微波仿真功分器_2010_MTT_GeneralizedPo.

1、3832 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL. 58, NO. 12, DECEMBER 2010 Analytical Design Method of Multiway Dual-BandPla nar Power Dividers With Arbitrary Power Divisio n Yon gle Wu, Stude nt Member, IEEE, Yua nan Liu, Member, IEEE, Qua n Xue, Senior Member, IEEE, Shula n Li, and C

2、uip ing Yu problem of un equal power divisi on and dual-ba nd applicati ons rema in un resolved. On the other hand, gen eralized un equal two-way 5 and multiway 6 power dividers were reported, while the dual-ba nd applicati ons were not con sidered. Rece ntly, a new N-way meta-material power divider

3、 has bee n prese nted in 7. Although this N-way meta-material power divider 7 has a pla nar structure, it is only for low-freque ncy (less than 1.5 GHz due to the operating frequency limitation of the practical lumped elements and single-band applications. In recent years, many novel dual-band distr

4、ibuted-circuit power dividers with equal 8 -12 or unequal power divisions 13, 14 were developed. The main limitation of these dual-band power dividers is that they all have merely twoway con?guration. In general, the design of wideband power dividers only focuses on its operati on cen ter-freque ncy

5、 and ban dwidth. However, the cen ter freque ncy ratio of dual band is one of sig ni ?ca nt paameters, which are used as desig n goals in the desig n of dual-ba nd power dividers. Mea nwhile, the performa nee at the freque ncies betwee n these desired two bands is not con sidered in in itial require

6、me nts. In order to realize gen eralized Wilk inson power dividers with various features in clud ing multiple ways, un equal power divisi on, dual-ba nd applicati ons and pla nar structures, we proposed a no vel and complete desig n methodology in this paper. This gen eralized Wilk inson power divid

7、er is con structed by in corporati ng the exte nded dual-ba nd un equal (or equal power divider cells, the recomb inant structures and the two-secti on dual-freque ncy tran sformers. The desig n theories and procedures for this proposed power dividers are give n. As typical examples, circuit con ?gu

8、rati ons and closed-form desig n equati ons of three-way and fourway dual-ba nd un equal pla nar power dividers are obta in ed. For theoretical veri?catio n, several ideal examples with differe nt dual-ba nd applicati ons and various power divisi ons are prese nted based on the give n an alytical de

9、sig n methods, and the corresp ondingcalculated electrical parameters and simulated results are provided in details. For further experime ntal veri?cati on, a fabricated microstrip threeway power divider operat ing at both 0.6 and 2.45 GHz with a power dividi ng ratio of 3:5:1 is dem on strated. Goo

10、d agreeme nt betwee n the simulated and measured results has bee n show n. II. BASIC CONSIDERATION OF MULTIWAY POWER DIVIDER PLANARCONFIGURATIONS The basic pla nar circuit structures for the proposed power dividers are illustrated in Fig. 1. As show n in Fig. 1(b, a recomb inant desig n con cept 15

11、has been applied to obtain a novel three-way dual-band arbitrary planar power divider, where the rightmost two-way dual-ba nd arbitrary (un equal Abstrac In this paper, a no vel closed-form desig n method of gen eralized Wilk inson power dividers is proposed. By using this method, the power divider

12、could be designed to be arbitrary-way (N-way with arbitrary power divisi on, and arbitrary dual-ba nd operati ons in a pure pla nar structure. A previous dual-ba nd un equal Wilk inson power divider is exte nded to arbitrary term inal impeda nces case, thus, it can be used to con struct multiway pla

13、 nar power dividers through the comb in ati on of the two-sect ion dual-freque ncy tran sformers. To obta in threeway (or any odd-way power dividers with dual-ba nd and un equal power divisi on features, a new developed recomb inant structure is employed. This recomb inant structure con sists of a t

14、wo-way dual-ba nd un equal power divider/comb iner without any isolati on structures. Furthermore, the complete desig n procedures and an alytical equati ons of these proposed gen eralized power dividers are prese nted. To verify our proposed desig n approach in theory, several three-way and four-wa

15、y power dividers with differe nt dual-ba nd applicati ons and various power divisi ons are desig ned and simulated. Fin ally, a practical three-way power divider operating at both 0.6 and 2.45 GHz with a power dividing ratio of 3:5:1 is fabricated in microstrip tech no logy as a typical example. The

