Analysis and designs of symmetrical six port microstrip couplers

ANALYSIS AND DESIGNS OF SYMMETRICAL SIX-PORT MICROSTRIP COUPLERS CHEN YUAN NATIONAL UNIVERSITY OF SINGAPORE 2008 ANALYSIS AND DESIGNS OF SYMMETRICAL SIX-PORT MICROSTRIP COUPLERS CHEN YUAN (B.Eng., Shanghai Jiao Tong University) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2008 Acknowledgements I would like to express my sincere gratitude to my supervisor, Prof. Yeo Swee Ping, for his guidance and encouragement throughout my PhD project. It has been a very pleasant experience to study and research under his supervision. I would also like to extend my appreciation to Mr. Sing Cheng Hiong and Ms. Lee Siew Choo for their kind assistance in fabrication and measurements. I would like to thank my fellow course-mates and postgraduate students in Microwave Laboratory for their friendship and knowledge sharing. Finally, I would like to take this opportunity to thank my family for their constant love and support. i Table of Contents Acknowledgements .i Table of Contents .ii Abstract v List of Figures .vi List of Tables . xiii List of Symbols .xiv Chapter Introduction 1.1 General Background 1.2 Project Tasks 1.3 Outline of Thesis 1.4 Original Contributions .6 Chapter 2.1 General Overview Symmetrical Six-Port Junctions .7 2.1.1 Five-way power dividers 2.1.2 Directional couplers (for use in six-port reflectometers) .10 2.1.3 Six-port crossovers .13 2.2 Review of Related Research 15 2.3 Choice of Modeling Tool .17 Chapter Eigenmode Models 20 3.1 Eigenmode Analysis 20 3.2 Transmission-Line Formulation .24 3.2.1 Arc of ring line .25 3.2.2 Single ring structure .27 ii 3.2.3 Star structure 28 3.2.4 Single-ring-with-star structure .30 3.2.5 Single-ring-with-rotated-star structure .31 3.2.6 Double-ring structure .36 3.2.7 Double-ring-with-rotated-link structure .37 3.2.8 Double-ring-with-star structure .38 3.2.9 Adding step transformers .41 3.2.10 Adding linear tapers .42 3.2.11 Rings with non-uniform widths .43 3.3 Summary 44 Chapter 4.1 Design Considerations .47 Validation of Models .47 4.1.1 Prototype (single-ring-with-rotated-star structure) .48 4.1.2 Prototype (double-ring-with-rotated-link structure) .53 4.2 Optimization Process .59 4.2.1 Search algorithm 60 4.2.2 Optimization constraints 63 4.3 Fabrication Tolerances .65 4.4 Summary 72 Chapter Six-Port Directional Coupler for Six-Port Reflectometer Application 73 5.1 First-Order Analysis .73 5.2 Design Targets for Optimization .81 5.3 Intermediate Coupler Designs 87 5.4 Finalized Coupler Design 95 5.5 Summary 104 iii Chapter Six-Port Power Divider 106 6.1 First-Order Analysis .106 6.2 Optimization Targets .112 6.3 Prototype Coupler 113 6.4 Summary 119 Chapter Six-Port Crossover .120 7.1 First-Order Analysis .120 7.2 Optimization Targets .125 7.3 Prototype Crossover .129 7.4 Summary 133 Chapter Four-Port Crossover .134 8.1 First-Order Analysis .136 8.2 Optimization Targets .139 8.3 Prototype Crossover .141 8.4 Sensitivity Analysis .144 8.5 Summary 153 Chapter Conclusions 154 9.1 Principal Findings 154 9.2 Suggestions for Future Work .156 References 158 iv Abstract Transmission-line analysis has been employed to derive closed-form eigen-admittance expressions that can be used to predict the scattering coefficients of symmetrical sixport microstrip couplers which may be implemented in a diversity of structural forms. The compilation of these analytical formulas forms the basis of the computer model that is embedded within the design optimization software which is based on Genetic Algorithm. The wide range of add-on design options that are available (including the central star and/or second ring in various combinations with linear tapers and/or step transformers) provides greater flexibility in the optimization search for symmetrical six-port microstrip couplers that are suitable for selected applications. Laboratory measurements have confirmed that the resulting six-port prototypes meet the design specifications over bandwidths of 49% for six-port reflectometer application, 36% for five-way power division/combination application and 6% for three-way crossover application. The experience gained during the analysis and design of the six-port crossover has proven to be useful during the