Mode-matching analysis and design of substrate integrated waveguide T-junction diplexer and corner filter

Transcription

1 NTERNATONAL JOURNAL OF NUMERCAL MODELLNG ELECTRONC NETWORK, DEVCE AND FELD nt. J. Nuer. Model. 015; Published online 16 October 014 in Wiley Online Library (wileyonlinelibrary.co)..030 Mode-atching analysis and design of substrate integrated waveguide T-junction diplexer and corner filter Zaza Kordiboroujeni, and Jens Borneann Departent of Electrical and Coputer Engineering, University of Victoria, Victoria, BC, V8W Y Canada UMMARY The ode-atching technique is deployed in this paper in order to analyze and design a substrate integrated waveguide (W) T-junction diplexer in Ku-band. The diplexer has bandwidths of 4.1% and 3.79% at and GHz, respectively. Also in Ku-band, an W corner filter is analyzed and designed with the sae technique. Analytical results are copared with siulated data obtained fro coercially available field solvers such as CT Microwave tudio and ANY HF. Excellent agreeent between analytical and siulated data is achieved. Copyright 014 John Wiley & ons, Ltd. Received 6 May 014; Revised 4 epteber 014; Accepted 9 epteber 014 KEY WORD substrate integrated waveguide; ode-atching techniques; diplexer; filter; T-junction; corner. 1. NTRODUCTON The advent of substrate integrated circuit technology, and specifically substrate integrated waveguide (W) technology, has introduced a new layout to efficiently design icrowave and illieter-wave structures. ntegrable with other planar topologies, these copact and high Q-factor structures can easily be fabricated at a low cost. Nuerous efforts in the area of design and analysis of passive W coponents, including diplexers, have been undertaen in the past few years. One of the essential passive coponents in front-end systes is the diplexer, which provides needed separation between transit and receive bands. The first diplexers based on W technology are reported in 005 [1,]. An X-band W diplexer using asyetric dual-ode iris filters in a branchingport configuration is proposed in [1]. The bands of the diplexer are located at 9.7 and 10.3 GHz, respectively, and three-pole in-band filters are used at each branch [1]. A siilar configuration with single-ode iris filters operates at C-band []. The bands of this diplexer are located at 5.4 and 5.96 GHz using five-pole and four-pole channel filters, respectively []. n 007, a diplexer designed with triplet technology is presented [3]. The diplexer has input and output ports on opposite sides of the substrate and uses iris filters, including a trisection, at 1.1 and GHz, respectively [3]. Also in 007, a diplexer operating at K-band uses dual ode W filters with circular and elliptic cavities [4]. The diplexer bands are located at 5 and 6 GHz, respectively [4]. An W triplexer with bands located at 1.9,.018, and.35 GHz is reported in 009 [5], but the insertion loss in one of the channels is in the order of 7 db. n 011, a T-junction diplexer with iris filters is presented in [6] with bands located at 59.8 and 6. GHz, respectively; however, the perforance is not verified by easureents. Also in 011, the T-junction W diplexer in [7] uses copleentary split-ring resonators at C-band. The channels of this C-band diplexer are located at 4.7 and 5.8 GHz. n 013, a K-band W diplexer with bands located at and 19 GHz is introduced [8], which has been designed using an efficient Correspondence to Zaza Kordiboroujeni, Departent of Electrical and Coputer Engineering, University of Victoria, Victoria, BC, V8W Y, Canada. E-ail zordi@ece.uvic.ca Copyright 014 John Wiley & ons, Ltd