16、 measured results of the fabricated power divider verify our proposed idea. In dex TermArbitrary power division, dual-band, dual-frequency, multiway, planar, unequal, Wilkinson power divider. I. INTRODUCTION P OWER dividers are widely used in many commu nication circuits such as power ampli?ers and

17、antenna arrays. For example, the popular th-pert powerdivider with a pla nar structure is a two-way Wilk inson divider 1. The Wilk inson divider1 in cludes multiway applicati on, but the 3-D ?oati ng com mon node makes its pla nar impleme ntati on become very dif?cult, and the an alyzed structure ca

18、n not satisfy arbitrary dual-ba nd applicati ons. On one hand, several N-way pla nar power dividers have bee n investigated in 2 -4, but the Manuscript received June 05, 2010; revised August 01, 2010; accepted August 08, 2010. Date of publicati on November 09, 2010; date of curre nt versi on Decembe

19、r 10, 2010.This work was supported in part by Nati onal High Tech no logy Research and Developme nt Program of China un der 863 Program, No. 2008AA01Z211, Importa nt Natio nal Scie nee and Techn ology Speci?c Projects un der No. 2010ZX03007-003-04, and BUPT Excelle nt Ph.D. Stude nts Foun dation und

20、er CX200901 and CX201021. Y. Wu, Y. Liu, S. Li, and C. Yu are with the School of Electronic Engin eeri ng, Beiji ng Un iversity of Posts and Telecom muni cati ons, 100876 Beiji ng, China (e-mail: wuy on gle138; .c n; lishula .c n; yucuiping. Y. Wu and Q. Xue are with the State

21、Key Lab of Millimeter Waves, Departme nt of Electro nic Engin eeri ng, City Un iversity of Hong Kong, Hong Kong (e-mail: .hk. Color versions of one or more of the ?gures in this paper are available on li ne at . Digital Object Ide nti?er 10.1109/TMTT.2010.2086

22、712 0018-9480/$26.00 ? 2010 IEEEWU et al.: MULTIWAY DUAL-BAND PLANAR POWER DIVIDERS 3833 Fig. 1.Basic pla nar con? gurati ons of multiway dua-ba nd pla nar power dividers with arbitrary power divisi on. (a Stan dard model of un equal or equal dual-ba nd power divider cells. (b Three-way dual-ba nd a

23、rbitrary pla nar power divider. (c Four-way dual-ba nd arbitrary pla nar power divider. power divider is used as a recomb inant structure (“recomb ineiFig. 1(b. Since the phases of the two tran smissi on ways W1 and W2 are the same, the isolati on eleme nt can be safely ignored because it con tribut

24、es no thi ng to affect ing the exter nal performa nee in this gen eralized divider. Therefore, we can provide a large separatio n betwee n two sides of tran smissi on ways, W1 and W2, in the practical layout;thus, this layout will avoid un desired parasitic effects betwee n them and will not degrade

25、the power combiner' s ef?ciencies. Twobdnd impedanee transformers with equal electrical le ngths are utilized to make all the output sig nals in-phase and the output ports matched at the desired two ban ds. In additi on, note that all the output ports can be isolated effectively because each two

26、-way dual-ba nd un equal power divider cell in the whole circuit has ideal isolation performanee. As shown in Fig. 1(c, a typical four-way dual-ba nd arbitrary power divider can be obta ined by directly in terc onn ect ing three basic two-way dual-ba nd un equal power divider cells. It is n ecessary

27、 to point out that additi onal in terc onn ect ing tran smissi on lines can be used betwee n two adjace nt power divider cells. Whe n the nu mber of ways in creases, the pla nar con? gurati ons of multiway dual-ba nd arbitrary power dividers will become more ?exible. For example, there are three typ

28、ical pla nar con? gurati ons of ?veway gen eralized power dividers, which are shown in Figs. 2(a-2(c. Similarly, additional interconnecting transmission lines should be used to obtain in-phase characteristics in dual-band applications. Here, there are two kinds of in terc onn ect ing tran smissi on

29、lin es: 1 compulsory lines which are used as phase shifters to achieve in-phase (such as Line 1 in Fig. 2 or as impedance transformers to realize dual-ba nd match ing (such as Line 2 in Fig. 2; 2 optio nal li nes (not show n in Figs.1 and 2 which are just used to modify the total external characteri

