Values of the passive elements used to shift the center frequency of the tunable BAW-SMR filter towards higher frequencies and their quality factors.
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More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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These aspects of forest fire are the subject of this book. I realize, however, that the contents in it can only be an incentive for the reader to learn more, in an interesting aspect. I assume that this book will be valuable to researchers as well as students who are interested in different aspects connected to forest fires, not only from the ecological point of view but also from the social one. 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They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide.",isbn:null,printIsbn:"978-953-51-0871-9",pdfIsbn:"978-953-51-6289-6",doi:"10.5772/45654",price:139,priceEur:155,priceUsd:179,slug:"digital-filters-and-signal-processing",numberOfPages:322,isOpenForSubmission:!1,hash:"ad19128b3c5153cd5d30d16912ed89f3",bookSignature:"Fausto Pedro García Márquez and Noor Zaman",publishedDate:"January 16th 2013",coverURL:"https://cdn.intechopen.com/books/images_new/3198.jpg",keywords:null,numberOfDownloads:21594,numberOfWosCitations:13,numberOfCrossrefCitations:9,numberOfDimensionsCitations:14,numberOfTotalCitations:36,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"March 22nd 2012",dateEndSecondStepPublish:"April 12th 2012",dateEndThirdStepPublish:"July 9th 2012",dateEndFourthStepPublish:"August 8th 2012",dateEndFifthStepPublish:"November 7th 2012",remainingDaysToSecondStep:"9 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:"Edited by",kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"22844",title:"Prof.",name:"Fausto Pedro",middleName:null,surname:"García Márquez",slug:"fausto-pedro-garcia-marquez",fullName:"Fausto Pedro García Márquez",profilePictureURL:"https://mts.intechopen.com/storage/users/22844/images/system/22844.jpeg",biography:"Fausto Pedro García Márquez has been accredited as Full Professor at UCLM, Spain since 2013. He also works as a Honorary Senior Research Fellow at Birmingham University, UK, Lecturer at the Postgraduate European Institute, and has worked as Senior Manager in Accenture (2013-2014). He obtained his European PhD with a maximum distinction. He is a holder of the Runner Prize for Management Science and Engineering Management Nominated Prize (2020), Advancement Prize (2018), First International Business Ideas Competition 2017 Award (2017), Runner (2015), Advancement (2013) and Silver (2012) by the International Society of Management Science and Engineering Management (ICMSEM), and Best Paper Award in the international journal of Renewable Energy (Impact Factor 3.5) (2015). He has published more than 150 papers (65 % ISI, 30% JCR, and 92% internationals), some recognized as follows: “Applied Energy” (Q1, as “Best Paper 2020”), “Renewable Energy” (Q1, as “Best Paper 2014”), “ICMSEM” (as “excellent”), “International Journal of Automation and Computing” and “IMechE Part F: Journal of Rail and Rapid Transit” (most downloaded), etc. He is an author and editor of 25 books (Elsevier, Springer, Pearson, Mc-GrawHill, IntechOpen, IGI, Marcombo, AlfaOmega, etc.), and 5 patents. He is also an Editor of 5 International Journals and Committee Member of more than 40 International Conferences. He has been a Principal Investigator in 4 European Projects, 6 National Projects, and more than 150 projects for universities, companies, etc. He is an European Union expert in AI4People (EISMD) and ESF. He is Director of www.ingeniumgroup.eu. His main interest are: artificial intelligence, maintenance, management, renewable energy, transport, advanced analytics, and data science.",institutionString:"University of Castile-La Mancha",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"10",totalChapterViews:"0",totalEditedBooks:"10",institution:{name:"University of Castile-La Mancha",institutionURL:null,country:{name:"Spain"}}}],coeditorOne:{id:"155714",title:"Dr.",name:"Noor",middleName:null,surname:"Zaman",slug:"noor-zaman",fullName:"Noor Zaman",profilePictureURL:"https://mts.intechopen.com/storage/users/155714/images/5120_n.png",biography:"Dr. Noor Zaman acquired his degree in Engineering in 1998, and Master’s in Computer Science at the University of Agriculture at Faisalabad in 2000. His academic achievements further extended with Ph.D. in Information Technology at University Technology Petronas (UTP) Malaysia. He has vast experience of 16 years in the field of teaching and research. He is currently working as an Assistant Professor at the College of Computer Science and Information Technology, King Faisal University, in Saudi Arabia since 2008. He has contributed well in King Faisal University for achieving ABET Accreditation, by working as a member and Secretary for Accreditation and Quality cell for more than 08 years. He takes care of versatile operations including teaching, research activities, leading ERP projects, IT consultancy and IT management. He headed the department of IT, and administered the Prometric center in the Institute of Business and Technology (BIZTEK), in Karachi Pakistan. He has worked as a consultant for Network and Server Management remotely in Apex Canada USA base Software house and call center.\n\nDr. Noor Zaman has authored several research papers in indexed journals\\\\international conferences, and edited six international reputed Computer Science area books, has many publications to his credit. He is an associate Editor, Regional Editor and reviewer for reputed international journals and conferences around the world. He has completed several international research grants\\\\funded projects and currently involved in different courtiers. 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In telecommunication systems, all filters and resonators that constitute the RF part have the tendency to be integrated on the same chip that contains the information treatment.
In order to achieve miniaturization, bulk acoustic wave (BAW) technology is presented. BAW filters are very sensitive to surface contamination, and can exhibit very small sizes. In addition, BAW resonators could be fabricated using compatible material CMOS and BiCMOS [1]. In this context and in order to compensate the variation due to the fabrication process, the work presented in this paper focuses on the tuning of BAW-SMR resonators and filters.
