新型人造傳輸線之研究及其於超寬頻感測節點之微型化射頻模組的應用

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(1)行政院國家科學委員會專題研究計畫成果報告新型人造傳輸線之研究及其於超寬頻感測節點之微型化射頻模組的應用(第 2 年) 研究成果報告(完整版). 計計執執. 畫畫行行. 類編期單. 別號間位. ：個別型： NSC 97-2221-E-011-019-MY2 ： 98 年 08 月 01 日至 99 年 07 月 31 日：國立臺灣科技大學電機工程系. 計畫主持人：馬自莊計畫參與人員：碩士班研究生-兼任助理人員：王宸晟碩士班研究生-兼任助理人員：許紘偉碩士班研究生-兼任助理人員：邱皇欽碩士班研究生-兼任助理人員：蔡志偉碩士班研究生-兼任助理人員：林家輝碩士班研究生-兼任助理人員：吳政勳博士班研究生-兼任助理人員：賴季暉. 報告附件：出席國際會議研究心得報告及發表論文. 處理方式：本計畫涉及專利或其他智慧財產權，2 年後可公開查詢. 中. 華. 民. 國 99 年 10 月 07 日.

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(4) Abstract This project is a two-year project aiming at developing miniaturized key microwave components using novel artificial transmission lines in microstrip/stripline/coplanar waveguide (CPW) forms with double-layer or multi-layer fabrication process. The developed miniaturized microwave components can be integrated into the RF front-end circuit for future applications. By utilizing quasi-lumped elements in microstrip, stripline and CPW forms, several novel artificial transmission lines have been developed and investigated thoroughly. The artificial line in microstrip form is realized using double layer fabrication process, and is applied to the development of the miniaturized quadrature hybrid coupler, six-port junction, dual-mode ring bandpass filter, CPS-to-microstrip line transition, and etc. The synthesized lines in CPW form, also using the double layer process, are designed and applied to the development of miniaturized backward-wave edge-coupled directional coupler, backward-wave broadside-coupled directional coupler, forward-wave edge-coupled directional coupler, rat-race coupler, and dual-mode bandpass filter. The artificial line in stripline form is developed using six-layer printed circuit board fabrication process. The artificial line in stripline form is a little bit complicated, but rendering similar size reduction capability when compared with its microstrip counterpart. Multilayer broadside coupler, broadside Marchand balun are demonstrated using artificial lines in stripline form. On the other side, an impulse-radio-based RF front-end module for ultra-wideband communication is developed in this project based a novel compact microwave sampler. By using the equivalent time sampling (ETS) theory, two transmission data rate, 90 and 270 kbps, are demonstrated with various bit patterns. The experimental results reveal that the transceiving module has a coverage range up to 4.5 m. In the two year project, 6 SCI papers in international top journals and 3 conference papers in IMS have been published. There are two additional journal papers currently under review.. Keywords: artificial transmission line, multi-layer printed circuit board, microwave key components, RF front-end.

(5) Outline ύЎᄔा .......................................................................................................... 2 Abstract ............................................................................................................. 3 Chapter 1. Introduction ................................................................................... 5. Chapter 2. A Miniaturized Multilayer Marchand Balun Using Coupled. Artificial Transmission Lines ......................................................................... 10 Chapter 3. Novel Uniplanar Synthesized Coplanar Waveguide and the. Application to Miniaturized Rat-race Coupler ............................................... 20 Chapter 4 Miniaturized Coupled-line Couplers Using Uniplanar Synthesized Coplanar Waveguides ..................................................................................... 32 Chapter 5. A Miniaturized Dual-mode Ring Bandpass Filter ....................... 66. Chapter 6 Novel Synthesized Microstrip Line with Quasi-Elliptic Response for Harmonic Suppressions ............................................................................. 77 Chapter 7 An Impulse-radio Ultrawideband RF Front-end Module with A New Multilayer Microwave Sampler............................................................ 116 Chapter 8. Conclusion................................................................................. 138.

(6) Chapter 1 Introduction 1.1 Chapter Outline This project is a two-year project aiming at investigating and designing miniaturized microwave. components. using. novel. artificial. transmission. lines. in. microstrip/stripline/coplanar waveguide (CPW) forms with double-layer or six-layer printed circuit board fabrication process. By utilizing quasi-lumped elements, several novel artificial transmission lines in microstrip, stripline and CPW forms have been developed and investigated thoroughly. The artificial transmission lines in microstrip, stripline and CPW forms are applied to the development of the miniaturized microwave components,. including. quadrature. hybrid. coupler,. rat-race. coupler,. backward/forward-wave directional coupler, Marchand balun, six-port junction, dual-mode ring bandpass filter, CPS-to-microstrip transition, and etc. The design methodology, circuit configuration, simulated and measured results will be introduced and discusses carefully in the following chapters. In Chapter 2, a miniaturized Marchand balun is investigated. The Marchand balun is realized on a six-layer printed circuit board by integration of two coupled artificial transmission line sections. An additional artificial line is inserted in-between the coupled lines for compensating the asymmetry. With the help of the even odd mode analysis, the electrical characteristics of the coupled lines are investigated in detail. The proposed balun has the smallest occupied size among the previous designs on printed circuit boards. It features excellent amplitude and phase imbalance, and a comparable return loss bandwidth as well. By utilizing quasi-lumped components, we propose a novel slow-wave uniplanar synthesized coplanar waveguide (USCPW) in Chapter 3. The physical length of a.

(7) 90-degree uniplanar synthesized coplanar waveguide (USCPW) is less than one-twentieth of a guided wavelength. A lumped equivalent circuit model is proposed to explain the complicated behavior of the synthesized line. The design concept, propagation characteristics, equivalent circuit model, and simulated and measured results are carefully studied. Based on the new synthesized coplanar waveguide, a novel miniaturized rat-race coupler is demonstrated. The proposed design is merely 7.2% the size of a conventional coupler, which is the smallest one ever reported in coplanar waveguide form using printed circuit board technology. The response of the miniaturized coupler is experimentally verified in Chapter 3. In Chapter 4, a novel slow-wave synthesized coplanar waveguide, namely the uniplanar synthesized coplanar waveguide, is investigated. Quasi-lumped coplanar waveguide inductors and capacitors are used in synthesizing the new slow-wave structure. The synthesis method, lumped equivalent circuit model, and simulated and experimental results are discussed. The synthesized line, featuring excellent miniaturization capabilities, has a moderate quality factor. The slow wave factor is 7.5, while the unloaded quality factor is 30-60. By utilizing the synthesized coplanar waveguide, three novel miniaturized coupled-line directional couplers are proposed and experimentally verified. With the help of even odd mode analysis, design charts are summarized for understanding of the developed miniaturized couplers. When compared with previous designs, the miniaturized couplers show comparable performance, but significantly reduced sizes. Additionally, they have quasi-square appearances, which are suitable for circuit integration in cascade connection. A novel miniaturized dual-mode ring bandpass filter is proposed in Chapter 5. The miniaturization is accomplished by slow-wave synthesized microstrip lines in an asymmetrical form. At the input/output ports, two saw-toothed coupling structures with quarter-wavelength open-circuited stubs are used to provide tight coupling. The.

(8) miniaturized filter features a very compact size and the in-band responses are comparable to its conventional counterpart. The design methodology, circuit topology, and simulated and measured results are investigated and compared. A novel synthesized microstrip line with quasi-elliptic response is proposed in Chapter 6. By utilizing quasi-lumped elements, the proposed synthesized lines are capable of reducing the circuit size with good slow-wave property. Benefitted from the quasi-elliptic response, signal suppression capability is introduced to the synthesized line at the harmonic frequencies. The design concept, circuit geometry, equivalent lumped circuit model, and simulated and measured results are carefully investigated and discussed. Based on the new synthesized microstrip line, a miniaturized quadrature hybrid coupler with harmonic suppressions is designed as a demonstrated example. The signal rejection levels are higher than 20 and 40 dB at the second and third harmonics, respectively. At the mean time, the size reduction percentage is 50%. The designed hybrid coupler is applied to develop a miniaturized six-port junction, possessing the excellent harmonic suppression capability. In Chapter 7 we develop a new impulse-radio-based RF front-end module for ultrawideband communications. The proposed transceiving module is designed based a novel compact microwave sampler. The microwave sampler consists of a multilayer magic-T and a balanced sampling bridge. By utilizing a wideband microstrip-to-slotline Marchand balun, the newly proposed magic-T features an improved bandwidth of 94.2 %. The design concept, circuit topology, and experimental results of the magic-T and microwave sampler are investigated in the first half of this chapter. By utilizing the equivalent time sampling theory, in the second half of this chapter we investigate an impulse-radio-based ultrawideband transceiving front-end module. Two transmission data rates, 90 and 270 kbps, are demonstrated with various bit patterns. The experimental results reveal that the transceiving module has a coverage range up to 4.5 m. The circuit.

