DUAL-BAND MICROWAVE COMPONENTS AND THEIR APPLICATIONS. Jin Shao. Thesis Prepared for the Degree of MASTER OF SCIENCE UNIVERSITY OF NORTH TEXAS

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1 DUAL-BAND MICROWAVE COMPONENTS AND THEIR APPLICATIONS Jin Shao Thesis Prepared for the Degree of MASTER OF SCIENCE UNIVERSITY OF NORTH TEXAS December 011 APPROVED: Hualiang Zhang, Major Professor Miguel F. Acevedo, Committee Member Hyoung Soo Kim, Committee Member Shengli Fu, Graduate Program Coordinator Murali Varanasi, Chair of the Department of Electrical Engineering Costas Tsatsoulis, Dean of the College of Engineering James D. Meernik, Acting Dean of the Toulouse Graduate School

2 Shao, Jin. Dual-band Microwave Components and their Applications. Master of Science (Electrical Engineering), December 011, 68 pp., 3 tables, 3 illustrations, references, 91 titles. In general, Dual-Band technology enables microwave components to work at two different frequencies. This thesis introduces novel dual-band microwave components and their applications. Chapter presents a novel compact dual-band balun (converting unbalanced signals to balanced ones). The ratio between two working frequencies is analyzed. A novel compact microstrip crossover (letting two lines to cross each other with very high isolation) and its dual-band application is the subject of chapter 3. A dualfrequency cloak based on lumped LC-circuits is introduced in chapter 4. In chapter 5, a dual-band RF device to detect dielectric constant changes of liquids in polydimethylsiloxane (PDMS) microfluidic channels has been presented. Such a device is very sensitive, and it has significantly improved the stability. Finally, conclusion of this thesis and future works are given in chapter 6.

3 Copyright 011 by Jin Shao ii

4 ACKNOWLEDGEMENTS I would like to thank my major advisor Dr. Hualiang Zhang for his encouragement, knowledge, mentoring, and support throughout my M.S. study. He brought me into the microwave research field, and he helped me find the joy of research. It is my honor to be his student. I would also like to thank all of my friends and lab mates for their company, support, and discussion. These are all very valuable parts in my memory. Thanks to my thesis committee members Dr. Miguel F. Acevedo and Dr. Hyoung Soo Kim and other faculty and staff members of the electrical engineering department for their training and support. Finally, I want to thank all of my family members for their support and love. They give me the power of action, meaning of life. To them I dedicate this thesis. iii

5 TABLE OF CONTENTS Page ACKNOWLEDGEMENTS... iii LIST OF TABLES... vi LIST OF ILLUSTRATIONS... vii Chapters 1.INTRODUCTION Motivation Contributions of the Thesis Overview of the Thesis....A COMPACT DUAL-BAND COUPLED-LINE BALUN WITH TAPPED OPEN- ENDED STUBS Introduction...5. Theoretical Analysis Design Procedure Prototype Fabrication and Measurement Conclusion A NOVEL COMPACT MICROSTRIP CROSSOVER AND ITS DUAL-BAND APPLICATION Introduction Proposed Single-Band Crossover...0 iv

6 3.3 Proposed Dual-Band Crossover Experimental Results Conclusion DUAL-FREQUENCY ELECTROMAGNETIC CLOAKS ENABLED BY LC-BASED METAMATERIAL CIRCUITS Introduction Theoretical Analysis Simulation Results Conclusion DUAL-BAND RADIO-FREQUENCY DEVICE FOR SENSING DIELECTRIC PROPERTY CHANGES IN MICROFLUIDIC CHANNELS Introduction Operating Principle Measurement Results Conclusion CONCLUSION AND FUTURE WORK Conclusion Future Work...55 REFERENCES...56 v

7 LIST OF TABLES Page.1 Calculated stub impedance of proposed balun Fractional bandwidth under different K and corresponding Z1 and θ Calculated LC-loaded circuit parameters for each layer when f1 = 3 GHz and f = 5 GHz...41 vi

8 LIST OF ILLUSTRATIONS Page.1 Modified Marchand balun with a short-ended port (a) Equivalent circuit under even-mode excitation...7. (b) Equivalent circuit under odd-mode excitation Calculated Zoe and Zoo under different Zs (Zout=50 Ω) Calculated Zoe and Zoo under different Zout (Zs = 30 Ω) (a) Calculated even-odd mode impedance with different n for Zs=110 Ω (b) Calculated even-odd mode impedance with different n for Zs=80 Ω (a) Schematic-level simulation results of dual-band balun for GSM system (b) Schematic-level simulation results of dual-band balun for IEEE standard Layout of the proposed dual-band balun Experimental prototype for proposed balun Comparison between simulated and measured results for proposed dual-band balun Comparison between simulated and measured results for proposed dual-band balun Circuit configuration of proposed single-band crossover Reduced networks under different excitations Simulation result of S31 with K = 1.5, K = 1.0 and K = vii

9 3.4 Configuration of proposed dual-band crossover Computed impedances of Za and Zb under different frequency ratios (a) Simulated results of the dual-band crossover: 1 and 1.9 GHz (b) Simulated results of the dual-band crossover: 1 and.3 GHz (c) Simulated results of the dual-band crossover: 1 and.8 GHz Top view of the proposed single-band and dual-band crossovers Simulated and measured results of magnitude of S11 and S31 (single-band crossover) Simulated and measured results of magnitude of S1 and S41 (single-band crossover) Simulated and measured results of magnitude of S11 and S31 (dual-band crossover) Simulated and measured results of magnitude of S1 and S41 (dual-band crossover) Schematic of the proposed dual-band cloak The general circuit model with the analogy to the effective medium (a) Schematics of the LC-loaded circuits for the medium in θ direction (b) Schematics of the LC-loaded circuits for the medium in z direction The proposed LC-loaded circuit with multiple resonances to suppot dual-frequency operation (a) The E-field distributions of the proposed dual-frequency cloak at 3GHz...40 viii

10 4.5 (b) The E-field distributions of the proposed dual-frequency cloak at 5GHz (c) The E-field distributions of the proposed dual-frequency cloak at 4GHz (a) The calculated differential scattering cross sections of the proposed cloak along with the results for the bare PEC at 3GHz (b) The calculated differential scattering cross sections of the proposed cloak along with the results for the bare PEC at 5GHz Calculated normalized total scattering cross section of the proposed dual-frequency cloak over the frequency range from GHz to 6 GHz Schematic of the proposed dual-band RF dielectric measurement device A tapped stub structure Photo of the fabricated dual-band RF dielectric measurement device with PDMS microfluidic channels (a) Measured S1 using the proposed dual-frequency RF sensor at first operating frequency (b) Measured S1 by using the proposed dual-frequency RF sensor at second operating frequency...5 ix