This work is divided in two parts. The first part consists of designing BAW-SMR (Solidly Mounted Resonator) filters. In the second part, we propose the use of two methods to tune this type of filters. Thus, we present the design methodology, the study, and the experimental realization of the BAW-SMR tunable filters.
The bulk acoustic wave resonator is basically constituted by a piezoelectric layer sandwiched between two electrodes (Fig.1). The application of an electric field between the two electrodes generates a mechanical stress that is further propagated through the bulk of the structure (acoustic wave). The resonance condition is established when the acoustical path (in thickness direction) corresponds to odd integer multiples of the half acoustic wavelength. The bulk acoustic wave resonator is basically constituted by a piezoelectric layer sandwiched between two electrodes (Fig.1) [2, 3].
The bulk acoustic wave resonator fabrication over silicon substrates imposes its acoustical isolation, confining the acoustic waves into the main resonant structure. Two configurations are proposed: the membrane suspended structure (FBAR – Film Bulk Acoustic wave Resonator) [3], where the resonator is suspended by an air-bridge (Fig.1a); and the solidly-mounted structure (SMR – Solidly Mounted Resonator), where the resonator is mounted over a stack of alternating materials (Fig.1b). This stack is built on a Bragg reflector basis and it has an acoustic mirror behavior [2-3]. Both, air and acoustic mirror, present an optimum discontinuity for reflecting the acoustic waves at the interface with the bottom electrode, confining waves into the main resonant structure.
In the solidly mounted resonator (SMR), the piezoelectric is solidly mounted to the substrate (Fig.1.b). Some means must be used to acoustically isolate the piezoelectric from the substrate if a high quality factor (Q) resonance is to be obtained. In effect, the quarter wavelength layers act as a reflector to keep waves confined near the piezoelectric transducer film [4]. The effect of the reflector on mechanical displacement is to cause the wave amplitude to diminish with depth into the reflector. The number of layers required to obtain a satisfactory reflection coefficient is dependent on the mechanical impedances between layers and, to a lesser extent, the substrate [5]. The number of layers is best determined by an analysis of the resonance response as a function of the number of layers versus resonator ‘Q’ and coupling coefficient.
a) Film Bulk Acoustic Resonator (FBAR). (b) Solidly Mounted Resonator (SMR).
An important effect of the reflector layers, as demonstrated by Newell [4], is a partial lateral stiffening of the piezoelectric plate that minimizes plate wave generation and spurious resonances normally observed in free plates. However, real resonator structures are inherently 3D and some form of radiation beyond the simple thickness dimension is to be expected. If energy leaves the resonator structure, through radiation, then it counts as a loss mechanism. Reflections of lateral waves at the edge of the resonator can lead to standing waves and spurious responses. The SMR approach requires that the substrate be smooth in order to proceed with the fabrication of reflectors, electrodes, and piezoelectric film [5].
The Modified Butterworth-Van-Dyke (MBVD) model is an electrical schematic around resonance (Fig.2). The elements Ra, La, Ca present the series resonance and the insertion losses. The capacity C0 represents the piezoelectric material between the two electrodes.
SMR-MBVD model.
The impedance characteristic of a measured BAW-SMR is shown in Fig.3. In this graph, it can be observed that the SMR presents mainly two resonance pulsations: the series resonance (fs), when the electrical impedance approaches to zero, and the parallel resonance (fp), when the electrical impedance approaches to infinity. For all other frequencies far from the resonances, the SMR presents static capacitor behavior. fs is adjusted according to the thickness of the piezoelectric layer and it is spaced by the parallel resonance fp. The instantaneous frequency deviation between the two resonances is determined by the electromechanical coupling coefficient of the piezoelectric layer. The quality factor of the measured BAW-SMR is 192.5 and its active area is 16800 µm2. This relatively small quality factor is due to some technological problems.
Impedance characteristic of a measured BAW-SMR.
The electrical impedance of an SMR is obtained by solving the acoustic boundary problem and applying the transmission line theory [6]. The electrical SMR impedance can be simplified and expressed by the following equation:
where ‘s’ is the complex variable: s = jw.
The association of external passive components (L, C) to the resonators was made in two parts. First, the resonators analyses have been carried out using on-wafer measurements. Then, these results have been associated with the capacitors and inductors. The combination of experimental results and modeling of passive elements constitutes the final response of the tuned resonators.
The addition of the capacitors (having an intrinsic quality factor ‘Q’ > 140) to the SMR circuitry doesn’t affect severely the quality factor of the overall design. The resonator’s electromechanical coupling coefficient is described indirectly by the capacitor ratio C0/Ca as determined by the resonator physical configuration and piezoelectric material properties [7]. When changing the electromechanical coefficient of the piezoelectric material, the bandwidth changes. Our goal is to tune the capacitor ratio C0/Ca by adding series or parallel capacitors to the resonator. Thus, controlling this ratio will enable us to control the electromechanical coefficient, and as a sequence the bandwidth of the resonator.
2.3.1.1. Series capacitor association
The performance analysis of the association of series capacitor to the SMR is based on the BVD model (Fig.4). The analysis of the frequency response of the series capacitor associated to the SMR will lead us to (2) presented below:
Where‘s’ is the complex variable: s = jw.
From (2), it is possible to notice the insertion of a pole and zero to the frequency response of the simple resonator. The extraction of the poles and zeroes values of (2), will lead us to (3) & (4) shown below.
Impedance response of the measured BAW-SMR with series capacitor.
From (3) & (4), it may be noted that the capacitor added in series with the BAW resonator affects only the series resonance frequency. It is inversely proportional to fs. To illustrate this theoretical study, responses with different values of capacitors added in series with the measured BAW-SMR are shown in Fig.4.
2.3.1.2. Parallel capacitor association
The analysis of the frequency response of the parallel capacitor associated to the SMR will lead us to (5), presented below.
