DESIGN OF MULTI BAND MICROWAVE DEVICES USING COUPLED LINE TRANSMISSION LINES Sri Katakam Thesis Prepared for the Degree of MASTER OF SCIENCE UNIVERSITY OF NORTH TEXAS May 2015 Thesis Committee Dr. Hualiang Zhang, Major Professor Dr. Hyoung Soo Kim, Committee Member Dr. Xinrong Li, Committee Member Dr. Shengli Fu, Interim Chair of Dept. of Electrical Engineering Dr. Costas Tsatsoulis, Dean of the College of Engineering Dr. Mark Wardell, Dean of the Toulouse Graduate School ProQuest Number: 10034708 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest 10034708 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 Katakam, Sri. Design of multi band microwave devices using coupled line transmission lines. Master of Science (Electrical Engineering), May 2015, 38 pp., 2 tables, 26 illustrations, references, 41 titles. Multi band technology helps in getting multiple operating frequencies using a single microwave device. This thesis presents the design of dual and tri band microwave devices using coupled transmission line structures. Chapter 2 presents the design of a novel dual band transmission line structure using coupled lines. In chapter 3, Design of a dual band branch line coupler and a dual band Wilkinson power divider are proposed using the novel dual band transmission line structure presented in the previous chapter. In chapter 4, Design of a tri band transmission line structure by extending the dual band structure is presented. The Conclusion and future work are presented in chapter 5. Copy right 2015 Sri.Katakam ii ACKNOWLEDGEMENTS I would like to express my heartfelt gratitude to my major professor Dr.Hualiang Zhang, for his continuous support, knowledge sharing and mentoring throughout my master’s study. It is a great honor working with him. I would like to thank my committee members Dr. Xinrong Li and Dr. Hyoung Soo Kim and all the professors in EE department for their training and support during my study at UNT. I would like to thank all my lab mates and friends for their support, company and cooperation. I would like thank my family for their love and support throughout my study. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS .......................................................................................................... iii LIST OF FIGURES .................................................................................................................... vi LIST OF TABLES..................................................................................................................... viii Chapters INTRODUCTION ....................................................................................................................... 1 1.1 Introduction .................................................................................................................. 1 1.2 Contribution to Thesis .................................................................................................. 2 1.3 Overview of Thesis ...................................................................................................... 2 DUAL BAND COUPLED LINE TRANSMISSION LINE DESIGN ................................................ 4 2.1 Introduction....................................................................................................................... 4 2.2 Design and Simulation Results ......................................................................................... 5 2.3 Conclusion.......................................................................................................................10 APPLICATION OF DUAL BAND TRANSMISSION LINES FOR MICROWAVE DEVICES ........11 3.1 DUAL BAND COUPLER ..................................................................................................11 3.1.1 Introduction ...............................................................................................................11 3.1.2 Design and Simulation results ...................................................................................12 3.1.3 Conclusion ................................................................................................................18 3.2 DUAL BAND WILKINSON POWER DIVIDER .................................................................19 3.2.1 Introduction ...............................................................................................................19 3.2.2 Design and Simulation results ...................................................................................20 iv 3.2.3 Conclusion ................................................................................................................25 TRI-BAND TRANSMISSION LINE STRUCTURE .....................................................................26 