Wave solutions in different media (no bounds considered).
\\n\\n
Dr. Pletser’s experience includes 30 years of working with the European Space Agency as a Senior Physicist/Engineer and coordinating their parabolic flight campaigns, and he is the Guinness World Record holder for the most number of aircraft flown (12) in parabolas, personally logging more than 7,300 parabolas.
\\n\\nSeeing the 5,000th book published makes us at the same time proud, happy, humble, and grateful. This is a great opportunity to stop and celebrate what we have done so far, but is also an opportunity to engage even more, grow, and succeed. It wouldn't be possible to get here without the synergy of team members’ hard work and authors and editors who devote time and their expertise into Open Access book publishing with us.
\\n\\nOver these years, we have gone from pioneering the scientific Open Access book publishing field to being the world’s largest Open Access book publisher. Nonetheless, our vision has remained the same: to meet the challenges of making relevant knowledge available to the worldwide community under the Open Access model.
\\n\\nWe are excited about the present, and we look forward to sharing many more successes in the future.
\\n\\nThank you all for being part of the journey. 5,000 times thank you!
\\n\\nNow with 5,000 titles available Open Access, which one will you read next?
\\n\\nRead, share and download for free: https://www.intechopen.com/books
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Preparation of Space Experiments edited by international leading expert Dr. Vladimir Pletser, Director of Space Training Operations at Blue Abyss is the 5,000th Open Access book published by IntechOpen and our milestone publication!
\n\n"This book presents some of the current trends in space microgravity research. The eleven chapters introduce various facets of space research in physical sciences, human physiology and technology developed using the microgravity environment not only to improve our fundamental understanding in these domains but also to adapt this new knowledge for application on earth." says the editor. Listen what else Dr. Pletser has to say...
\n\n\n\nDr. Pletser’s experience includes 30 years of working with the European Space Agency as a Senior Physicist/Engineer and coordinating their parabolic flight campaigns, and he is the Guinness World Record holder for the most number of aircraft flown (12) in parabolas, personally logging more than 7,300 parabolas.
\n\nSeeing the 5,000th book published makes us at the same time proud, happy, humble, and grateful. This is a great opportunity to stop and celebrate what we have done so far, but is also an opportunity to engage even more, grow, and succeed. It wouldn't be possible to get here without the synergy of team members’ hard work and authors and editors who devote time and their expertise into Open Access book publishing with us.
\n\nOver these years, we have gone from pioneering the scientific Open Access book publishing field to being the world’s largest Open Access book publisher. Nonetheless, our vision has remained the same: to meet the challenges of making relevant knowledge available to the worldwide community under the Open Access model.
\n\nWe are excited about the present, and we look forward to sharing many more successes in the future.
\n\nThank you all for being part of the journey. 5,000 times thank you!
\n\nNow with 5,000 titles available Open Access, which one will you read next?