11 CHAPTER 1 INTRODUCTION 1.1 Motivation With the rapid advance in wireless communications, the design of many passive circuits is facing new challenges including compact size, wide bandwidth, and multi-band operations. For example, high data-rate wireless communication systems, such as worldwide interoperability for microwave access (WiMAX) and wireless local area network (WLAN), require bandwidths up to several hundred megahertz and flexibility in operating across multiple frequency bands. Among all of these new requirements, dualband operation is very important. It can lead to both size and cost reduction of the whole system. Due to these reasons, dual-band technology is the subject of research at component level, system level, and product level (new apple TV works at.4ghz and 5GHz). As an important topic, the concept of invisible cloak has drawn much attention in the physics and materials science fields. Many novel methods have been presented to realize invisible cloaks. By implementing dual-band technology, a cloak can simultaneously operate at two frequencies, which can greatly improve its performance. Dielectric measurement is widely used to identify biological and chemical samples. Because of the advantages of simple operation, instant testing, and no chemical modification, dielectric measurement has also drawn much research attention. For radio- 1

12 frequency (RF) dielectric measurement devices, since a vector network analyzer is normally needed to collect the measurement data, RF dielectric measurement devices have the potential of integration and parallelization. By combining dual-band technology with microfluidics, the resulting dual-band RF dielectric measurement devices can be used to detect dielectric change at two frequencies. Overall, this process will enhance the stability of the devices. 1. Contribution of Thesis In general, dual-band technology enables microwave components to work at two different frequencies. This thesis introduces novel dual-band microwave components. To be specific; 1) A compact dual-band balun (converting unbalanced signals to balanced ones) is designed, including full design equations. The ratio between two working frequencies is analyzed. ) A four port symmetric dual-band crossover (letting two lines cross each other with very high isolation) is introduced for the first time. 3) For cloaking applications, a microwave dual-band cloak is designed based on lumped LC-circuits. 4) For RF dielectric measurement device, a dual-band RF sensor is designed and fabricated. It has significantly enhanced the stability of the sensor. 1.3 Overview of Thesis This thesis presents two microwave dual-band components, a dual-frequency cloak, and a dual-band RF sensor.

13 Chapter presents a novel compact dual-band balun. The proposed structure is based on modified Marchand balun (with the fourth port shorted). To achieve the desired dual-band operation, two additional open-ended stubs are added to the two balanced ports of the modified Marchand balun. Explicit design equations are then derived using evenodd mode analysis. Finally, to verify the design concept, a microstrip balun operating at 0.9 and GHz is fabricated on Duroid RO310 printed circuit board. Measurement results are in good agreement with the theoretical predictions. A novel compact microstrip crossover and its dual-band application is the subject of chapter 3. The proposed single-band crossover has a compact size, an easily controlled bandwidth, and a flexible frequency ratio between the two working frequencies. The design equations are derived using the even-odd mode method. The final design equation is very simple. To verify the design concepts, both a single band crossover working at 1 GHz and a dual-band crossover working at 1 and.3 GHz are fabricated and tested. The measurement results agree well with the design theory. A dual-frequency cloak based on lumped LC-circuits is introduced in Chapter 4. Multiple LC-resonant tanks are employed to satisfy the specific conditions for dualfrequency operations. In this way, the designed cloak features greatly reduced scattering cross sections at the two working frequencies simultaneously. In addition, explicit design equations are derived for the developed circuit systems. Based on these formulas, the range of the realizable frequency ratio of the presented cloak (the ratio between the two operating frequencies) is discussed. To verify the theoretical predictions, full-wave 3

14 electromagnetic simulations are carried out. A good consistency between the numerical results and the design theory is achieved. In chapter 5, a dual-band RF device to detect dielectric changes in polydimethylsiloxane (PDMS) microfluidic channels is introduced. Such a device, which consists of two dual-band Wilkinson power dividers (working at GHz and 5GHz) and two 90 o dual-band transmission lines (provide 180 o phase difference at two operation frequencies), is very sensitive, and it has significantly improved the stability. Compared with the recently reported RF sensor [88], the proposed device provides detections at two frequencies so that the measurement stability is enhanced while holding the same measurement sensitivity (-80dB cancellation level). Dual-band technology is very attractive because it can be used to design dualband microwave components; moreover, it also can be implemented into other related research fields. Finally, conclusion of this thesis and future works are given in chapter 6. 4

15 CHAPTER A COMPACT DUAL-BAND COUPLED-LINE BALUN WITH TAPPED OPEN-ENDED STUBS.1 Introduction A balun is a microwave device for converting unbalanced signals to balanced ones, and vice versa [1]-[3]. Such conversion is attractive, especially for differentialmode RF / microwave circuits, since it will lead to improved signal timing and reduced electromagnetic interference and noise. Baluns can also be used as 180 o hybrids, which further extends their applications [4]. The conventional baluns can be categorized into two types, namely, active and passive baluns. For active baluns, the transistors employed will consume more energy [5]. As for passive baluns, they can be further classified as lumped-type and distributed-type baluns [6]-[8]. The disadvantage of lumped-type balun is its difficulty to maintain the 180 o phase difference and equal magnitude responses between the two signals. The distributed-type Marchand balun features low loss, uniplanar structure, and low cost [9]. Therefore, this kind of balun is attractive for practical applications. Meanwhile, with the rapid advance in wireless communications, the design of many passive circuits is facing new challenges including compact size, wide bandwidth and multi-band operations. For example, high data-rate wireless communication systems, 5

16 such as worldwide interoperability for microwave access (WiMAX) and wireless local area network (WLAN), require wide bandwidths up to several hundred megahertz and flexibility of operating in multiple frequency bands. Among all of these new requirements, multi-band operation is very important. It can lead to both size and cost reduction of the whole system. For balun design, different topologies have been studied for size reduction [10]- [13] and bandwidth enhancement [14]-[16]. Research on multi-band baluns, however, is limited. A dual-band balun is achieved by replacing the uniform coupled-lines with tapered coupled-lines in a Marchand balun [17]. Another dual-band balun has been proposed using stepped impedance resonators in the coupled-line Marchand balun [18]. This structure features multiple coupled units that need careful tuning and tight control of the prototype fabrication. In [19], based on the conventional Marchand balun, a dualband balun was achieved by attaching two open stubs. Apart from the Marchand-type balun, another dual-band balun based on branch line structure has also been proposed in [0] and [1]. This design has a good performance and it is easy to fabricate. This chapter proposes and demonstrates a novel compact structure of dual-band baluns. In this structure, two open-ended stubs are connected at the balanced ports of a modified Marchand balun. By adjusting stub impedances and coupled-line even-odd mode impedances, the desirable equal-amplitude and out-of-phase responses can be achieved at two operating frequencies. For the purpose of experimental demonstration, a microstrip balun working at 0.9 and GHz is fabricated on printed circuit boards (PCB). The measurement results verified our design concept. 6