4.1 Introduction......................................................................................................................26 4.2 Design and simulation results ..........................................................................................27 4.3 Conclusion.......................................................................................................................31 CONCLUSION AND FUTURE WORK ......................................................................................32 5.1 Conclusion.......................................................................................................................32 5.2 Future work .....................................................................................................................32 v LIST OF FIGURES Fig: 2.1 Topology of Coupled line Structure……………………………………………4 Fig: 2.2 Equivalent circuit model of the coupled lines…………………………………5 Fig: 2.3 Proposed Dual band transmission line structure………………………….....6 Fig: 2.4 Topology of proposed dual band transmission line in hyper lynx 3D………8 Fig: 2.5a Simulation S11 parameter of the proposed structure…………………….…8 Fig: 2.5b Simulation S21 parameter of the proposed structure……………………….9 Fig: 2.5c Simulation phase of S21 parameter of the proposed structure…………….9 Fig: 3.1 A simple Branch line coupler………………………………………………….11 Fig: 3.2 General schematic of proposed dual-band branch line coupler…………..12 Fig: 3.3 Modified schematic of dual band branch line coupler for simulation……..14 Fig: 3.4a Simulated and measured return loss (S11) of the coupler………………..14 Fig 3.4b Simulated and measured insertion& coupled loss (S21 & S31) of the coupler……………………………………………………………………………15 Fig: 3.5 Photo of fabricated dual band coupler……………………………………….16 Fig: 3.6 Simulated and measured phase difference between output ports of the coupler………………………………………………………………………………….…16 Fig: 3.7 Normalized impedances at different frequency ratios ……………………..17 vi Fig: 3.8 Basic Wilkinson power divider…………………………………………………..19 Fig: 3.9 Replacement of a quarter wavelength transmission line with dual band transmission line……………………………………………………………………………20 Fig: 3.10 Proposed dual band Wilkinson power divider………………………….........21 Fig: 3.11 Modified schematic of dual band Wilkinson power divider for simulation...22 Fig: 3.12 Simulation return loss (S11) of the proposed structure………………………23 Fig: 3.13 Simulation (S21&S31) of the output ports of the power divider………………24 Fig: 3.14 Simulation Phase difference between output ports of the power divider…..24 Fig: 4.1 Proposed Tri-band transmission line structure………………………..............26 Fig: 4.2 Topology of proposed tri band transmission line in hyper lynx 3D………......29 Fig: 4.3 Simulation return loss (S11) of the tri band structure…………………………..30 Fig: 4.4 Simulation insertion loss (S21) of the tri band structure………………………..30 vii LIST OF TABLES Table: 3.1 Comparison between simulated and measured insertion loss values…15 Table: 3.2 Comparison between S-Parameters at output ports……………………..23 viii CHAPTER 1 INTRODUCTION 1.1 Introduction Recent advancements in the field of communications resulted in increased demand for high efficient microwave devices. This led the research field to search for new options for reducing the cost, size and flexibility of the devices. Design of multi-band and wide band microwave devices is one of the major ways to satisfy needs of the communication world. The current high data rate devices like WLAN require larger bandwidth and the flexibility to operate at multiple frequencies. Design of dual, tri and quad band microwave devices is an important aspect and therefore is the current field of interest for the researchers. Usage of Microstrip to design microwave devices is restricted because of high losses, low output yield and lesser power handling capacity. But, micro strip lines are less expensive than a wave guide. Coupled line structures are more useful than a conventional transmission lines. Design of coupled lines in an inhomogeneous medium like microstrip will result in increased usability of these structures in microwave devices as they increase the efficiency of microwave devices. Design of multi band structures using these structures will result in development of low cost devices with size adaptability. 1 1.2 Contribution to Thesis This thesis provides design of novel dual and tri band microwave devices. 1) A dual band transmission line structure using coupled lines has been designed along with design equations. 2) Two microwave devices i.e., a branch line coupler and a Wilkinson power divider are designed and fabricated. 