Impedance response of the measured BAW-SMR with parallel capacitors.
From (5), it is possible to notice the displacement of the poles of the device’s resonance frequency. The extraction of the poles and zeroes values of (5), will guide us to (6) & (7) as shown below.
It is noticed from (6) & (7) that the capacitor added in parallel with the BAW resonator affects only the parallel resonance frequency. It is inversely proportional to fp. Fig.5 presents the final responses of the measured BAW-SMR with different values of capacitors added in parallel.
The association of inductors to the BAW resonators could be realized in series or parallel. We should note that in the case of VLSI-CMOS, these inductors are characterized by a small quality factor with respect to the BAW (400 to 1000) which degrades the quality factor of the overall circuitry, and they occupy a relatively large size.
2.3.2.1. Series inductor association
The performance analysis of the assembly of the inductors in series with the SMRs is based on the BVD model. The analysis of the frequency response of the series inductors associated to the SMR will lead us to (8).
From (8), it is possible to notice the insertion of a zero to the resonator frequency response. The extraction of the poles and zeroes values from (8), will bring (9) & (10). Based on these equations, we can see that the values of the poles are not deteriorated. However, from (9), we notice that the association of series inductors to the SMR will modify the zeroes, and only the series resonance frequency is affected. It is inversely proportional to fs.
Impedance response of the measured BAW-SMR with series inductors.
To illustrate this theoretical study, impedance behavior of the measured BAW-SMR with different values of inductors associated in series is shown in Fig.6.
2.3.2.2. Parallel inductor association
Based on the same procedure used above, the analysis of the frequency response of the parallel inductors associated to the SMR will lead us to (11), presented below.
From (11), it is possible to notice the insertion of a pole to the resonator frequency response and the displacement of another. Also, we can notice the composition of a double pole near the frequency response of the device. The extraction of the poles and zeroes values from (11), will lead us to (12) & (13).
From (12) & (13), we can see that that the inductor added in parallel with the BAW resonator affects only the parallel resonance frequency. It is inversely proportional to fp. Fig.7 presents the final responses of the measured BAW-SMR with different values of inductors associated in parallel.
Impedance response of the measured BAW-SMR with parallel inductors.
Impact of the quality factor of the inductors added in series with the BAW resonator on the series quality factor ‘Qs’ of the overall resonator circuitry (SMR+L).
The addition of inductors to the BAW-SMR increases the insertion losses and degrades the quality factor of the overall circuitry. Fig.8 illustrates the influence of inductors added in series with the SMR on the overall quality factor of the assembly.
Bulk acoustic wave filters are basically divided in three topologies: ladder, lattice and ladder-lattice (Fig.9) [3].
Bulk acoustic wave resonator filter topologies: (a) ladder stage, (b) lattice stage and (c) ladder-lattice stage.
Ladder filter are characterized by an unbalanced operation mode and very small size able to deliver very high selectivity filtering responses, however presenting low rejection or isolation out-of-band. Typically, ladder bulk acoustic wave filters are quite effective for blocking signals close to the passband, but poor at rejecting undesired bands [3-4].
On the other hand, lattice bulk acoustic wave filters are characterized by a balanced operation mode. In contrast to the first one, this topology presents typically a low selectivity close to the passband, followed by a high rejection out-of-band. They present slower roll off coefficient and higher rejection. Thus, lattice networks are not interesting to block signals close to the passband, but they are more effective for rejecting undesired bands [3].
Ladder-lattice bulk acoustic wave filters are also characterized by a balanced operation mode. Ladder-lattice filters ally advantages of both network types, enabling high isolation at undesired bands and steep responses close to the passband [3]. This topology is able to strongly reduce the linearity constraints of the receiver RF chain. Fig.10 shows a comparison between the typical theoretical transmission responses (S21) of these three network types.
Theoretical transmission responses for main bulk acoustic wave (BAW) filter topologies.
The ladder filter is an association of resonators in series and in parallel. The shunt resonators are loaded and their resonance frequencies are smaller than the series resonators. Ladder BAW topology presents a good selectivity which enables to block undesired signals near the pass band. In this context, and in order to support the theoretical study, a tunable BAW-SMR ladder filter was designed for the 802.11b/g standard (2.40 – 2.48 GHz). The resonators and filters were fabricated at the CEA-Leti in the framework of the project ‘EPADIM’. The filter is composed of five SMRs, associated in ladder topology. The filter stack can be divided into resonators’ layers and Bragg reflector’s layers. The resonator’s layers are composed by the classical couple AlN-Mo [8]. However, in contrast to [8], the Bragg reflector was implemented using an exclusive dielectric stack composed by SiOC:H and SixNy [9].
Microphotography of the Ladder BAW-SMR for the 802.11b/g standard.
The acoustical performance of the fully dielectric stack is comparable to the traditional SiO2-W reflectors; however, it strongly reduces the coupling between resonators through the Bragg reflector. Furthermore, the filter stack was realized on a high resistive silicon substrate in order to reduce losses due to the capacitive coupling [10].
In order to optimize the filter performance, a double resonator and apodized geometries have been used. Indeed, double resonators present large electrodes’ areas, which results in lower resistive losses. Also, the filter resonators present apodized geometries in order to avoid spurious resonances caused by the parasitic lateral acoustic modes [11]. Fig.11 and 12 show the microphotography and a comparison between the measured and simulated results of the tunable ladder BAW-SMR filter, respectively. The filter occupies a small area and has reduced dimensions (1035*1075 µm2). Electromagnetic simulation of the overall filter structure has been performed using the ADS-Momentum software. Next, the acoustical effects have been considered using the Mason Model [12] and included in the simulations.
Comparison between measured and simulated results of the 802.11b/g ladder BAW-SMR filter.