follow-up extension to analyze and design a four-port crossover. With its reduced structural complexity, the resulting four-port prototype is able to yield a measured bandwidth of 20% that is wider than that of its six-port counterpart. In addition, the first-order analysis performed for each of these applications has been found to provide valuable insight into the coupler’s behavior to help in steering the design optimization iterations. v List of Figures Figure 2.1: Input- and output-wave arrangements for symmetrical six-port coupler Figure 2.2: Schematic diagram of six-port reflectometer 11 Figure 2.3: Intersection of circles (with centers qk) in complex Γ plane 13 Figure 3.1: Input and output waves for coupler when operating in eigenmode of order m = 0, 1, 2, 3, 4, as portrayed in (a), (b), (c), (d), (e) and (f) respectively 21 Figure 3.2: Transmission line model for eigenmode analysis of single-ring structure 25 Figure 3.3: Single ring structure 27 Figure 3.4: Equivalent circuit for single-ring structure (where terminals X-X at left end have to be wrapped around for connection to terminals Y-Y at right end) .27 Figure 3.5: Star structure 28 Figure 3.6: Single-ring-with-star structure 30 Figure 3.7: Equivalent circuit for single-ring-with-star structure (where terminals X-X at left end have to be wrapped around for connection to terminals Y-Y at right end) .31 Figure 3.8: Single-ring-with-rotated-star structure 31 Figure 3.9: Equivalent circuit for single-ring-with-rotated-star structure (where terminals X-X at left end have to be wrapped around for connection to terminals Y-Y at right end) .32 Figure 3.10: Transmission line model for eigenmode analysis of single-ring-withrotated-star structure .32 vi Figure 3.11: Double-ring structure 36 Figure 3.12: Double-ring-with-rotated-link structure 37 Figure 3.13: Possible double-ring-with-star structures 39 Figure 3.14: Adding steps on (a) spokes of star junction, (b) ring-to-ring links, and (c) external arms .41 Figure 3.15: Step transformer 42 Figure 3.16: Linear taper 43 Figure 3.17: Coupler structures with non-uniform width for (a) outer ring and (b) inner ring .43 Figure 4.1: Prototype based on single-ring-with-star structure 48 Figure 4.2: Variation of magnitude of γ for Prototype 49 Figure 4.3: Variation of magnitude of α with frequency for Prototype 49 Figure 4.4: Variation of magnitude of β with frequency for Prototype 50 Figure 4.5: Variation of magnitude of τ with frequency for Prototype .50 Figure 4.6: Variation of phase of γ with frequency for Prototype 51 Figure 4.7: Variation of phase of α with frequency for Prototype 51 Figure 4.8: Variation of phase of β with frequency for Prototype 52 Figure 4.9: Variation of phase of τ with frequency for Prototype 52 Figure 4.10: Prototype based on double-ring-with-rotated-links structure .54 Figure 4.11: Variation of magnitude of γ with frequency for Prototype .55 Figure 4.12: Variation of magnitude of α with frequency for Prototype 55 Figure 4.13: Variation of magnitude of β with frequency for Prototype 56 Figure 4.14: Variation of magnitude of τ with frequency for Prototype .56 Figure 4.15: Variation of phase of γ with frequency for Prototype 57 vii Figure 4.16: Variation of phase of α with frequency for Prototype 57 Figure 4.17: Variation of phase of β with frequency for Prototype 58 Figure 4.18: Variation of phase of τ with frequency for Prototype 58 Figure 4.19: Magnitude variations of (a) γ (b) α (c) β (d) τ with frequency for different inner-ring widths: ooo +5 mil, ··· –5 mil, ××× +10 mil, +++ – 10 mil 66 Figure 4.20: Magnitude variations of (a) γ (b) α (c) β (d) τ with frequency for different inner-ring radii: ooo +5 mil, ··· –5 mil, ××× +10 mil, +++ –10 mil .67 Figure 4.21: Magnitude variations of (a) γ (b) α (c) β (d) τ with frequency for different outer-ring widths: ooo +5 mil, ··· –5 mil, ××× +10 mil, +++ – 10 mil 68 Figure 4.22: Magnitude variations of (a) γ (b) α (c) β (d) τ with different outerring radii: ooo +5 mil, ··· –5 mil, ××× +10 mil, +++ –10 mil .69 Figure 4.23: Magnitude variations of (a) γ (b) α (c) β (d) τ , with frequency for different ring-to-ring link widths: ooo +5 mil, ··· –5 mil, ××× +10 mil, +++ –10 mil .70 Figure 5.1: First-order variations of γ and β with Φ a