3) A tri band transmission line structure is developed by attaching stubs to the dual band coupled line structure. The design equations are provided and simulation results are derived. 1.3 Overview of Thesis In this thesis, two dual band microwave devices and a tri band transmission line structure are proposed. In chapter 2, design of a novel dual band transmission line is presented. Dual band operation is achieved by adding two quarter wave length open circuit stubs to a coupled line which are identical and parallel to each other. Design equations are derived using ABCD parameters. The ideally designed structure is simulated using ADS EM simulator and the practical simulation is done in Hyper Lynx 3D EM. In chapter 3, implementation of the dual band structure is done with microwave devices. First, we have designed a dual band branch line coupler which is highly useful in mixers and modulators. The conventional quarter wavelength transmission line of the branch line coupler has been replaced with the dual band transmission line to achieve dual band operation. Flexibility of the device is observed by examining the frequency ratio of the two arbitrary frequencies. To verify the design, a branch line coupler operating at 0.95GHz and 1.52 GHz is designed and fabricated on a Roger’s board. The simulated 2 and measured results show good agreement with each other. Later, a dual band Wilkinson power divider is designed using the same dual band transmission line structure. The designed structure is simulated in Hyper Lynx 3D EM and the simulated results at the two output ports are almost equal in both magnitude and phase. In chapter 4, a tri band transmission line structure is designed by attaching two /8 transmission lines to the proposed dual band structure. Closed form design equations are derived using ABCD parameters and the designed structure is simulated with fullwave electromagnetic simulator. Finally, in chapter 5, conclusion and future work are presented. 3 CHAPTER 2 DUAL BAND COUPLED LINE TRANSMISSION LINE DESIGN 2.1 Introduction Electromagnetic coupling which exists between parallel coupled transmission lines in an inhomogeneous medium like microstrip shows large variation with that of a homogeneous medium. The difference is mainly because of the even and odd mode excitation signals traveling with different phase velocities. The difference in the phase velocities prevents the formation of pure TEM wave propagation. For the above condition, two identical microstrip transmission lines of length “l” and width “w” are coupled and are separated by a gap “g”. The schematic below shows the topology of the proposed structure. Fig: 2.1 Topology of Coupled line Structure Here V1, V2, V3 & V4 are the voltage inputs at the four ports respectively. By considering the voltage inputs at ports 2 & 3 equal to 0 and by even-odd mode analysis, the equivalent circuit from the above model becomes 4 Fig: 2.2 Equivalent circuit model of the coupled lines The ABCD parameters for this equivalent circuit is A = D= B = + + 2 + 2 +2 ( − )) ( 2( +) C =j 2 + (2.1) (2.2) (2.3) 2.2 Design and Simulation Results Many dual band transmission line designs using conventional quarter wavelength transmission lines have been proposed recently. In this proposed transmission line design, two open circuited stubs with electrical length θ are attached to the two ends of the coupled line structure in the form of a Pi-Shape. The structure of the proposed dual band transmission line is shown in Fig. 2.3. 5 Za, Port 1 Port 2 Z1, Z1, Fig: 2.3 Proposed Dual band transmission line structure Here Za, = (Zoe, e, Zoo, o) By considering the ABCD parameters of the proposed structure, we have � + 1 0 + �� 2 1 + � = � 2 + 2 +2 ( − )) ( For = = , (2.4) becomes 1 � 0 � � 1 2 (+) � 2 2 + (+) 2 For + = , (2.5) results in − 2( +) + 1 � � − 2 2 0 1� � 1 � � (2.4) (2.5) (2.6) For a quarter wavelength transmission line, A=D=0 i.e. − 2 = 0 Hence = 2 2 6 0 � 1 (2.7) The total ABCD matrix of the proposed structure becomes � 0 � = � 2 2 0 �=� 0 ± 1 To satisfy dual band operation, the necessary condition is ± 0 � (2.8) 1 = ±2 (2.9a) 2 = ±2 (2.9b) Here 1 and 2 are the electrical lengths at the two desired operating frequencies. The above design equations can be solved using 2 = ± 1 , = 1,2,3,4 … … … And 1 2 = 1 2 (2.10a) (2.10b) By considering the two operating frequencies pre-assigned, we can deduce the electrical lengths from equations (2.10a) and (2.10b). We can further calculate the impedance values from (2.7), (2.9a) and (2.9b). The two operating frequencies taken into consideration are 1 GHz and 1.6 GHz with 2 � =1.6. Using the design equations presented above, the impedances and electrical 1 lengths of all the stubs have been calculated. The values are, for = 50, 1 = 1 , 1 = 138.46 , 1 =150.8, Z1=59.18. The above configuration is simulated with the commercial electromagnetic simulator HyperLynx 3D EM. Fig. 2.4 shows the proposed transmission line design. 