17 . Theoretical Analysis A 3-port balun circuit can be obtained by terminating one port of a symmetrical 4- port network with arbitrary port impedances [17]. Fig..1 illustrates an example of realizing 3-port baluns based on 4-port network, with short termination at one specified port. All the coupled-line sections are quarter-wavelength long. It is noted that the modified Marchand balun is realized with short-termination. Port1 Port Port4 s/c Port 3 Fig..1 Modified Marchand balun with a short-ended port 4. θ s θ s θ c T e θ c T o Γ e Y out Γ o Y out Y in Y in Y even Y odd (a) (b) Fig.. (a) Equivalent circuit under even-mode excitation. (b) Equivalent circuit under odd-mode excitation. 7

18 To achieve dual-band operation, two additional stubs are attached at two balanced ports of the modified Marchand baluns. The electrical length of the coupled line section in this balun is θ c, and the length of the shunted stubs is θ s. An intuitive explanation of the design concept is that these shunted stubs introduce a transmission zero in the pass-band so that the fundamental band splits into two separate operating bands. In addition, it is found that θ s must be an integer multiple of θ c. Impedance of the stub and the even-odd mode impedances are functions of input/output impedances of the balun. Detailed mathematical derivations of these parameters will be provided now. Even- and odd-mode circuits are shown in Fig..(a) and (b). Γ e and Γ o are the input reflection coefficients of the even- and odd-mode circuits, while T e and T o are the corresponding transmission coefficients. Γ is the reflection coefficient of port 4. The following equations have been derived for synthesizing this kind of 3-port baluns [17]. T e (1 ( e o ) o ) 0 (-1a) e o ( e e o o ) 0 (-1b) Equation (-1a) ensures that S 1 = S 31, while the second equation (-1b) considers the matching condition at port 1 (input port), S 11 = 0. These equations imply that, to achieve perfect amplitude and phase balance, the balun has to present a transmission stop for the even-mode circuit, that is T e = 0. When it comes to the oddmode circuit, the solution will vary depending on the termination of port 4. In practice, a useful condition is: 8

19 9 1 e and 3 1 o (-) By substituting Y even, Y odd and Y in (defined in Fig..) into (-1b), more insightful conclusions are obtained [18]: in odd even Y Y Y 1 1 (-3) In our case, the even-mode circuit (Fig..(b)) of proposed dual band balun structure is naturally a transmission stop network for all bands. In fact, this is one of the ten typical two-port coupled-line structures discussed in [19]. The odd-mode circuit is to be discussed below to show how to derive Y even and Y odd. First, we write the ABCD matrix of the even mode circuit, then from the ABCD matrix, S 11 can be derived. Finally, from S 11 we can derive Y even. The odd mode derivation follows the same procedure. After that, we separate real and imaginary parts of derived admittance and list them as follows: Y even (real) = (-4) Y even (imaginary) = (-5) Y odd (real) = (-6) ] ) [( 16 ] ) ( [ ) ( ) ( 1 3 out s s s s out s s out Y t Y c a t Y c a b a e b a e Y t Y c d a b a c Y a 3 16 ] ) ( ) ( )[ ( 16 3 ] ) ( [ ) ( 4 out s s s s out s s s s Y c a t Y c a t Y c a b a e b a e c d Y a t Y c a t Y c a e b a c b a a ] ) [( 16 ] 8 [ 4 ] 4 4 [ 4 out s s s s out s s out s s out Y t Y d t Y d c a c a Y d b t Y Y d t Y d c a Y c a

20 Y odd (imaginary) = (-7) ac{ b a d a cys ts 4d [( Ys ts) 4 ac[ a c 8d Ys ts] 16d ( Y s Y t s ]} 4b Yout ) out c Ys t s Y odd and Y even are even- and odd-mode admittances of the coupled-line unit, a = Y odd + Y even, b = Y odd - Y even, c = sin(θ s ), d = sin(θ c ), e = cos(θ c ),Y s is admittance of the stub (with a length of θ s as shown in Fig..). θ c and θ s are electric lengths of the coupled-line sections and the shunted stubs, respectively. Y odd and Y even are then derived as functions of θ c, θ s, Y in, Y out and Y s, assuming: s n c (-8) We can predict the following proprieties of Y even and Y odd versus θ c : They are periodic and symmetrical in nature with period equating to π, since θ c and π - θ c give the same expression. This is the intrinsic property of proposed structures for dual band operation. Fig..3 Calculated Z oe and Z oo under different Z s (Z out =50 Ω). 10

21 Fig..4 Calculated Z oe and Z oo under different Z out (Z s = 30 Ω). Applying Eqs. (-1) (-8), Fig..3 shows the solutions of Z oe, Z oo (characteristic impedance for the even and odd modes) in a Ω system. We set n=1 for the most compact design. It can be seen that the proposed balun could be realized by practical values of Z oe and Z oo with θ c between 30 o and 60 o as well as 10 o and 160 o depending on the values of stub impedance Z s. In general, the required values of Z oe and Z oo increase with increasing Z s. For θ c in the 0 o to 90 o range, Z oo decreases monotonically with increasing θ c, while Z oe decreases first and then increases rapidly, in which a minimum value exists. Fig..4 shows the solutions in impedance transforming system (input and output ports have different impedance). In Fig..4, the output-input impedance ratio is not less than 1, when the ratio increases, the distance between even and odd mode impedances decreases, leading to a decreased coupling coefficient. This implies a higher impedance transformation ratio that is easier to implement in practice. 11

22 Z 0e, Z 0o ( ) Z 0e, Z 0o ( ) The above discussion is based on an n = 1 situation, which means that the stub and the coupled line have the same length. For a larger n, larger design flexibility can be achieved. Fig..5 shows the even-odd mode impedances when n equals to 1, and 3. These parameters are calculated in a Ω system. In Fig..5(a), the shunted stub impedance (Z s ) is 110 Ω. We can see that n = 1 case only covers 57 o to 70 o for θ c, n = case covers 33 o to 43 o while n = 3 case covers o to 30 o. Fig..5(b) shows the calculated results when stub impedance (Z s ) is 80 Ω. Compared with results shown in Fig..5 (a), the practical frequency range changes somewhat with different n. But the overall trend stays the same. These examples show clearly the influence of n on the proposed designs Ω n=1 Z 0e n=1 Z 0o n= Z 0e n= Z 0o n=3 Z 0e n=3 Z 0o Ω n=1 Z 0e n=1 Z 0o n= Z 0e n= Z 0o n=3 Z 0e n=3 Z 0o c (Degree) c (Degree) (a) (b) Fig..5 (a) Calculated even-odd mode impedance with different n for Z s =110 Ω and (b) Z s =80 Ω. 1

