I. Introduction. Young Yun, Jang-Hyeon Jeong, Hong Seung Kim, and Nakwon Jang

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1 Basic RF Characteristics of Fishbone-Type Transmission Line Employing Comb-Type Groun Plane (FTLCGP) on PES Substrate for Use in Flexible Passive Circuits Young Yun, Jang-Hyeon Jeong, Hong Seung Kim, an Nakwon Jang In this work, a fishbone-type transmission line employing a comb-type groun plane (FTLCGP) was fabricate on polyethersulfone (PES) substrate, an its RF characteristics were thoroughly investigate. Accoring to the results, it was foun that the FTLCGP on PES showe perioic capacitance values much higher than other types of transmission lines ue to a coupling capacitance between the signal line an groun, which resulte in a reuction of wavelength an line with. Using the theoretical analysis, we also extracte the banwith characteristic of the FTLCGP on PES. Accoring to the result, the FTLCGP structure showe a cut-off frequency of 8 GHz. Keywors: Fishbone-type transmission line employing comb-type groun plane, FTLCGP, polyethersulfone, PES, Monolithic Microwave Integrate Circuit, MMIC. Manuscript receive Feb. 7, 14; revise Mar. 1, 14; accepte Apr. 1, 14. This research was financially supporte by the Ministry of Eucation, Science Technology (MEST) an National Research Founation of Korea (NRF) through the Human Resource Training Project for Regional Innovation. This work was supporte by the National Research Founation of Korea (NRF) grant fune by the Korea government (MSIP) (14R1AA1A ). Young Yun (corresponing author, yunyoung@kmou.ac.kr) an Jang-Hyeon Jeong (jjh1@ kmou.ac.kr) are with the Department of Raio Communication Engineering, Korea Maritime an Ocean University, Busan, Rep. of Korea. Hong Seung Kim (hongseung@kmou.ac.kr) is with the Department of Nano Semiconuctor Engineering, Korea Maritime an Ocean University, Busan, Rep. of Korea. Nakwon Jang (nwjang@kmou.ac.kr) is with the Department of Electrical an Electronics Engineering, Korea Maritime an Ocean University, Busan, Rep. of Korea. I. Introuction Flexible electron evices have been employe for applications such as flexible isplays, smart tags, an wearable proucts [1]. Recently, RF applications of flexible electron evices have rawn attention ue to the eman for the evelopment of folable wireless communication evices. Compare with other flexible materials, polyethersulfone (PES) showe better heat-resisting properties an higher transparency [] [3]. In aition, PES shows goo waterresistant qualities []. For these reasons, PES has been employe in flexible Monolithic Microwave Integrate Circuits (MMICs) [4] [5]. The coefficient of thermal expansion an glass transition temperature of PES is 49.1 ppm/k an 8 C, respectively, an the ielectric loss tangent an relative permittivity of PES is.1 an 3.5, respectively. Silicon substrate is a wiely use commercial semiconucting material. So, the electrical characteristics of many new materials are often compare to those of silicon. The electrical properties of PES were also compare with the silicon substrate. Accoring to our previous results, [4] [5], it was foun that the insertion loss of PES was much lower than that of silicon substrate. To reuce the size of the RF evice on semiconucting substrate, we shoul use a transmission line with a short wavelength. However, the wavelength of the transmission line on PES was much longer than that on conventional semiconucting substrate, such as silicon, ue to its low effective permittivity [4]. Usually, a transmission line 18 Young Yun et al. 15 ETRI Journal, Volume 37, Number 1, February 15

2 with low impeance is require for the impeance matching of a transistor in high frequency ue to the low input an output impeance of transistors. However, the transmission line on PES showe a characteristic impeance much higher than that shown on conventional semiconucting substrate. For a PES substrate of thickness m, a coplanar waveguie having a line with of 5 m an gap (a gap between line an groun) of 65 m on the PES showe a characteristic impeance higher than 1. Therefore, a transmission line with a very wie line with is require to perform the impeance matching of transistors with low input an output impeance [4]. For this reason, the passive components on a PES substrate have to be a little larger in size than those on a conventional semiconucting substrate. To solve the above problem, the fishbone-type transmission line (FTTL) was propose, an its RF characteristics were evaluate [4]. Accoring to the results in [4], the FTTL on the PES showe an effective permittivity ( eff ) that was much higher than that shown by a conventional coplanar waveguie on PES, an this resulte in a reuction in wavelength. In aition, the FTTL on the PES showe a lower characteristic impeance than that of the coplanar waveguie on PES ue to an enhancement of the perioic capacitance. Recently, we have propose a fishbone-type transmission line employing a comb-type groun plane (FTLCGP) for a further reuction of the RF evice on PES [5]. The size of the impeance transformer employing the FTLCGP was highly reuce compare with the conventional one [5]. For application to various on-chip components on flexible MMICs, the basic characteristics of the FTLCGP structure on PES shoul be thoroughly explore. However, an extensive investigation of the basic characteristics of the FTLCGP structure on PES has not yet been performe. In this work, basic RF characteristics of FTLCGP on PES are theoretically stuie using a simple equivalent circuit an close-form equations. Concretely, RF characteristics such as impeance an banwith are extracte from the theoretical analysis, which offere a esign guieline for passive components employing FTLCGP. Accoring to our results, we foun that the theoretical results showe goo agreement with the experimental ones. The basic RF characteristics of the FTLCGP structure obtaine from the experimental an theoretical analysis inicate that the FTLCGP structure can be effectively use for a evelopment of RF components on flexible PES substrates. II. FTLCGP Structure on PES Figure 1 shows the structure of the FTTL [4] on PES. The conventional coplanar waveguie has only a perioical X Groun plane Top view Y Y W Signal line I X Groun plane (Cross-sectional view of X-X irection) GND plane Signal line PES substrate (Perioical inuctance an capacitance for FTTL structure) L a L L a L Fig. 1. Structure of FTTL on PES [4]. L a L GND plane capacitance,, between line an groun plane, while the FTTL has an aitional perioical shunt capacitance, [4]. In aition, the coplanar waveguie has only a perioical inuctance, L a, ue to the current flowing across the signal line, while the FTTL has an aitional inuctance, L, ue to the current flowing across the. The FTTL on PES showe a much higher perioic capacitance an inuctance than that of a conventional coplanar waveguie on PES, which le to a reuction of wavelength an characteristic impeance [4]. In this work, a moifie structure, FTLCGP, was fabricate on PES for a further reuction of wavelength an characteristic impeance. The wavelength an characteristic impeance of a transmission line can respectively be expresse as follows [6]: π π, LC (1) Z L () C, where, L, an re the angular frequency, perioic series inuctance, an shunt capacitance of the transmission line, respectively. In particular, C is a perioic shunt capacitance ue to a coupling between the signal line an groun. From the above equations, we can see that the perioic shunt capacitance between the signal line an groun shoul be increase to reuce wavelength an characteristic impeance. In the propose FTLCGP, a perioic groun structure was employe to enhance the perioic shunt capacitance. Figure shows the structure of the FTLCGP. As shown in this figure, the FTLCGP consists of a fishbone-type center line an comb-type groun planes. The fishbone-type center line consists of a signal line an perioic metal strips (s), an the comb-type groun plane consists of a groun plane an perioic groun strips (PGSs). The s are place alternately with the PGSs. Therefore, compare with the FTTL, the FTLCGP has an aitional shunt capacitance between the signal line an groun (C b ) ue to an electromagnetic coupling between the ETRI Journal, Volume 37, Number 1, February 15 Young Yun et al. 19

3 Y. FTLCGP on PES PGS W X Groun plane Signal line Y l Groun plane PGS X (Cross-sectional view of X-X irection) GND plane Signal line PES substrate C b GND plane (Cross-sectional view of Y-Y irection) C b Capacitance (pf/mm).15.1 FTTL on PES CPW on PES Fig. 3. Measure equivalent perioic shunt capacitance per unit length of various transmission lines on PES. L a L PGS Fig.. Structure of FTLCGP on PES. PES substrate (Perioic inuctance an capacitance for FTLCGP structure) C b L a L L a L C b C b s an PGSs, which increases the total perioic shunt capacitance. Therefore, the total perioic shunt capacitance of the FTTL an FTLCGP can be expresse as follows: C C C, (3) FTTL a C C C C. (4) FTLCGP a b In the FTTL structure, there is a coupling capacitance between the