30、stic and enhance implementation ?exibility of the proposed power dividers such Fig. 2. Three typical pla nar con? gurati ons of ?veway dual-ba nd pla nar power dividers with arbitrary power divisio n (More additi onal in terc onn ecti ng tran smissi on lines can be used betwee n two adjace nt power

31、divider cells. These tran smissi on lines are n ot show n here because they are unn ecessary. as the in terc onn ect ing tran smissi on lines discussed in 16. This is beyo nd the poi nt discussed in this paper. III. PLANAR CIRCUIT AND DESIGN THEORY OF THE EXTENDED DUAL-BAND UNEQUAL POWER DIVIDER CEL

32、L The closed-form desig n equatio ns of two kinds of two-way dual-ba nd un equal power dividers have bee n proposed by the authors in 13, 14. Accord ing to the measured freque ncy performa nce of the microstrip examples in 13, 14, the basic two-way dualband unequal power divider cell without output

33、ports-matching structures (“ PDCell ” for short give n in 14 are chose n and exte nded to replace the dual-ba nd un equal power divider cell in Fig. 1(a. The exte nded PDCell will be used in the follow ing sect ions because its dual-ba nd operati ng freque ncy ban dwidth is relatively wide while the

34、 isolatio n structure is opti on al (desig n ?exibility. Fig. 3 shows the circuit con? guratio n of the extended PDCell. Its terminal impedances are arbitrary real values. In other words, and can be ?exibly de?ned their values are not limited to accord ing to differe nt desig n requireme nts. In add

35、iti on, we assume that the cen ter freque ncies of the desig nated dual band are3834 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 Fig. 3. Extended two-way dual-band unequal power divider with generalized terminal impedances. is the power dividing-ratio is of t

36、he output ports 3 and 2 in Fig. 3, and the de?ned ratio of term inal impeda nces. Since the isolati on structures in Fig. 3 should be chose n accord ing to the freque ncy ratio , the parameter values of the different isolation structures (the parallel RLC, the pure resistor R and the series RLC are

37、calculated by differe nt an alytical equati ons. To express these equati ons in simple form, two in termediate variables are de?ned as (4 and ( is the frequency ratio. It is also interesting that three kinds of isolation structures (the parallel RLC, the pure resistor R, and the series RLC should be

38、 chose n accordi ng to the cen ter freque ncy-ratio of the desig ned dual band for the PDCell. Note that the pure resistor R is only used when the frequency ratio equals to three. In fact, this special case is the traditi onal two-way sin gle band un equal Wilk inson power divider 14. Thus, on ly tw

39、o isolatio n structures in clud ing parallel and series RLC are show n in Fig. 3 for achiev ing arbitrary dual-ba nd applicati ons. For obta ining arbitrary power dividi ng with lossless transmission, ideal isolation and matching at dual band simultaneously, the analysis method of the tran smissi on

40、 line theory and circuit theory, as prese nted in 13, 14, can be applied. The ?nal results are smmarized in this section without process details since the similar an alysis was published in 14. To begi n with, the electrical le ngths of transmission lines shown in Fig. 3 are discussed. For simplicit

41、y in the design, all theelectrical le ngths of differe nt secti on tran smissi on lines are de?ned to as show n in Fig. 3. In fact, the electrical lengths can be different for each section transmission line (such as and in this PDCell. The required value of electrical lengths at the ?rst frequency c

42、an be determined by using the following equation (1 where is arbitrary positive integer, such as 1,2, 3, etc. Furthermore, ano ther variable used to calculate parameters is de?ned as (2 Fin ally, the gen eral closed-form desig n parameters equati ons for the exte nded PDCell show n in Fig. 3 are der

43、ived in the follow ing discussi on. For the power divider show n in Fig. 3, the characteristic impeda nces of tran smissi on lines can be calculated by (3 where (5 where (6 Note that the value of (4 will be always positive based on (3. Then, accord ing to the an alysis of tran smissi on line and cir

44、cuit theory 13, 14, the equati ons for isolation structures including two variables and are obtained as follows. , the parallel RLC isolation structure is When used, the values of the resistor, inductor, and capacitor are (7 When , the pure resistor R isolation structure is used, the value of the re