The filter design was realized for implementation in SiP context. The performances of the tunable BAW-SMR filter are in concordance with the simulation results. Mainly, the filter fulfills the requirements for the WLAN 802.11 b/g standard, presenting -3.3 dB of insertion loss, -12.7 dB of return loss and a selectivity higher than 33 dB at ± 30 MHz of the bandwidth. The filter high insertion losses are mainly due to the low resonators quality factor obtained in the fabrication (Q = 200). Therefore, these losses can be strongly reduced using mechanical energy concentration techniques in the resonator acoustical cavity [13].
The shunt resonators of the ladder filter determine the position of the zeroes at the left of the center frequency and the series resonators determine the position of the zeroes at the right of the center frequency. Thus, changing the impedance of the parallel and series resonators leads to a change in the zeroes’ positions.
Ladder BAW-SMR filter.
Based on this theory and in order to tune the BAW-SMR filter (Fig.13), we propose to add passive elements to the shunt and series resonators that constitute the filter.
To shift the center frequency of the filter towards higher frequencies we have to move all the zeroes towards these frequencies. Thus, we have added inductors in parallel with the series resonators and capacitors in series with the shunt resonators that constitute the ladder BAW-SMR filter (Fig.14).
Tunable BAW-SMR filter with inductors added in parallel with the series resonators and capacitors added in series with the shunt resonators.
Table 1 presents the values and the quality factor of the external passive elements used in the circuitry designed to move the center frequency of the tunable BAW-SMR filter towards higher frequencies.
Value | Quality Factor ‘Q’ | |
Capacitors | C1= C2=2.2 pF | 140 |
Inductors | L1=3.9 nH | 47.7 |
L2=5.6 nH | 40 | |
L3=4.7 nH | 45 |
Values of the passive elements used to shift the center frequency of the tunable BAW-SMR filter towards higher frequencies and their quality factors.
The tunable BAW-SMR filter and the passive components are mounted on a FR4 substrate as shown in Fig.15.
Tunable BAW-SMR filter and passive elements mounted on FR4 PCB.
Fig.16 shows the simulation results of the tunable filter. The insertion loss (IL = -2.4 dB) obtained in the simulation is due to quality factors of resonators (Q = 500). The return loss (RL) is -10 dB, and the out of band rejection is 26 dB at 2.0 GHz. The simulation results shows that a shift of +1% of the initial central frequency (2.44 GHz) is obtained.
Simulation of tunable BAW filter with inductors added in parallel with the series resonators and capacitors added in series with the shunt resonators.
Comparisons between the measurements of the tunable filter with the original one are shown in Fig.17 and Fig.18.
Shift towards higher frequencies: Comparison of transmission characteristic (S21)between the tunable BAW-SMR filter (passive elements added) and the original one.
Based on the measurements of the tunable filter, we can note -4.5 dB of insertion losses and a shift of +0.6% of the center frequency (2.44 GHz) towards the higher frequencies (Fig.17). As well, a return loss of -7 dB is obtained (Fig.18). The filter high insertion losses are mainly due to the low resonators quality factor obtained in the fabrication (Q = 200) and to the low quality factor of the passive element used. Moreover, the parasitic capacitors generated by the FR4 PCB and the bonding wires used to connect the tunable filter with the passive elements caused a reduction of 15 MHz to the bandwidth of the tunable filter.
Shift towards higher frequencies: Comparison of reflexion characteristic (S11) between the tunable BAW-SMR filter (passive elements added) and the original one.
This time and in order to shift the center frequency of the filter towards lower frequencies, we have to move all the zeroes towards these frequencies.
Tunable BAW-SMR filter with capacitors added in parallel with the series resonators and inductors added in series with the shunt resonators.
Thus, we have added capacitors in parallel with the series resonators and inductors in series with the shunt resonators that constitute the ladder BAW-SMR filter (Fig.19). Table 2 presents the values and the quality factor of the external passive elements used.
Value | Quality Factor ‘Q’ | |
Capacitors | C1=2.2 pF | 140 |
C2=1 pF | 200 | |
C3=2 pf | 150 | |
Inductors | L1=L2=2.2 nH | 57 |
Values of the passive elements used to shift the center frequency of the tunable BAW-SMR filter towards lower frequencies and their quality factors.
As same as before, the tunable BAW-SMR filter and the passive components are mounted on a FR4 substrate. Fig.20 shows the simulation results of the tunable filter.
The insertion loss (IL = -2.4 dB) obtained by simulation is due to quality factors of resonators (Q = 500). In addition the return loss (RL) is -9.5 dB, and the out of band rejection is 16 dB at 2.0 GHz (Fig.20). The simulation results shows that a shift of -1% of the initial central frequency (2.44 GHz) is obtained. A comparison between the measurements of the tunable filter with the original one is shown in Fig.21.
Based on the measurements of the tunable filter, we can note -4.5 dB of insertion losses and a shift of -1.3% of the center frequency (2.44 GHz) towards the lower frequencies (Fig.21). In addition, the parasitic capacitors generated by the FR4 PCB and the bonding wires used to connect the tunable filter with the passive elements caused a reduction of 13 MHz to the bandwidth of the tunable filter.
Simulation of tunable BAW filter with capacitors added in parallel with the series resonators and inductors added in series with the shunt resonators.
Shift towards lower frequencies: Comparison between the tunable BAW-SMR filter (passive elements added) and the original one.
As a conclusion, one should note that in contrast to [13], where lumped elements (inductors or capacitors) were proposed to be added at a time, in this paper the use of capacitors and inductors together have shown how to shift the center frequencies towards higher or lower frequencies.
To validate the concept of digitally tuning BAW filters using passive elements controlled by CMOS transistors, we present in this part the use of CMOS switches at the terminals of capacitors (Fig.22) [6].