23 .3 Design Procedure The design procedure of the proposed dual-band balun could be summarized as the following steps: (1): The electric length of the coupled line is 90 o at the middle frequency of two operating bands. The length of coupled line should be designed first. (): Due to the linear relation between frequency and electrical length or physical length, we can calculate the electrical length at lower frequency and higher frequency band as ( f / f 1 ) 90 and ( f / f ) 90, respectively. According to input-output impedances of the system, we can get different combinations of even-odd mode impedances at smaller and larger electrical lengths with respect to lower and higher frequency bands for different n values. These impedances are the same due to the symmetrical properties. In practice, we should choose the smallest n and appropriate stub impedance which can satisfy design requirements and ensure that the resulting even-odd mode impedances can be realized in practical fabrication. (3): According to n, we can compute the lengths of shunted stubs. From stub impedance and even-odd mode impedances, we can finally calculate the physical dimensions of proposed balun. Table.1 shows some typical combinations of dual operation frequencies. Since GSM system and IEEE standards are often used, corresponding design parameters for them are listed in this table. It could be easily implemented using different fabrication techniques. The schematic-level simulation results are shown in Fig

24 S_Parameters [db].4 Prototype Fabrication and Measurement To demonstrate the feasibility of implementing our design concept, to validate the analytical results, and to evaluate the performance of proposed structures, a balun was fabricated for Ω system. For this balun, it can be realized by symmetrical lines such as stripline (using multilayer substrate technologies). For microstrip realization, however, special attention is required due to its nature of unequal even and odd mode phase velocities. This undesired property could degrade the performance of fabricated dual-band balun. Table.1 Calculated stub impedance of proposed balun. f 1 (MHz) f (MHz) n Z s Z oe Z oo Θ c (at f 1 ) o o o o S 11 (900 / 1800) S 1 (900 / 1800) S 11 (850 / 1900) S 1 (850 / 1900) S 11 (900 / 1900) S 1 (900 / 1900) f [GHz] (a) 14

25 S_Parameters [db] S 11 S 1 / S f (GHz) Fig..6 Schematic-level simulation results of dual-band balun for (a) GSM system, and (b) (b) IEEE standard. Fig..7 shows a physical layout of proposed dual-band balun. An experimental prototype fabricated on Duroid RO310 printed circuit board is shown in Fig..8. L s Port 1 S L s1 Port 3 Port W s W c L c Fig..7 Layout of the proposed dual-band balun. W c = 1.78mm, W s = 0.7mm, L c = 0mm, L s1 = 3.8mm, L s = 14mm. 15

26 S_Parameters [db] S_Parameters [db] S_Parameters [db] Fig..8 Experimental prototype of the proposed balun. According to the design procedures described above, a set of even-odd mode impedances associated with stub impedances were calculated for a dual-band balun working at 0.9 GHz and GHz. Both coupled-line section and shunted stub have an electric length of 90 o at 1.45 GHz, which is the middle frequency of the two operation bands. 0-0 Measurement -40 Simulation S 11 S 1 S f [GHz] -80 f [GHz] f (GHz) Fig..9 Comparison between simulated and measured results for proposed dual-band balun. 16

27 Absolute Value of Phase Difference [Degree] Fig..9 shows measured and full-wave simulated amplitude responses of the dual-band balun. The overall measured result shows a good agreement with the simulated one. The measured S 1 and S 31 are -.85 / db at 0.9 GHz, and / -3.7 db at GHz, respectively. According to the measurement, S 1 and S 31 are close to each other with less than 1. db amplitude difference over a 0.3 GHz bandwidth and 1.6 db over a 1 GHz bandwidth. Fig..10 shows the phase characteristics of proposed balun. At two operation frequency bands, the phase differences are within o. Finally, it is worth to point out that the proposed dual-band balun can be easily redesigned to support other working frequencies with different frequency ratios, although they have a higher loss (as shown in Fig..9) and a narrower bandwidth compared with conventional single-band designs. The narrower bandwidth is due to the additional shunted stubs. The higher loss is most likely due to the additional cables we used to measure the Ω system as shown in Fig f [GHz] Measurement f [GHz] f (GHz) Simulation Fig..10 Simulated and measured phase difference for proposed dual-band balun. 17

28 .5 Conclusion A dual-band balun with shunted stubs has been presented. Detailed theoretical calculations of this new balun are included. To verify the design concept, an experimental prototype has been fabricated and measured. The measurement results match with the simulations. The proposed dual-band balun features compact size and large design flexibility. It can be easily scaled for other working frequencies. In the future, more flexibility of proposed baluns will be introduced by adjusting the locations of shunted stubs. 18

29 CHAPTER 3 A NOVEL COMPACT MICROSTRIP CROSSOVER AND ITS DUAL-BAND APPLICATION 3.1 Introduction A crossover is a microwave device, which allows two lines to cross each other with very high isolation [1]-[3]. It has been widely used in antenna array systems. In the past, a crossover was achieved by 3D or multilayer substrates, which increases the complexity as well as the cost of the fabricated devices. To address this issue, recently, many novel fully planar single-band crossovers have been reported [4]-[8]. In [4], a four-port crossover based on the double-ring design is proposed, which has also been reanalyzed by transmission line theory in [5]. In [6], a symmetric four-port crossover is reported. In [7] and [8], microstrip crossovers are designed based on the branch-line structure. Meanwhile, with the rapid advance in modern communications, the design of many passive components is facing new challenges: low cost, compact size, and multiband operations. Among these requirements, multi-band technology is very important. It can lead to both size and cost reductions. Up to now, many microwave components have been engineered to achieve dual-band operations [9]-[36]. However, very few dual-band crossovers have been proposed so far [37]. Therefore, to meet the stringent 19

30 communication system requirement, more novel dual-band crossovers need to be proposed. In this thesis, a novel crossover and its dual-band application are investigated. The proposed crossover has many advantages: 1) it features simple structure and concise design equations; ) its bandwidth can be easily controlled; 3) it is easy to implement for dual-band operation; and 4) the frequency ratio between two working frequencies is flexible. To verify our design concept, a single band crossover working at 1GHz and a dual-band crossover working at 1 and.3 GHz are designed, fabricated, and characterized. The measured results agree well with the simulated results. 3. Proposed Single-Band Crossover. Fig. 3.1 shows the schematic diagram of proposed single-band crossover, where PP and QQ (as shown in Fig. 3.1) are two symmetric planes. Among the new crossover, there are two critical parts, namely, the outside microstrip lines and the inner crossed microstrip lines. Q Port 1 Z 1, θ 1 Z 1, θ 1 Port Z1, θ 1 Z, θ Z 1, θ 1 Z, θ Z, θ P P Z1, θ 1 Z, θ Z 1, θ 1 Port 4 Z 1, θ 1 Z 1, θ 1 Q Port 3 Fig. 3.1 Circuit configuration of proposed single-band crossover. 0