7 Topology of proposed dual band transmission line in Hyper Lynx 3D EM. The simulated S-parameter results of the above structure are shown in Fig. 2.5. 0 -10 S11(dB) -20 -30 -40 -50 -60 0.50 S11 0.75 1.00 1.25 1.50 1.75 2.00 Freq(GHz) Fig: 2.5a Simulated S11 parameter of the proposed structure 8 5 S21 0 -5 -10 S21(dB) -15 -20 -25 -30 -35 -40 -45 -50 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Freq(GHz) Fig: 2.5b Simulated S21 parameter of the proposed structure Ang S21 150 100 Phase 50 0 -50 -100 -150 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Freq(GHz) Fig: 2.5c Simulated phase of S21 parameter of the proposed structure From the figure above (Fig: 2.5a), we observed a significant return loss (S11<-40 dB) at both of the operating frequencies, which indicates good impedance matching. From Fig: 2.5b, it is observed that the insertion loss is approximately equal to 0 dB at the two 9 operating frequencies. The Phase S21 at these frequencies as shown in Fig: 2.5c is 89.5o and 90.8o respectively. 2.3 Conclusion From all the above observations, the proposed dual band quarter wavelength transmission line design works pretty well at the proposed frequencies. 10 CHAPTER 3 APPLICATION OF DUAL BAND TRANSMISSION LINES FOR MICROWAVE DEVICES 3.1 DUAL BAND COUPLER 3.1.1 Introduction Branch line couplers are 3dB couplers with a 90o phase difference between through and coupled output ports. They are also called quadrature hybrids. The basic function of a branch line coupler is that power entering from port 1 is divided between ports 2 & 3 with a 90o phase shift. The basic configuration of a typical branch line coupler is shown in Fig: 3.1. /(√2) Port 1 Port 2 Port 4 Port 3 /(√2) A simple branch line coupler In Fig: 3.1, Zo is the normalized characteristic impedance, which is normalized to 50Ω. 11 In the past, usage of coupled lines in an inhomogeneous medium has been discussed [1]. There are certain designs on development of single band branch line couplers using coupled lines [2]. Designs of dual-band structures using different non-coupled and coupled transmission line structures have also been proposed [3-19]. However, further performance improvement is needed for the design of dual band structures. 3.1.2 Design and Simulation results In the proposed work, the conventional quarter wavelength transmission line of the branch line coupler is replaced with the dual band transmission line from the previous chapter to design a dual band branch line coupler. The structure of the proposed dual band coupler is shown in Fig: 3.2. Za2, Port 1 Z1, Z2, Port 2 Z2, Za1, Z1, Z1, Za1, Z2, Z2, Z1, Port 3 Port 4 Za2, 12 Figure: 3.2 General schematic of proposed dual-band branch line coupler (Za1 = impedance of the coupled line used for the 50 Ω branch; Za2 = impedance of the coupled line used for the 35.35 Ω branch; Z1 = impedance of the open circuited stub used for the 50 Ω branch; Z2 = impedance of the open circuited stub used for the 35.35 Ω branch). From the dual band transmission line design above, the design equations for the impedances within the proposed coupler are = 2 2 1 = 2 (3.1) (3.2) By using the proposed dual-band transmission line structure, we have designed the dual-band coupler by replacing the 50Ω transmission line with a 50Ω quarter wavelength Pi-shaped coupled line structure and 35.35Ω transmission line with a 35.35Ω quarter wavelength Pi-shaped coupled line structure in a conventional branch line coupler. To validate the performance of the proposed dual band coupler, an experimental prototype has been designed and fabricated. For simplicity of the simulation, the open circuited stubs Z1 and Z2 are combined to form Z (Z = Z1 ∥Z2). The two working frequencies under considerations are 0.95GHz and 1.52GHz. Here 2 � =1.6. For these 1 values, using the design equations presented above, the impedances and electrical lengths of all the stubs have been calculated. The values are, for = 50, 1 = 0.95, 1 = 138.46 , 1 =150.8 , Z1=59.18 and for = 35.35, 1 = 0.95, 1 = 138.46 , Z2 = 106.62 Z2=41.85. From Z1 and Z2, we get Z=24.5165 and 1 = 138.46 . 13 The dielectric constant and thickness of the PCB substrate are 2.2 and 0.7871mm, respectively. The loss tangent is 0.001. The HyperLynx 3D EM design layout for the proposed dual band coupler is shown in Fig: 3.3. Fig: 3.3 Modified schematic of dual band branch line coupler for simulation 0 -5 S11(dB) -10 -15 -20 S11 Mea S11 Sim -25 0.6 0.8 1.0 1.2 freq(GHz) 14 1.4 1.6 Fig: 3.4a Simulated and measured return loss (S11) of the coupler. 