When a transistor is ON, the capacitor is short circuited, and when a transistor is OFF, the capacitor will be considered in series with the shunt resonator. Thus, the bandwidth and the characteristics of the filter will be modified. The circuitry of the filter, capacitors, transistors and the associated “bonding wires” are shown in Fig.22.
Tunable BAW-SMR using CMOS transistors.
The BAW-SMR filter used in this study is a fifth order filter designed for the W-CDMA standard in the ladder topology. This topology is composed by the resonator in series and parallel, the parallel resonators are loaded and their resonance frequencies are smaller than the series resonators. The die photography of the tunable BAW-SMR filter is shown in Fig.23. The filter has reduced size, and the die area is 1450*985 μm². Moreover, many passive pads connecting the filter with the active chip were taken in consideration.
Microphotography of ladder BAW-SMR for the W-CDMA standard.
Fig.24 presents the comparison between the measurement and the simulation of the BAW-SMR filter. Electromagnetic simulation of the overall filter structure has been accomplished by using the ADS-Momentum software, where the acoustical effects have been included using the Mason Model. The filter is designed for implementation in SiP context. As shown in Fig.24, the measurements are in concordance with the simulations. However, the filter fulfills the requirements for the W-CDMA standard, exhibiting -2.77 dB of insertion loss, -8.75 dB of return loss and selectivity higher than 38 dB at 40MHz offset from the operating frequency.
Simulation and measurement results of the W-CDMA ladder BAW-SMR filter.
To adjust the bandwidth of the BAW filter, a chip is realized in 65nm CMOS technology. This chip is composed by the capacitors mounted in series with the MOS transistor, and these transistors are controlled by a 2 to 4 decoder (Fig.25).
Circuitry of the tuning mechanism.
Fig.26 shows the layout of the tuning circuit. In symbolize the pad for connection with ladder filter. VG, Vdd1, Vdd2 and GND correspond to the gate voltage, the command of decoder and the ground respectively. The size of the Silicon area is 335*330μm².
Layout of the tuning mechanism.
The tuning is attained by controlling the MOS transistors and capacitors in series with shunt resonators. Each transistor is open or short circuited by obtaining different outputs of the 2 to 4 decoder. Table 3 shows the truth table of the realized decoder. A, B, E symbolize the input of a decoder commanded by Vdd1, Vdd2 and VG respectively, Sn (n = 0, 1, 2 or 3) represent the output of this decoder used to control Qn. All transistors used in the tuning mechanism are provided by STMicroelectronics (CMOS 65 nm). The width and length of the gate are: W = 50 μm and L = 0.06 μm. The main parasitic elements are taken into account in the simulation (Cgs, Cgd, Cds and Ron). The length of bonding wire is 2 mm. It represents an inductive effect of approximately 2 nH at 2 GHz. Ron of the MOS transistor is function of its dimensions and of the gate voltage (VG). Thus, with an external adjustment of VG, Ron value is regulated.
A | B | E | S0 | S1 | S2 | S3 |
0 | 1 | 0 | 0 | 0 | 1 | |
0 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 0 | 0 |
X | X | 0 | 0 | 0 | 0 | 0 |
Truth table of the 2 to 4 decoder.
Fig.27 shows the microphotography of the association of the ladder filter with the active chip. The devices are connected with bonding wires. The capacitors C1, C2 and C3 values are fixed to achieve 12, 9 and 6 MHz tuning range, respectively. When the output S0 of the decoder is ON, the transistor Q0 is ON and all of the capacitors are short circuited. When the output Sn (n = 1, 2 or 3) is ON, the transistor Qn is ON and the capacitor Cn will be considered in series with the shunt resonators.
Microphotography of the digitally tunable ladder BAW-SMR for the W-CDMA standard.
The comparison between the simulation and the measurement results is shown in Fig.28. of the tunable BAW-SMR filter combined with the active chip presents a tuning range of 12 MHz, when the output S3 of the decoder is ON. It show also -1.52 dB of insertion loss and 12 dB of the out-band rejection at 1.85 GHz. This out-band rejection is improved by 3 dB. This degradation is due to the length of bonding wire associating the active chip and PCB [10].
Comparison between the simulation and the measurement of the digitally tunable BAW filter.
In this paper, the impedance behavior of the BAW-SMR has been shown. Also, the effects of the addition of passive elements (L, C) to this type of resonators have been illustrated. In addition, a tunable BAW-SMR filter realized in a ladder topology used for the 802.11b/g standard (2.40 - 2.48 GHz) was shown. Mainly, the filter fulfilled the requirements for the WLAN 802.11 b/g standard, presenting a measured -3.3 dB of insertion loss, -12.7 dB of return loss and selectivity higher than 33 dB @ ± 30 MHz of the bandwidth. This tunable BAW-SMR filter has reduced dimensions (1035*1075 μm2). Moreover, the center frequency of this tunable filter was shifted towards higher and lower frequencies by adding passive elements. Measured shifts of -1.3% of the center frequency (2.44 GHz) towards lower frequency and +0.6% of the center frequency towards higher frequencies were obtained. Furthermore, digitally tunable BAW-SMR filter implementation was shown. The tunable filter was designed for the W-CDMA standard. The filter fulfilled the requirements for the WCDMA standard, presenting a measured -2.77 dB of insertion loss, -8.75 dB of return loss and selectivity higher than 38 dB @ ±40 MHz of the bandwidth. Moreover, the center frequency of this tunable filter is digitally shifted towards higher frequencies by adding capacitors in series with transistors that act as switches. These switches are controlled by a 2to4 decoder, and they are added to the shunt resonators.
IMS laboratory is acknowledged for all facilities offered and the access to obtain the filter measurements. Also, CEA-LETI (Grenoble, France) and STMicroelectronics (Crolles, France) are acknowledged for the technology access and filter fabrication.
