Design of Power Dividers using Defected Microstrip Structure and an Analytically Calculated Characteristic Line Impedance

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1 , pp Design of Power Dividers using Defeted Mirostrip Struture and an Analytially Calulated Charateristi Line Impedane Jongsik Lim Department of Eletrial Engineering, Soonhunhyang University, Rep of Korea Abstrat In this work, a defeted mirostrip struture (DMS), methods to alulate the new harateristi impedane of DMS line, and, as an appliation example, a design of mirowave wilkinson power dividers using DMS pattern are desribed. DMS patterns are inserted for the desirable effets of periodi struture suh as size-redution and inreased line width for high harateristi impedane. In order to alulate the proper harateristi impedane of DMS mirostrip line, the quarter-wavelength transformer model method and an analyti alulation method are adopted. As an example, the DMS mirostrip line with 70.7 harateristi impedane is designed, alulated and inserted into the wilkinson power divider. The size of designed power divider with DMS patterns is only 82% of a referene power divider omposed of normal mirostrip lines, while the iruit performanes are very well preserved even after the size-redution. Keywords: defeted mirostrip struture, DMS, power dividers 1. Introdution Reently, perturbation strutures suh as photoni band gap (PBG) and defeted ground struture (DGS) for mirostrip lines have been widely studied as planar periodi strutures, whih modify the harateristi impedane and dimensions of mirostrip lines. Due to the perturbation strutures, equivalent iruit elements per unit length, i.e., indutane and apaitane, of mirostrip line inrease, and related physial phenomenon ours. So the harateristi impedane of mirostrip line inreases for a given line width and slow-wave effet is observed. Those properties might be applied to high frequeny iruits for sizeredution or performanes improvement [1-6]. However, in the ase of PBG, it is not easy to define a unit setion and to extrat the equivalent iruit elements of PBG patterns beause a lot of periodi patterns are required on the ground plane. This drawbak has prevented ones from applying PBG patterns to mirowave and radio frequeny (RF) iruits. To the ontrary, there are some superior advantages in DGS ompared to PBG suh as; 1) less DGS elements are required for the similar effets, 2) it is easy to define a unit element and to model the equivalent iruit, and 3) DGS patterns have a great potential of appliability. However, DGS patterns should be ethed off from the ground plane of mirostrip lines, and this has been known as a ritial disadvantage of DGS so far [4-7]. Defeted mirostrip struture (DMS) has been proposed reently in order to solve the drawbak of DGS while making use of the advantages of DGS [8,9]. In other words, the mirostrip lines with DMS patterns have the same pros of previous PBG and DGS, and do not ISSN: IJCA Copyright 2014 SERSC

2 have the ons mentioned above beause perturbation patterns are realized not on the bottom side ground plane, but in the mid of signal line on the upper side of mirostrip lines. So it is neessary to study the appliations of DMS to mirowave and RF iruits beause of the representative drawbak of DGS an be eliminated by replaing it with DMS. In this study, a high frequeny wilkinson power divider is designed, fabriated and measured to present an example of appliation of DMS. The designed power divider has a smaller size ompared to the normal one due to the equivalent additional indutane and apaitane of the inserted DMS pattern, although the performanes of the size-redued power divider are quite omparable to the original ones. In order to design the power divider with DMS pattern, the appropriate harateristi impedane of DMS mirostrip line should be provided, beause it is required to omplete the design. In this work, an analyti alulation method is disussed and the obtained line impedane is applied to design the power divider. 2. DMS Mirostrip Line and the Quarter-wave Transformer Method Fig.1 shows the pattern of defeted mirostrip struture (DMS) adopted in this work. This DMS pattern is realized on the signal plane of mirostrip line on the upper plane, so the ground plane is not touhed. Considering the previous strutures of PBG and DGS for mirostrip lines, the DMS pattern is very omparative beause it is a ritial drawbak of PBG and DGS to pattern them on the bottom ground plane. This bottom patterning leads to two representative negative effets. The first one is the signal leakage problem. Beause the PBG and DGS patterns are realized in the mid of bottom ground plane by ething them off, it is easily predited for the signal to leak through the ethed patterns on the ground plane. The seond problem ours when the iruits with PBG and DGS patterns are inserted into metalli housing. If they are plaed on the pakage, the bottom ground plane with PBG and DGS patterns must ontat the metalli surfae. In most ases, the metalli housing ats as the bulky ground. So the advantages of PBG and DGS disappear in ondutive housing. However in Figure 1, the DMS pattern is inserted on the upper mirostrip line. Figure 1. Mirostrip line with defeted mirostrip struture pattern in this work The slot-like DMS pattern in Figure 1 has additional equivalent indutive and apaitive elements. The oupling in slots results in the apaitane, and the outer length of slots indutane. It is noted that the adding of indutane is dominant over the inrease of apaitane beause the length of outer slot-boundary is muh longer than that of oupling setion. The added equivalent indutane and apaitane aused by the DMS pattern make the eletrial length of DMS mirostrip line longer than that of normal mirostrip line without DMS for a given physial length. This means it is possible to redue the 12 Copyright 2014 SERSC