s. However, to contribute to a reuction in wavelength, the coupling capacitance shoul exist between the signal line an groun, because the C in (1) an () is the shunt capacitance between the signal line an groun. From (1) an (), we can obtain the following equation: L 1 π C. (5) Z Z Z Using (5), we extracte the perioic shunt capacitance. Figure 3 shows the perioic capacitance of the various transmission lines on PES. For a fabrication of FTTL an FTLCGP on PES, titanium (Ti) was eposite on the PES to provie goo ahesion firstly, an then gol (Au) was eposite over the Ti to reuce the resistance; the total combine thickness of the Au an Ti was m. For the FTTL, the length an with of a is 16 m an 3 m, respectively, an the signal line with, W, is 7 m. For the FTLCGP, the length an with of both the s an the PGSs is 16 m an 3 m, respectively; the istance between the s an PGSs is 3 m; an the signal line with W is 7 m. As shown in this figure, FTLCGP exhibits a much higher capacitance than other structures. Concretely, the FTLCGP shows capacitance values ranging from.18 pf/mm to.19 pf/mm in the frequency range 5 GHz to 5 GHz, while the FTTL shows capacitance values ranging from.1 pf/mm to.137 pf/mm in the same frequency range. The above results reveal that using the FTLCGP structure leas to a further reuction of wavelength an characteristic impeance ue to an enhancement of the perioic capacitance. III. RF Characteristics of FTLCGP Structure on PES Table 1 shows the wavelengths for various transmission lines on PES an silicon substrate. As shown in this table, the FTLCGP on PES exhibits shorter wavelengths than other transmission lines. In particular, compare with the FTTL on PES, the FTLCGP on PES shows a further reuction of the wavelength. The wavelength of the FTTL on PES is.3 mm at 5 GHz, while the wavelength of the FTLCGP on PES is 1.91 mm at the same frequency, which is 85.7% of the FTTL on PES. Compare with other transmission lines, the wavelength of the FTLCGP on PES is respectively 48.5% an 77.% of the coplanar waveguie on PES an of the coplanar waveguie on silicon, at 5 GHz. From Fig., we can see that an increase in the length of a results in an enhancement of the perioical shunt capacitance, ue to an increase to the open stub length, an an enhancement of coupling capacitance C b, ue to an increase in the coupling area between a an PGS. Therefore, the characteristic impeance of the FTLCGP, Z, can be easily controlle by changing the length of the s, because Z epens on the perioic shunt capacitance an series inuctance of the transmission line, as shown in (). The epenence of Z on the length of a is shown in Fig. 4, where the signal line with W was fixe at 7 m. For a 13 Young Yun et al. ETRI Journal, Volume 37, Number 1, February 15

4 Table 1. Wavelengths of various transmission lines on PES an silicon substrate. Frequency FTLCGP on PES FTTL on PES CPW on PES CPW on silicon 1 GHz 9. mm 9.79 mm 18. mm 1.4 mm GHz 4.81 mm 5.11 mm 9.9 mm 5.71 mm 3 GHz 3.5 mm 3.56 mm 6.33 mm 3.99 mm 4 GHz.4 mm.76 mm 4.85 mm 3.4 mm 5 GHz 1.91 mm.3 mm 3.94 mm.48 mm Characteristic impeance () FTTL on PES FTLCGP on PES length (µm) Fig. 4. Characteristic impeance of FTLCGP structure on PES. comparison, we also plotte the Z of the FTTL. As shown in this figure, an FTLCGP with various characteristic impeance can be realize on PES substrate by changing only the length of the s. From the above result, we must pay attention to one important result. As mentione before, the transmission line on the PES showe a much higher characteristic impeance than that on a conventional semiconucting substrate. Therefore, a transmission line with a very wie line with is require for low impeance matching applications [4]. The FTTL on PES showe a characteristic impeance that was lower than that of a conventional coplanar waveguie on PES [4]. Accoring to the above result, however, the FTLCGP shows a further reuction of characteristic impeance compare with the FTTL, which originates from an increase in the perioic shunt capacitance. In other wors, compare with the FTTL, the perioic shunt capacitance of the FTLCGP was enhance ue to the coupling between s an PGSs, an from (), we can see that an increase to the perioic shunt capacitance reuces the characteristic impeance. Therefore, if a transmission line with the same characteristic is fabricate on PES, then the line with of FTLCGP is much narrower than the FTTL. Concretely, the length of the FTLCGP with a Z of 61 is.15 mm, an the total line with is.37 mm, while the length of the FTTL with