalent circuit is a short-circuited tee.

6. II. EXCITATION AND INTERCO - NNECTION OF RESONATORS 5 Fig. 1. Evanescent suspended bandpass resonator (series transmission pole). Fig. 2. Evanescent suspended bandstop resonator (shunt transmission zero).

7. II. EXCITATION AND INTERCO - NNECTION OF RESONATORS 6 Fig. 6. Z versus ln(W =W ) for various values of H. Fig. 5. Surface-wave line configuration. Enclosure width is W, line and dielectric widths are W, high dielectric-constant substrate thickness is d ("r > 10), support thickness is H, and "r = 2. For surface wave,H >W.

8. 7 Fig. 7. Bandpass case: F = 1.03 GHz (measured), 0.93 GHz (simulated), dielectric constant = 25 in simulation, 20 actual, substrate thickness is 0.004 in Fig. 8. Bandstop case: F = 1:82 GHz (measured), 1.65 GHz (simulated), dielectric constant = 25 in simulation, 20 actual, 0.004 in thick. III. RESONATORS

9. 8 Fig. 9. (a) Bandpass and bandstop resonators. (b) Two resonator bandpass types using either transmission line or lumped inverters. III. RESONATORS

10. IV. OPERATIONAL COMMENTS 當加入此介質時，既可在低頻產生共振的效果，無須用大型的共 振電容來產生。 當加入介質並不會犧牲原本的諧振架構，且頻帶很寬，這是本結 構之最大特點；因為寄生元件並不會因此而變差，而是超過截止 頻率時才會導致而成。 截止頻率低於截止節不影響由該 feedlines 的介質加載。 在某些時候，它的目的是使用鐵的電介質的諧振器的執行。 9

11. V. FILTERS AND CONCLUSIONS 在多個濾波器中，運用 2-6 個條狀型設計；梯字型與交叉耦合方 式的結構。可運用於 400 MHz 至 4 GHz 製作於封閉面積所小化織架構，該方法也適用於 “ 在一晶片式 ” 可 從 100 MHz 到 10GHz 。在某些情況下，由基本長度的諧振與表面 波浪線可代表一個逆變器。 在更近的實現，互連傳輸集中等值線已被替換，可謂以上。 許多拓撲結構是可能的，包括交叉耦合帶通諧振器，個別傳輸零 點放在拒諧振器，等諧振網絡 10

12. 11 Fig. 10. One proposed multiresonator connection. Fig. 11. Transformation of a series transmission line shown in (a) into a low-pass pi-equivalent shown in (b). is in radians, ! is filter center frequency in radians. Final values are adjusted via optimization. V. FILTERS AND CONCLUSIONS

13. 12 Fig. 12. Propagatingwave comparison. Equivalent frequency principle: higher K shortens wavelength and has same effect as higher frequency with low K increases reactance of below cutoff resonator. V. FILTERS AND CONCLUSIONS

14. REFERENCES J. Papapolymerou, J. Cheng, J. East, and L. Katehi, “A micromachined high-Q X-band resonator,” IEEE Microwave Guided Wave Lett., vol. 7, pp. 168–170, June 1997. R. Snyder, “New application of evanescent waveguide to filters,” Trans Microwave Theory Tech., vol. MTT-25, pp. 1013–1021, Dec. 1977. G. Goubau, “Surface-wave lines,” Proc. IRE, vol. 39, pp. 619–624, 1951. R. Snyder, “Quasi-elliptic compact high-power notch filters using a mixed lumped and distributed circuit,” Trans. Microwave Theory Tech., vol. 47, pp. 518–522, Apr. 1999. 13

15. 本人對看法 此篇論文對於濾波器的架構與設計，是由 L-C 組合而成。 運用微帶性的材料，例如 : 共面波導（ CPW ）， coplanar stripline (CPS), Goubau lines (surface-wave structures), waveguide, etc. ，均可由此產生再 1GHz 以下的小尺寸結構 來使用。 當加入寄生元件時，不會改變任何現象，既可保持原來既 有優良之效果。