(9) configuration, modulation scheme, and system performance of the front-end module are discussed thoroughly. The tradeoff for increasing the data rate is discussed at the end of this chapter as well. In the final chapter, Chapter 8, we will conclude this project with a summary.. 1.2 Self evaluation In this project, six international SCI papers in IEEE Transactions on Antennas and Propagation [J-1], IEEE Transactions on Microwave Theory and Techniques [J-2], IEEE Microwave and Wireless Components letters [J-3]-[J-4], Electronic Letters [J-5], and Progress In Electromagnetics Research [J-6] were published. Three conference papers were presented in 2008/2010 IEEE MTT International Microwave Symposiums (IMSs) [C-1]-[C-3]. Two additional journal papers are currently under review by IEEE Microwave and Wireless Components letters and IEEE Transactions on Microwave Theory and Techniques [J-7]-[J-8]. Seven graduate students, receiving their master degrees within these two years, were involved in this project. The achievement of this two-year project is fruitful. By utilizing quasi-lumped elements fabricated on double-layer or six-layer printed circuit board fabrication process, novel artificial transmission lines in microstrip, stripline and coplanar waveguide (CPW) forms have been developed and investigated thoroughly. The new designs are applied to the development of miniaturized quadrature hybrid couplers, rat-race couplers, backward/forward-wave directional coupler, Marchand baluns, six-port junction, dual-mode ring bandpass filters, CPS-to-microstrip transition, and etc. All designs give rise to very compact sizes, which are commonly less than one-half the sizes of the second smallest ones ever reported in literature using printed circuit board technology. At the meantime, an impulse-radio-based RF front-end module for ultra-wideband communication was developed in this project, as well. By utilizing the.

(10) equivalent time sampling theory, two transmission data, 90 and 270 kbps, were experimentally demonstrated with various bit patterns. The experimental results reveal that the transceiving module has a coverage range up to 4.5 m. The researches in this project provide not only innovative designs but excellent performances when compare with conventional designs. In the following chapters, the details of each individual design will be introduced and discussed..

(11) Chapter 2 A Miniaturized Multilayer Marchand Balun Using Coupled Artificial Transmission Lines 2.1 Introduction Recently, the ever increasing demands for miniaturized microwave components have imposed new design challenges to circuit engineers. The Marchand balun, a core component in microwave circuits with balanced signals, generally occupies a bulky size owing to the two quarter-wavelength coupled lines. Various advanced designs have been proposed in the literatures [2.1]-[2.7]. The goal of this chapter is to develop a new miniaturized Marchand balun using multilayer printed circuit board fabrication process. By utilizing two coupled artificial transmission lines (ATLs), the proposed balun demonstrates a very compact size of 0.218 ǘ 0.44 Og2. The artificial transmission line used is a modification of the design in [2.8]-[2.9]. As compared with a conventional stripline structure, the required physical length of an artificial line can be substantially reduced whereas its electrical properties remain the same. In Section 2.2, the circuit configuration of the novel miniaturized balun is introduced. By means of the even odd mode analysis, the coupled artificial line is investigated in detail in Section 2.3. The simulated and experimental results are discussed in Section 2.4. A comparison between the proposed design and previous works is tabulated as well. This chapter is concluded with a brief summary in Section 2.5.. 2.2 Circuit configuration Figure 2.1 illustrates the circuit layout of the miniaturized Marchand balun. The balun was fabricated on a six-layer printed circuit board with Rogers RO4003C substrates..

(12) The dielectric constant is 3.38 and the loss tangent is 0.0027. To enhance the coupling between the coupled lines, the spacing between metal layers M3 and M4 is 8 mil. The substrate thicknesses between all other layers, on the other side, are 20 mil. An enlargement of the proposed Marchand balun is shown in Fig. 2.2 along with the circuit dimensions. The Marchand balun consists of two coupled artificial transmission lines and an additional artificial line for compensation. It has been shown that in the first-order approximation, the uncoupled artificial transmission line can be represented by line inductors, parallel-plate capacitors, and interdigital capacitors [2.8]-[2.9]. The synthesis procedure for an uncoupled unit-celled artificial transmission line has also been discussed in [2.8]-[2.9]. By applying the synthesis procedure together with the even odd mode analysis, the even- and odd-mode lumped equivalent circuit models of the coupled-line section can be achieved along with their associate characteristic impedances. The coupling coefficient and the impedance matching of the coupled lines, which are directly related to the even- and odd-mode characteristic impedances, can be therefore determined. This synthesis procedure can be repeated for various inductance and capacitance values until the coupled lines meet the design goal, i.e. Zc = 50 ohm and C = 4.8 dB, the theoretical coupling coefficient for optimal impedance matching with all ports being terminated by 50 ohms. On the other hand, due to the physical separation of the two balanced output ports, i.e. ports 2 and 3, an additional artificial transmission line is inserted in-between the two coupled lines for compensating the asymmetry. In the design, the even- and odd-mode characteristic impedances of each of the two coupled lines are first derived using the analysis method discussed in Section 2.3. The electrical parameters are then substituted into software Agilent ADS to determine the required electrical length and characteristic impedance of the compensated line for optimizing the balanced output response. In the ADS simulation all lines are modeled by ideal lines for simplicity. Finally, the.

(13) compensated line is physically realized by an artificial transmission line using the synthesis procedure given in [2.8]-[2.9]. A post-integration tuning process is inevitably necessary to account for the parasitic coupling. According to the simulation, the compensated line has a characteristic impedance of 45 ohms and a phase delay of 40 degrees at the center operating frequency. Three stripline-to-conductor-backed coplanar waveguide transitions are connected to the input/output ports for measuring purpose. In a back-to-back configuration, the insertion loss of the transition is less than 1 dB over the band of concern. The vias around the ports are used to suppress higher order modes. Although not shown in Fig. 2.1, the Marchand balun is surrounded by a row of vias to prevent potential exterior interference during measurement.. 2.3. Analysis of the coupled artificial line section The electrical parameters of a coupled artificial transmission line can be analyzed. with the help of even odd mode analysis. The plane of symmetry lies in the middle plane between metal layers M3 and M4. In the analysis, it can be replaced by either a magnetic or an electric wall, which corresponds to the even and odd modes, respectively, of the coupled line section. The simulated two-port S-parameters of both modes can be readily achieved and converted into ABCD matrices with a system impedance Z0. Meanwhile, the ABCD matrix of an ideal lossless transmission line with a physical length L is well known [2.10, chap 4]. It is therefore routine to verify that the even- and odd-mode propagation constants and characteristic impedances of the coupled artificial line can be easily derived by equating each entry in the ABCD matrices representing the even- and odd-mode circuits to the corresponding entry in the ABCD matrix for an ideal lossless transmission line. Table I summarizes the calculated electrical parameters of the coupled artificial line used in the proposed balun. The simulator is Ansoft HFSS 10.1. Although the losses are taken into account in the full-wave simulation, for simplicity they have.

(14) been neglected in the calculation of the electrical parameters. The center frequency is 1.9 GHz. It is shown that the calculated coupling coefficient, C, is 5.1 dB, close to the theoretical value of 4.8 dB. In addition, the coupled-line section reveals good impedance matching. The slight deviation from the ideal values is reasonable, taking into account the fine and complicated structure of the miniaturized coupled artificial lines and the ever-existing parasitic coupling. The ideal case of Zc = 50 ohms and C = 4.8 dB is taken as the initial design goal in developing the coupled line sections. A tuning process is required to optimize the response after the whole circuit integration. The artificial couple line also features a slow wave factor (SWF) of 3.31 [2.8], which is nearly twice than that of a conventional stripline in the same substrate. The calculated ratio between the evenand odd-mode characteristic impedances remains better than 3.5 over the frequency band of interest, an important factor for achieving balanced signals at the balun outputs.. 2.4 Simulated and experimental results The 40A-GSG-400-DP-W probe heads from Picoprobe® are used for measurement. A full two-port SOLT calibration was carried out to shift the reference planes to the probe tips. During the measurement the non-contacted ports are terminated by two 100 chip resistors in parallel for impedance matching. The measured 10 dB return loss (RL) bandwidth is 1.43–2.58 GHz, i.e., a fractional bandwidth of 60%. The maximum return loss is 24.5 dB, and the minimum insertion loss is 3.4 dB. The insertion loss deviates from the ideal value only by 0.4 dB. In the 10 dB return loss bandwidth, the phase imbalance is less than 1.5Ʊ, and the amplitude imbalance is smaller than 0.5 dB. The discrepancy between the simulated and measured results can be mostly attributed to the nonideal effects of the ignored finite conductor thicknesses. The fabrication tolerance and the uncertainty of the termination resistors may contribute to the discrepancy as well. Due to the unequal even- and odd-mode phase velocities, the ever-existing forward-wave.