\n\nRead, share and download for free: https://www.intechopen.com/books
\n\n\n\n
\n'}],latestNews:[{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"}]},book:{item:{type:"book",id:"293",leadTitle:null,fullTitle:"Practical Applications and Solutions Using LabVIEW™ Software",title:"Practical Applications and Solutions Using LabVIEW™ Software",subtitle:null,reviewType:"peer-reviewed",abstract:"The book consists of 21 chapters which present interesting applications implemented using the LabVIEW environment, belonging to several distinct fields such as engineering, fault diagnosis, medicine, remote access laboratory, internet communications, chemistry, physics, etc. The virtual instruments designed and implemented in LabVIEW provide the advantages of being more intuitive, of reducing the implementation time and of being portable.\nThe audience for this book includes PhD students, researchers, engineers and professionals who are interested in finding out new tools developed using LabVIEW.\nSome chapters present interesting ideas and very detailed solutions which offer the immediate possibility of making fast innovations and of generating better products for the market. The effort made by all the scientists who contributed to editing this book was significant and as a result new and viable applications were presented.",isbn:null,printIsbn:"978-953-307-650-8",pdfIsbn:"978-953-51-5551-5",doi:"10.5772/819",price:139,priceEur:155,priceUsd:179,slug:"practical-applications-and-solutions-using-labview-software",numberOfPages:488,isOpenForSubmission:!1,isInWos:1,hash:"8709b37736bf2d4359e98e5542cae86c",bookSignature:"Folea Silviu",publishedDate:"August 1st 2011",coverURL:"https://cdn.intechopen.com/books/images_new/293.jpg",numberOfDownloads:134081,numberOfWosCitations:37,numberOfCrossrefCitations:28,numberOfDimensionsCitations:50,hasAltmetrics:0,numberOfTotalCitations:115,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 3rd 2010",dateEndSecondStepPublish:"December 1st 2010",dateEndThirdStepPublish:"April 7th 2011",dateEndFourthStepPublish:"May 7th 2011",dateEndFifthStepPublish:"July 6th 2011",currentStepOfPublishingProcess:5,indexedIn:"1,2,3,4,5,6,7",editedByType:"Edited by",kuFlag:!1,editors:[{id:"6084",title:"Prof.",name:"Silviu",middleName:null,surname:"Folea",slug:"silviu-folea",fullName:"Silviu Folea",profilePictureURL:"https://mts.intechopen.com/storage/users/6084/images/293_n.jpg",biography:"Folea, C., Silviu, PhD, is professor at the Technical University of Cluj-Napoca, Automation Department, Romania. His research interests include: embedded systems - hardware and software, reconfigurable systems, data acquisition, wireless networks and low power sensors. His software interests include LabVIEW graphical programming for Real Time and FPGA modules with courses taught at bachelor and master degree.\nProfessor Folea has twenty-three years of design experience in the embedded systems domain and in university teaching. IEEE Senior Member.",institutionString:null,position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Technical University of Cluj-Napoca",institutionURL:null,country:{name:"Romania"}}}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"599",title:"Computer Simulation",slug:"numerical-analysis-and-scientific-computing-computer-simulation"}],chapters:[{id:"17619",title:"Virtual Instrument for Online Electrical Capacitance Tomography",doi:"10.5772/19523",slug:"virtual-instrument-for-online-electrical-capacitance-tomography",totalDownloads:3087,totalCrossrefCites:0,totalDimensionsCites:2,signatures:"Zhaoyan Fan, Robert X. 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\r\n\tPolyimide is nowadays fully acknowledged as one of the most efficient polymers in many industries for its excellent thermal, electrical and mechanical properties, as well as for its easy processability. Particularly, in the Electronic and Electrical Engineering industries, polyimide is widely used for decades thanks to its very good dielectric and insulating properties at high electric field and high temperature up to 250°C in long term-service.
\r\n\t
\r\n\tSince its discovery in the mid-50’s, a wide range of applications from low to high voltage appeared, putting polyimide as a key material to design more performing and reliable electrical devices and systems. On another hand, polyimide appears also essential for the development of new electronic devices where further considerations such as high power density, integration, higher temperature, thermal conduction management, energy storage, reliability or flexibility are required in order to sustain the growing electrical energy consumption needs of the global society.
\r\n\tConsequently, polyimide materials have and will have to face new exciting fundamental, technological and environmental challenges among which:
\r\n\t• a better understanding of its intrinsic electrical properties to identify current limitations and propose new advanced device designs,
\r\n\t• the development of innovative composites and nanocomposites structuration to tailor its physical properties by involving classical and original nanoparticles such as graphene layer, carbon nanotubes, metal, silicates, nitrides, etc.,
\r\n\t• the development of polyimide composites for energy storage, thermal management, reinforced nanodielectrics and corona-resistant nanocomposites,
\r\n\t• the development of new low and ultra-low dielectric constant polyimide for microelectronics (fluorinated polyimides, nanoporous, mesoporous),
\r\n\t• the development of new higher temperature reliable polyimide (high glass transition, high degradation temperature),
\r\n\t• the emergence of solvent-free processes to fit with environmental purposes
\r\n\tMoreover, many challenges regarding the aging mechanisms understanding under single or multiple constraints and the realistic lifetime prediction using robust physical modelling is a ubiquitous questioning in most of the electronic industries.