2 498 Z. KORDBOROUJEN AND J. BORNEMANN ode-atching technique (MMT) proposed for W structures [9, 10]. The W diplexer is siilar in configuration to [3] and [5], but operates at a significantly higher frequency. n all W diplexers entioned earlier, except for the one reported in [8], the optiization and tuning steps of the W diplexer design are carried out using full-wave siulators. This is a tedious and cubersoe tas, considering the large nuber of optiization paraeters present in W diplexer designs. n contrast, the MMT approach adopted in [8] for designing W diplexers is an order of agnitude faster than coercially available field solvers. However, the presented MMT analysis cannot be directly applied for the analysis of W structures including T-junctions and corners. n this paper, the MMT approach presented in [9,10], in conjunction with a new approach for deploying MMT in analyzing W T-junctions, is adopted in order to design and analyze W T-junction structures, such as an W T-junction diplexer operating at Ku-band. The diplexer bands are placed at and GHz, using five-pole and four-pole filters, respectively. After presenting the analytical ethod for W T-junction structures, as the next step, one of the branches in the T-junction is short circuited, and W corners are investigated. An W corner filter at Ku-band is designed based on the proposed ethod.. THEORY ubstrate integrated waveguide structures are planar realizations of conventional rectangular waveguides. As a result, the field patterns inside these structures are siilar. However, as there is only a reduced set of odes in W structures [11], that is, only TE 0 odes, the odal analysis techniques, such as the MMT, are a proper choice for the analysis of these structures. This section starts with an overview of the MMT analysis of W structures and is followed by the proposed technique for analyzing W T-junctions..1. Mode-atching analysis of W structures Figure 1(a) shows the W topology with its structural paraeters. On a specific dielectric with h as the substrate height and r as the substrate relative perittivity, the ain structural paraeters of an W structure are the diaeter of the etal posts (d), the space between the in a row (via pitch p), and the W width, a W. n the design of W structures, the ratio of the via diaeter to the via pitch, d p, is chosen so that the electroagnetic field is copletely bound inside the structure and iniu leaage occurs (05 < d=p < 08 [1]). As a result of that, we bound the W structure inside a larger rectangular waveguide with the sae height as the W structure (Figure 1(b)), in order to apply the MMT. nside a waveguide with electric walls (E.W.), for the TE 0 set of odes, the agnetic vector potential can be expressed as (suppose that the cross section of the structure is in x y plane, cf. Figure 1(a)) E A h D A h E a D X p Zh T h.x/ hf e j C B e Cj i (1) (a) (b) Figure 1. (a) W circuit with its structural paraeters; and (b) a typical W structure with square vias surrounded by a larger rectangular waveguide.

3 MMT ANALY AND DEGN OF W T-JUNCTON DPLEXER AND CORNER FLTER 499 (a) (b) Figure. (a) Discontinuities between an all-dielectric waveguide and an N-furcated waveguide fored by N 1 via holes; and (b) discontinuity between a waveguide port and an W structure. in which Z h is the wave ipedance of the TE 0 ode and is equal to p Zh D r! ()! is the angular frequency, is the pereability of free space, a is the width of the waveguide, and is the wave propagation constant for the TE 0 wave in the -direction and is given by D s! r (3) a v c in which v c is the speed of light in free space. F and B are the aplitudes of forward and bacward traveling waves in the structure (see Figure (a)), and T h represents the dependence of the potential on cross-sectional coordinates; which for TE 0 odes, we only have an x dependence of T h. T h can be expressed as (note that the origin has been placed in the iddle of the cross section) T h.x/ D A cos a x C a Because in MMT all odes have to be noralized to the sae power, for exaple, 1 W in each region, we have (4) A D a r ah (5) For the electric and agnetic fields in this region, we have EE Dr.A h a / O H) E y (6) and EH D 1 A ao x C A a O (7) For copleting the MMT, subject to the boundary conditions at the discontinuity, electric and agnetic fields at both sides of a discontinuity relate to each other and for the -paraeters of the junction.

4 500 Z. KORDBOROUJEN AND J. BORNEMANN.1.1. Discontinuity between an all-dielectric waveguide and an N-furcated waveguide. Figure (a) presents the discontinuity between an all-dielectric waveguide and an N-furcated waveguide with N 1 via holes. Please note that we apply the MMT for the analysis of W structures with rectangular/square vias. The size of the vias in Figure (a) is exaggerated in order to deonstrate forward and bacward traveling waves in each region. For this type of discontinuity, EE and EH are calculated by Equations (6) and (7), and at the discontinuity, the boundary condition of perfect electric conducting vias should be applied. By atching E y over the entire discontinuity (suppose that it is placed at D 0), we have s X! D X N X A 0 0 s! sin A N Ń a N x C sin a N.x x N / and by atching H x in each individual region, we obtain F 0 C B 0 F N C BN (8) s X 0! A 0! 0 D X Ń s! A N! Ń a N sin sin a N.x x N / x C a 0 F 0 C B 0 F N C BN (9) We ultiply both sides of Equation (8) by sin 0.x C / and integrate fro to. This results in the following equation F 0 C B 0 D X N M N F N C B N (10) or in atrix forat F 0 C B 0 D M 1 M M N 6 4 F 1 C B 1 F N C B N in which M D M 1 M M N. Also, we ultiply both sides of Equation (9) by sin 0 a N.x x N / and integrate fro x N to x N C a N, leading to the following equation M N T F 0 B 0 D F N B N.N ties/ (11) or in atrix forat 3 M 1 T M T F 0 B 0 D M N T F 1 B 1 F N B N 3 7 5