0 S21 & S31(dB) -20 -40 -60 S21-Mea S31-Mea S21-Sim S31-Sim -80 -100 0.6 0.8 1.0 1.2 1.4 1.6 freq(GHz) Fig 3.4b Simulated and measured insertion& coupled loss (S21 & S31) of the coupler. Figure 3.4 provides the simulated and measured results of S-parameters of the designed dual band coupler. From Fig: 3.4a, we can observe that return loss (S11) is less than -22dB at 0.95GHz and less than -18dB at 1.52GHz. From Fig: 3.4b, the simulated and measured results of S21 & S31 are given. The following table shows a comparison between these results. Frequency S21 S31 0.95GHz -3.6dB(sim) -3.6dB(sim) 0.95GHz -4.1dB(mea) -3.8dB(mea) 1.52GHz -3.6dB(sim) -3.7dB(sim) 15 1.52GHz -4.1dB(mea) -4.1dB(mea) Table: 3.1 Comparison between simulated and measured insertion loss values. The photo of the fabricated dual band coupler is shown in Fig: 3.5. Fig: 3.5 Photo of fabricated dual band coupler. As shown in Fig: 3.6, the phase difference between the two output ports (2&3) is -90.1° at 0.95 GHz and 89.7° at 1.52 GHz, respectively. PD mea PD sim 300 Phase Difference(PD) 200 100 0 -100 -200 16 -300 0.6 0.8 1.0 1.2 freq(GHz) 1.4 1.6 Fig: 3.6 Simulated and measured phase difference between output ports of the coupler. The bandwidth of the coupler is about 50 MHz at two design frequencies assuming that the mismatches between amplitude and phase values are less than 0.5 dB and 1°. In Fig: 3.7, the required impedances (note: they are normalized to 50 Ω) of the proposed coupler under different frequency ratios are also plotted. For practical issues, the impedance values taken into consideration are between 20 Ω and 120 Ω for open circuited stubs (Z) and 200 Ω to 350 Ω for coupled line structures (Zx). In addition to the frequency ratio range shown in Fig: 3.7, the coupler is also able to work well for the frequency ratio above 2. Z Zx 6.0 5.5 Normalized Impedance 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1.3 1.4 1.5 1.6 frequency ratio 17 1.7 1.8 Fig: 3.7 Normalized impedances at different frequency ratios (Here Zx = Impedance of coupled line structure; Z =Impedance of open circuit stub). 3.1.3 Conclusion Closed form design equations of dual band branch line couplers are derived using ABCD matrices. An experimental prototype has been fabricated and measured. The simulated and measured results show good agreement with each other, validating the proposed design theory. 18 3.2 DUAL BAND WILKINSON POWER DIVIDER 3.2.1 Introduction Invented by Ernest Wilkinson, Wilkinson power dividers are a specific class of power dividers where it achieves isolation between the two output ports. The two output ports are equal in magnitude and phase. By matching the output ports, the Wilkinson power divider can be lossless by dissipating reflected power from the outputs. The basic form of a Wilkinson power divider is shown in Fig: 3.8. Fig: 3.8 Basic Wilkinson power divider Here Zo is the characteristic impedance of the transmission line (Zo = 50Ω). The two stubs of the above structure are chosen to be of quarter wavelength. R is the resistance isolating the two output ports 2& 3. 19 When a signal enters port 1, it is split into equal-amplitude, equal-phase output signals at ports 2 and 3. Since each end of the isolation resistor between ports 2 and 3 is at the same potential, no current flows through it and therefore the resistor is decoupled from the input. The two output port terminations will add in parallel at the input, so they must be transformed to 2xZ0 each at the input port to be combined to Z0. 3.2.2 Design and Simulation results A dual band Wilkinson power divider is designed with the help of the dual band transmission line presented in the previous chapter. Specifically, the quarter wavelength transmission lines in the conventional Wilkinson power divider are replaced with the proposed dual band transmission line. Fig: 3.9 Replacement of a quarter wavelength transmission line with dual band transmission line The equivalent impedance values from the dual band transmission line structure (Equations 3.1 &3.2) are = 2 2 1 = 2 20 The structure of the proposed dual band Wilkinson power divider is shown below. Fig: 3.10 Proposed dual band Wilkinson power divider The above structure is simulated using HyperLynx 3D EM simulator with a dielectric constant 2.2, substrate thickness 0.787 mm and loss tangent 0.0001. The two open circuit stubs of transmission line are joined due to the design complexity near port 1. By taking the two frequencies into consideration as 2 � =1.8, and using the design 1 equations presented above, the impedances and electrical lengths of all the stubs have 21 been calculated. They are Z1 = 142.2Ω, Zx = 180.85Ω, θ = 124.12o. All the above values are determined by considering the characteristic impedance Zc = 50Ω. The EM simulator model of the designed dual band Wilkinson power