\r\n\tThis book will target to review both the state-of-the-art and new researches on Polyimide for Electronic and Electrical Engineering Applications. It will present interdisciplinary chapters on the state of knowledge of each topic under consideration through a combination of overviews and original unpublished research. Chapter proposals related to one of the following topics and their keywords (but not only restricted to them) are very welcome to be submitted for this book publication project:
\r\n\t• General Considerations and Technological Processes of Polyimide for Electronics and Electrical Systems
\r\n\tProcessability, Photosensitive and non-photosensitive polyimide, Curing temperature,
\r\n\tSpin-coating, Dip-coating, Extruded enameled wires, Other casting methods
\r\n\t• Polyimide in Microelectronic Applications
\r\n\tDielectric properties, Intermetal layer, Ultra Large-Scale Integration (ULSI), Low-k dielectrics, Fluorinated polyimide, Nanoporous polyimide, Flexible substrates, Thin film transistors, LCD devices, sensors and actuators (gas, humidity, pressure, tactile…)
\r\n\t• Polyimide in Medium and High Voltage Applications
\r\n\tElectrical insulation properties (conduction, breakdown), Digital isolators, Power electronics and devices, Power modules, Power integration, Passivation, Packaging, High voltage power systems, Enameled wires for fed-inverter rotating machine
Microwaves pervade the whole universe; this was discovered by quite an accident by R. W. Wilson and A. A. Penzias in 1964 [1, 2, 3]; microwaves seem to bathe the earth and the space from all directions. Microwaves, also, pervade today’s world of high technology [4, 5]. They are of tremendous scientific interest, and they are, just, indispensable in today’s communication [6], military [7], medical [8], domestic appliances, scientific instruments [9, 10] (electron spin resonance, ESR/ferromagnetic resonance spectroscopy, FMR), microwave passive instruments [11, 12, 13, 14, 15], radars, spaceships, satellites, and so forth; they are also found in many industries such as automobile, data, memory and computer processing, and microwave instrumentation [14, 15]; the signal processing in the range of 5–50 GHz is quite interesting for security, military, and communication applications [15, 16]. Modern microwave communication especially mobile communication and satellites requires high performance band-stop filter having high frequency selectivity, smaller size, high stop band attenuation, and low insertion loss [15, 17]. A good account of different applications is found in [17].
Most impressive, they are already playing an important role in the development of smart cities along with smart transportation, smart energy, smart health care, and so forth [18]. Figure 1 shows an electromagnetic spectrum, making emphasis on the microwave region and the definition of its different bands. Figure 2 shows an assortment of pictorial representations of some of the modern applications of microwaves.
The electromagnetic spectrum, making emphasis on the microwave region and its different bands.
The microwaves in the electromagnetic spectrum range from 300 MHz (1 m) to 300 GHz (1 mm) [
In Figure 3, we show one of the most impactful applications of microwaves as the signals coming in and out from magnetic microwire sensors implanted in injured-surgery patients in order to follow postoperatory recovery [8]. The microwave beam should penetrate a considerable section of tissue then “hit” the magnetic wire, film, or rod, reflecting in many directions. Some microwaves will get back to the horn entrance of the transceiver, then detected and processed. The technology already exists and is already in use in atmospheric sciences [21] and in gun radars to detect speedy objects. These applications cannot be carried out with laser, for example, as laser light cannot penetrate tissue as microwaves do. It should be noted that in all the above examples, microwaves and radar work in open spaces and “hit” a target, and then some of the reflected beams are detected. Absorption in the medium itself and by obstacles reduces the reading at the detectors. There are also a great number of uses of microwaves inside tubes, pipes, and cavities. More controlled energy flux is attained and precision measurements can be done. We treat them after we give the fundamentals of the physics involved.