(15) component in the coupled artificial lines becomes apparent and eventually deteriorates the balanced response for frequencies beyond 3 GHz. As compared with previous works, the proposed balun has the smallest occupied size. In addition, it features excellent in-band amplitude and phase balance, and a comparable 10 dB return loss bandwidth. The superiority of the proposed design over previous works is clearly verified. The dimensions of the proposed miniaturized balun were determined using Ansoft HFSS. In the simulation the conductors were modeled by infinitely thin perfect conductors due to insufficient computing resource. The parameters associated with the coupled line sections are lATL = 4.3, ll1 = 1.6, ll2 = 0.5, ll3 = 1.225, lc1 = 1.15, lc2 = 1, wC1 = 0.6, wd = 0.2, and gd = 0.2. The parameters related to the compensated line are lcomp = 4, ll4 = 1.6, lc3 = 2, lc4 = 1.4, wC2 = 1.6, and wC3 = 0.4. The feeding structure has dimensions of lcpw = 1.15, wcpw = 1.2, and ls = 0.65. All units are in millimeters. The widths of both line inductors and interdigital fingers are 0.2 mm. The spacing between the fingers is 0.2 mm as well. The balun features a very compact size of 18.725 ǘ 3.8 mm2, or equivalently, 0.218 ǘ 0.044 Og2. Here Og is referred to as the guided wavelength of a 50 ohm stripline in the same substrate. Figure 2.3 illustrates the simulated and measured S-parameters of the Marchand balun at all ports. The simulation was completed by HFSS while the measurement was performed using an Agilent performance network analyzer E8362B along with a probe station. The 40A-GSG-400-DP-W probe heads from Picoprobe® are used for measurement. A full two-port SOLT calibration was carried out to shift the reference planes to the probe tips. During the measurement the non-contacted ports are terminated by two 100 ohm chip resistors in parallel for impedance matching. The measured 10 dB return loss (RL) bandwidth is 1.43 – 2.58 GHz, i.e., a fractional bandwidth of 60 %. The maximum return loss is 24.5 dB, and the minimum insertion loss is 3.4 dB. The insertion loss deviates from the ideal value only by 0.4 dB. The measured amplitude and phase.

(16) imbalance between the two output ports is illustrated in Fig. 2.4. In the 10 dB return loss bandwidth, the phase imbalance is less than 1.5 degrees, and the amplitude imbalance is smaller than 0.5 dB. The discrepancy between the simulated and measured results can be mostly attributed to the nonideal effects of the ignored finite conductor thicknesses. The fabrication tolerance and the uncertainty of the termination resistors may contribute to the discrepancy as well. Due to the unequal even- and odd-mode phase velocities, the ever-existing forward-wave component in the coupled artificial lines becomes apparent and eventually deteriorates the balanced response for frequencies beyond 3 GHz. Table II compares the 10 dB return loss bandwidth, occupied size, in-band amplitude and phase imbalance of the proposed Marchand balun to various previous designs on printed circuit boards [2.1]-[2.7]. Here “in-band” is referred to as the 10 dB return loss bandwidth. The data are estimated from the figures in the literatures. As compared with previous works, the proposed balun has the smallest occupied size. It is almost one-third the size of the second smallest one. In addition, it features excellent in-band amplitude and phase balance, and a comparable 10 dB return loss bandwidth. The superiority of the proposed design over previous works is clearly verified.. 2.5 Conclusion In this chapter a novel multilayer miniaturized Marchand balun has been analyzed and experimentally verified. The balun is realized by utilizing two coupled artificial transmission lines. In comparison with previous works, the miniaturized balun features the smallest cirucit size and excellent in-band amplitude and phase balance. The proposed design can be applied to MMIC fabrication process as well. With better line resolution, which is 0.1 mm in the current design, it is believed that the size reduction precentage of the proposed scheme can be further improved..

(17) Fig. 2.1 Circuit layout of the miniaturized Marchand balun. Three-dimensional view and the cross-sectional view. h1 = h3 = 40 mil, and h2 = 8 mil.. Fig. 2.2 Detail geometries of the miniaturized Marchand balun..

(18) Fig. 2.3 Simulated and measured S-parameters of the proposed miniaturized Marchand balun.. Fig. 2.4 Measured amplitude and phase imbalance of the miniaturized Marchand balun..

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(20) References [2.1] R. Phromloungsri, M. Chongcheawchamnan, and I. D. Robertson, “Inductively compensated parallel coupled microstrip lines and their applications,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 9, pp. 3571–3582, Sep. 2007. [2.2] K. S. Ang and I. D. Robertson, “Analysis and design of impedance transforming planar Marchand baluns,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 2, pp. 402–406, Feb. 2001. [2.3] W. M. Fathelbab and M. B. Steer, “New classes of miniaturized planar. Marchand baluns,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, pp. 1211–1220, Apr. 2005. [2.4] Z.-Y. Zhang, Y.-X. Guo, L. C. Ong, and M. Y. W. Chia, “A new planar balun,” in IEEE MTT-S Int. Dig., Long Beach, CA, Jun. 12–17, 2005, pp. 1207–1210. [2.5] M. Chongcheawchamnan, C. Y. Ng, M. S. Aftanasar, I. D. Robertson, and J. Minalgiene, “Broadband CPW Marchand balun using photoimageable multilayer thick-film,” Electron. Lett., vol. 37, no. 20, pp. 1228–1229, Sep. 2001. [2.6] L. K. Yeung, W.-C. Cheng, and Y. E.Wang, “A dual-band balun using broadside-coupled coplanar striplines,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 8, pp. 1995–2000, Aug. 2008. [2.7] L. K. Yeung and K.-L. Wu, “A dual-band coupled-line balun filter,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 11, pp. 2406–2411, Nov. 2007. [2.8] C.-W.Wang, T.-G. Ma, and C.-F. Yang, “A new planar artificial transmission line and its applications to a miniaturized Butler matrix,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2792–2801, Dec. 2007. [2.9] T.-G. Ma, C.-W.Wang, R.-C. Hua, and J.-W. Tsai, “A modified quasi-Yagi antenna with a new compact microstrip-to-coplanar strip transition using artificial transmission lines,” IEEE Trans. Antennas Propagat, to be published. [2.10] D. M. Pozar, Microwave Engineering, 3rd ed. New York: Wiley, 2005..

(21) Chapter 3 Novel Uniplanar Synthesized Coplanar Waveguide and the Application to Miniaturized Rat-race Coupler 3.1 Introduction The coplanar waveguide (CPW), which was first introduced in 1969, has become one of the most reliable planar transmission lines in microwave and millimeter wave applications. The coplanar waveguide features a simple fabrication process with scalable dimensions, wide attainable characteristic impedances, and realizable series/shunt stubs. The surface mounted devices can be easily mounted on a coplanar waveguide as well. Recently, due to the urgent demands of highly integrated systems, circuit miniaturization with slow-wave synthesized or artificial transmission lines has drawn intensive attention in the microwave community. Miniaturized microwave components can improve the utilization of resources and reduce the fabrication cost. Many researchers have been devoted themselves to investigating the miniaturization techniques for transmission lines [3.1]-[3.6]. In [3.1], periodic loaded stubs were applied to develop artificial transmission lines in microstrip form. The LC ladder network [3.2] and the complementary-conducting-strip (CCS) [3.3] are the common ways to realize synthesized lines in MMIC process. Artificial transmission lines based on quasi-lumped microstrip inductors and capacitors were introduced and studied in [3.4]. Synthesized transmission lines in coplanar waveguide form have been realized by series and shunt stubs in [3.5]-[3.6]. In this subproject, a novel synthesized coplanar waveguide, namely the uniplanar synthesized coplanar waveguide (USCPW), is proposed and investigated. The new design, which is composed of quasi-lumped meander line inductors and interdigital capacitors in.