3 physial length of mirostrip line for the same eletrial length by inserting DMS pattern. This is the priniple in reduing the size of iruit by inserting any periodi or perturbation struture into normal transmission lines [10]. It is well known that the harateristi impedane (Z ) of transmission lines is determined by (1) L Z C (1) where L and C are the equivalent indutane and apaitane per unit length of transmission lines [-13]. Then the harateristi impedane of DMS line an be expressed by (2). L L Z, DMS C C (2) Beause the added indutane (L) is larger than added apaitane (C), it is true that Z.DMS > Z,normal, where Z.DMS and Z,normal are the harateristi impedanes of DMS and normal mirostrip lines, respetively. So, if the line impedane is required to be preserved even after DMS patterns have been inserted, the line width should be inreased. This is one of very important advantages in pratial appliations. One simple example may be presented here with a dieletri substrate of whih dieletri onstant ( r ) and thikness (H) are 2.2 and 31mils, respetively. This substrate has been seleted to design the DMS mirostrip line shown in Figure 1. Figure 2 represents the predited S-parameters whih have been simulated on Ansys HFSS (high frequeny struture simulator). The line width 2.38mm orresponds to the width of the normal 50 mirostrip line. However the harateristi impedane of the DMS mirostrip line in Fig. 1 is no more 50 beause the S in Figure 2 is not perfet within the passband. Figure 2. Simulated S-parameters of the DMS mirostrip line The harateristi impedane of DMS line (Z.DMS ) an be found using the quarterwave transformer method [14]. Figure 3 and Eqs. (3)-(5) are useful for alulating Z.DMS. Figure 3 shows the transmission line model of the DMS line with the length of quarter-wave at the enter frequeny (F o ). When is /2 or a quarter-wave length at F o, the magnitude of refletion oeffiient ( ) is maximum, so the relation between and S in (3) is effetive. One is known, Z in is alulated by (4). Finally, Z.DMS is alulated from (5). Here, Z o is the referene impedane or termination impedane. Copyright 2014 SERSC 13

4 Figure 3. Equivalent iruit model to determine the harateristi impedane of the DMS line S [ ] 20log (3) db 1 Z in Z o (4) 1 1 Z, DMS ZinZo Z (5) o 1 Sine the simulated S is -9.5dB in Fig. 2, the orresponding line impedane an be alulated. It turns to be around 70 from (1)-(3), and this is a meaningful value beause wilkinson power dividers require transmission line elements with 70.7 of line impedane [13]. In addition, it is noted that the width of 70.7 normal mirostrip line is only 1.37mm, while that is 2.38mm in DMS line as shown in Figure 1. The 70.7, and its harateristi impedane was verified through the S-parameter measurement. Figure 4(a) and (b) show the photograph of the fabriated DMS mirostrip line and measured S-parameters. The measurement has been performed using an Agilent E5071B vetor network analyzer. The measured S is exatly the same as the predited one in Figure 2. Therefore it an be said that the design of 70.7 DMS line with 2.38mm of line width has been verified. Figure 4 (a) -parameters (a)photo (b)sparameters (b) 14 Copyright 2014 SERSC