Fluid-solid two-phase flows are important in many geophysical problems such as sediment erosion, transport and deposition in rivers or coastal environment, debris flows, scour at river or marine structures, and submarine landslides. Behaviors of fluid-solid two-phase flows are very different from those of liquid-gas two-phase flows where bubbles are dispersed in the liquid or droplets dispersed in the gas. Vast numbers of experiments on various scales have been carried out for different applications of fluid-solid two-phase flows; these experiments have advanced our understanding of bulk behaviors of some important flow characteristics. However, development of measurement techniques suitable for collecting data that contribute to understanding important physics involved in fluid-solid two-phase flows is a still-evolving science. With the modern computer technology, many data that are not obtainable currently in the experiment can be easily produced by performing time-dependent, multidimensional numerical simulations. Of course, empirical closure models required to close the governing equations still need high-quality experimental data for model validation.
\nNumerical approaches to two-phase flows include Eulerian-Eulerian approach, direct numerical simulations (DNS) based on Eulerian-Lagrangian formulations (Lagrangian point-particle approach), and fully resolved DNS approach [1]. Fully resolved DNS can resolve all important scales of the fluid and particles, but these simulations are currently limited to about 10 k uniform-size spheres on a Cray XE6 with 2048 cores [2], and it is not practical to use this method to model large-scale geophysical flow problems in the foreseeable future [1]. Lagrangian point-particle approach uses Eulerian formulation for the fluid phase and Lagrangian formulation for tracking the instantaneous positions of the particles. Lagrangian point-particle simulations make use of semiempirical relationships to provide both hydrodynamic force and torque acting on each particle and thus avoid modeling processes on scales smaller than Kolmogorov scale [1], making it possible to include more particles and run in a domain larger than that for fully resolved DNS. The application of Lagrangian point-particle approach is crucially dependent on the availability and accuracy of such semiempirical relationships. A recent study shows that good results can be obtained for about 100k uniform-size spherical particles in a vertical channel flow [3]; however, using this approach to investigate large-scale two-phase flow problems is still beyond the current computing capacity. Two-phase Eulerian-Eulerian approach treats both the fluid and particle phases as continuum media and is suitable for solving large-scale two-phase flow problems.
\nEulerian-Eulerian two-phase flow models based on large-eddy-simulations solve a separate set of equations describing conservation of mass, momentum, and kinetic energy for each phase [4, 5, 6, 7] and thus have the potential to consider all important processes involved in the interactions between the two phases through parameterization of particle-scale processes. This chapter introduces the basics of Eulerian-Eulerian two-phase flow modeling, its implementation in the finite-volume framework of OpenFOAM®, and two applications in geophysical flow problems.
\nLet us consider a mixture of fluid and solid particles. Fluid can be gas, water, or a mixture of water and gas. In DNS and Lagrangian point-particle approaches to two-phase flows, the flow field is solved by solving the Navier-Stokes equations, and the motion of each particle is determined by the Newton’s equation of motion. In Eulerian-Eulerian two-phase flow approaches, however, the motions of individual particles are not of the interest, and the focus is on the macroscopic motion of the fluid and solid particles instead. For this purpose, the solid particles are modeled as a continuum mass through an ensemble averaging operation, which is based on the existence of possible equivalent realizations. After taking ensemble average, the mixture of fluid and particles consists of two continuous phases: the fluid (water, gas, or a mixture of water and gas) is the fluid phase, and the solid particle is the solid phase. Both phases are incompressible. The motions of the fluid and solid phases are governed by their own equations, which are obtained by taking ensemble average of the microscopic governing equations for each phase [8]. Even though some aspects of fluid-solid interaction can be considered through the ensemble average, the ensemble averaging operation itself, however, does not explicitly introduce any turbulent dispersion in the resulting equations. To consider the turbulent dispersion in the Eulerian-Eulerian description of the fluid-solid two-phase flows, another averaging operation (usually a Favre average) is needed to consider the correlations of turbulent components [5, 9].
\nAt the microscopic scale, the fluid-solid mixture is a discrete system. The purpose of performing an ensemble averaging operation is to derive a set of equations describing this discrete system as a continuous system at the macroscopic scale, where the typical length scale should be much larger than one particle diameter.
\nIn the Eulerian-Eulerian approach to two-phase flows, it is assumed that the equations governing the motion of phase \n
and
\nwhere \n
where \n
Because the fluid phase and the solid phase are immiscible, at any time \n
The volumetric concentration of phase \n
There are several methods to derive the ensemble averaged equations governing the motion of phase \n
where \n
The ensemble averaged equations governing the motion of phase \n
and
\nThe resulting equations governing the ensemble average motion of phase \n
and
\nwith
\nNote that \n
which is the density of the interfacial force [8]. Physically, \n
After using Eq. (3) for \n
and
\nwhere \n
and \n
For compressible materials \n
Now we examine the limiting case where the fluid-solid system is at its static state. Because the phase functions for the two phases satisfy \n
for the fluid phase, and
\nfor the solid phase.
\nBecause \n
which, physically, is the buoyancy acting on the solid phase. Now Eq. (18) becomes
\nwhich states that the weight of the solid particles is supported by the buoyancy and the interparticle forces. Therefore, the ensemble pressure of the solid phase can be written as \n
For brevity of the presentation, we shall denote simply \n
and
\nThe ensemble averaged equations governing the motion of the solid phase are
\nand
\nwhere \n
To close the equations for the fluid and solid phases, closure models are needed for \n
It is remarked here that the definitions of the ensemble averages given in Eq. (14) do not consider the contribution from the correlations between the fluctuations of the velocities and the fluctuations of phase functions at microscopic scale; therefore, the effects of turbulent dispersion are not directly included in the ensemble averaged equations describing the motion of the each phase. In the literature, two approaches have been used to consider the turbulent dispersion: (i) considering the correlation between the fluctuations of \n
In the absence of the turbulent dispersion from \n
This expression for \n
where \n
The volumetric concentration and the velocities can be written as
\nwhere the Favre averages are defined as
\nand the overline stands for an integration with respect to time over a time scale longer than small-scale turbulent fluctuations but shorter than the variation of the mean flow field.