and Φ b 79 Figure 5.2: First-order variations of α and τ with ψ .80 Figure 5.3: Schematic diagram of symmetrical six-port coupler configured as six-port reflectometer .82 Figure 5.4: Two possible six-port reflectometer configurations based on symmetrical six-port coupler together with directional coupler 85 viii -10 -10 -20 -20 magnitude (dB) magnitude (dB) Chapter Four-Port Crossover -30 -30 -40 -40 -50 -50 -60 0.9 0.95 1.05 frequency (GHz) -60 1.1 0.9 0.95 (a) 1.05 frequency (GHz) 1.1 (b) 90 phase (deg) magnitude (dB) -10 -90 -20 0.9 0.95 1.05 frequency (GHz) -180 1.1 (c) Figure 8.10: Variations of (a) | γ |, (b) | α |, (c) | β | and (d) phase of 0.9 0.95 1.05 frequency (GHz) 1.1 (d) β for different outer-ring radii: ××× +0.2 mm, +++ –0.2 mm, ooo original 151 -10 -10 -20 -20 magnitude (dB) magnitude (dB) Chapter Four-Port Crossover -30 -30 -40 -40 -50 -50 -60 0.9 0.95 1.05 frequency (GHz) -60 1.1 0.9 0.95 (a) 1.05 frequency (GHz) 1.1 (b) 90 phase (deg) magnitude (dB) -10 -90 -20 0.9 0.95 1.05 frequency (GHz) -180 1.1 (c) Figure 8.11: Variations of (a) | γ |, (b) | α |, (c) | β | and (d) phase of 0.9 0.95 1.05 frequency (GHz) 1.1 (d) β for different ring-to-ring link widths: ××× +0.3 mm, +++ –0.3 mm, ooo original 152 Chapter Four-Port Crossover Similar to the earlier findings we obtained during our pilot study in Section 4.3 on the symmetrical six-port coupler, it can be inferred from the simulation plots presented in Figure 8.7 - Figure 8.11 that the symmetrical four-port coupler we proposed in Figure 8.2 and Table 8.1 should be insensitive to fabrication tolerance up to ±0.2 mm with the bandwidth remaining at 20%. Even for incremental variations between ±0.2 mm and ±0.5 mm, the bandwidth of our proposed coupler still does not fall below 16%. Among the five key dimensions included in our simulation tests, our four-port crossover design is particularly sensitive to changes in the width and radius of its outer ring but it is least sensitive to any change in the width of its inner ring. Among the three scattering coefficients, γ appears to be the most sensitive to dimension variations while β is clearly the least sensitive even for fabrication tolerances up to ±0.5 mm. 8.5 Summary Instead of resorting to non-planar crossover structures (such as air-bridge and underpass crossings), we have proposed a symmetrical four-port microstrip coupler (based on the double-ring structure and linear tapers) that is able to function as a planar fourport crossover over a 20% bandwidth (from 0.92 GHz to 1.12 GHz) with in-line insertion loss less than dB and off-line isolation and return loss better than the usual 20 dB limits. With reduced structural complexity, this four-port prototype is less sensitive to incremental changes of ±0.2 mm in its physical dimensions when compared with its six-port counterpart in Chapter 7. 153 Chapter Conclusions Chapter Conclusions 9.1 Principal Findings We have attained the various objectives set out at the inception of our research. Summarized below are our principal findings/achievements during the course of the investigations: ● We have successfully developed in Chapter an easy-to-use computer model for the analysis and design of symmetrical six-port microstrip couplers in Chapters 5-7. Transmission-line analysis has been utilized to derive closedform expressions which we systematically compiled for a diversity of coupler structures when operating in various eigenmodes. The fabrication of selected prototypes for laboratory measurements has allowed us to verify the accuracy of the numerical results generated by our computer model which we have since found to be flexible enough for extension (after some minor adaptation) to the analysis and design of symmetrical four-port microstrip couplers in Chapter 8. ● The special properties of the symmetrical four- and six-port couplers suggest the possibility of various applications as discussed in Section 2.1. For each of the selected applications, the first-order analysis we performed (prior to the design process) has provided us with valuable insight into the behavior of a reasonably good coupler design that still manifests some minor departures from the ideal case. We have utilized these first-order findings to help steer the 154 