5 3. Calulation of Charateristi Impedane of DMS Line using an Analyti Method In order to design the power divider with DMS pattern, the appropriate harateristi impedane of DMS mirostrip line should be provided, beause it is required to omplete the design. In this work, an analyti alulation method is disussed and the obtained harateristi impedane (Z ) is applied to design the power divider. Even though the above method an be used to find the new Z of DMS line, it is a drawbak for one to apply the method only at the enter frequeny where the eletrial length () is /4 or /2. So the alulated line impedane is valid only at the enter frequeny. However, harateristi impedane of transmission lines is a very important fator in pratial appliations at all required frequeny band, beause all of high frequeny iruits should have the targeted performanes within the designated band, and this is guaranteed by adopting the proper transmission line elements. Therefore when DMS patterns are ombined to the normal mirostrip line, it is essential to alulate the Z as exat as possible for suessful appliation to high frequeny iruits and systems. Figure 5 shows the blok diagram of a DMS line, of whih harateristi impedane, eletrial length, phase onstant, and physial length are Z,,, and l, respetively [15]. Aording to the basi transmission line theories, the input impedane (Z in ) is expressed as (6) and (7). S whih orresponds to the input oeffiient of the DMS line is shown in eq. (8), beause Z in plays a role of load when the input signal is injeted from port1. Figure 5. Blok diagram for finding the harateristi impedane of DMS mirostrip line Z z S in in Zo jz tan Z (6) Z jz tan o 1 jz tan z z j tan (7) zin 1 rs jis z 1 (8) in where z in =Z in /Z o and z =Z /Z o, and rs and is are the real and imaginary part of the S, respetively. Copyright 2014 SERSC 15

6 If (7) is inserted into (8), then (9) is obtained. It is noted that the real and imaginary parts should be zero if (9) is valid. So (10) and () are produed with the quadrati equation form of ax 2 +bx+=0 for z. z z z 1tan is j2 z is z 1tan rs z 1tan 0 2z rs (9) 2 2 2rs tan is 2is tan rs z 1 0 z 1 1 rs 1 rs 0 Beause Z is the harateristi impedane of the mirostrip line, so it must be a real value. Then (10) an be ignored in this study beause, in some ases, we may get an imaginary determinant value from (10) depending on rs, is, and tan. By the way, in (), the magnitude of rs is always less than 1 beause transmission lines are passive elements. Then the third term of (), whih orresponds to of the quadrati equation, is always negative. Hene, determinant D is always positive, and two real solutions of () exist. Then the optimum solution is one of them, and the other one will turn out to be improper. The analyti method has been applied to the S-parameters shown in Figure 4 to find the more aurate Z of the DMS line. The alulated impedanes at various frequenies are around 70.7 at 1GHz as depited in Figure 6. It is noted that, in the above quarterwave transformer method, the alulated line impedane is reliable only at around the enter frequeny where the eletrial length is /4. However, in Figure 6, the alulated line impedanes using the analyti method are less frequeny-dependent. This means the obtained impedanes are more reliable over broad band ontaining enter frequeny. In Figure 6, one an find the Z of the DMS line of Figure 4 (a) at other frequenies. (10) () Figure 6. Calulated harateristi impedane of DMS line in Figure 4 using the analyti method 4. Design of the Size-redued Wilkinson Power Divider using DMS Line The DMS line designed above has been applied to design a size-redued wilkinson power divider. Agilent Advaned Design System (ADS) has been adopted in order to simulate the iruit level design and predit the primitive performanes of the divider. Figure 7(a) shows 16 Copyright 2014 SERSC