the same Z is.3 mm, Table. Insertion loss of FTLCGP an coplanar waveguie on PES with a length of /4. Frequency FTLCGP on PES CPW on PES 1 GHz 1.59 B 1.34 B GHz 1.75 B 1.55 B 3 GHz 1.13 B 1.69 B 4 GHz 1. B 1.53 B an the total line with is.53 mm. The above results inicate that using the FTLCGP can lea to a further reuction of evice size on PES. Until now, various types of perioic structures have been stuie for application to RF circuits [7] [13]. In particular, a slow-wave structure with an FTLCGP was fabricate on a PCB for use with a low-impeance transmission line in S-ban [7]. The slow-wave structure successfully operate as a transmission line up to S-ban. However, slow-wave structures on conventional PCBs, such as Teflon, show very narrow ban characteristics an very high losses in high-frequency ranges. However, the FTLCGP fabricate on PES showe a very low loss up to the millimeter wave range. Table shows the insection loss of the FTLCGP an coplanar waveguie on PES. For a fair loss comparison, two transmission lines of the same electrical length shoul be compare, because the wavelengths of the two transmission lines are ifferent from each other. Therefore, the loss of two transmission lines of length /4 were compare. As shown in this table, the FTLCGP on PES shows a low loss, which is comparable to the coplanar waveguie on PES. Concretely, the FTLCGP on PES shows a loss of 1 B to 1.75 B in the range 1 GHz to 4 GHz, an the coplanar waveguie on PES shows a loss of 1.34 B to 1.69 B in the same frequency range. This low loss of the transmission lines on PES originates from the goo electrical insulating properties of PES [4]. The above results inicate that the FTLCGP can be employe for application in flexible passive evices up to the millimeter wave frequency ue to its low loss characteristic. Incientally, the insertion loss of the FTLCGP ecreases from GHz to 4 GHz. This result is cause by the characteristic of the attenuation constant,. It is known that the attenuation constant of a transmission line on semiconucting substrate saturates in a certain frequency range [13], which causes a ecrease in the rate of insertion loss per wavelength. Figure 5 shows the measure propagation constant () of the FTLCGP an of the other types of transmission lines on PES an silicon substrate. Accoring to our previous results [4], the FTTL on PES exhibite a higher than that exhibite by other types of transmission lines ue to its strong slow-wave ETRI Journal, Volume 37, Number 1, February 15 Young Yun et al

5 Propagation constant (ra/mm) FTLCGP on PES FTTL on PES CPW on silicon CPW on PES Fig. 5. Measure propagation constant of various transmission lines on PES an silicon substrate. characteristic [4]. As shown in Fig. 5, however, the FTLCGP exhibits a higher than that exhibite by the FTTL. Concretely, the FTLCGP on PES shows values of ranging from.68 ra/mm to 3.8 ra/mm in the range 1 GHz to 5 GHz, while the FTTL on PES shows values of ranging from.64 ra/mm to.8 ra/mm in the same frequency range. The above result is ue to the high perioic capacitance value of the FTLCGP. Accoring to transmission line theory, is proportional to the square root of the perioic capacitance, which can be expresse in the following equations [6]: (6) eff LC, where,, an eff represent the permittivity of air, permeability, an effective permittivity of the transmission line, respectively. From (6), we can see that the higher the value of the perioic capacitance, the higher the value of. As shown in Fig. 3, the FTLCGP showe a higher perioic capacitance value than that of the FTTL, which le to a higher value of. The larger the value of for the FTLCGP, the shorter the wavelength, as shown in Table 1. We also investigate the effective permittivity eff of the FTLCGP on PES. The eff was obtaine from the following equation: π 1 eff, (7) where an represent the wavelength of the transmission line an permeability of air, respectively. Figure 6 shows the effective permittivity eff of the FTLCGP an other types of transmission lines. As shown in Fig. 6, the FTLCGP isplays a higher effective permittivity than that isplaye by the FTTL an coplanar waveguie on PES, ue to its strong slow-wave characteristic. Concretely, the FTLCGP isplays an eff of 9.46 to 1.6 in the range 5 GHz to 5 GHz, while the FTTL isplays an eff of 7. to 9.5 in the same frequency range. In particular, the FTLCGP on PES exhibits a higher eff than that exhibite eff FTLCGP on PES CPW on silicon FTTL on PES CPW on PES Fig. 6. Effective permittivity eff of various