45、sistor is (8 When , the series RLC isolation structure is used, the values of the resistor, inductor, and capacitor are (9 Because the desig n 9 in clude two unknown variables and for the PDCell, these equations are more general than the analytical ones in 14. In addition, the results of (3-9 will b

46、e the same with the ones in 14 whe n and . This characteristic means that the results prese nted in this secti on can be used to desig n gen eralized power dividers with ?exible term inal impeda nces. Using the closedformWU et al.: MULTIWAY DUAL-BAND PLANAR POWER DIVIDERS 3835 Fig. 4. Typical power

47、distributio ns of mutil-way (N-way dual-ba nd un equal pla nar power dividers. design (1 (9, we can de?ne and code a very useful mathematical function for parameter calculatio n, whose ma in expressi on is (10 where the in depe ndent variables in the are the de?ned or known values (desig n goals and

48、 the calculated resulfedepe ndent variables are the desired desig n parameters. Therefore, the desig n does not n eed any optimization algorithm; it seems that the total procedure is simple and effective. IV. THEORETICAL DESIGN GUIDELINE OF MULTI-WAY DUAL-BAND UNEQUAL PLANAR POWER DIVIDERS The theor

49、etical desig n guideli ne of the proposed gen eralized Wilk inson power dividers is discussed in this sect ion. Fig. 4 shows a typical multiway dual-ba nd un equal pla nar power divider with power de?n iti ons. A. Power Con siderati ons As discussed above, the proposed gen eralized Wilk inson power

50、divider simulta neously has four mai n characteristics: pla nar structure if impleme nted by microstrip or stripline, multiple ways, arbitrary power dividing, and dual-band operations. In order to obtain all these characteristics in one structure, the two-side power distributions of the total genera

51、lized Wilkinson power divider shown in Fig. 4 should have the followi ng relatio nships (11 In Fig. 4, the in put and output power for in ternal two-way dual-ba nd un equal or equal power divider cells should satisfy the follow ing equati on: (12 The (11 and (12 in dicate that all of the power divid

52、er and comb iner cells don' s have any tran smissi on loss in the desig n procedure. B. Desig n Procedure Assume that it is required to design an N-way dual-band planar power divider with a power divid ing ratio of Fig. 5. Proposed gen eral circuit for three-way dual-ba nd arbitrary pla nar powe

53、r dividers. . Based on the above discussi on, the desig n procedure of multiway dualband un equal pla nar power dividers in cludes the follow ing steps, which are as follows. 1 Whe n the value of is de?ned and ?xed, the con? gurati on can be chose n accord ing to the desig n con cept of pla nar con?

54、 gurati on in Secti on II. The basic con? gurati on structures as show n in Figs. 1 and 2 are preferred. 2 Accord ing to con servati on of en ergy, there is a relati on ship betwee n the power divid ing ratio and power distributi ons, which is give n by (13 3 Once the values of are calculated, the t

55、otal power distributi ons are obta ined by comb ining gen eral (11 and (12, thus, the no rmalized power divid ing ratio and term inal impedances (some of them should be chosen manually are easily obtained by using the relationship between power dividing ratio and terminal impedances given in (3. 4 T

56、he basic power divider cell, n amely, PDCell in Fig. 3, is chose n, and all of the electrical parameters are obtained using the closed-form design (-9 or (10. 5 Based on the type of tran smissi on lines such as microstrip or stripli ne and the speci?c substrate shuas FR4 or RT Duroid series, all of

57、planar circuit dimensions are obtained using transmission line calculators. Un til now, the total desig n of the required power divider is ?ni shed. Fin ally,we can draw the practical prin ted circuit board (PCB. 6 Of course, many kinds of commercial full-wave simulation tools such as Sonnet, HFSS,

58、CST, and XFDTD can be used to verify the S-parameter performa nee of the desig ned PCB power dividers. If the full-wave electromag netic simulated results are not perfect, the dime nsions maybe are optimized carefully. However, this step is not necessary in this paper since the design parameters are

59、 the best one in theory.3836 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 Fig. 6 (Continued. Simulated S-parameters results of Examples C (c1 and c2. sig n guideli ne give n in Sectio n IV. The proposed structure with all parameters and several simulated examples are discussed. A. The Design Circuit Structure and its Design Equations