5 MMT ANALY AND DEGN OF W T-JUNCTON DPLEXER AND CORNER FLTER 501 M T is the transpose of M. n the aforeentioned equations, atrix M N is related to the ipedance atrix Z N K, adittance atrix Y 0, and coupling integral J N by q q M N D Diag Y 0 J N Diag Z N (1) and the coupling integral is J N D p a0 a N Z xn Ca N x N sin x C sin a N.x x N /dx (13) Fro this M atrix, the -paraeters, which are relating incident and reflected wave aplitudes as 6 4 B 0 F F N D Π6 4 F 0 B B N can be derived as 11 D MM T C 1 MM T 1 D MM T C 1 M D T 1 1 D M T. 11 / (14) D M T 1 where denotes the unit atrix. The axiu nuber of odes in each individual section is set by a axiu frequency. With this axiu frequency, f ax, the nuber of odes in a waveguide section with width a N is deterined as an f ax ax D ceiling (15) in which v p is the wave propagation speed in the dielectric, and the ceiling function aps a real nuber to the sallest following integer. According to our investigations, setting this f ax equal to 40 ties the cutoff frequency of the input/output ports, f c, results in an acceptable accuracy. f c is specified at the beginning of the design and deterines the operation frequency band..1.. Discontinuity between waveguide ports and an W structure. Figure (b) represents the discontinuity fro a waveguide port to an W structure. The boundary between two structures is treated as a perfect agnetic conductor (PMC). n this case, EE and EH are calculated by Equations (6) and (7). However, as the boundary condition is a PMC, for atching, we have to ultiply both sides of the equation for H x by sin 0 x C and integrate fro to (see Figure (b)) and for E y by sin 0 a 1 x C a 1 and integrate fro a 1 to a 1. n this case, the coupling integral is v p.j / D p a0 a 1 Z a1 a 1 sin x C sin a 1 x C a 1 dx (16) The M atrix and -paraeters are calculated as in Equations (1) and (14).

6 50 Z. KORDBOROUJEN AND J. BORNEMANN.1.3. MMT analysis of ultiport W structures. f there is ore than one waveguide port at the input or output of the structure, the procedure of calculating the atrix is predoinantly based on the ethod presented earlier for two-port W structures. After calculation of the total odal atrix of the discontinuities involved (sae procedure as that presented for two-port structures), the desired -paraeters of the ultiple port structure (M C N port structure) with M input ports and N output ports, ij, are extracted fro the coputed overall odal two-port scattering atrix as total D 4 3 port 11 port 1 5 port 1 port M 1.M C1/ 1.M CN/ 1 M.MC1/.MCN/ D M1 MM M.MC1/ M.MCN/.M C1/1.M C1/M.M C1/.M C1/.M C1/.M CN/ (17).M CN/1.M CN/M.M CN /.M C1/.M CN /.M CN/.. MMT for W T-junctions Mode-atching technique analysis of a waveguide T-junction is previously reported in the literature. For exaple, it is suggested in [13] that three short circuits with different lengths be used to terinate each port three ties, and then an MMT approach is deployed. However, this approach coputes the - paraeters of the fundaental ode only. The generalized odal scattering atrix for ode-atching probles involving discontinuity-distorted ulti-port junctions is presented in [14]. However, the presented ethod requires very coplex coputations. n this section, an efficient MMT approach for the analysis of W T-junctions is presented. The MMT analysis presented in subsection.1. cannot directly be deployed for the analysis of W T-junctions. For the -paraeters calculations of the W T-junction (Figure 3(c)), we first add a waveguide corner (Figure 3(b)) to this T-junction and then calculate the -paraeters of this new W structure with one input port and two output ports (Figure 3(a)) fro the theory presented in ection.1. Now, we subtract the -paraeters of the waveguide corner [15] fro that calculated -paraeters in order to achieve the desired -paraeter of the W T-junction in Figure 3(c) [16]. The (a) (b) (c) Figure 3. -paraeter calculation of an W T-junction (c) based on subtraction of the -paraeters of the waveguide corner (b) fro the -paraeters of an W structure with one input port and two output ports (a).