(22) coplanar waveguide form, can be synthesized in a simple and systematic way. When compared with a conventional coplanar waveguide with identical characteristic impedance and electrical length, the proposed synthesized line is about one-sixth the length of the conventional one. In Sec. 3.2, the circuit layout and electrical characteristics of the newly proposed synthesized line are carefully discussed. A miniaturized rat-race coupler is developed in this paper to demonstrate the size reduction capability of the proposed uniplanar synthesized coplanar waveguide (USCPW).. 3.2 Uniplanar synthesized coplanar waveguide The coplanar waveguide is distributive in nature but can be modeled by cascaded sections of alternatively connected series inductance and shunt capacitance. A synthesized coplanar waveguide can be realized with high slow-wave effects by replacing the series inductance and shunt capacitance in a conventional coplanar waveguide with quasi-lumped components. The circuit layout and the equivalent lumped circuit model of the proposed slow-wave uniplanar synthesized coplanar waveguide (USCPW) are shown in Figs. 3.1 and 3.2, respectively. Here, a 50-ohm 90-degree uniplanar synthesized coplanar waveguide (USCPW) is demonstrated as a design example. It will be referred to as a unit cell in the following discussion. As shown in Fig. 3.1, two meander line inductors, which are symmetrical with respect to the center of the unit cell, are used to replace the series inductance in a conventional line. In the first order approximation, the meander line inductor can be represented by a lumped network consisting of a series inductor Lul and four parasitic shunt-to-ground capacitors Cul, as indicated in Fig. 3.2. The quasi-lumped interdigital capacitors on each side of the meander line inductor, on the other hand, can be accounted for by a shunt-to-ground capacitor Cuc. Two series inductors Luc are added to the circuit model to account for the additional current paths flowing through the connection lines of the interdigital capacitors. Two short conventional.

(23) 50-ohm coplanar waveguides are attached to each side of the unit cell for phase adjustment between the actual phase of the unit cell and the targeted value. To simplify the analysis, the lumped equivalent circuit model in Fig. 3.2 can be rearranged as a simple L-section with an equivalent series inductance Ls and a shunt-to-ground capacitance Cp, where. and. Ls. 2 Lul 2 Luc. (3.1). Cp. 2Cuc 8Cul .. (3.2). With (1) and (2), the characteristic impedance Zc and guided wavenumber g of the unit cell can be derived by [3.4] Zc. and. Eg. Ls / C p. (3.3). Z Ls C p / lu 8 .. (3.4). Here, lu8 is the physical length of the unit cell. It is routine to verify that as Ls and Cp rise proportionally, the guided wavenumber in (3.4) can be dramatically raised whereas the characteristic impedance in (3.3) keeps unchanged. The required physical length of the synthesized coplanar waveguide is, in turn, significantly reduced. On the other hand, the electrical properties of the synthesized line remain principally the same as its conventional counterpart. The approximate equations (3.1)-(3.4) provide very accurate results as long as the unit cell is electrically small when compared with the guided wavelength. The 50-ohm 90-degree unit cell was designed on a 0.508-mm RO4003C substrate. The relative dielectric constant is 3.55 and the loss tangent is 0.0027. Air bridges are attached to suppress the unwanted slotline mode. At the center frequency, 915 MHz, the occupied area of the unit cell is merely 10.6 mmġ× 12.75 mm, or equivalently, 0.041 gġ× 0.05 g. Here g is referred to as the guided wavelength of a 50-ohm coplanar waveguide on the same substrate at 915 MHz. The dimensions of the unit cell are wcpw = 3 mm, scpw.

(24) = 0.2 mm, lcpw = 0.3 mm, wu1 = 0.2 mm, wu2 = 3.3 mm, wu3 = 2 mm, wu4 = 0.7 mm, wu5 = 0.4 mm, wu6 = 9.75 mm, lu1 = 0.3 mm, lu2 = 0.2 mm, lu3 = 0.6 mm, lu4 = 2.2 mm, lu5 = 0.4 mm, lu6 = 0.3 mm, lu7 = 10 mm, lu8 = 10.6 mm, and su1 = su2 = su3 = 0.2 mm. For the sake of easy mounting of SMA adapters, two additional 5 mm long coplanar waveguides are connected to each side of the unit cell. The additional lines are deembedded using the TRL calibration technique during the measurement. The lumped equivalents of each quasi-lumped component can be readily extracted. Each quasi-lumped component is treated as a two-port network in the extraction, and the associate port definitions are indicated in Fig. 3.2. The details are not shown here due to the limited space. For the 50-ohm. 90-degree unit cell, the extracted values are Lul = 5.58 nH, Cul = 0.095 pF, Cuc = 1.73 pF, and Luc = 2.48 nH. The calculated, simulated and measured characteristic impedances and phase delays of the 50-ohm 90-degree uniplanar synthesized coplanar waveguide (USCPW) are shown in Fig. 3.3. The simulation was carried out by the Ansoft HFSS, while the measurement was taken by an Agilent E8363B network analyzer with the TRL calibration included. The calculated parameters were achieved by the Agilent ADS along with the equivalent lumped circuit model and the extracted element values. By utilizing the S-parameters, the characteristic impedance of the unit cell is evaluated by [3.4], Zc. Re( Z o. (1 S11 ) 2 S212 . ) (1 S11 ) 2 S 212. (3.5). Referring to Fig. 3.3, excellent agreement between the simulated and measured results can be observed. The measured characteristic impedance and phase delay are 51.8 ohms and -90.5° at the center frequency. The measured bandwidth with the variations of the characteristic impedance < 5% is 110 MHz. The phase response is linear over the frequency band of concern. The calculated results using lumped circuit model agree well with the measured ones. The correctness and effectiveness of the lumped equivalent.

(25) circuit model are therefore verified. By applying the same design procedure, an additional 90-degree uniplanar synthesized coplanar waveguide (USCPW) was designed, simulated and measured, as shown in the inset of Fig. 3.4. The characteristic impedance is 70.7 ohms at 915 MHz. The dimension of the 70-ohm unit cell is 0.043 gġ × 0.043 g. The simulated and measured characteristic impedances and phase delays are shown in Fig. 3.4. Excellent agreement between the results is observed as well. At 915 MHz, the measured characteristic impedance and phase delay are 73.1 ohms and -89.9 degrees, respectively. The slow wave factors of the unit cells reach up to 7.5, while the quality factors are around 30. The 70-ohm unit cell will be applied to the miniaturized rat-race coupler in the following section.. 3.3 Miniaturized Rat-race Coupler To demonstrate the miniaturization capability of the proposed uniplanar synthesized coplanar waveguide (USCPW), a novel miniaturized rat-race coupler was developed and experimentally verified on a 0.508-mm RO4003C substrate. The center frequency is 915 MHz. The design procedure is simple. By replacing the conventional 90-degree transmission lines in a rat-race coupler with the 70-ohm uniplanar synthesized coplanar waveguides (USCPWs), a miniaturized rat-race coupler can be readily achieved. The circuit layout is illustrated in Fig. 3.5, which is a directly scaled version of the developed coupler. Additional air bridges are applied to suppress the higher order modes. In the proposed design, the 3Og/4 line is realized by three cascaded 70-ohm unit cells. To minimize the occupied area, the three cascaded unit cells for the 3Og/4 line are arranged in parallel with the remaining three synthesized unit cells. All unit cells are in the same form, and their electrical lengths are a little bit less than 90 degrees to account for the interconnection effects. The ports are inserted in-between the unit cells, and two.