7 the shemati design of the divider in whih the HFSS simulation results of the DMS line are inluded, and the simulated S-parameters. (a) Figure 7. Shemati design of the size-redued power divider and simulated S- parameters (a)shemati design (b)s--parameters of the power divider using ADS Two 70 DMS mirostrip lines in Figure 4(a) are inserted to onsist of the wilkinson divider. Figure 7(b) shows the predited S-parameters of the designed divider. Exellent performanes in power dividing, mathing, and isolation are observed. Figure 8. Layout of power dividers using DMS mirostrip line(upper) and normal one(lower) Figure 8 shows the layouts of size-redued wilkinson power divider using DMS miorstrip line. A normal design of power divider is also presented in Figure 8 for omparison of size. In order to present the effet of DMS in size-redution, 1GHz has been seleted as the design frequeny. As has been desribed already, the width of DMS line is fixed to 2.38mm in the DMS divider whether it is 50 or 70.7 line. The dimensions of DMS in the size-redued divider are the same as those in Figure 1. It is lear to desribe the effet of DMS pattern by omparing two dividers in Figure 8. Eliminating the port feeding lines with 50, one an ompare the pure divider area (b) Copyright 2014 SERSC 17

8 designated by dotted boxes. Those are 534mm 2 and mm 2 for the size-redued divider and normal one. The size of DMS divider is only 82% of normal one. The size - redution is aused by the slow-wave effet due to the added equivalent iruit element of the DMS patterns. (a) Figure 9. Eletromagnetially simulated S-parameters of the DMS power divider using HFSS (a)s-parameters (b)phase differene Figure 9(a) shows the eletromagnetially simulated S-parameters of the DMS power divider using HFSS. All performanes required for power dividers suh as power dividing ratio(s21, S31), mathing at ports(s, S22, S33), and isolation between output ports(s32) are exellent. In addition, Figure 9(b) shows the phase differene between two output ports is almost zero, whih is lose to an ideal ase. 5. Fabriation and Measurement The DMS power divider has been fabriated pratially and is illustrated in Figure 10. The 70.7 DMS line in Figure 4(a) has been adopted in the final layout. The substrate with the dieletri onstant of 2.2 and thikness of 31mils has been seleted for the design and fabriation. (b) Figure 10. Fabriated power divider using DMS Figure presents the measured S-parameters of the fabriated DMS divider. The input power has been equally divided and delivered to output ports. The measured S21 and S31 are -3.07dB and -3.08dB, respetively, so the insertion loss is less than 0.1dB. The mathing (S, S22, and S33) and isolation performane (S32) are less than -20dB, whih means very good performanes. It is observed that the measured S-parameters 18 Copyright 2014 SERSC