Chapter Conclusions design optimization iterations in order to search for suitable prototypes in Chapters 5-8. ● Resembling a six-port directional coupler, the symmetrical six-port coupler we analyzed and designed in Chapter has met our optimization targets for sixport reflectometer application. The results we obtained from the intermediate designs explored in Section 5.3 have shown that it is possible to increase the coupler’s bandwidth via structural modifications. We note from the measured scattering-coefficient data, which agree with the corresponding plots generated by our computer model, that our final prototype yields a bandwidth of 49% which (to the best of our knowledge) is the widest that has been reported thus far. ● In contrast to the simple design with a bandwidth of only 10% reported by Riblet and Hansson [24], the second symmetrical six-port coupler which we analyzed and designed has been found in Chapter to be suitable for five-way power division/combination over a wider bandwidth of 36%. Prototype tests have confirmed that there is excellent agreement between the predicted and measured results. It is also possible for us to adapt the optimization process to design couplers that meet other power division/combination specifications instead. ● Yet another application is the third symmetrical six-port coupler we analyzed and designed to function as a six-port crossover (which, to the best of our knowledge, is the first planar component to be ever proposed for three-way crossover application). The bandwidth we measured for this novel prototype is only 6%; actually, the predicted results presented in Section 7.3 indicate that it 155 Chapter Conclusions should be possible for us to obtain a wider bandwidth for such a design (if not for the deviation between the predicted and measured results near the design frequency). ● It should be easier to design symmetrical four-port couplers because of their reduced structural complexity. Extending beyond the six-port crossover design attempted in Chapter 7, we have also analyzed and designed in Chapter a four-port crossover with a measured bandwidth of 20%. The sensitivity test results indicate that this four-port prototype is less sensitive to incremental changes of ±0.2 mm in its main physical dimensions than for its six-port counterpart. Apart from our N = and N = prototypes (reported in Chapters 5-7 and Chapter respectively), we would like to point out that our computer model can be readily adapted for the analysis and design of other symmetrical N-port couplers (especially for N ≥ 7). 9.2 Suggestions for Future Work We would like to offer the following suggestions for future work that may be of interest to other researchers: ● The accuracy of the numerical results generated by our computer model is limited by the validity of the two assumptions in Section 3.2 which we had to incorporate during our transmission-line formulation to derive the eigenmode expressions. It would be helpful if these two assumptions may be dispensed but the computational speed of the resulting model (which has to be embedded 156 Chapter Conclusions within the design optimization software) should not be delayed due to numbercrunching. ● It is also possible to expand the diversity of coupler options available for designers by including, for example, third and even fourth rings, stubs on rings, or lumped capacitances/inductances. The concern, however, is that increasing the prototype’s structural complexity may lead to a deterioration of numerical accuracies. ● We have designed, fabricated and tested prototypes implemented in microstrip. It should also be possible to extend the general analysis in Chapter to other implementations such as stripline and coplanar waveguide. 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Theory Tech., vol. 42, pp. 376-382, Mar. 1994. 166 [...]