\nThe averaged equations for the mean flow fields of the two phases are obtained by taking the following steps: (i) substituting Eq. (25) with Eq. (26) in Eqs. (22) and (24), (ii) substituting Eq. (27) in the equations obtained at step (i), and (iii) taking average of the equations obtained at step (ii) to obtain the following equations:
\nfor the fluid phase, with \n
and
\nfor the solid phase, with \n
It is remarked here that the terms \n
In order to close these averaged equations, closure models are required for the following terms: \n
where \n
For brevity of the presentation, the symbols representing Favre averages are dropped hereinafter, and the final equations governing the conservation of mass and momentum of each phase are
\nfor the fluid phase and
\nfor the solid phase.
\nThe stress tensor for the fluid phase \n
The viscous stress tensor \n
where \n
The stress tensor \n
where \n
with \n
The equations governing \n
and
\nwhere coefficients \n
where \n
with \n
It is remarked here that the presence of solid particles in the turbulent flow may either enhance (for large particles) or reduce (for small particles) the turbulence [18]. The \n
The closure models for \n
where \n
For solid particles in a compact bed, the formula proposed by Hsu et al. [19] can be used to compute \n
where \n
The closure models for \n
The kinematic viscosity of the solid phase \n
where \n
Based on an analysis of heavy and small particles in homogeneous steady turbulent flows, Hinze [20] suggests that \n
and
\nwhere the coefficient \n
For dense fluid-solid two-phase flows, the visco-plastic rheological characteristics depend on a dimensionless parameter \n
Following the work of Boyer et al. [22], Lee et al. [16] assumed
\nwhere \n
where \n
which considers the solid phase in its static state as a very viscous fluid and
\nwhere \n
The drag force between the two phases is modeled through the particle response time \n
The first model is based on particle sedimentation in still water, which can be simplified as a one-dimensional problem, where the steady sedimentation assures that there are no stresses in both the solid and fluid phases in the vertical direction \n
and
\nwhere \n
Because net volume flux through any horizontal plane must be zero, we have
\nCombining Eqs. (59) and (61) yields
\nSubstituting Eqs. (61) and (62) into Eq. (60) leads to
\nwhere the solid-phase velocity \n
where the coefficient \n
The terminal velocity of a single particle \n
where \n
where \n
It is remarked that Eq. (64) is validated only for \n
Another model for particle response time can be derived by examining the pressure drop in the steady flow through a porous media. For a one-dimensional problem of a horizontal, steady flow through porous media, the terms containing the stresses of the fluid phase disappear, and Eq. (38) reduces to
\nwhere the horizontal coordinate \n
For this problem, Forchheimer [29] suggested
\nwhere \n
Comparing Eqs. (69) and (70) and using Eq.(71) give
\nwhere \n
For flow in a porous media, the particle response time can also be related to its permeability \n
where \n
When the flow is very slow, Eqs. (70), (71), and (73) suggest that
\nwhich means that the particle response time can be related to the permeability.
\nEquation (64) is validated only for \n
where \n
Combining Eqs. (63), (76), and (66)–(67) gives
\nWe stress that \n
where \n
For given values of \n
This section introduces how to use OpenFOAM® to solve the governing equations with the closure models presented in the previous section. OpenFOAM® is a C++ toolbox developed based on the finite-volume method; it allows CFD code developers to sidestep the discretization of derivative terms on unstructured grids.
\nTo avoid numerical noises occurring when \n
and
\nThe solutions of Eqs. (80) and (81) are expressed in the following semidiscretized forms:
\nwhere \n
If Eq. (83) is directly used to calculate \n
which is corrected by the following corrector
\nThis predictor-corrector scheme can improve the numerical stability by introducing a numerical diffusion term. To see this, we combine Eqs. (39) and (85) to obtain the following equation describing the evolution of \n
The right-hand side of Eq. (86) now has a diffusive term introduced by the numerical scheme. High sediment concentration and large \n
For the velocity-pressure coupling, Eq. (82) is similarly solved using a predictor \n
which is corrected by the following corrector
\nSubstituting Eq. (88) into Eq. (37) gives a pressure equation. However, when using this pressure equation to simulate air-water flows, numerical experiments have shown that the lighter material is poorly conserved [36]. The poor conservation of lighter material can be avoided by combining Eqs. (37) and (39) into the following Eq. (37):
\nand using Eq. (89) to correct \n
and combine Eqs. (83) and (88)–(90) to obtain the following equation
\nThe numerical diffusion term on the right-hand side of Eq. (91) can help improve the numerical stability.
\nThe prediction-correction method presented here deals with velocity-pressure coupling and avoids the numerical instability caused by high concentration. The turbulence closure \n
When \n
An iteration procedure is needed to solve the governing equations at each time step for the values of \n
Compute \n
Solve Eq. (86) for \n
Compute \n
Compute \n
Compute \n
Solve Eq. (91) for \n
Repeat Eqs. (5)–(7) for \n
Compute \n
Set \n
Repeat Eqs. (1)–(10) with the updated \n
Solve Eqs. (45) and (46) for \n
Figure 1 is a flowchart showing these 12 solution steps.
\nA flow chart showing the solution procedure using OpenFOAM®.