9 are in exellent agreement with the predited ones. Therefore it an be said that the design of size-redued wilkinson power divider using DMS has been ompleted suessfully. Figure. Measured S-parameters of the fabriated DMS power divider 6. Conlusion A defeted mirostrip struture and two methods to find the harateristi impedane of mirostrip line with DMS have been disussed. Due to the additional equivalent indutane of DMS, a slow-wave effet arises and the harateristi impedane of DMS line inreases. So the line width of DMS line should be broader than before DMSinsertion for the harateristi impedane to be the same. The first alulation method to find the harateristi impedane of DMS line adopts /4 transformer theories, and reliable at the enter frequeny. The other method uses an analyti approah utilizing the S-parameters of DMS line, refletion oeffiient, and input impedane of DMS line. Unlikely to the first way, frequeny-insensitive harateristi impedane values are obtained over broad frequeny band rather than only at the enter frequeny. Finally, a size-redued wilkinson power divider has been designed and fabriated suessfully using the DMS line. The harateristi impedane of DMS line has been alulated by two methods, and turned out to be around 70.7, whih is essential value for wilkinson dividers. The measured performanes of the divider are exatly the same as the simulated S-parameters. The size of the fabriated DMS divider is only 82% of the normal one while the performanes have been well preserved. There was no leakage or ground ontat problem in the designed DMS divider, and also no performanes degradation, either. The insertion loss at two output ports was order of 0.1dB, whih is so small value, and all mathing and isolation performanes were exellent. It is expeted that DMS pattern has a great potential for further appliation to mirowave iruits without the well-known drawbaks of PBG and DGS. Referenes [1] V. Radisi, Y. Qian and T. Itoh, IEEE Mirowave Guide Wave Letters, vol. 8, (1998), pp. 13. [2] I. Rumsey, M. Piket-May and P. Kelly, IEEE Mirowave Guide Wave Letters, vol. 8, (1998), pp [3] S. G. Mao and M. Y. Chen, IEEE Mirowave and Wireless Components Letters, vol., (2001), pp [4] C. Kim, J. Park, D. Ahn and J. Lim, IEEE Mirowave Guide Wave Letters, vol. 10, (2000), pp. 131 [5] J. Lim, C. Kim, Y. Lee, D. Ahn and S. Nam, IEE Eletronis Letters, vol. 38, (2002), pp Copyright 2014 SERSC 19

10 [6] J. Lim, C. Kim, D. Ahn, Y. Jeong and S. Nam, IEEE Transations on Mirowave Theory and Tehniques, vol. 53, (2005), pp [7] J. Koo, S. Oh, M. Hwang, C. Park, Y. Jeong, J. Lim, K. Choi and D. Ahn, A New DGS Unequal Power Divider, Proeedings of the 37th European Mirowave Conferene, Munhen, Germany, (2007) Otober. [8] J. Mendez, H. Aguilar, F. Sanhez, I. Ruiz, V. Lopez and R. Herrera, Mirowave Optial Tehnology Letters, vol. 43, (2004), pp. 481 [9] G. Chaudhary, Y. Jeong, J. Lim, C. Kim, D. Kim, J. Kim and J. Park, DMS harmoni termination load network for high effiieny power amplifier appliations, Proeedings of the 40th European Mirowave Conferene, Paris, Frane, (2010) Otober. [10] J. Lim, J. Park, Y. Lee, D. Ahn and S. Nam, IEEE Mirowave and Wireless Components Letters, vol. 12, (2002), pp [] K. Gupta, R. Garg, I. Bahl and P. Bhartia, Mirostrip Lines and Slotline 2/e, Arteh House, Boston, (1996). [12] W. Hayt Jr., and J. Buk, Engineering Eletromagnetis 7/e, MGraw-Hill, New York, (2006). [13] M. Pozar, Mirowave Engineering 3/e, John Wiley and Sons, In., New York, (2005). [14] J. Lim, C. Kim, J. Park, D. Ahn and S. Nam, IEE Eletronis Letters, vol. 36, (2000), pp [15] J. Lim, J. Lee, J. Lee, S. Han, D. Ahn and Y. Jeong, Progress In Eletromagnetis Researh, vol. 106, (2010), pp Jongsik Lim Authors Jongsik Lim reeived the B.S. and M.S. degrees in eletroni engineering from Sogang University, Seoul, Republi of Korea, in 1991 and 1993, respetively, and the Ph.D. degree in eletrial engineering from Seoul National University, Seoul, in In 1993, he joined ETRI, Daejeon, Korea, and was with them in the Satellite Communiation Division as a senior member of researh staff. Sine Marh 2005, he has been with the Department of Eletrial Engineering, Soonhunhyang University, Choongnam, Korea, as a faulty member. His urrent researh interests inlude the design of the passive and ative iruits for RF/mirowave and millimeter-wave with MIC/MMIC tehnology, modeling of ative devies, design of high-power amplifiers for mobile ommuniations, appliations of periodi struture to the RF/mirowave iruits, and modeling of passive struture having periodi strutures. 20 Copyright 2014 SERSC

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