31 Z ee Z 1, θ 1 Z, θ O/C Z 1, θ 1 Z, θ O/C Z eo (Z eo ) Z 1, θ 1 S/C Z 1, θ 1 Z, θ S/C Z oo Z 1, θ 1 S/C Z 1, θ 1 S/C Fig. 3. Reduced networks under different excitations. Since the designed crossover is symmetric to both PP and QQ planes, it can be analyzed using Even-Odd mode analysis method [38]. Under suitable even- / odd-mode excitations, the reduced networks with their equivalent load impedances (Z ee, Z eo, Z oe, and Z oo ) are shown in Fig. 3.. From equivalent load impedances and port impedance (Z 0 ), the reflection coefficients under different excitations can be expressed as: Where: Zee ee, eo, oe, oo Z Z ee, eo, oe, oo ee, eo, oe, oo Z Z j Z j Z 1 tan 1 Z 1 tan Z 1 Z tan 1 tan 0 0 (3-1) (3-) 1

32 Z eo Z eo j Z 1 Z 1 tan 1 tan Z 1 Z tan Z tan 1 j Z 1 1 tan 1 1 (3-3) Zoo j Z tan 1 1 (3-4) The S-parameters of this device can be derived as [5]: S 11 ee eo 4 oe oo (3-5) S 1 ee eo 4 oe oo (3-6) S 13 ee eo 4 oe oo (3-7) S 14 ee eo 4 (3-8) For crossover application, if signal is coming from port 1, the expected S- parameters are: S 11 = S 1 = S 14 = 0, S 13 = 1, the corresponding relations between reflection coefficients are: oe oo ee oo eo oe (3-9) To satisfy the requirement of, we need to make sure that Z ee equals to Z oo. ee oo From the reduced networks (as shown in Fig. 3.), we can observe that when θ equals to 90 o, the corresponding Z ee and Z oo are equivalent. To ensure oo eo, the following equations can be derived from (3-3) and (3-4): K 3 Z Z t1 Z 1 Z t t Z 1 Z t Z Z t t 1 Z t (3-10)

33 Magnitude of S 31 (db) Where K = Z 0 / Z 1, t 1 = tan θ 1, t = tan θ. Substituting θ = 90 o into (3-10), since and eo are automatically equal in the proposed structure, the final equation can be expressed eo as: K 1 t t 1 1 (3-11) From Eq. (3-11), we can see that the proposed single-band crossover has very simple design equation, and its bandwidth can be easily controlled by applying different values of K. The impedance of Z is not related to the final result at design frequency. In the following discussion, Z and θ are fixed to 50Ω and 90 o, port impedance Z 0 is fixed to 50Ω. Also, the parameter K is very important for the proposed crossover design. Considering the limitations about microstrip transmission lines and the possible solutions of equation (3-11), K is limited from 0.8 to.5. To verify the design equation, Fig. 3.3 shows simulation results of S 31 when K = 1.5, 1, 0.8. The corresponding Z 1, θ 1 are obtained by solving equation (3-11). From the simulation results, we can easily see that different K results in different bandwidth. More information about K and bandwidth is listed in Table K=1.5 K=1.0 K= Frequency (GHz) Fig. 3.3 Simulation results of S 31 with K = 1.5, K = 1.0, and K =

34 Table 3.1 Fractional bandwidth under different K and corresponding Z 1 and θ 1 K Z 1 [Ω] θ 1 [degree] -10dB FBW [%] -0dB FBW [%] Proposed Dual-Band Crossover Structurally speaking, the proposed single-band crossover is composed of an outside microstrip line (Z 1, 8θ 1 ), and four inner 90 o crossed microstrip lines (Z, θ ). In order to realize the proposed dual-band crossover, we need to replace the Z a, θ a Z a, θ a Z b, θ b Port 1 Z 1, θ 1 Z 1, θ 1 Port Z 1, θ 1 Z, θ Z 1, θ 1 Z, θ Z, θ Z 1, θ 1 Z, θ Z 1, θ 1 Port 4 Z 1, θ 1 Z 1, θ 1 Port 3 Fig. 3.4 Configuration of proposed dual-band crossover. 4

35 inner and outside microstrip lines of proposed single-band crossover with dual-band microstrip lines. Since many dual-band 90 o microstrip lines had been reported [36]-[38], in this paper, we focus on designing a dual-band arbitrary degree (θ 1 ) microstrip line by employing a T-shape structure. Fig. 3.4 shows the structure of proposed dual-band crossover. Z a, θ a, Z b, θ b are characteristic impedances and electrical lengths of series and shunt sections of the T- shape structure. Such structure is used to realize the dual-frequency θ 1 phase change transmission line. The ABCD-matrix of T-shape structure has been given in [35]: A T D T cos Za sin acos a asin a Zb tan b (3-1) B T j Z a Z cos sin j a a a sin atan b Z b (3-13) C T j sin acos b j cos atan b Z Z a (3-14) From equations (3-1)-(3-14) we can see that by replacing θ a and θ b with nπ+ θ a and mπ+ θ b, the resulting matrices are the same. This is the key on how we can make the T-shape structure work at dual-frequency. In other words, through the design process, we need to make sure that θ a and θ b are the electrical lengths at first frequency (f 1 ), and nπ+ θ a and mл+ θ b are the electrical lengths at second frequency (f ). After some derivations, θ a and θ b can be calculated by the ratio of two desired frequencies: b a f 1 f1 f f 1 (3-15) b f1 f1 f f 1 (3-16) 5

36 In the following discussion, we will introduce an example when K = 1. From Table 3.1, the values of Z 1 and θ 1 are fixed to be 50 Ω and o. Now we need to make sure our T-shape structure is equivalent to a transmission line (with Z = 50 Ω and θ 1 = o ) at dual-frequency. The ABCD-matrix of this transmission line is: A C B j D j (3-17) The design procedures of T-shape structure can be summarized as follows: 1. Using equations (3-15) and (3-16) to calculate θ a and θ b at two working frequencies f 1 and f. Here, n and m start from 1 for compactness.. Substituting equations (3-1), (3-13), and (3-14) into (3-17) to get the values of Z a and Z b. 3. Determining whether the impedances of Z a and Z b are achievable by using microstrip line. If it is not, go back to step 1, and increase the values of n and m. 4. Computing the physical dimensions of proposed T-shape structure based on Z a, θ a, Z b, and θ b. So far, the T-shape (K=1) dual-band transmission line has been introduced. Even though different values of K will affect equation (3-17), the design procedures are the same. Finally, by replacing inner crossed transmission lines with dual-band 90 o transmissions (as shown in Fig. 3.4), a novel dual-band crossover is designed. Since the inner dual-band 90 o microstrip lines (Z, θ, as labeled in Fig. 3.4) can be realized by T shape, modified T shape (with short end) or step-impedance structures 6

37 Impedance of Z a and Z b (ohm) [40-41] (which has very wide frequency ratio), the frequency ratio of proposed dual-band crossover is determined by the ratio of outside dual band Z 1, θ 1 transmission line Frequency Ratio ( f / f 1 ) Z a Z b Fig. 3.5 Computed impedances of Z a and Z b under different frequency ratios. Due to the limitations of achievable microstrip impedances, any dual-band structures have limited frequency ratios. Following the introduced four steps to calculate impedances of Z a and Z b under different frequency ratios, it is found that the T-shape structure features flexible frequency ratio with realistic microstrip impedance. Fig. 3.5 shows the computed impedances of Z a and Z b under different frequency ratios. For different values of K, the realizable frequency ratio range needs to be recalculated following the procedure discussed before. Fig. 3.6 shows simulation results of the magnitude of S 11, S 1, and S 31. Three dual-band crossovers are designed to work at: 1 and 1.9 GHz, 1 and.3 GHz, and 1 and.8 GHz. For these crossovers, the design parameters of dual-band 90 o microstrip liness 7