(26) compensated coplanar waveguide sections are added to the junctions of ports 1 and 3 to compensate for the parasitic effects due to the closely arranged interdigital capacitors and CPW feed lines. The geometric parameters associated with the interconnections are lr1 = 25.3, lr2 = 59.8, lr3 = 15.95, lr4 = 43.8, lr5 = 0.5, lr6 = 0.4, lr7 = 5.35, lr8 = 0.55, lr9 = 2.85, lr10 = 1.35, and lrf = 8. All units are in millimeters. The dimension of the miniaturized rat-race coupler is 15.95 mmġ× 43.8 mm, or equivalently, 0.068 g × 0.188 g. When compared with a conventional design, the size reduction percentage reaches up to 92.8%. The simulated and measured S-parameters at the sum and difference ports are illustrated in Fig. 3.6(a) and (b), respectively. The phase differences between the output ports are shown in Fig. 3.7. Fairly good agreement between the simulated and measured results is observed. The slight discrepancy can be attributed to the fabrication tolerance, the parasitic effects of air bridges, and the ignored finite conductor thickness in the simulation. At the center frequency, the return losses at the sum and difference ports are lower than 24 dB. The measured isolation between the input ports is 27 dB. As the sum port (port 1) is excited, the measured |S21| and |S31| are -3.37 and -3.34 dB, respectively, at the center frequency. The simulated and measured phase differences between S21 and S31 are -0.55 and -3.23 degrees. When the signal is injected into the difference port (port 4), the measured |S24| and |S34| are -3.23 and -3.11 dB, and the simulated and measured phase differences are 180.6 and 177.6 degrees, respectively, at 915 MHz. From 870 to 1005 MHz, the miniaturized rat-race coupler simultaneously satisfies the following specifications: the return loss and isolation > 15 dB, the amplitude imbalance < 0.8 dB and the phase imbalance < 6 degrees. This is equivalent to a fractional bandwidth of 15%. According to the experimental results, the electrical response of the miniaturized rat-race coupler is comparable to that of a conventional design. The circuit size, on the other side, is dramatically reduced..

(27) 3.4 Conclusion By utilizing quasi-lumped coplanar waveguide components, a novel slow-wave synthesized coplanar waveguide, namely the uniplanar synthesized coplanar waveguide (USCPW), has been proposed and investigated in this paper. The occupied size of a 90-degree unit cell is merely 0.002 g2. A lumped equivalent circuit model, which is capable of explaining the complicated behavior of the uniplanar synthesized coplanar waveguide (USCPW), has been proposed and discussed. The lumped equivalents are given as well. Based on the new synthesized coplanar waveguide, a novel uniplanar miniaturized rat-race coupler has been developed and experimentally verified. The proposed coupler is merely 7.2% the size of a conventional design. The circuit response, on the other hand, is comparable to the conventional one. To the authors’ knowledge, the proposed rat-race coupler is the smallest design in coplanar waveguide form using printed circuit board technology. The promising potential of the proposed uniplanar synthesized coplanar waveguide (USPCW) for circuit miniaturization is clearly unveiled..

(28) (a). (b) Fig. 3.1. Circuit layout of the unit cell of the uniplanar synthesized coplanar waveguide. (a) Three-dimensional view. (b) Top view.. Fig. 3.2. Lumped equivalent circuit model..

(29) Fig. 3.3. Calculated, simulated, and measured characteristic impedances and phase delays of the 50-ohm uniplanar synthesized coplanar waveguide (USCPW).. Fig. 3.4. Simulated and measured characteristic impedances and phase delays of the 70-ohm uniplanar synthesized coplanar waveguide (USCPW)..

(30) Fig. 3.5. Circuit layout of the miniaturized rat-race coupler.. (a).

(31) (b) Fig. 3.6. Simulated and measured S-parameters of the miniaturized rat-race coupler. (a) Sum port. (b) Difference port. Fig. 3.7. Simulated and measured phase differences of the miniaturized rat-race coupler..

(32) References [3.1]. K. W. Eccleston and S. H. M. Ong, “Compact planar microstripline branch-line. and rat-race couplers,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 10, pp. 2119-2125, Oct. 2003. [3.2]. P.. Kangaslahti,. P.. Alinikula. and. V.. Porra,. “Miniaturized. artificial-transmission-line monolithic millimeter-wave frequency doubler,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 4, pp. 510-518, Apr. 2000. [3.3]. C.-C. Chen and C.-K. C. Tzuang, “Synthetic quasi-TEM meander transmission. lines for compacted microwave integrated circuits,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 6, pp. 1637-1647, Jun. 2004. [3.4]. C. W. Wang, T. G. Ma and C. F. Yang, “A new planar artificial transmission line. and its applications to a miniaturized butler matrix,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2792–2801, Dec. 2007. [3.5]. C.-T. Lin, C.-L. Liao, and C. H. Chen, “Finite-ground coplanar waveguide. branch-line couplers,” IEEE Microw. Wireless Comp. Lett., vol. 11, no. 3, pp. 127-129, March 2001. [3.6]. T. Fujii, I. Ohta, T. Kawai and Y. Kokubo, “Miniature broad-band CPW 3-dB. branch-line couplers in slow-wave structure,” IEICE Trans. Electron., vol. E90-C, no. 12, pp. 2245–2253, Dec. 2007.

(33) Chapter 4 Miniaturized Coupled-line Couplers Using Uniplanar Synthesized Coplanar Waveguides 4.1 Introduction Passive microwave components, principally developed by transmission lines, are large in size and have become the major bottleneck in realizing highly integrated systems. To tackle this problem, slow-wave artificial transmission lines have drawn a great deal of attention in the microwave community, because of their capability of miniaturization and cost reduction. In literature, the artificial transmission line is also known as the synthesized transmission line. Investigations on the miniaturizations of transmission lines, based on slow wave structures, have been found in [4.1]-[4.8]. When compared with other size reduction techniques [4.9]-[4.11], the slow-wave artificial transmission line provides a simple and systematic way to synthesize miniaturized components without the need of surface mounted devices, via holes, or photonic bandgap structures. Meanwhile, the coupled-line couplers, an important building block in microwave systems, have been investigated intensively in past decades [4.12]. Advanced directional couplers in CPW form have been reported in both edge-coupled and broadside-coupled configurations. Edge-coupled CPW couplers with interdigital capacitor loading, floating finite-extent backed conductor, and composite right/left-handed lines have been reported in [4.7], [4.13], and [4.14], respectively. Broadside-coupled CPW couplers with defected ground structure, dielectric overlay, and hexagonal slot were investigated in [4.15]-[4.17]. These advanced designs are capable of improving the coupling strength, reducing the occupied size, or widening the operating bandwidth. Nevertheless, except for [4.7], the physical lengths of the previously reported couplers are all one-quarter wavelength long. This is unacceptable in modern applications and further miniaturization is required..

(34) We proposed a novel slow-wave synthesized coplanar waveguide, namely, the uniplanar synthesized coplanar waveguide, in [4.8]. The new design is composed of quasi-lumped coplanar waveguide (CPW) meander line inductors and interdigital capacitors. The synthesized line is only one-sixth the length of a conventional CPW, with identical characteristic impedance and electrical length. The preliminary results, including the circuit layout and equivalent lumped circuit model, have been introduced in [4.8]. A miniaturized rat-race coupler, which is merely 7.2% the size of a conventional one, was developed as a demonstration of the miniaturization capability of the new synthesized line. In the first part of this paper, i.e., Sec. 4.2, the electrical characteristics of the new synthesized line are investigated in greater detail. The explicit synthesis procedure, which was not discussed in [4.8], is given along with the extraction method for each individual component in the equivalent circuit model. The attenuation constants, slow wave factors, and quality factors of the synthesized coplanar waveguides are compared to those of a conventional CPW. Synthesized coplanar waveguides, with alternative layouts but identical in-band responses, are discussed in terms of the transmission coefficients as well. By utilizing the uniplanar synthesized coplanar waveguide, in the second half of this paper, i.e., Sec. 4.3, three novel miniaturized coupled-line couplers, including a 10-dB backward-wave edge-coupled CPW coupler, a 6-dB backward-wave broadside-coupled CPW coupler, and a 3-dB forward-wave CPW coupler, are proposed and experimentally verified. The even odd mode analysis is applied to achieve the design charts with respect to the geometric parameters of the synthesized coupled lines. For a specific coupling coefficient, the dimensions of the miniaturized couplers can be determined in accordance with the design charts. The miniaturized backward-wave couplers are approximately one-third the size of their corresponding conventional designs. The responses, on the.