divider is shown in Fig: 3.11. Fig: 3.11 Modified schematic of dual band Wilkinson power divider for simulation In Fig: 3.11, the ports 4 and 5 are localized ports for MMIC to connect the 100Ω resistor to the output ports of the power divider. The simulated S-parameter results of the proposed structure is 22 5 0 -5 -10 S11(dB) -15 -20 -25 -30 -35 -40 -45 0.50 S11 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Freq(GHz) Fig: 3.12 Simulated return loss (S11) of the proposed structure We can observe that the return loss (S11) at the two frequencies is S11 = -31.2 dB at 1 GHz and S11 = -36.4 dB at 1.8 GHz. The following table shows the comparison of S21 and S31 at the two output ports Frequency S21 S31 1 GHz -3.21dB(sim) -3.19dB(sim) 1.8 GHz -3.26dB(sim) -3.23dB(sim) Table: 3.2 Comparison between S-Parameters at output ports As shown in Table: 3.2 and Fig: 3.13, the magnitude difference between S21 and S31 at the two frequencies is less than 0.1dB showing an equal division of power between the two output ports. 23 5 S21 S31 0 -5 -10 S21(dB) -15 -20 -25 -30 -35 -40 -45 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Freq(GHz) Fig: 3.13 Simulation (S21 & S31) of the output ports of the power divider 3.0 Ang S31-Ang S21 Phase Difference(Deg) 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 0.75 1.00 1.25 1.50 1.75 2.00 Freq(GHz) Fig: 3.14 Simulation Phase difference between output ports of the power divider 24 The phase difference between the two output ports is shown in Fig: 3.14. We can observe the phase difference between the two output ports is less i.e., around 0.5 at the two operating frequencies. 3.2.3 Conclusion A dual band Wilkinson power divider using coupled line structure has been proposed and designed. Theoretical and simulation analysis show a good match with each other. 25 CHAPTER 4 TRI-BAND TRANSMISSION LINE STRUCTURE 4.1 Introduction Design of tri band microwave devices has always been challenging as theoretical analysis to design a tri band transmission line structure is quite complex. Very few tri band transmission line structures have been developed recently. Some of these designs are implemented with the use of inductors and capacitors, and some are realized with the use of resistors. There are also tri band designs with the use of extended stubs. In this chapter, we presented a novel design of a tri band transmission line structure, which is achieved by attaching two stubs to the two ends of the dual band transmission line structure presented in the chapter 2. The figure below shows the structure of the proposed tri band transmission line. Fig: 4.1 Proposed Tri-band transmission line structure 26 The stub Z1 is connected to the dual band transmission line to realize the tri band operation. Here the electrical length for the extended stub is half the electrical length of the coupled line structure. 4.2 Design and simulation results By considering the ABCD parameters of the proposed tri band transmission line, it is derived as: � �= �2 1 �2 1 � � � � 2 2 �2 � 1 0 �2 1� � �2 1 � 2 1 � = 1 2 2 1 + 0 + 1� � 2 + 2 + 2 +2 ( − )) ( 2( +) + �× + 1 �2 � �2 (4.1) For = = , (4.1) becomes �= �2 1 �2 1 � � � � 2 �2 � 1 0 � � 2 1 (+) (+) 2 1 � � 0 �2 �� 1 �2 1 �2 � �2 1 (4.2) = � �2 �2 1 1 �2 − 2 �� 2 �2 27 2 − 2 �� �2 �2 1 1 �2 �2 (4.3) � The ABCD matrix of a quarter wave length transmission line is 0 � � = � ± ± 0 � (4.4) By equating the equivalent ABCD parameters to that of the quarter wavelength transmission line, we have 2 = 2 2� − 1 − � 41 (4.5) And by taking Z1 as the required characteristic impedance for simplicity, we have Zx in the form of a quadratic equation of degree 2. 2 �2 + 21 2 2 �2� + [212 2 − 412 − 1 2] + �412 2 − 413 2 �2� = 0 (4.6) From equations 4.5 & 4.6, two possible solutions for the electrical length are available between 0 and π by taking the values of Z1, Z2 &Zx as constant. The relationship between electrical length θL and two arbitrary operating frequencies f1 and f2 is given by: = �1 + 2 (4.7) 1 There is a special condition for θ=π/2 where the given circuit can be realized as a quarter wavelength transmission line with electrical length π/2 and impedance equal to 28 the characteristic impedance. The frequency associated with this quarter wavelength transmission line is f3 which is the average of the two arbitrary operating frequencies. 