38 Magnitude of S 11, S 1, and S 31 (db) Magnitude of S 11, S 1, and S 31 (db) (equivalent to Z and θ at dual-frequency) are derived from [36], and the values of Z a, θ a, Z b, and θ b are calculated from four design steps. The simulated port isolation (S 1 ) and return loss (S 11 ) are very good at two working frequencies for all three dual-band crossovers. 0 f 1 f S 11 S 1-30 S Frequency (GHz) (a) 0 f 1 f S 11 S 1 S Frequency (GHz) (b) 8

39 Magnitude of S 11, S 1, and S 31 (db) f 1 f S 11 S 1-30 S Frequency (GHz) (c) Fig. 3.6 Simulated results of three dual-band crossovers: (a) 1 and 1.9 GHz, (b) 1 and.3 GHz, and (c) 1 and.8 GHz. 3.4 Experimental Results To verify our design concept, a single band crossover operating at 1GHz and a dual-band crossover working at 1 and.3ghz were fabricated on Duroid 5880 substrate with a dielectric constant of. and thickness of mm. Fig. 3.7 shows the top view of fabricated single band and dual band crossovers. For the single band crossover, we choose K = 1. The corresponding Z 1 and θ 1 are 50 Ω and o, and Z and θ are 50 Ω and 90 o. Simulated and measured results of the proposed single band crossover are shown in Fig. 3.8 and Fig

40 Magnitude of S 11 and S 31 (db) Fig. 3.8 shows the simulated and measured results of S 11 and S 31. Fig. 3.9 shows the simulated and measured results of S 1 and S 41. Since the structure of proposed crossover is bisymmetric, the simulated S 1 and S 41 are the same. For the dual band crossover, Z a, Z b, θ a, θ b are calculated to be: 4.47 Ω, 3.44 Ω, o and o, respectively. Z a, Z b, θ a, θ b are calculated to be: Ω, Ω, o and o, respectively. Fig. 3.7 Top view of the proposed single-band and dual-band crossovers Simulated S Simulated S 11 Measured S 31 Measured S Frequency (GHz) Fig. 3.8 Simulated and measured results of magnitude of S 11 and S 31 (single-band crossover). 30

41 Magnitude of S 11 and S 31 (db) Magnitude of S 1 and S 41 (db) 0 Measured S 1 Measured S Simulated S 1 and S Frequency (GHz) Fig. 3.9 Simulated and measured results of S 1 and S 41 (magnitude of single-band crossover). Fig and Fig show simulated and measured S 11 and S 31 of the dual-band crossover. Fig. 3.9 shows simulated and measured results of S 1 and S 41. It is observed that measurement results match well with simulation results, verifying our design concept Measured S 11 Measured S 31 Simulated S 11 Simulated S Frequency (GHz) Fig Simulated and measured results of S 11 and S 31 (magnitude of dual-band crossover). 31

42 Magnitude of S 1 and S 41 (db) 0 Measured S 1 Measured S 41 Simulated S 1 and S Frequency (GHz) Fig Simulated and measured results of S 1 and S 41 (magnitude of dual-band crossover). 3.5 Conclusion A novel crossover and its dual-band application have been presented. For single band crossover, the final design equation has been derived, and the corresponding bandwidth performance is discussed. The design procedure of a dual band crossover is introduced, and its realizable frequency ratio is discussed. To verify the design concept, both a single band and a dual-band crossover are fabricated and measured. Good agreement has been achieved between the measurement and simulation results. 3

43 CHAPTER 4 DUAL-FREQUENCY ELECTROMAGNETIC CLOAKS ENABLED BY LC-BASED METAMATERIAL CIRCUITS 4.1 Introduction With the development of metamaterials, the concept of invisible cloak has drawn much attention as an important topic. By the aid of cloaking structures, waves can propagate through the target with very small perturbations to the total fields. Many methods have been proposed for this purpose. In [4], anomalous localized resonance is used to achieve the cloaking effect. Alu and Engheta [43]-[44] propose to use plasmonic shell as a cloak to reduce the total scattering cross section of a particle. Especially, spatial coordinate transformation method has been widely employed since its appearance [45]- [49]. These ideas have also been extended to other applications such as electromagnetic wormholes [50], field concentrator [51], field rotator [5], and beam forming [53]-[54]. Meanwhile, recent advance in complex systems has imposed more stringent system requirements including dual-frequency operation [55]-[68]. As for cloak s applications, it is noted that most of the proposed cloaking structures can only work at single frequency due to the causality constraints imposed by metamaterials [69]. To relax this limitation, Chen et al. [70] show a cloak design with broader bandwidth, which is realized by the sacrifice of scattering cross section. Meanwhile, Alu and Engheta [71] propose to us 33

44 multilayered plasmonic shells to cancel the scattering at different frequencies, leading to multi-frequency cloaks. After that, several multi-frequency cloaks have been achieved by using different methods [7]-[75]. In this thesis, we demonstrate how to construct a dualfrequency cloak based on the coordinate transformation method. Metamaterials based LC-circuits are proposed to realize the desired parameters at different frequencies, where the concept of multiple resonances is applied. A cylindrical cloak with ten layers is studied. Each layer of the cloak is then approximated by the proposed circuit. The simulation results show the desired dual-frequency operation of the whole cloak. The same concept can be also applied for other cloaking structures designed by spatial coordinate transformation method for multiple-frequency operations. y μ r are replaced by the proposed metamaterial based LC-circuits for each layer r R 1 x R ε z, μθ are replaced by the conventional metamaterial based LCcircuits Fig. 4.1 Schematic of the proposed dual-band cloak. 34

45 4. Theoretical Analysis The general schematic of the cloak studied is shown in Fig It is cylindrical in shape. Applying the coordinate transformation r = R 1 + r (R R 1 )/R, the original cylindrical region, 0 r R, is compressed into a concentric cylindrical shell, R 1 r R, where r is the coordinate in the original space and r is the coordinate in the transformed space. By doing this, the region 0 r R 1 (the dark grey area marked in Fig. 4.1) is excluded from the transformed space so that anything can be placed into it without affecting the wave propagation in the whole space, resulting in the cloaking of the region. After the transformation, the relative permeability and permittivity in the cloaking shell are expressed as: r R1 r r (4-1) r r (4-) r R 1 r (4-3) r R 1 To study the performance of the cloaks, time harmonic plane waves with transverse-electric (TE) polarization, transverse-magnetic (TM) polarization, or mix of both of them are excited. Without a loss of generality, in the following, we will focus our analysis on TE case. The same theory can be easily extended to other cases. It is found that, under the TE illuminations, wave propagations depend on three parameters, namely, μ r, μ θ and ε z. For single frequency cloak, these parameters are calculated by Eqs. (4-1) 35