Microwaves as the signals coming in and out from magnetic microwire sensors implanted in injured-surgery patients in order to follow postoperatory recovery [
But, why are they (microwave) everywhere in this world and out of this world? It is because of the peculiarity of their electromagnetic properties and the way they interact with matter. They started to propagate through the universe at the epoch of recombination in the cosmic evolution. The cosmic microwave background (CMB) is the most ancient relic we have today of the beginning of the universe in the form of a big bang [24, 25]. It is the oldest electromagnetic radiation, older than visible light [26]. When atoms and nuclei appeared for the first time in the universe, microwaves started to interact with them immediately. Microwaves interact with atoms, nuclei, protons, electrons, molecules, clusters of molecules, and so forth. At the macroscopic scale, microwaves interact with all kinds of matter: rocks, gases, clouds, liquids (water and oceans), dielectrics, plasmas, ionosphere, metals, magnetic matter, and so on. It gets reflected, transmitted, and very frequently absorbed. Microwaves make atoms rotate (rotational excitation) and make electric dipoles jiggle frenetically, and when electric dipoles are part of dielectric materials, microwaves heat them. Microwaves make magnetic dipoles rotate and jump up magnetic energy states. The free electrons in metallic objects absorb greatly microwaves.
Microwaves interact with matter, microscopically, through its constituent atoms, conduction electrons if present, and atomic magnetic dipoles if present. Yet, macroscopically, the effects of microwaves on matter are well described by the four Maxwell equations and the electrodynamic properties of matter: ϵ (electric permittivity), μ (magnetic permeability), and σ (electrical conductivity).
The interactions of microwaves with matter are of many kinds. The general electrodynamic properties of matter, ϵ, μ, and σ, determine completely their behavior when microwaves “hit” them. More specifically, the electric permittivity, ϵ, carries information on the polarization of a dielectric specimen (water, vapor, clouds, wood, glass, and so on) and is related to the number of electric dipoles as χ = Nα/(ϵ0 − Nαb) and P = (ϵ – ϵ0) E, and ϵ = (1 + χ) ϵ0, with P = ϵ0χE and α the molecular polarizability of the medium and is generally anisotropic, i.e., αx ≠ αy ≠ αz; hence χ in general is anisotropic and is represented by a tensor in matrix form. Electric dipoles absorb greatly microwaves because these cause the electric dipoles to execute damped oscillations at the GHz frequency. The damped motion brings with it a complex ϵ = ϵ’ – i ϵ” which is also a function of frequency [27, 28], in which ϵ” takes account of the energy losses.
The magnetic permeability, μ, carries information on the magnetization capacity of a material that carries a number N of magnetic dipoles. They are related by μ = μ0(1 + χm),
We describe here, in a nutshell form, the fundamental physics involved in the interactions of microwaves with matter with emphasis on magnetic matter. Today science and technology are able to produce, control, direct, and amplify microwaves in the laboratory and in devices and high-technology instruments and equipments [9, 11, 19, 21]. The electromagnetism of microwave devices and instruments is an integral part of today’s technological world. And the electrodynamics of microwaves is governed by Maxwell’s equations as applied to ϵ, μ, and σ materials. We present these equations and the partial differential wave equations that are obtained from them with the expressions of their solutions.