3 = 1 +2 (4.8) 2 By taking the two frequencies into consideration and by solving the quadratic equation for Zx and putting it in Z2, we get the required impedance values at the given electrical lengths. By taking f1 and f2 as 1.5 GHz and 3 GHz, we have θ = 60o, Zx = 117Ω, Z1 = 70.7Ω & Z2 = 32.6Ω. The third frequency f3 is 2.25GHz. A tri band transmission line structure has been designed using the above obtained values. It is simulated using the HyperLynx 3D EM simulator. The design parameters taken into consideration are dielectric constant =2.2, substrate thickness = 0.787mm and loss tangent of 0.0001. The figure below shows the EM simulator model for the tri band transmission line structure. Fig: 4.2 Topology of proposed tri band transmission line in hyper lynx 3D 29 The S-parameter simulation results are shown in the following graphs (Fig: 4.3 and Fig: 4.4). 0 -20 -30 S11 -40 1.0 1.5 2.0 2.5 3.0 3.5 Freq(GHz) Fig: 4.3 Simulated return loss (S11) of the tri band structure 5 S21 0 -5 -10 S21(dB) S11(dB) -10 -15 -20 -25 -30 -35 1.0 1.5 2.0 2.5 3.0 3.5 Freq(GHz) Fig: 4.4 simulated insertion loss (S21) of the tri band structure 30 We can observe that the return loss (S11) at these three operating frequencies is at least -20 dB. The insertion loss (S21) at the three frequencies is less than 0.9 dB. 4.3 Conclusion In this chapter, a tri band transmission line structure has been designed by extending a dual band transmission line structure. Closed form design equations have been derived and the simulated results are in good agreement with the theoretical calculations at the three proposed frequencies. 31 CHAPTER 5 CONCLUSION AND FUTURE WORK 5.1 Conclusion In this thesis, a few novel approaches of designing multi band microwave devices using coupled line structure have been discussed. A new design of dual band transmission line (working at 1 and 1.6GHz) has been proposed. Based on the proposed dual band transmission line structure, two dual band microwave devices have been designed. First a dual band branch line coupler (working at 0.95 and 1.52GHz) is designed and tested. Second, a dual band Wilkinson power divider (working at 1 and 1.8GHz) is designed. By extending the dual band transmission line with two stubs, a tri band transmission line has been designed. For all the designs, the theoretical and practical results show good agreement with each other. 5.2 Future work In the future, more designs of dual band and multi band transmission lines are to be investigated. Efforts should be put in reducing the design complexity of the circuit. Usage of coupled line structures in multiband microwave devices with both symmetrical and asymmetrical structures needs to be studied. 32 REFERENCES [1] G. L. Matthaei, E. Young, and E. M. T. Jones, “Microwave Filters, ImpedanceMatching Networks, and Coupling Structures,” Norwood, MA, USA: Artech House, 1980. [2] D. M. Pozar, “Microwave Engineering”, 2nd. ed, New York: Wiley 1998. [3] H. Zhang and K. J. Chen, “A stub tapped branch-line coupler for dual-band operations,” IEEE Microw. Wireless Compon. Lett, vol. 17, no. 2, pp. 106 – 108, Feb. 2007. [4] N. Zheng, L. Zhou and W.-Y. Yin, “A Novel dual band π-Shaped branch line coupler with stepped impedance stubs,” Progress in Electromagnetics Research Letters., vol. 25, pp. 11-20, 2011. [5] H. Zhang, Y. Peng, and H. Xin, “A tapped stepped-impedance balun with dual-band operations,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 119-122, 2008. [6] H. Kim, B. Lee, and M.-J. Park, “Dual-band branch-line coupler with port extensions,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 3, pp. 651-655, Mar. 2010. [7] X. Wang, W.-Y. Yin, and K.-L. Wu, “A dual-band coupled-line coupler with an arbitrary coupling coefficient,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 4, pp. 945-951, Apr. 2012. [8] K.-K. M. Cheng and Y. Sung, “A Novel Dual-Band 3-dB Branch-Line Coupler Design With Controllable Bandwidths,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 3, pp. 3055 – 3061, Oct. 2012. 33 [9] K.-S. Chin, C. K.-M. Lin, Y.-H. Wei, T.-H. Tseng, and Y.-J. Yang, “Compact DualBand Branch-Line and Rat-Race Couplers With Stepped-Impedance-Stub Lines,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 5, pp. 1213 – 1221, May 2010. [10] L. K. Yeung, W. Cheng, and Y. E. Wang, “A dual-band balun using broadsidecoupled coplanar striplines,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 8, pp. 1995-2000, Aug. 2008. [11] L. K. Yeung, “A Compact Dual-Band 90° Coupler With Coupled-Line Sections,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 9, pp. 2227 – 2232, Sept. 2011. [12] J. Shao, H. Ren, B. Arigong, C. Li, and H. Zhang, “A fully symmetrical crossover and its dual-freuqnecy application,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 8, pp. 2410-2416, Aug. 2012. [13] Y. Li, S. Sun and F. Yang, “Dual-band hybrid patch coupler with embedded spiral open stubs”, In Proceedings of APMC 2012, Vol. 2, December 4-7, 2012, pp. 169 – 171. [14] C. C. Leong, W. W. Choi and K. W. Tam, “A tunable dual-band DGS stub tapped branch-line coupler,” In Proceedings of APMC 2010, Vol. 2, December 7-10, 2010, pp. 1252 – 1255. [15] H. Zhang and X. Hao, “Design of dual-band Wilkinson power dividers with flexible frequency ratios,” In IEEE MTT-S Int. Microw. Symp. Dig., 2008, pp. 1223-1226. [16] K.