46 (4-3) and can be emulated using well defined metamaterial structures. In practice, for the ease of implementation, permittivity and permeability are further reduced to: R r R 1 z ( ), 1, r ( ) (4-4) R R1 r In Eq. (4-4), both μ θ and ε z are constant and can be realized with conventional substrate. As for μ r (the permeability in the r-direction), it is found that, when r is close to R 1, the required permeability is quite small (close to 0), which cannot be realized using conventional materials. Therefore, metamaterials are employed to realize this parameter [47]. However, as mentioned before, due to the causality of metamaterials, the designed parameters can be satisfied only at single assigned frequency. For dual-frequency or multiple-frequency operations, metamaterials with different structures are required. In general, two types of metamaterials are widely used, one is composed of metal wires and split-ring resonators [76] and the other is based on LC-loaded transmission line networks [77]-[81]. In our case, we find that it is possible to employ the second type metamaterial to achieve dual-frequency operation of the cloak. A typical illustration of this type of metamaterials is shown in Fig. 4., where Z is the impedance of the circuit in series and Y is the admittance of the circuit in shunt. Due to analogy between the circuits and the electromagnetic wave propagation models, we have: Y (4-5) j 0 Z (4-6) j 0 36

47 Fig. 4. The general circuit model with the analogy to the effective medium. Fig. 4.3 Schematics of the LC-loaded circuits for the medium in (a) θ direction and (b) z direction. Applying Eqs. (4-5) and (4-6), μ θ and ε z can be realized by the LC-loaded circuits shown in Fig And relations between the lumped components and the permittivity and permeability are: 37

48 L, 0 C 0 (4-7) z Cz, 0 Lz z 0 (4-8) where is length of the total LC-circuit and other parameters are labeled in Fig From Eqs. (4-7) and (4-8), the resulting μ θ and ε z are not dependent on the frequency and further calculations show that both of them can be realized by a lumped inductor and a capacitor with practical values. Therefore, they are suitable for dual-frequency cloak applications. However, for μ r, due to its very small value at the region close to the inner boundary (r = R 1 as shown in Fig. 4.1), it is impossible to achieve the desired parameter using the conventional LC-loaded circuit as shown in Fig. 4.3 (e.g. if μ r = 0.00, the corresponding inductor should be as small as 0.05 nh with = 0.01m, which is not practical). This motivates us to propose the circuit as shown in Fig. 4.4 to satisfy the assigned conditions for μ r at two distinct frequencies. Fig. 4.4 The proposed LC-loaded circuit with multiple resonances to support dualfrequency operation. 38

49 Based on Eqs. (4-5) and (4-6) and after some derivations, the effective permittivity and permeability of proposed circuit systems (as shown in Fig. 4.4) are expressed as: 1 L1 L r L0 0 1 L1C 1 1 LC (4-9) C r r (4-10) 0 Two additional LC-resonant tanks are added to the original circuits. Both of these LC-resonators contribute to the effective permeability of the medium. By exploiting the additional freedom introduced by these circuits, it is possible to realize unconventional permeability at two different frequencies. Physically, this behaves similarly as a twocomponent system [8] and it is a metamaterial with very flexible properties. 4.3 Simulation Results To prove the theoretical predictions of the proposed dual-frequency cloak, we have designed a prototype as shown in Fig. 4.1, where R 1 = 0.1 m and R = 0. m. This concentric cloaking shell is further decomposed into ten layers so that each layer has a uniform thickness of 0.01 m. In the θ- and z-directions, materials are constructed by the LC-loaded circuits as shown in Fig Applying Eq. (4-4), μ θ = 1 and ε z = 4 are held for all of these ten layers. Plugging these values into Eqs. (4-7) and (4-8) with = 0.01 m, it is found that L θ = 1.6 nh, C θ = 0.35 pf, L z = 1.6 nh and C z = 0.35 pf. In the r- direction, the permeability is a function of position. With Eq. (4-4), the calculated μ r values are: , 0.018, , 0.067, , 0.159, 0.155, , 0.111, 39

50 0.373, respectively, for the ten layers from inside to outside. Each layer is then approximated by the proposed LC-circuits as shown in Fig. 4.4 with different LCcomponent values. For a dual-frequency system, one parameter of particular note is the ratio between the two working frequencies (f / f 1 ). In our case, the range of this ratio is constrained by the practical values of inductors and capacitors. Fig. 4.5 The E-field distributions of the proposed dual-frequency cloak at different frequencies (a) 3 GHz (first working frequency, f 1 ), (b) 5 GHz (second working frequency, f ), (c) at 4 GHz. 40

51 Based on Eqs. (4-4)-(4-10), a numerical algorithm is applied to calculate the corresponding circuit components values with different frequency ratios. It is found that, for the ratio from f / f 1 = 4 GHz / 3 GHz to f / f 1 = 9 GHz / 3 GHz or even higher, the proposed dual-frequency cloaks work well (e.g. for frequency ratio within this range, the dual-frequency cloak can work properly). Some of the typical calculation results are listed in Table 4.1, for which L 0 = 1.6 nh and C r = 0.88 pf. Based on above calculations, a dual-frequency cloak working at 3 GHz and 5 GHz is designed and its performance is simulated by the full-wave simulator COMSOL Multiphysics. In the simulations, plane waves are incident from the left to the right with the frequency range from to 6 GHz. Perfectly matched layers (PML) boundaries and scattering boundaries are placed on all four sides of the simulation domain to remove Table 4.1 Calculated LC-loaded circuit parameters for each layer when f 1 = 3 GHz and f = 5 GHz. Layer C 1 = C (pf) L 1 (nh) L (nh)

52 Differential Scattering Cross Section (dbsm) Differential Scattering Cross Section (dbsm) GHz Case proposed cloak bare PEC cylinder Scattering Angle (degree) (a) GHz Case bare PEC cylinder proposed cloak Scattering Angle (degree) (b) Fig. 4.6 The calculated differential scattering cross sections of the proposed cloak along with the results for the bare PEC, (a) at 3 GHz and (b) at 5 GHz. undesired reflections. Simulated E-field distributions of this cloak are shown in Fig 4.5 at different frequencies. As desired, at 3 and 5 GHz as shown in Fig. 4.5 (a) and (b), the incident waves are bent smoothly around the cloaked area with small perturbations to the far fields (due to singular values of the designed parameters). Meanwhile, at other 4