Richard Feynman (from Feynman’s Lectures, Vol. 2, Chap. 21): “So here is the center of the universe of electromagnetism, the complete theory of electricity and magnetism, and of light; a complete description of the fields produced by any moving charges; and more. It is all here. Here is the structure built by Maxwell, complete in all its power and beauty. It is probably one of the greatest accomplishments of physics. To remind you of its importance, we will put it all together in a nice frame:”
He states such definite statements once he obtains the general solutions for the electric potential, V, and the vector potential,
We are not concerned here in the detail deduction of Maxwell’s equations, nor the deduction of electromagnetic waves from them. Reflection and refraction and absorption of microwaves in conducting magnetic and dielectric materials are presented in graphical form along with the principal equations that govern them. The deduction of such results is too long, and they are developed in a number of excellent, well-established textbooks [27, 28, 29, 30, 31, 32, 33]. The deduction of electromagnetic fields and waves from Maxwell’s equations does not impose any restriction on the wavelength-frequency, as shown in Figure 1. The result is quite general, but we are interested and focused on microwaves interacting with
All the elements of both material electrodynamic tensors are in general dependent on frequency,
Remember that
From Maxwell’ equations inhomogeneous wave equations are obtained for the fields
Far from the microwave sources (centimeters, meters, kilometers, and, even, light years), we can safely drop the “source” terms, and homogeneous partial differential equations are left:
It should be stressed that these identical wave equations describe attenuated waves. This comes naturally from the third term that includes magnetic permeability, electric conductivity, and the first time derivative of each field. The solutions of these equations are readily obtained by separation of variables [27]. The detailed deduction of these mathematical expressions is lengthy and elaborated; after such work, we find the fields to be transverse and plane-polarized for which the x-direction for
Wave solutions in different media (no bounds considered).
Here we show in the form of a table (deductions are given in [27, 28, 31]) the solutions for E and H for propagation in free space and in a dielectric material and in a conducting material. In this concise form, we highlight the most relevant features and parameters of the solutions. When we put back the solutions found for a σ, μ,
In the ideal case of propagation of microwaves in air, the phenomenon of attenuation (absorption of microwave energy,
In the modern microwave Wi-Fi, military, radar communication systems, the microwaves have to travel through “free space” to reach detectors and receivers, but it is pretty common in urban areas that the propagation encounters obstacles, such as buildings, windows, walls, bridges, metallic structures, and fog. At the surface of those obstacles, reflection, absorption, refraction, and dispersion of the microwaves occur. When microwaves hit obstacles, energy is irremediably lost at these obstacles. This fact could be used to detect that precisely an obstacle is present and fine measurements of the reflected or refracted microwave energy could give valuable information on the electromagnetic character (
Microwaves bounce back from virtually any material. (a) The Wi-Fi signal being reflected and refracted from anything can be in an urban city area. Wi-Fi and radar signals are commonly present in the air in any city. These microwaves hit buildings, windows, fog, hot air, street floors, and so forth; at all times they are reflected (R), absorbed (A), and refracted (T) [
The general boundary conditions the electromagnetic fields,
Boundary conditions for the magnetic field
Since medium 1 sustains the incident and reflected fields,
When boundaries are present on purpose or as an inevitable obstacle, the incident microwaves reflect and refract, and the formal treatment will conduct us to Snell law and the Fresnel equations for incidence with
Incident, reflected, and transmitted microwaves at any kind of interface. (a)
The incident wave with magnetic vector in the incidence plane. Snell laws demand that the reflected and transmitted magnetic vectors are also in the same plane. The arrows indicate the directions of the vectors involved. The Poynting vectors
In Figure 6a, medium 1 is the space where we want to propagate some microwave signal and medium 2 being a window, a wall, water, wood, concrete, metallic sheets, a building in front of us, etc. A very common situation is when sunlight shines and goes through a glass window; in this case most of the light goes through and illuminates the room. And yet, part of it is reflected, and part is absorbed (the energy of which heats up the glass window itself). A second very common situation generated by the modern wireless communication technology is the Wi-Fi signal (it plays exactly the same role as the sunshine in the above illustration). The typical Wi-Fi signal is around 2.3 GHz, and the newest cable boxes are delivering to our home rooms ≈5.2GHz with about 1 W power.