7 MMT ANALY AND DEGN OF W T-JUNCTON DPLEXER AND CORNER FLTER 503 final -paraeters of the W T-junction (structure ()) in ters of the -paraeters of the structures () and () are as follows 11 D W D 1 14 W D 1 T 13 D 14 W D 31 T 1 D 1 4 W D 1 T D 4 W D 4 W D T 3 (18) 31 D 33 3 D D W D W D T W T T where W D h C i 1 34 (19) For the analysis of W corners, one of the branching ports of the W T-junction is short-circuited (e.g., port in Figure 3(c)), and the final -paraeters of the W corner can be extracted fro the -paraeters presented in Equation (18) as b1 a 3 " # corner 11 1 corner D D 1 corner corner a1 b 3 corner 11 D 11 C corner 1 D 13 C corner 1 D 31 C corner D 33 C 3 3 (0).3. Analysis of W structures with circular vias The MMT analysis presented in the previous sections is applicable to W coponents with square vias. However, in order to analyze W structures with circular vias, which are ore coon in practice, an equivalence between circular vias and square vias has been established [10]. Based on this equivalence, any circular via with diaeter of d can be approxiated by a square via with side length l as l D.l inner C l outer /= D d.1= p C 1/= (1) in which l inner and l outer are the side lengths of inscribed and circuscribed squares of the circular via, respectively, as shown in Figure 4. Based on the MMT analysis presented in this section, the perforance of an W T-junction with circular vias (Figure 5(a)) is analyzed in Ku-band.

8 504 Z. KORDBOROUJEN AND J. BORNEMANN Figure 4. The circle with diaeter d circle and inscribed and circuscribed squares with side lengths l inner and l outer, respectively. (a) Figure 5. (a) W T-junction with circular vias in Ku-band. The structure is analyzed with MMT (solid line), and the results are copared with CT data (dashed line) (b). (b) For the design of an W coponent, first, the cutoff frequency f c, substrate perittivity r,andd=p ratio (05 < d=p < 08 [1]) are specified. Once the effective waveguide width of W (W equi ) is calculated, the W width (a W ) can be calculated based on [17]. n this paper, the substrate is chosen as RT/duroid 600 with r D 94 and height h D f c D 107 GHz results in W equi D 8514, and with p D 1 and d D 06444, the W width is a W D 9. The side length of the square vias in the MMT analysis is l D 055. The MMT results for the W T-junction with square vias are copared with the siulated data fro CT Microwave tudio for the W structure with equivalent circular vias (Figure 5(b)). Reasonable agreeent is achieved between MMT and CT data, which proves the validity of the proposed analytical approach.

9 MMT ANALY AND DEGN OF W T-JUNCTON DPLEXER AND CORNER FLTER 505 Figure 6. W filter for the lower channel of the W T-junction diplexer. The structure is analyzed with MMT (solid line), and the results are copared with the CT data (dashed line). Figure 7. W filter for the higher channel of the W T-junction diplexer. The structure is analyzed with MMT (solid line), and the results are copared with the CT data (dashed line). 3. W DPLEXER DEGN The design of the T-junction diplexer starts with the design of two channel filters. The first channel filter with the bandpass located at the lower frequency band is a five-pole filter and has 4.1% bandwidth at GHz. This W filter is designed and analyzed based on the MMT for W structures with square vias, and the analytical data is copared with siulated data with circular vias fro CT in Figure 6. The other filter operating at the higher frequency band is a four-pole filter and has 3.79% of bandwidth at GHz. Figure 7 shows the layout of the filter along with the coparison between analytical and siulated data. Now, the diplexer is fored based on the two presented channel filters. The diplexer is optiized with the analytical approach presented, which saves us significant aount of tie, as the presented technique is faster than coercially available field solvers by an order of agnitude [8]. The layout of the final optiized diplexer is presented in Figure 8(a). The designed diplexer is siulated in CT Microwave tudio and also ANY HF, and the agreeent between the analytical and siulated data validates the presented ode-atching based technique for the analysis of W coponents including a T-junction (Figure 8(b)). 4. W CORNER FLTER After validation of the presented technique for analyzing W T-junctions, one of the branches of the T-junction is being short circuited, and an W corner, along with an W corner filter, is designed and analyzed. The W corner layout along with its perforance is presented in Figure 9. Also, the W corner filter, which is a four-pole iris filter, and its -paraeters are presented in Figure 10. Please note that the discrepancy observed between MMT data and siulation data in Figure 10 is because the atrix inversion in Equation (0) liits the nuber of odes considered in the MMT analysis. Other than that, for both W corner and W corner filter, the analytical data is in good agreeent with the siulated data, which prove the validity of the analytical ethod.