... the analysis and design of six- port crossovers allows us to extend the scope of investigation to the analysis and design in Chapter 8 of four -port crossovers (which are easier to handle because of their relative structural simplicity) 1.3 Outline of Thesis The thesis consists of nine chapters After the introductory discussion in Chapter 1, we provide a general overview of symmetrical six- port couplers. .. component of their six- port reflectometer circuit However, the structural simplicity of their prototypes did not offer much flexibility for bandwidth broadening and the practical utility of these designs is thus restricted to narrow-band circuits To improve the design of the symmetrical six- port coupler, we also look at what the other researchers had previously attempted for the case of symmetrical four- and. .. are the symmetrical five- and six- port junctions The symmetrical five -port junction has already benefited from the efforts of many researchers after the introduction of the six- port reflectometer as a simple alternative approach to measuring the reflection coefficients of one -port components (followed by the proposal to use the dual six- port scheme to measure the scattering coefficients of two -port components)... easier to design (because of the reduced number of isolated ports), we have expanded the scope of investigation in Chapter 7 to additionally consider the analysis and design of the symmetrical four -port coupler 5 Chapter 1 Introduction in Chapter 8 As expected, the measured bandwidth of our prototype for four -port crossover application is wider than that obtained for its six- port counterpart in Chapter... we have additionally expanded our scope of investigation to cover symmetrical four -port couplers in Chapter 8 for use as four -port crossovers (which are easier to analyze and design in view of their reduced structural complexity) 2.2 Review of Related Research As mentioned in Chapter 1, the symmetrical six- port coupler actually belongs to the general family of symmetrical N -port junctions Such junctions... core component of a six- port reflectometer capable of optimum measurement performance Although it is possible to adapt the optimization targets so as to search for a six- port directional coupler instead, the focus of our design optimization efforts is on a prototype suitable for six- port reflectometer application The analysis and design reported in Chapter 6 are for a symmetrical six- port coupler to... [29, 31-33] Many designs are available in the literature based on a diversity of structures and configurations [34, 35] Among them are the symmetrical N -port junctions where the designs for the less common N = 5 and N = 6 versions have already been reported by other researchers For the symmetrical fiveport family, waveguide and microstrip prototypes have been designed by Chang et al [36] and Wang et al... for the analysis and design of planar crossover structures Wight et al [58] attempted to cascade two hybrids for crossover application but the bandwidth of their composite prototype is limited The range of options at our disposal in Chapter 3 offers opportunities for other novel six- port crossover designs in Chapter 7 Since it is more common to find crossovers with four instead of six ports, we have... basis The possibility of designing the symmetrical six- port coupler to function as a six- port crossover is considered in Chapter 7 For this novel application, we have found it difficult to improve the bandwidth of our narrow-band design since there is a need to arrange for four of the coupler’s ports to be electrically isolated from the port with the input wave Noting that four -port crossovers ought... are also compact in size and light in weight With relative ease of integration, microstrip implementation can accommodate more complicated structures such as the diversity of microstrip structures considered in Chapter 3 for the symmetrical six- port coupler As mentioned in Sub-Section 2.1.1, the first prototype reported for a symmetrical sixport coupler was designed by Riblet and Hansson [24] as a power . ANALYSIS AND DESIGNS OF SYMMETRICAL SIX- PORT MICROSTRIP COUPLERS CHEN YUAN NATIONAL UNIVERSITY OF SINGAPORE 2008 ANALYSIS AND DESIGNS OF SYMMETRICAL SIX- PORT MICROSTRIP. variations of γ and β with a Φ and b Φ 79 Figure 5.2: First-order variations of α and τ with ψ 80 Figure 5.3: Schematic diagram of symmetrical six- port coupler configured as six- port. variations of α and β with a Φ and b Φ 126 Figure 7.2: First-order variations of γ and τ with a Φ and ψ 127 Figure 7.3: Proposed design for symmetrical six- port microstrip coupler