When the obstacle (medium 2) is made of materials that are also ferromagnetic or ferrimagnetic (ferrites), the absorption will increase considerably because the magnetic moments of the material absorb energy from the Wi-Fi waves. Conductors (materials with free electrons) will absorb Wi-Fi wave energy by virtue of the term JE which becomes Joule heating. Abstracting the cases mentioned above, we consider, as the first case, the incidence of a plane electromagnetic wave on the interface of two media as shown in Figure 7; the incident electric field is of the form
The reflected and the refracted waves are
As the simple example illustrated in Figure 6b, given by Feynman [29], shows “A large imaginary part of the index of refraction (or equivalently a large imaginary component of k, k”) means a strong absorption. So there is a general rule that if any material gets to be a
But in our case the three fields must be identical functions of space and time at any point on the interface [27, 28, 29, 32, 33]. From such requirement, it follows that
Now we proceed to determine the quantities
We have four unknowns: (
At any point and at any time at the interface. Likewise, continuity of the tangential component of the magnetic field requires
which becomes
Algebraic Eqs. (20) and (21) are readily solved for unknowns E0r and E0t:
Using (20)
where N indicates that E is normal to the incidence plane and/or H is in the plane of incidence.
In the case the three H vectors are perpendicular to the plane of incidence, Figure 8, we have:
After some algebra and rearranging terms, we obtain E0t/E0i. Hence:
Here P denotes that the
Both media are dielectric and magnetic, and the magnetic field component
And obviously
The whole subject of reflection, refraction, and absorption of microwaves at the interface of air and a conducting (σ), magnetic (μ), and dielectric (
When research in this area does not involve necessarily open spaces, and transmission losses should be avoided, what can we do to reduce losses, dispersion, and uncontrolled reflections of microwaves while propagating? Or what can be done to control and measure such dispersions, absorptions, and reflections? The answer is whenever possible, guide the microwaves (Figure 9).
It is well known that very good conductors (metallic) reflect electromagnetic waves with a minimum of losses (these losses are due to Joule effect on the free electrons that are within the skin depth only) (see Table 1
Rectangular waveguides made of very good conducting metals (copper, silver, gold, and brass) sustaining different patterns of
Since the beginnings of the microwave technology, previous to world war II, it is well known that metallic hollow pipes with internal, mirror-polished walls can sustain propagation of some particular electromagnetic (EM) modes, TM (transverse magnetic), and TE (transverse electric) and cannot sustain other EM modes [27, 28, 29, 37, 38].
A universal condition is that one significant dimension, ξ, of the hollow pipe be exactly a multiple of an integer number of half the wavelength of the microwave to be transmitted through it. Hence ξ = nλ/2 determines the “size” of the cross section of a rectangular or a cylindrical waveguide. λg = c/νnm is the wavelength inside the waveguide. All the theory is consequence of the solutions to Maxwell’s equations, under boundary conditions at the walls of the mirror-polished metallic surfaces of the microwaveguide. The particular deductions of the mathematical expressions of the valid
Standard sizes of rectangular waveguide | |||||
---|---|---|---|---|---|
Waveguide name | Frequency band name | Recommended frequency band of operation (GHz) | Cutoff frequency of lowest-order mode (GHz) | Cutoff frequency of next mode (GHz) | Inner dimensions of waveguide opening (mm) |
EIA | |||||
WR650 | L-band (part) | 1.15–1.72 | 0.908 | 1.816 | 165.1 × 82.55 |
WR340 | S-band (part) | 2.20–3.30 | 1.736 | 3.471 | 86.36 × 43.18 |
WR229 | C-band (part) | 3.30–4.90 | 2.577 | 5.154 | 58.17 × 29.08 |
WR90 | X-band | 8.20–12.40 | 6.557 | 13.114 | 22.9 × 10.2 |
WR42 | K-band | 18.00–26.50 | 14.051 | 28.102 | 10.7 × 4.32 |