10 506 Z. KORDBOROUJEN AND J. BORNEMANN (a) Figure 8. Diplexer T-junction layout (a), along with -paraeters (b). The structure is analyzed with MMT (solid line), and the data are copared with siulated data fro CT (dashed line) and also HF (dash-dotted line). (b) Figure 9. Layout and perforance of an W corner. MMT data (solid line) have been copared with CT data (dashed line). Figure 10. Layout and perforance of an W corner filter. MMT data (solid line) have been copared with CT data (dashed line).

11 MMT ANALY AND DEGN OF W T-JUNCTON DPLEXER AND CORNER FLTER CONCLUON The MMT with square vias is a powerful approach for the analysis of W coponents, including filters, T-junctions, and corners. The presented technique is deonstrated by coparing MMT results using square vias with CT and HF siulations eploying circular vias. Very good agreeent is achieved for the T-junction diplexer and the corner filter, thus verifying the MMT-based analysis and design procedure. ACKNOWLEDGEMENT The authors would lie to acnowledge the support of this wor fro the National cience and Engineering Research Council of Canada (NERC). REFERENCE 1. Chen X, Hong W, Cui T, Wu K. ubstrate integrated waveguide (W) asyetric dual-ode filter and diplexer. nternational Journal of Electronics 005; 9(1) Hao ZC, Hong W, Chen JX, Chen XP, Wu K. Planar diplexer for icrowave integrated circuits. EE Proceedings - Microwaves, Antennas and Propagation 005; 15(6) Han,WangX,FanY,YangZ, He Z. The generalized Chebyshev substrate integrated waveguide diplexer. Progress n Electroagnetics Research 007; Tang HJ, Hong W, Chen JX, Luo GQ, Wu K. Developent of illieter-wave planar diplexers based on copleentary characters of dual-ode substrate integrated waveguide filters with circular and elliptic cavities. EEE Transactions on Microwave Theory and Techniques 007; 55(4) Hou D, Hong W, Tian L, Liu J, Tang H. A planar triplexer based on substrate integrated waveguide technology for TD-CDMA applications, Asia-pacific Microwave Conference (APMC) Proceedings, ingapore, Deceber 009; Athanasopoulos N, Maris D, Voudouris K. Developent of a 60 GHz substrate integrated waveguide planar diplexer, EEE MTT- nternational Microwave Worshop eries on Millieter Wave ntegration Technologies (MW) Proceedings, itges, pain, October 011; Dong Y, toh T. ubstrate integrated waveguide loaded by copleentary split-ring resonators for iniaturized diplexer design. EEE Microwave and Wireless Coponents Letters 011; 1(1) Kordiboroujeni Z, Borneann J. Mode atching design of substrate integrated waveguide diplexers, EEE MTT- nternational Microwave yposiu (M) Digest, eattle, WA, UA, June 013; Borneann J, Taringou F, Kordiboroujeni Z. A ode-atching approach for the analysis and design of substrate-integrated waveguide coponents. Frequenz - Journal of RF/Microwave Engr., Photonics and Counications 011; Kordiboroujeni Z, Borneann J, ieverding T. Mode-atching design of substrate-integrated waveguide couplers, Asia-Pacific yposiu on Electroagnetic Copatibility (APMEC) Proceedings, ingapore, May 01; Xu F, Wu K. Guided-wave and leaage characteristics of substrate integrated waveguide. EEE Transactions on Microwave Theory and Techniques 005; 53(1) Deslandes D, Wu K. Accurate odeling, wave echaniss, and design considerations of a substrate integrated waveguide. EEE Transactions on Microwave Theory and Techniques 006; 54(6) Liang XP, Zai KA, Atia AE. A rigorous three plane odeatching technique for characterizing waveguide T-junctions, and its application in ultiplexer design. EEE Transactions on Microwave Theory and Techniques 1991; 39(1) Labay VA, Borneann J. Generalized odal scattering atrix of discontinuity-distorted waveguide ultiport junctions. nternational Journal of Nuerical Modelling Electronic Networs, Devices and Fields 1997; 10(3) Kühn E. A ode-atching ethod for solving field probles in waveguide and resonator circuits. Archiv fuer Eletroni und Uebertragungstechni 1973; Beyer R, Arndt F. The generalized scattering atrix separation technique cobined with the MM/FE ethod for the efficient odal analysis of a coprehensive class of 3D passive waveguide circuits, EEE MTT- nternational Microwave yposiu (M) Digest, Orlando, FL, UA, May 1995; Kordiboroujeni Z, Borneann J. Designing the width of substrate integrated waveguide structures. EEE Microwave and Wireless Coponents Letters 013; 3(10)