transmission lines on PES an silicon substrate. by the coplanar waveguie on silicon substrate in a frequency range higher than 1 GHz. Therefore, for the fabrication of passive components, using the FTLCGP enables a further reuction of component size compare with other types of transmission lines, because the higher the eff of the semiconucting substrate, the smaller the component size on the semiconucting substrate [6]. From Fig. 6, we can see that the coplanar waveguie on silicon substrate exhibits a strong frequency ispersion characteristic. Generally, a slow-wave moe of propagation, as well as a quasi-transverse electromagnetic (quasi-tem) moe, exists on oxie/silicon substrate, which leas to a strong frequency ispersion characteristic [13]. On the other han, the transmission line on PES exhibits a very weak frequency ispersion characteristic ue to its ominant quasi-tem moe on the metal/highinsulating substrate structure [14]. Notably, in spite of its composite perioic structure, the FTLCGP exhibits a frequency epenency that is weaker than that exhibite by the FTTL an has goo frequency ispersion characteristics comparable to the coplanar waveguie on PES. This can be explaine as follows. As mentione before, there is a coupling capacitance between the s of the FTTL structure. However, this coupling capacitance is only a parasitic capacitance, an as such, it cannot contribute to a reuction of wavelength. Therefore, this parasitic capacitance causes a relatively strong frequency ispersion characteristic. However, there is a coupling shunt capacitance between the signal line an groun in the FTLCGP, which is a part of the equivalent shunt capacitance of the transmission line, not a parasitic capacitance. This shunt capacitance oesn t cause a strong frequency ispersion, an it only contributes to a reuction of wavelength [6]. The above results reveal that the FTLCGP structure on PES can be effectively use for broaban applications ue to its very weak frequency ispersion characteristic. Using the effective permittivity equation moel 13 Young Yun et al. ETRI Journal, Volume 37, Number 1, February 15

6 of the coplanar waveguie, we also extracte the relative permittivity of the PES from the effective permittivity shown in Fig. 6. Accoring to the result, the relative permittivity of the PES was 3.4 to 3.6 in the above frequency range. IV. Theoretical Analysis of FTLCGP Structure on PES In this work, the RF characteristics of the FTLCGP on PES were theoretically stuie using a simple equivalent circuit [6] an close-form equations. Concretely, RF characteristics, such as impeance an banwith, were extracte from the simple theoretical analysis. The FTLCGP structure can be expresse as the perioically loae line shown in Figs. 7(a) an 7(b), an C FTLCGP is the perioical capacitance of the FTLCGP structure, which is shown in Fig. 3. In this figure, is the length of a unit cell in the perioic structure, which for the FTLCGP, is equal to 1 m. The perioically loae line shown in Fig. 7(a) can also be expresse by the perioical susceptance, jb, shown in Fig. 7(b). The perioical susceptance jb is given by jb j C / Y j C Z, (8a) FTLCGP FTLCGP b C Z (8b) FTLCGP, where an Z are the angular frequency an characteristic impeance of the transmission line without perioic structure, respectively. For a theoretical analysis of the transmission line employing FTLCGP, we begin by stuying the propagation characteristics of the equivalent circuit shown in Fig. 7(b). Each unit cell of this line is of length, with a shunt susceptance across the C FTLCGP Z, k I n I n jb jb jb jb jb V n (a) Unit cell (b) Fig. 7. Equivalent circuit of FTLCGP structure on PES: (a) an equivalent circuit with perioically loae capacitor C b an (b) an equivalent circuit with perioically loae susceptance jb. C FTLCGP C FTLCGP C FTLCGP C FTLCGP V n+1 mipoint of this length, an the susceptance jb is normalize to the characteristic impeance, as shown in (8b). From Fig. 7(b), we can relate the voltages an currents on either sie of the nth unit cell using the following ABCD matrix: Vn A BVn 1, I n C D I (9) n1 where A, B, C, an D are the matrix parameters for the unit cell shown in Fig. 7. The unit cell consists of two lines of length / an susceptance b. In aition, in (9), I n an V n are the current an voltage at the input of nth unit cell shown in Fig. 7, respectively, an I n+1 an V n+1 are the current an voltage at the output of the (n+1)th unit cell, respectively. The matrix parameters can be given by [6] k k k k cos jsin cos jsin A B 1 C D k k jb 1 