-S. Chin, Y.-H. Wei, T.-Y. Lin and C.-C. Chang, “Dual-band rat-race coupler with arbitrary power-split ratios,” In 4th International HSIC forum 2012, May 10-11, 2012, pp. 1 – 4. 34 [17] F. Lin and Q.-X. Chu, “A novel compact dual-band branch-line coupler,” In Proceedings of APMC 2010, Vol. 2, December 7-10, 2010, pp. 2595 – 2597. [18] Y. Liu W. Chen and Z. Feng, “Compact dual-band branch-line and rat-race couplers with stepped coupled-line,” In proceedings of CJMW 2011, April 20-22, 2011, pp. 1 – 4. [19] K. Kumari and T. Raghuvir , “Compact fractal shaped, unequal length branch-line coupler for dual-band applications” In Twentieth National Conference on Communications (NCC) 2014, February 28 -March 2, 2014, pp. 1 – 5. [20] H. Zhang and X. Hao, “Designs of dual-band Wilkinson power dividers with flexible frequency ratios,” IEEE MTT-S Int. Microw. Sump. Dig., 2008, pp. 1223- 1226. [21] J. Shao, H. Zhang, C. Chen, S. Tan, and K. J. Chen, “A Compact Dual-Band Coupled-Line Balun with Tapped Open-Ended Stubs,” Progress In Electromagnetics Research C, vol. 22, pp. 109–122, 2011. [22] J. Shao, H. Zhang, Y. Lin, and H. Xin, “Dual-Frequency Electromagnetic Cloaks Enabled by Lc-Based Metamaterial Circuits,” Progress In Electromagnetics Research, vol. 119, pp. 225–237, 2011. [23] H. Zhang and K. J. Chen, “A Stub Tapped Branch-Line Coupler for Dual-Band Operations,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 2, pp. 106–108, Feb.2007. 35 [24] F. L. Wong and K. K. M. Chen, “A Novel, Planar, and Compact Crossover Design for Dual-Band Applications,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 3, pp. 568573, Mar. 2011. [25] J. Shao, H. Zhang, Y. Lin, and H. Xin, “Dual-Frequency Electromagnetic Cloaks Enabled by LC-Based Metamaterial Circuits,” Progress In Electromagnetics Research, Vol. 119, 225-237, 2011. [26] Qaroot A., N. Dib, and A. Gheethan, "Design Methodology of Multi-Frequency UnEqual Split Wilkinson Power Divider Using Transmission Line Transformers," Progress In Electromagnetics Research B, vol. 22, 1-21, 2010. [27] Wu, Y., Y. Liu, S. Li, C. Yu, and X. Liu, "Closed-Form Design Method of an NWay Dual-Band Wilkinson Hybrid Power Divider," Progress In Electromagnetics Research, PIER 101, 97-114, 2010. [28] Heidari, A. A., and M. Heyrani, and M. Nakhkash, "A Dual-Band Circularly Polarized Stub Loaded Microstrip Patch Antenna for GPS Applications," Progress In Electromagnetics Research, PIER 92, 195-208, 2009. [29] Wu, Y., Y. Liu, and S. Li, "Dual-Band Modified Wilkinson Power Divider Without Transmission Line Stubs and Reactive Components," Progress In Electromagnetics Research, PIER 96, 9-20, 2009. [30] J. T. Kuo, T. H. Yeh, and C. C. Yeh, “Design of microstrip bandpass filters with a dual-passband response,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, pp. 13311337, Apr. 2005. 36 [31] Wu, Y., Y. Liu, and S. Li, "An Unequal Dual-Frequency Wilkinson Power Divider with Optional Isolation Structure," Progress In Electromagnetics Research, PIER 91, 393-411, 2009. [32] Wang X. H., L. Chen, X. W. Shi, Y. F. Bai, L. Chen, and X. Q. Chen, "Planar DualFrequency Power Divider Using Umbrella-Shaped Resonator," J. of Electromagn. Waves and Appl., vol. 24, 597-606, 2010. [33] Li J. C., J. C. Nan, X. Y. Shan, and Q. F. Yan, "A Novel Modified DualFrequency Wilkinson Power Divider with Open Stubs and Optional Isolation," J. of Electromagn. Waves and Appl., vol. 24, 2223-2235, 2010. [34] Abu M., M. K. A. Rahim, O. Ayop, and F. Zubir, "Triple-Band Printed Dipole Antenna with Single-Band AMC-HIS," Progress In Electromagnetics Research B, vol. 20, 225-244, 2010. [35] Vegesna S., and M. Saed, "Novel Compact Dual-Band Bandpass Microstrip Filter," Progress In Electromagnetics Research B, vol. 20, 245-262, 2010. [36] R. E. Collin, Foundations for Microwave Engineering, 2nd ed. New York: McGrawHill, 1992. [37] H. Zhang and X. Hao, “Dual-band branch-line balun for millimeter-wave applications,” IEEE MTT-S Int. Microw. Sump. Dig., 2009, pp. 717-720. 37 [38] Lin Z., and Q. X. Chu, "A Novel Approach to the Design of Dual-Band Power Divider with Variable Power Dividing Ratio Based on Coupled-Lines," Progress In Electromagnetics Research, PIER 103, 271-284, 2010. [39] H. Zhang and K.J. Chen, “Design of dual-band rat-race couplers,” IET Microw, Antennas Propag., Vol. 3, no. 3, pp. 514-521, 2009. [40] Y. C. Chiou and J. T. Kuo, private communication Jul. 2011. [41] C. Collado, A. Grau, and F. D. Flaviis, “Dual-band Bulter matrix for WLAN systems,” IEEE MTT-S Int. Microwave Symp. Dig., June. 2005. 38

1/--страниц