(35) other hand, remain almost unaltered. The design methodology, even odd mode analysis, design charts, and experimental results will be investigated thoroughly.. 4.2 Uniplanar Synthesized Coplanar Waveguide A. Circuit Configuration and Synthesis Procedure The circuit layout and equivalent lumped circuit model of the uniplanar synthesized coplanar waveguide are shown in Figs. 4.1 and 4.2, respectively. Here, a 50-ohm 90-degree synthesized line, which will be referred to as a unit cell in the following discussion, is demonstrated as an example. As shown in Fig. 4.1, the meander line inductors for replacing the series inductance in a conventional CPW are arranged symmetrically, with respect to the center of the unit cell. In the first order approximation, each of the meander line inductors can be represented by a network consisting of a series lumped inductor Lul and four parasitic shunt capacitors Cul, as indicated in Fig. 4.2. The interdigital capacitors on each side of the meander line inductors can be summed up as a shunt capacitor Cuc. Two series lumped inductors Luc are then added to the model to account for the additional current paths flowing through the connection lines of the interdigital capacitors. The short conventional 50-ohm CPWs on each side of the unit cell are used for phase adjustment between the actual phase of the unit cell and the targeted value. The lumped circuit model in Fig. 4.2 is too difficult to analyze directly due to the complicated interconnections. To simplify the analysis, the circuit model can be approximately rearranged as a simple L-section with an equivalent per-unit-cell series inductance Ls and per-unit-cell shunt-to-ground capacitance Cp, where Ls. and. Cp. 2 Lul 2 Luc. (4.1). 2Cuc 8Cul .. (4.2).

(36) With (4.1) and (4.2), the characteristic impedance Zc and guided wavenumber Eg of the unit cell can be estimated by [4.4]. Zc and. Ls C p. E g Z LsC p / lu 8 ,. (4.3) (4.4). where lu8 is the physical length of the unit cell. As Ls and Cp in (4.1)-(4.2) rise proportionally, the guided wavenumber in (4.4) can be dramatically increased whereas the characteristic impedance in (4.3) remains invariant. The physical length of the unit cell, with a specific electrical length, is hence significantly reduced. The approximate expressions (4.1)-(4.4) provide very accurate results as long as the unit cell is electrically small when compared with the guided wavelength. The synthesis procedure for a uniplanar synthesized coplanar waveguide with an arbitrary electrical length and characteristic impedance is straightforward. First, the lumped equivalents of each individual quasi-lumped component should be extracted. As indicated in Fig. 4.2, each quasi-lumped component can be treated as a two-port network; the associate port definitions (P1, P2, P1’, and P2’) are shown in the figure. The. S-parameters of each two-port network can be simulated by a full-wave EM simulator, e.g., Ansoft HFSS. For the interdigital capacitors, the simulated S-parameters are de-embedded to the reference planes t and t c , as indicated in Fig. 4.2. Using the simulated S-parameters, the corresponding Y or Z matrix can be retrieved by standard matrix operations; its associated - or T-equivalent circuit network can be obtained at the same time. The lumped equivalents of each quasi-lumped component can be determined by the - or T-equivalent circuit parameters. After determining all element values of the equivalent circuit model, the characteristic impedance and propagation constant of the unit cell can be calculated using (4.1)-(4.4). The phase delay of the synthesized line is.

(37) T. E g lu 8 .. (4.5). By repeating the extraction procedure, a set of design curves versus the dimensions of the meander line inductors and interdigital capacitors could be retrieved. This, in turn, helps determine the dimensions of a unit cell with specific electrical properties. A post-integration tuning process might be required to account for the parasitic coupling effects of the closely arranged quasi-lumped elements. These design curves are easy to build and similar to Fig. 4.2 in [4.4]. They will not be repeated for brevity. B. Experimental Results and Discussion The 50-ohm 90-degree unit cell was developed on a 0.508-mm RO4003C substrate. The relative dielectric constant is 3.55 and the loss tangent is 0.0027. Air bridges are used to suppress the unwanted slotline mode. For easy mounting of SMA adapters, two additional 5-mm CPWs are connected to each side of the unit cell. The additional lines are de-embedded using the Thru-Reflect-Line (TRL) calibration technique in the measurement. The dimensions of the unit cell are summarized in Table I for easy reference. The subscript “u” represents the parameters associated with the unit cells. At a center frequency of 915 MHz, the occupied size of the unit cell, including the finite-extent ground plane, is merely 10.6 mmġ× 12.75 mm, or equivalently, 0.041 g × 0.05 g. It is only one-sixth the length of a conventional CPW with the same electric length. Here, g is the guided wavelength of a 50-ohm CPW on the same substrate at 915 MHz. The finite-extent ground plane, whose width is set equal to that of the signal trace of a 50-ohm CPW, accounts for the return current path on the ground plane. The simulated, measured, and calculated S-parameters of the unit cell are shown in Fig. 4.3(a). The full-wave simulation was carried out by the Ansoft HFSS, while the measurement was taken by an Agilent E8363B network analyzer. The calculation, on the other side, was completed by the Agilent ADS, using the equivalent circuit model in Fig. 4.2. The extracted element values are Lul = 5.58 nH, Cul = 0.095 pF, Cuc = 1.73 pF, and Luc.

(38) = 2.48 nH. By utilizing the S-parameters, Fig. 4.3(b) shows the characteristic impedance of the 50-ohm unit cell from 0.5 to 1.3 GHz using [4.18] Zc. Re( Z 0. (1 S11 ) 2 S 212 ). (1 S11 ) 2 S 212. (4.6). In (4.6), the S-parameters can be derived from full-wave simulation, measurement, or model calculation. Fig. 4.3(b) also shows the phase delay of the synthesized line. Excellent agreement between the results is observed. The measured characteristic impedance and phase delay are 51.8 ohms andġ Į90.5°, respectively, at the center frequency. Within a bandwidth of 110 MHz, the variation of the characteristic impedance is less than 5%. To synthesize a 50-ohm 90-degree CPW, the layout in Fig. 4.1 is not the only approach. As illustrated in Fig. 4.4(a), by cascaded connection of two 45-degree unit cells, three 30-degree unit cells, or four 22.5-degree unit cells, a 50-ohm 90-degree synthesized line can be realized, as well. At the center frequency, all synthesized lines have the same electrical properties. However, their out-of-band transmission responses are dramatically different, as shown in Fig. 4.4(b). The unit cell is naturally a lowpass filter whose cutoff frequency is inversely proportional to the square root of the product of the per-unit-cell inductance Ls and per-unit-cell capacitance Cp. As the per-unit-cell inductance and capacitance become larger, the cutoff frequency moves toward a lower frequency range. Accordingly, the 90-degree line formed by a single unit cell has the lowest cutoff frequency among the designs. The synthesized line, using four cascaded unit cells, on the other hand, features the steepest fall-off rate in addition to the highest cutoff frequency; this is because the four cascaded 22.5-degree unit cells can be approximated by an eighth-order lowpass filter, inherently having good frequency selectivity in the transition region..

(39) Two additional 90-degree unit cells were obtained using the same synthesis procedure. At 915 MHz, the characteristic impedances of the additional cells are 35.4 and 70.7 ohms. The geometric parameters are also summarized in Table I. The sizes of the 35-ohm and 70-ohm unit cells are 0.042 g × 0.06 g and 0.043 g × 0.043 g, respectively. For the 35-ohm synthesized line, the meander line inductors are replaced by straight line inductors, as the required series inductance is relatively low. The attenuation constants, g, and guided wavenumbers, g, of the 35-, 50-, and 70-ohm unit cells can be determined by [4.18] e. where. J g lu 8. 1 S112 S 212 (1 S112 S 212 ) 2 (2 S11 ) 2 2 S 21 ,. Jg. D g jE g .. (4.7) (4.8). In Fig. 4.5, the normalized attenuation constants, (dB/Og), and normalized guided wavenumbers, (Eg/k0), of the unit cells are compared to those of a conventional 50-ohm CPW. The results are simulated by Ansoft HFSS. The normalized guided wavenumber (Eg/k0) is known as the slow wave factor of a transmission line. At the center frequency, the slow wave factors of the synthesized lines are 7.5, five times higher than that of a conventional CPW. The attenuation constant in Fig. 4.5, on the other side, is normalized by the guided wavelength. This represents the power dissipated by a transmission line in one guided wavelength. The power dissipation of the synthesized line, though higher than that of a conventional CPW, is still in an acceptable range if its promising miniaturization capability is simultaneously taken into consideration. The unloaded quality factors,. Eg/2Dg, show similar results. At the center frequency, the unloaded quality factors of the 35-, 50-, and 70-ohm unit cells are 66, 31 and 27, respectively; this is good enough for components developed for circuit miniaturization..