jsin cos k k jsin cos b b b (cos k sin k) j(sin k cos k ), b b b j(sin k cos k ) (cos k sin k) (1a) k LC (1b) a eff, where an are the permeability an permittivity of air, respectively. The effective permittivity eff is shown in Fig. 6. In Fig. 7, the transmission line with a length of / can be expresse by an LC equivalent circuit, an the was consiere when the propagation constant (k) of the line itself was calculate using (1a) an (1b). Using the propagation constant of the guie wave on the perioically loae microstrip line gives V (11a) n 1 Vne, I n 1 Ine. (11b) Using (9), (11a), an (11b) gives [6] Vn A BVn 1 Vn 1e, I n C D I n1 In1e (1) Ae B Vn 1. C D e I n1 For a nontrivial solution, AD e A D e BC ( ). Since AD BC = 1 for a lossless network, the above equation can be expresse as 1 e ( A D) e e e ( A D). (13) ETRI Journal, Volume 37, Number 1, February 15 Young Yun et al

7 Using (1) an (3) gives e e ( AD) b cosh (cos k sin k), (14) where (1) was use for the values of A an D. Since the propagation constant of the guie wave on the perioically loae microstrip line consists of real an imaginary parts, it can be represente by j. (15) Thus, from (14) an (15), the following expression can be obtaine: b cosh coshcos jsinhsin cos k sin k. (16) Since the right-han sie of (16) is real, we shoul have either sinh = or sin =. If the attenuation constant is, then this correspons to the case of a non-attenuating propagation wave on the perioic structure an efines the passban of the structure. Then, (16) can be expresse as follows: b cosh j cos cos k sin k cos k Xksin k, (17a) CFTLCGPZ where X. (17b) eff Note that there are an infinite number of values of that can satisfy (17). If the attenuation constant is not zero, then the wave is attenuate along the line, an this case correspons to that of a stopban. In this case, (16) reuces to cosh cos k Xk sin k 1. (18) Thus, epening on the frequency an normalize susceptance values, the perioically loae line will exhibit either passbans or stopbans, an as such, it can be consiere as a type of filter. Figure 8 shows the passbans an stopbans calculate from (17) an (18). Using (8), (17), an (18), we can obtain the banwith of the pass- an stopbans from the - k graph of Fig. 8. The banwiths of the FTLCGP structure are summarize in Table 3. In this table, the first passban correspons to a practical banwith. From the table, we can see that the FTLCGP structure has a cut-off frequency of 8 GHz, which means that it can be use as a transmission line in millimeter wave an microwave frequencies. From (17), we can obtain the following equations: 1 cos (cos k Xk sin k), (19) π π 1 cos (cos k Xk sin k). () Table 3. Banwiths of FTLCGP structure on PES. Frequency range (GHz) Banwith (GHZ) First passban 8 8 First stopban Secon passban Secon stopban 861 1, n passban 1st stopban 1st passban k eff Fig. 8. Passbans an stopbans calculate from -k relations of (17) an (18). Propagation constant (ra/mm) Calculate Measure Fig. 9. Measure an calculate propagation constant of FTLCGP on PES. From the above equations, we can calculate the propagation constant an wavelength. Figures 9 an 1 show the propagation constant an wavelength calculate from the above equations, which were compare with measure results. Form this, we can see that the calculate results show goo agreement with the measure ones, which inicates that the above theoretical metho is fairly accurate. Besies the propagation constant of the waves on the perioically loae line, we are also intereste in the characteristic impeance for these waves. We can efine the characteristic impeance at the unit cell terminal as Vn 1 Z Z, (1) I B n1 134 Young Yun et al. ETRI Journal, Volume 37, Number 1, February 15

8 5 6 Wavelength (mm) Calculate Measure Characteristic impeance Z () (a) Fig. 1. Measure an calculate wavelength of FTLCGP on PES. since V n+1 an I n+1 in the above erivation are normalize quantities. Equation (1) can be expresse as ( Ae ) V BI. () n1 n1 If the ratio of voltage to current obtaine from () is substitute into (1), then we can obtain following equation: BZ ZB. (3) ( A e ) From (13), we can solve for e in terms of A an D to achieve the following: ( AD) ( AD) 4 e. (4) Because A is equal to D (A = D), using (1), (3), an (4) gives b b (sin k cos k ) Z ZB. (5) b 1 (cosk sin k) The characteristic impeance, Z B, can be calculate from (8) an (5). Figures 11(a) an 11(b) show the calculate characteristic impeance an measure return loss for the FTLCGP on PES. In Fig. 11(b), the return loss was measure with a port impeance