53 frequencies (e.g. 4 GHz as shown in Fig. 4.5 (c)), strong scattering is observed because the corresponding permeability and permittivity at those frequencies do not satisfy suitable cloak parameters. To further evaluate the performance of designed dual-frequency cloak, the differential scattering cross section of it is calculated at two working frequencies. The results are plotted in Fig. 4.6, where bistatic scattering is calculated as a function of the scattering angle φ. Also, in Fig 4.6, bistatic scatterings with bare PEC cylinder at those two operating frequencies are plotted for the purpose of comparison. It is observed that, at 3 GHz, scattering cross section at φ = 0º for the proposed cloak is 11 db lower than that of the bare PEC. For most of the other angles (scattering angle), scattering cross section of the cloaked area is reduced by the aid of the designed cloak. At 5 GHz, similar reductions of scattering cross sections are achieved. Besides, oscillations of the cloak s differential scattering cross sections in Fig. 4.6 are faster than that of the bare PEC. This indicates that zeroth order scattering is reduced by the proposed cloak at two operating frequencies. Finally, the normalized total scattering cross section (normalized to the bare PEC) of the proposed cloak is investigated. The results are plotted in Fig. 4.7 over the frequency range from to 6 GHz. It is observed that, at the working frequencies (3 and 5 GHz), the total scattering cross section of the cloak is only 30% and 16% of those of the bare PEC, respectively, demonstrating great scattering reductions. Deviated from the center frequency, we find that the total scattering cross section increases dramatically so 43

54 The Normalized Total Scattering Cross Section (%) that the bandwidth of the proposed cloak is narrow. This is due to the highly resonant property of proposed LC-loaded metamaterials. 300 proposed cloak PEC_case PEC_case PEC_case Frequency (GHz) Fig. 4.7 Calculated normalized total scattering cross section of the proposed dualfrequency cloak over the frequency range from GHz to 6 GHz. So far, the performance of the dual-frequency cloak is verified by the results presented above. In addition, it is worth pointing out that by applying the same design concept, it is possible to design cloak for multiple-frequency operations (e.g. triplefrequency, quadruple-frequency, etc.). For these applications, high order LC-based circuits similar to that shown in Fig. 4.4 but with multiple resonant tanks are needed to satisfy the corresponding requirements. Moreover, for practical implementations, several issues need to be considered including the losses of applied components and the physical size of corresponding components and interconnects. 44

55 4.4 Conclusion We have developed a dual-frequency electromagnetic cloak based on the LCloaded circuits. The limitations imposed by the causality and the extreme small value of permittivity / permeability for cloaking applications are relaxed by the proposed LCcircuit with multiple resonances. Full-wave simulations are then carried out to prove our design concept, where a cylindrical cloak working at 3 and 5 GHz is designed and simulated. The simulation results including the E-field distributions and the scattering cross sections show the desired dual-frequency operations of the cloak. Moreover, the proposed structures are suitable for other applications (e.g. field concentrator, beam forming, etc.) featuring dual-frequency operations. Based on the same concept, it is even possible to design cloaking structures with multiple-frequency operations. 45

56 CHAPTER 5 DUAL-BAND RADIO-FREQUENCY DEVICE FOR SENSING DIELECTRIC PROPERTY CHANGES IN MICROFLUIDIC CHANNELS 5.1 Introduction Dielectric measurement is widely used to identify biological and chemical samples. Because of the advantages of simple operation, instant testing, and no chemical modification, dielectric measurement has drawn much research attention. Many novel dielectric sensors have been investigated [83]-[84] so far. Especially, for the radiofrequency dielectric measurement devices, transmission lines [85] and antennas [86] were widely used in the past. These RF dielectric measurement devices have the potential of integration and parallelization. Recently, an RF dielectric measurement device [87], which consisted of a Wilkinson power divider and a rat-race hybrid, with two times more sensitivity than the previous research [86], was introduced. Based on the concept in [87], further research results about sensitivity improvements are reported in [88]. Meanwhile, in today s engineering field, dual-band technology has been well developed. Many novel dual-band components have been investigated such as: dual-band power divider [30], dual-band balun [89], and dual-band rat-race coupler [90]. Recently, the application of dual-band technology has been further extended to the area of 46

57 metamaterials, where dual-band invisible cloak was designed [91]. Since dual-band (or even multi-band) devices can support multiple operating frequencies, it is attractive for many system applications to realize both size and cost reduction, and improve system robustness. In this chapter, the dual-band technology is combined with the RF dielectric measurement device to provide two-frequency-band microfluidic detections. The proposed device is able to catch the dielectric change in PDMS channel at GHz and 5GHz, simultaneously. The direction of the resonant frequency shift at two working frequencies is consistent. This consistency can be employed to minimize the influence of incorrect testing data (which may be caused by background noise or operational error) to the measurement. In this way, stability improvement of the microfluidic RF dielectric measurement device can be achieved by using the proposed dual-band devices. Dual-band Wilkinson power dividers Dual-band 90 degree transmission line (+90 first frequency -90 second frequency) REF PDMS Channel Port 1 Port MUT PDMS Channel Dual-band 90 degree transmission line (-90 first frequency +90 second frequency) Fig. 5.1 Schematic of the proposed dual-band RF dielectric measurement device. 47

58 5. Operating Principle Fig. 5.1 shows the general schematic of proposed device. RF signal is coming from port 1 and goes to a dual-band Wilkinson power divider, which equally splits the power into two branches. These two branches are connected to two dual-band 90 o transmission lines (TL). In our design, the first dual-band 90 o TL provides +90 o phase shift at f 1, and -90 o phase shift at f. The second dual-band 90 o TL has opposite phase response at f 1 and f. After that, the two branches are connected to another dual-band Wilkinson power divider. It combines signals from two branches, which have the same power and 180 o difference at f 1 and f. Finally, the signal arrived at port. The magnitude of S 1 has minimal value at two resonant frequencies. When we set PDMS channels on these two branches and inject different samples into them, the resonant frequency of the whole device will shift at two frequency-bands. This property makes the proposed RF device very sensitive to detect small dielectric changes in PDMS channels. Fig. 5. A tapped stub structure. Fig. 5. presents the tapped stub structure which is used to equate quarterwavelength line in the proposed devices. The ABCD-matrix of the T-shape structure can be derived as: 48

59 A T D T cos Z a sin acos a asin a Zb tan b (5-1) B T j Z a Z cos sin j a a a sin atan b Z b (5-) C T j sin acos b Z a j cos atan b Z b (5-3) The design equations of using T-shape structure to achieve dual-band applications can be derived as: Z a f Z 0 tan a f1 (5-4) b f (5-5) f f 1 a f1 1 f f1 1 Z a tan atan b (5-6) Zb (5-7) 1 tan a where Z a, Z b, θ a and θ b are the impedances and electrical lengths of the branches and stubs, as shown in Fig. 5., and Z 0 is the impedance of the port. the T shape for the first path TL REF PDMS Channel the T shape for the power divider MUT PDMS Channel the T shape for the second path TL Fig. 5.3 Photo of the fabricated dual-band RF dielectric measurement device with PDMS microfluidic channels. 49