(40) 4.3 Miniaturized Coupled-line Couplers In this section, the uniplanar synthesized coplanar waveguides are used to develop novel miniaturized CPW couplers with a high degree of miniaturization and well-behaved circuit responses. With the help of even odd mode analysis, a 10-dB backward-wave edge-coupled directional coupler, a 6-dB backward-wave broadside-coupled directional coupler, and a 3-dB forward-wave edge-coupled coupler are designed and investigated consecutively in the following subsections. All designs were developed on a 0.508-mm RO4003C substrate with a center frequency of 915 MHz. A. Backward-wave edge-coupled coupler The circuit layout of the proposed miniaturized edge-coupled directional coupler is shown in Fig. 4.6(a). The coupler consists of two mutually coupled 90-degree uniplanar synthesized coplanar waveguides. To widen the operating frequency range, each of the coupled lines is formed by a cascaded connection of two 45-degree unit cells. Two interdigital capacitors, each with a finger length leo, are inserted in between the synthesized lines to activate the mutual coupling. The shunt-to-ground interdigital capacitors of each individual line, on the other side, are arranged only on one side of the synthesized line with a finger length lee. Rigorously speaking, the analysis of the synthesized edge coupler is involved, since this coupler lacks a plane of symmetry due to the interdigitated fingers. It makes the even odd mode analysis, the most straightforward way to extract the electrical parameters, failed to be applied directly. However, as indicated in [4.19], the mutual capacitors can be assumed to be approximately symmetrical with respect to the center line T-T’ without loss of generality. With this assumption, the proposed miniaturized coupler can be approximately analyzed using the even odd mode analysis, thus significantly reducing the design complexity. The equivalent circuit model for the synthesized edge coupler is depicted in Fig..

(41) 4.6(b). The per-unit-cell even- and odd-mode inductances and capacitances are given by. Even mode. Ce Le. Cp. (4.9). Ls Lm. (4.10). C p 2Cm. (4.11). Ls Lm. (4.12). Odd mode. Co Lo. To determine the even/odd-mode electrical parameters, including the characteristic impedances, effective dielectric constants, coupling coefficient, and lumped equivalents, the synthesized edge coupler is first treated as a full four-port network in a full-wave simulator. The simulated four-port S-parameters are then imported into the Agilent ADS. With the excitation arrangements shown in Fig. 4.7, the even odd mode analysis is completed, and the four-port S-parameters are converted into a pair of two-port. S-parameters representing the even- and odd-mode half circuits. By substituting the two-port S-parameters into (4.6), the impedances Zi can be derived by Zi. Z0. (1 S11e ( o ) ) 2 S212 e ( o ) (1 S11e ( o ) ) 2 S212 e ( o ). .. (4.13). In (4.13), the subscript e or o represents the even- or odd-mode two-port S-parameters. With the impedance Zi,, the even/odd-mode characteristic impedances can be evaluated by. and. Z 0o. Re( Z i ) 2. (4.14). Z 0e. 2 Re( Z i ) .. (4.15). Using (4.14) and (4.15), the coupling coefficient C of the synthesized edge coupler is,.

(42) C. Z0e Z0o . Z0e Z0o. (4.16). Similarly, the complex propagation constants associated with the even- and odd-mode half circuits can be extracted from the two-port S-parameters, as given by (4.17) in the bottom of the previous page. The even-/odd-mode effective dielectric constants are. H effe ( o ). ( E e ( o ) k0 ) 2 .. (4.18). Design charts for the synthesized edge coupler are derived and summarized in Fig. 4.8 using the even odd mode analysis and (4.13)-(4.18). Two geometric parameters, lee and leo, are studied to unveil their influence on the even-/odd-mode electrical parameters. The finger length, lee, determines the shunt-to-ground capacitor, Cp. It affects both evenand odd-mode characteristic impedances and effective dielectric constants. In contrast, the finger length leo only affects the mutual capacitor Cm. This, in turn, controls the odd-mode characteristic impedance and effective dielectric constant. The effective dielectric constants shown in Fig. 4.8(b) are relatively high, which indicates the outstanding miniaturization capability of the proposed design. In addition, for the case of leo = 2 mm and lee = 4.5 mm, the even- and odd-mode effective dielectric constants are nearly the same. This suggests that the phase velocities of both modes are equal, thus resulting in a directional coupler with high directivity. With the knowledge of even-/odd-mode characteristic impedances, the coupling coefficient of the miniaturized coupler can be evaluated using (4.16). The results are shown in Fig. 4.8(c). The maximum attainable coupling coefficient is around 8.5 dB. For tighter coupling, one may use broadside-coupled configuration or some advanced schemes, such as the tandem coupler and Lange coupler [4.20].. E e(o). Im[ln(. 2 2 2 2 1 S112 e ( o ) S 21 (1 S112 e ( o ) S 21 e(o) e ( o ) ) (2 S11e ( o ) ). 2 S 21e ( o ). ) / l e1 ]. (4.17).

(43) Additionally, the lumped values in Fig. 4.6(b) can be determined using the even-/odd-mode characteristic impedances and effective dielectric constants with the following equations,. Cp Cm. 1 (Co C p ) 2. Ce. H effe cZ 0 e. 1 ( H effo cZ 0 o H effe cZ 0 e ) 2. (4.19) (4.20). Ls. 1 2 ( Z 0 eCe Z 02oCo ) 2. (4.21). Lm. 1 2 ( Z 0 eCe Z 02oCo ) . 2. (4.22). A miniaturized 10-dB edge coupler was developed as a demonstration. The design begins with two uncoupled 50-ohm synthesized lines. From the design charts, the initial lengths of the interdigital fingers are leo = 2.5 mm and lee = 4 mm, which corresponds to a coupling coefficient of 9.75 dB. A post-integration iterative process is required to minimize the parasitic coupling between the connecting lines, to optimize the impedance matching, as well as to adjust the overall electrical length. The final dimensions are leo = 2.6 mm and lee = 4.1 mm. The dimensions of the unit cells are: lu1 = 0.45 mm, lu2 = 0.2 mm, lu3 = 0.6 mm, lu4 = 0 mm, lu5 = 0.4 mm, lu6 = 0.25 mm, wu1 = 0.2 mm, wu3 = 1.6 mm,. wu4 = 0.5 mm, wu5 = 0.4 mm, le1 = 11 mm, le2 = 1.1 mm, and we1 = 16.2 mm. The geometric parameters associated with the interconnections are le3 = 13 mm, we2 = 9.2 mm andġ e1 = 106.5°. The subscript “e” represents the parameters associated with the edge coupler. The calculated even- and odd-mode characteristic impedances are 73 and 37.1 ohms, while the even- and odd-mode guided wavenumbers are 144.6 and 158 rad/m, respectively, at the center frequency. The extracted lumped equivalents using (4.19)-(4.22) are Ls = 7.854 nH, Cp = 1.898 pF, Lm = 2.246 nH, and Cm = 1.089 pF. The occupied size of the synthesized edge coupler, including the finite-extent ground plane, is 11 mm × 19.2 mm, or equivalently, 0.043 g × 0.075 g. Instead of a long.

(44) and narrow appearance, like the design in [4.7], the proposed coupler has a quasi-square appearance, which makes the cascade-connected circuit components be able to be integrated in a more compact way. When compared with a conventional design, the miniaturized coupler shows a size reduction of 68%; moreover, it has an 83% decrease in the coupling length. Additionally, the proposed design is 30% the length and 90% the size of the coupler in [4.7]. The simulated and measured S-parameters are shown in Fig. 4.9(a)-(b), from 0.5 to 1.3 GHz. The simulated and measured phase differences between the output ports are depicted in Fig. 4.9(c). The agreement between the simulated and measured results is good. The discrepancy can be attributed to the fabrication tolerance, the parasitic effects of the bond wires, and the ignored finite conductor thickness in the simulation. At 915 MHz, the measured return loss and isolation (|S41|) are 22.1 and 23.0 dB. The measured |S21| and |S31| are -0.7 and -10.3 dB, respectively. At this frequency, the measured phase differences between S21 and S31 is 90.8°. The phase imbalance is less than 2 degrees over the entire band. From 720 to 1140 MHz, the miniaturized edge coupler simultaneously satisfies the following specifications: the variation of coupling coefficient 'C < 1 dB, the phase imbalance < 2 degrees, and the return loss and isolation > 20 dB. This corresponds to a factional bandwidth of 46 %. Table II compares the electrical performances of the proposed miniaturized edge coupler with those of the design in [4.7]. The data are estimated from the figures of [4.7]. The proposed design features a wider fractional bandwidth, lower power dissipation, and reduced size. B. Backward-wave broadside-coupled coupler The second design for demonstrating the minimization capability of the uniplanar synthesized coplanar waveguides is a backward-wave broadside-coupled directional coupler. The circuit layout is shown in Fig. 4.10. The coupled synthesized lines are arranged on the top and bottom layers of the substrate, which facilitates tight coupling.