of 58 from.1 GHz to 5 GHz, an the return loss values ware less than 5 B in this frequency range, which means that the measure characteristic impeance is 58. From this result, we can see that the calculate result shows goo agreement with the measure one. We also calculate the effective permittivity eff of the FTLCGP on PES. Using (7) an () leas to the following equation: eff 1 cos (cos k Xk sin k). (6) Return loss S11 -Port impeance: 58 -Frequency:.1 GHz 5 GHz Fig. 11. RF characteristic of FTLCGP structure on PES: (a) calculate characteristic impeance an (b) measure return loss at a port impeance of 58. eff Calculate Fig. 1. Measure an calculate effective permittivity eff of FTLCGP on PES. (b) Measure Using (6), we calculate the effective permittivity. Figure 1 shows the measure an calculate effective permittivity of the FTLCGP on PES. As shown in this figure, the calculate result shows goo agreement with the measure one. V. Conclusion In this work, we investigate the RF characteristics of the FTLCGP structure on PES substrate. The FTLCGP on PES exhibite much higher perioic shunt capacitance values than ETRI Journal, Volume 37, Number 1, February 15 Young Yun et al

9 those exhibite by other types of transmission lines ue to the coupling capacitance between the s an PGSs, which resulte in a further reuction of wavelength. For example, the wavelength of the FTLCGP on PES was 1.91 mm at 5 GHz, which was 85.7% of the FTTL on PES an 48.5% of the coplanar waveguie on PES. The characteristic impeance Z of the FTLCGP structure coul be easily controlle by changing only the length of the s. The FTLCGP showe a lower characteristic impeance than that shown by the FTTL ue to its higher perioic shunt capacitance, which resulte in a reuction of line with. Concretely, the total line with of the FTLCGP with a Z of 61 was.37 mm, while the total line with of the FTTL with the same Z was.53 mm. Accoring to the results, we can see that, compare with the FTTL, the FTLCGP is more suitable for RF applications ue to its shorter wavelength an narrower line with. The FTLCGP on PES exhibite a low loss of 1 B to 1.75 B in the range 1 GHz to 4 GHz, which was comparable to the conventional coplanar waveguie on PES. In aition, the FTLCGP structure exhibite a much higher propagation constant an effective permittivity eff than that exhibite by other types of transmission lines on PES ue to its strong slow-wave characteristic. Notably, in spite of its composite perioic structure, the FTLCGP showe a weaker frequency epenency than that shown by the FTTL, as well as a goo frequency ispersion characteristic comparable to the conventional coplanar waveguie on PES. The FTLCGP structure showe an eff of 9.46 to 1.6 in the range 5 GHz to 5 GHz. The above results reveal that the FTLCGP on PES can be effectively use with a broaban an low loss characteristic in RF components. The RF characteristics of the FTLCGP on PES were stuie using a simple equivalent circuit an close-form equations. RF characteristics, such as impeance an banwith, were extracte from the simple theoretical analysis, which offere a esign guieline for passive components employing FTLCGP. Accoring to the results, it was foun that the theoretical results showe goo agreement with the experimental ones. Using the theoretical analysis, we also extracte the banwith characteristic of the FTLCGP on PES. The FTLCGP structure showe a cut-off frequency of 8 GHz, which means that it can be use as a transmission line up to the millimeter wave frequency range. From these results, we can see that the FTLCGP structure on PES is a promising caniate for use with RF transmission lines on flexible substrates [] E. Celik et al., Carbon Nanotube Blene Polyethersulfone Membranes for Fouling Control in Water Treatment, Water Res., vol. 45, no. 1, Jan. 11, pp [3] R. Rajasekaran, M. Alagar, an C.K. Chozhan, Effect of Polyethersulfone an N, N'-Bismaleimio-4, 4'-Diphenyl Methane on the Mechanical an Thermal Properties of Epoxy Systems, Exp. Polymer Lett., vol., no. 5, 8, pp [4] Y. Yun, H.S. Kim, an N. Jang, Stuy on Characteristics of Various RF Transmission Line Structures on PES Substrate for Application to Flexible MMIC, ETRI J., vol. 36, no. 1, Feb. 14, pp [5] Y. Yun et al., A Miniaturize Impeance Transformer on PES for Flexible RFICs, Microw. J., vol. 57, no., Feb. 14, pp [6] D.M. Pozar, Microwave Engineering, Reaing, MA, USA: Aison-Wesley, 199. [7] T. Fujii et al., Miniature Broa-Ban CPW 3 B Branch-Line Couplers in Slow-Wave Structure, IEICE Trans. Electron., vol. E9-C, no. 1, Dec. 7, pp [8] D. Ahn et al., A Design of Low-Pass Filter Using the Novel Microstrip Defecte Groun Structure, IEEE Trans. Microw. Theory Techn., vol. 49, no. 1, Jan. 1, pp [9] F.