In the absence of the solid phase, the numerical scheme outlined here reduces to the “PIMPLE” scheme, which is a combination of the “pressure implicit with splitting of operator” (PISO) scheme and the “semi-implicit method for pressure-linked equations” (SIMPLE) scheme. Iterations need to be done separately to solve Eq. (80) for \n
To ensure the stability of the overall numerical scheme, the Courant-Friedrichs-Lewy (CFL) condition must be satisfied for each cell. The local Courant number for each cell, which is related to the ratio between the distance of a particle moving within \n
where in \n
This section briefly describes two examples that have been studied using the two-phase flow models described. The problem descriptions and numerical setups for these two problems are included here; for other relevant information, the reader is referred to Lee and Huang [35] and Lee et al. [38].
\nA sluice gate is a hydraulic structure used to control the flow in a water channel. Sluice gate structures usually have a rigid floor followed by an erodible bed. The scour downstream of a sluice gate is caused by the horizontal submerged water jet issuing from the sluice gate. It is of practical importance to understand the maximum scour depth for the safety of a sluice gate structure. Many experimental studies have been done to investigate the maximum scour depth and the evolution of scour profile (e.g., Chatterjee et al. [39]). For numerical simulations, this problem includes water (fluid phase) and sediment (solid phase) and is best modeled by a liquid-solid two-phase flow approach. In the following, the numerical setup and main conclusions used in Lee et al. [38] are briefly described. The experimental setup of Chatterjee et al. [39] is shown in Figure 2. To numerically simulate the experiment of [8], we use the same sand and dimensions to set up the numerical simulations: quartz sand with \n
A sketch of the experimental setup for scour induced by a submerged water jet.
Comparison of the computed scour depth with measurements of Chatterjee et al. [39].
The problem involves also an air-water surface, which can be tracked using a modified volume-of-fluid method introduced in [38]. A nonuniform mesh is used in the two-phase flow simulation because of the air-water interface, the interfacial momentum transfer at the bed, and the large velocity variation due to the water jet. The finest mesh with a vertical mesh resolution of \n
The scour process is sensitive to the model for particle response time used in the simulation. Because Eq. (72) can provide a better prediction of sediment transport rate for small values of Shields parameter, it is recommended for this problem. The two-phase flow model can reproduce well the measured scour depth and the location of sand dune downstream of the scour hole.
\nAnother application of the fluid-solid two-phase flow simulation is the simulation of the collapse of a deeply submerged granular column. The problem is best described as a granular flow problem, which involves sediment (a solid phase) and water (fluid phase). Many experimental studies have been reported in the literature on this topic. This section describes a numerical simulation using the fluid-solid two-phase flow model described in this chapter.
\nFigure 4 shows the experimental setup of Rondon et al. [40]. A 1:1 scale two-phase flow simulation was performed by Lee and Huang [35] using the fluid-solid two-phase flow model presented in this chapter. The diameter and the density of the sand grain are 0.225 mm and 2500 kg/m3, respectively. The density and the dynamic viscosity of the liquid are 1010 kg/m3 and 12 mPa s, respectively. Note that the viscosity of the liquid in the experiment is ten times larger than that for water at room temperature. For this problem, using a mesh of 1.0 × 1.0 mm and the particle response model given by Eq. (78), the fluid-solid two-phase flow model presented in this chapter can reproduce well the collapse process reported in Rondon et al. [40]. Figure 5 shows the simulated collapsing processes compared with the measurement for two initial packing conditions: initially loosely packed condition and initially densely packed condition.
\nA sketch of the experimental setup for the collapse of a deeply submerged granular column.
The simulated collapsing processes for the initially loose condition (a)–(d) and the initially dense condition (e)–(h). The lines represent contours of the computed concentrations, and the symbols were experimental data of Rondon et al. [40]. The figure is adapted from Lee and Huang [35].
The two-phase model and closure models presented in this chapter are able to deal with both initially loose packing and initially dense packing conditions and reveal the roles played by the contractancy inside the granular column with a loose packing and dilatancy inside a granular column with a dense packing. One of the conclusions of Lee and Huang [35] is that the collapse process of a densely packed granular column is more sensitive to the model used for particle response time than that of a loosely packed granular column. The particle response model given by Eq. (78) performs better than other models; this is possibly because the liquid used in Rondon et al. [40] is much viscous than water.
\nThis chapter presented a brief introduction to the equations and closure models suitable for fluid-solid two-phase flow problems such as sediment transport, submarine landslides, and scour at hydraulic structures. Two averaging operations were performed to derive the governing equations so that the turbulent dispersion, important for geophysical flow problems, can be considered. A new model for the rheological characteristics of sediment phase was used when computing the stresses of the solid phase. The \n
This material presented here is partially based upon work supported by the National Science Foundation under Grant No. 1706938 and the Ministry of Science and Technology, Taiwan [MOST 107-2221-E-032-018-MY3]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
\nIntechOpen’s Academic Editors and Authors have received funding for their work through many well-known funders, including: the European Commission, Bill and Melinda Gates Foundation, Wellcome Trust, Chinese Academy of Sciences, Natural Science Foundation of China (NSFC), CGIAR Consortium of International Agricultural Research Centers, National Institute of Health (NIH), National Science Foundation (NSF), National Aeronautics and Space Administration (NASA), National Institute of Standards and Technology (NIST), German Research Foundation (DFG), Research Councils United Kingdom (RCUK), Oswaldo Cruz Foundation, Austrian Science Fund (FWF), Foundation for Science and Technology (FCT), Australian Research Council (ARC).
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\n\nIn order to help Authors identify appropriate funding agencies and institutions, we have created a list, based on extensive research on various OA resources (including ROARMAP and SHERPA/JULIET) of organizations that have funds available. Before consulting our list we encourage you to petition your own institution or organization for Open Access funds or check the specifications of your grant with your funder to ascertain if publication costs are included. Where you are in receipt of a grant you should clarify:
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