(45) between the lines. Four conductor-backed coplanar waveguides are used to connect the coupled synthesized lines to SMA adapters. Additional bond wires can suppress the higher order modes. The vias around the coupler keep the ground planes in equal potential. With the same extraction procedure, the design charts for the synthesized broadside coupler are shown in Fig. 4.11. The coupled lines are investigated in terms of two variables, lbo and lbe. The length, lbo, determines the mutual capacitances between the synthesized lines on the top and bottom layers. This, in turn, controls the odd-mode characteristic impedance and effective dielectric constant. On the other hand, the even-mode parameters are adjusted by the length, lbe, which determines the shunt-to-ground capacitances of the lines. Differing from the edge-coupled coupler, here. lbo also affects the even-mode effective dielectric constant, whereas lbe has a negligible effect on the odd-mode parameters. Based on the even-/odd-mode characteristic impedances, Fig. 4.11(c) shows the calculated coupling coefficient of the synthesized broadside coupler. The maximum attainable coupling is around 3.2 dB, significantly larger than that achieved by the edge coupler. The maximum achievable coupling coefficient is principally limited by the degraded directivity when the difference between the even- and odd-mode phase velocities becomes large. This can be observed when lbo > 5 mm and lbe < 0.6 mm. For tighter coupling, e.g. a coupling coefficient greater than 3 dB, the substrate could be replaced by one with thinner thickness or higher dielectric constant. Additionally, since the broadside coupler is fully symmetric with respect to the middle plane of the substrate, the design charts in Fig. 4.11 are expected to have better accuracy than those in Fig. 4.8. For demonstration purpose, a miniaturized 6-dB broadside coupler was developed and experimentally verified. The initial dimensions of the interdigital fingers from the design charts are lbo = 3 mm and lbe = 1.6 mm. To compensate for the parasitic coupling.

(46) and to optimize the impedance matching, the length lbo is fine-tuned as 3.8 mm. The dimensions of the unit cells are: lu1 = 0.45 mm, lu2 = 0.2 mm, lu3 = 0.6 mm, lu4 = 0 mm, lu5 = 0.4 mm, lu6 = 0.25 mm, lb1 = 11 mm, lb2 = 1.1 mm, wu1 = 0.2 mm, wu3 = 2 mm, wu4 = 0.7 mm, wu5 = 0.4 mm, and wb1 = 10 mm. The geometric parameters associated with the interconnections are lb3 = 3.9 mm, lb4 = 1.4 mm, lb5 = 8.3 mm, sb = 0.2 mm, andġb = 40°. The subscript “b” represents the parameters associated with the broadside coupler. At the center frequency, the calculated even- and odd-mode characteristic impedances are 85.2 and 25.8 ohms, while the even- and odd-mode guided wavenumbers are 134.2 and 167.8 rad/m, respectively. The extracted lumped equivalents using (4.19)-(4.22) are Ls = 7.545 nH, Cp = 1.507 pF, Lm = 3.394 nH, and Cm = 2.358 pF. The size of the miniaturized broadside coupler, including the finite-extent ground plane, is 11 mm × 13 mm, or equivalently, 0.043 g × 0.051 g. When compared with a conventional broadside-coupled CPW coupler, it features a size reduction of 65%; in addition, it also has an 83% decrease in the coupling length. The miniaturized broadside coupler is merely 6% the size of the coupler in [4.15]. The simulated and measured S-parameters are shown in Fig. 4.12(a)-(b), while the simulated and measured phase differences between the output ports are depicted in Fig. 4.12(c). The agreement between the results is good. The measured center frequency shifts slightly to the lower frequency side. At 900 MHz, the measured return loss and isolation (|S41|) are 21.8 and 16.9 dB, respectively. The measured |S21| and |S31| are -1.6 and -6.1 dB at the center frequency. The measured phase differences between S21 and S31 at 900 MHz is 90.7°. According to Fig. 4.12(b), the phase imbalance is less than 2 degrees up to 1.1 GHz. From 580 to 1065 MHz, the broadside coupler meets the following specifications: the variation of coupling coefficient C < 1 dB, the phase imbalance < 2 degrees, and the return loss and isolation > 15 dB. This is equivalent to a factional bandwidth of 53%, comparable to the bandwidth of a conventional coupled-line coupler [Chap 6, 4.21]. The.

(47) comparison of the performances of the miniaturized broadside coupler and the design in [4.15] is shown in Table III. Although the coupler in [4.15] shows a very wide operation bandwidth and negligible in-band loss, it is 5.8 times the size of a conventional CPW design. C. 3-dB forward-wave edge-coupled coupler The last example is a 3-dB forward-wave edge-coupled directional coupler. A conventional forward-wave coupler generally requires a coupling length of several wavelengths. An alternative approach, resulting in compact size, was presented in [4.19] with microstrip technology. In this approach, the requirement of S11e = S11o = 0 for a 3-dB forward-wave directional coupler is satisfied with. Z 0e and. Z0. E o l 2E el S ,. (4.23) (4.24). where l is the coupling length of the coupler. With (4.23) and (4.24), the coupler is perfectly matched and isolated, respectively, at ports 1 and 3 at the center frequency. Meanwhile, at ports 2 and 4, the input power is equally split and the phases are in quadrature,. S21 (1 j ) 2 ,. S41. (1 j ) 2 .. (4.25) (4.26). This alternate forward-wave coupler is inherently a narrowband design. Fig. 4.13 shows the circuit layout of the miniaturized 3-dB forward-wave directional coupler using uniplanar synthesized coplanar waveguides. The proposed design adopts an edge-coupled configuration, as well. To satisfy the criterion (4.23), the even-mode characteristic impedance,. Z0 e. Le / Ce. ( Ls Lm ) / Cp ,. (4.27). should be lowered down by replacing the meander line inductors by straight line ones to.

(48) decrease the series inductance Ls. In the meantime, the finger length lee must be lengthened to increase the shunt capacitance, Cp, of the unit cells. Theoretically speaking,. Z0e should be chosen as close to 50 ohms (Z0) as possible. However, to avoid parasitic resonances, the length lee should not violate the quasi-lumped assumption, which requires the finger length to be shorter than one-tenth the guided wavelength. This sets a lower bound of the realizable even-mode characteristic impedance. In order to meet the condition of (24), the odd-mode guided wavenumber, Eo Z LoCo. Z ( Ls Lm )(C p 2Cm ) ,. (4.28). should be raised by lengthening the length leo to increase the mutual capacitance Cm. An iterative process is required, as lee simultaneously affects the odd-mode guided wavenumber. The extraction procedure in Sec. 4.3.A should be included to determine the even-/odd-mode electrical parameters during the iteration. In the current design, the optimized finger lengths are leo = 13.05 mm and lee = 6 mm, which correspond to an even-mode characteristic impedance (Z0e) of 60.8 ohms, and a ratio of 1.95 between the odd- and even-mode guided wavenumbers (Eo/Ee). The geometric parameters are lf1 = 11 mm, lf2 = 0.6 mm, lf3 = lf4 = 5 mm, wf1 = 28.85 mm, wf2 = 11.5 mm, wf3 = wf4 = 0.4 mm, and wf5 = 1.6 mm. The subscript “f” represents the parameters associated with the forward-wave coupler. The size of the miniaturized forward-wave directional coupler is 11 mm × 31.85 mm, or equivalently, 0.043 g × 0.125 g. This is only 60% the size and 32% the coupling length of the design in [4.19]. The simulated and measured S-parameters are shown in Fig. 4.14(a)-(b), while the phase differences between the output ports are depicted in Fig. 4.14(c). The agreement between the results is reasonably good. The ignored finite conductor thickness in the simulation is the most significant factor contributing to the discrepancy since the interdigital fingers are extraordinarily long. At the center frequency, i.e., 915 MHz, the measured return loss and isolation (|S31|) are 15.9 and 15.6 dB, respectively. The.