-R. Yang et al., A UC-PBG Structure an Its Applications for Microwave Circuits, IEEE Trans. Microw. Theory Techn., vol. 47, no. 8, Aug. 1999, pp [1] A.S. Anrenko, Y. Ikea, an O. Ishia, Application of PBG Microstrip Circuits for Enhancing the Performance of High- Density Substrate Patch Antennas, Microw. Opt. Techn. Lett., vol. 3, no. 5, Mar., pp [11] A. Lai an T. Itoh, Microwave Composite Right/Left-Hane Metamaterials an Devices, Asia-Pacific Microw. Conf., Suzhou, China, Dec. 4 7, 5, pp [1] J. Gao an L. Zhu, Per-Unit-Length Parameters of 1-D CPW Metamaterials with Simultaneously Series-n Shunt-L Loaing, Asia-Pacific Microw. Conf., Suzhou, China, Dec. 4 7, 5, pp [13] J.R. Long, Passive Components for Silicon RF an MMIC Design, IEICE Trans. Electron., vol. E86-C, no. 6, June 3, pp [14] J. Zhang an T.Y. Hsiang, Dispersion Characteristics of Coplanar Waveguies at Subterahertz Frequencies, Progress Electromag. Res. Symp., Cambrige, MA, USA, vol., no. 3, Mar. 6, pp References [1] Y. Sun an J.A. Rogers, Inorganic Semiconuctors for Flexible Electronics, Av. Mater., vol. 19, no. 15, Aug. 7, pp Young Yun et al. ETRI Journal, Volume 37, Number 1, February 15

10 Young Yun receive his BS egree in electronic engineering from Yonsei University, Seoul, Rep. of Korea in 1993; his MS in electrical an electronic engineering from Pohang University of Science an Technology, Pohang, Rep. of Korea in 1995; an his PhD in electrical engineering from Osaka University, Osaka, Japan, in From 1999 to 3, he worke as an engineer for the Matsushita Electric Inustrial Company Lt. (Panasonic), Osaka, Japan, where he was engage in the research an evelopment of monolithic microwave ICs (MMICs) for wireless communications. In 3, he joine the Department of Raio Communication Engineering, Korea Maritime an Ocean University, Busan, Rep. of Korea. He is currently a professor, an his research interests inclue esign an measurement for RF/microwave an millimeter-wave IC an esign an fabrication for HEMT an HBT. Since 8, he has serve as an associate eitor of the Institute of Electronics, Information an Communication Engineers (IEICE) in Japan an as an eitor of the Korean Society of Marine Engineering in the Rep. of Korea. He is the author an co-author of over 11 internationally publishe journal papers an 15 patents pening in RF/microwave evices an ICs. Nakwon Jang receive his BS, MS, an PhD egrees in electrical engineering from Yonsei University, Seoul, Rep. of Korea, in 199, 199, an 1999, respectively. From 199 to 1995, he was with Samsung Electronics, Yongin, Rep. of Korea, where he was involve in the esign of vieo-signal river circuits for p-si TFT LCDs. After completing his PhD, he worke as a senior engineer in the Semiconuctor R&D Division of Samsung Electronics, where he was engage in the research an evelopment of 4 MB an 3 MB FRAM. He joine the Korea Maritime an Ocean University as a professor in the Department of Electrical an Electronics Engineering in Busan, Rep. of Korea, in September 3. He is currently a professor, an his research interests inclue the esign an fabrication of LEDs an ZnO TFTs. He is the author an co-author of over 7 journal articles on semiconuctor evices. Jang-Hyeon Jeong receive his BS an MS egrees in raio communication engineering from the Korea Maritime an Ocean University, Busan, Rep. of Korea, in 1 an 1, respectively, an is currently working towar his PhD in raio communication engineering. Hong Seung Kim receive his BS, MS, an PhD egrees in materials science an engineering from the Korea Avance Institute of Science an Technology, Daejeon, Rep. of Korea, in 199, 1993, an 1999, respectively. He joine the Electronics an Telecommunications Research Institute, Daejeon, Rep. of Korea, in 1999 an has worke on the fabrication an evelopment of SiGe heterojunction bipolar transistors (HBTs) an InP/InGaAs HBTs for OEIC. From 1 to, he was a postoctoral research associate in electrical engineering at Cornell University, Ithaca, NY, USA, where he worke on three-imensional integration. In 3, he joine the Depaprtment of Nano Semiconuctor Engineering, Korea Maritime an Ocean University, Busan, Rep. of Korea. He is currently a professor, an his research interests inclue optoelectronic properties of ZnO-base evices, such as UV LEDs an transparent transistors. ETRI Journal, Volume 37, Number 1, February 15 Young Yun et al