WR22 | Q-band | 33.00–50.00 | 26.346 | 52.692 | 5.86 × 2.84 |
WR19 | U-band | 40.00–60.00 | 31.391 | 62.782 | 4.78 × 2.39 |
WR15 | V-band | 50.00–75.00 | 39.875 | 79.75 | 3.76 × 1.88 |
WR12 | E-band | 60.00–90.00 | 48.373 | 96.746 | 3.10 × 1.55 |
WR10 | W-band | 75.00–110.00 | 59.015 | 118.03 | 2.54 × 1.27 |
WR8 | F-band | 90.00–140.00 | 73.768 | 147.536 | 2.03 × 1.02 |
WR6, WR7, WR6, 5 | D-band | 110.00–170.00 | 90.791 | 181.583 | 1.65 × 0.826 |
Some of the most common rectangular waveguides and their frequency ranges and frequency cutoffs and inner dimensions (mm). The waveguide name WR stands for waveguide rectangular, and the number is the inner dimension width of the waveguide in hundredths of an inch (0.01 inch = 0.254 mm). The different microwave bands are given and can be correlated with the bands shown in Figure 1 (Taken from Wikipedia).
A plane electromagnetic wave propagating in a rectangular hollow waveguide. (a) The lines AB and CD are parallel to wave fronts for the wave propagating to the right and upward. Similarly, BC and DE are parallel to wave fronts traveling to the right and downward. The angle α is the angle of incidence; the broken line FCG represents a ray reflected at C. (b) A laboratory Q-band cylindrical waveguide.
Once we know the electromagnetic patterns that can be formed and sustained in hollow metallic pipes, as the one we show in Figure 11, how can we use them to probe material’s properties? The fundamental idea of how to measure electrodynamic properties (
Fundamental idea of how to measure electrodynamic properties (
To insert the specimen in the location we want, a hole is made on top of the guide and a material (dielectric,
Waveguides are used mainly to measure microwave transmission and energy transmission, T. A greater performance in the interaction of microwaves with (
Closed metallic boxes are a particular case of a bounded space but are an important one. When the wavelength of a particular microwave (v.gr. 3 cm, 11 cm, or 8 mm) is trapped inside a box made of very good conductors (copper, silver, gold), the microwave bounces back and forth between the walls, and a pattern of standing waves is formed. The energy absorption at the walls is very small, and by virtue of this property, such a box is, really, a container of electromagnetic energy, concentrated electromagnetic energy in a closed, finite space. The same way we store a beverage in an aluminum can, we can store electromagnetic energy in a similar can (see Figure 12).
A metallic can is commonly used to contain and to store a beverage. Similarly, a metallic can is used to sustain and store electromagnetic fields in the form of standing waves.
In electromagnetic cavities, the microwaves inside form maxima and minima at known distances, and the electromagnetic energy is stored efficiently. The main quantities that describe the electromagnetic behavior of a cavity are the standing wave electromagnetic fields
They are solved by separation of variables, the boundary conditions are periodic, and the separation constants become integer numbers: (k1, k2, k3) −> (n, l, m) in Cartesian coordinates, or (
If we are interested in the quantitative study of microwave dispersion, absorption, and reflection by some kind of materials, we produce standing wave patterns inside a resonant cavity, put inside the material to be studied, let the microwaves interact with it, and then measure its absorption by its reflection and its frequency shift (dispersion) by the change of the energy in the cavity (through the Q of the cavity) without and with material sample.
Examples of real microwave laboratory X-band and Q-band waveguides and cavities are as follows: the schematic representations of
Common rectangular X-band waveguides and cavities and microwave source box used in laboratory. (a) typically the microwaves are combined with static
The same kind of experimental setups we just briefly described for X-band waveguides and cavities can be very well carried out at other frequencies with the appropriate K, Ku, Q, L, and S microwave equipment. The hoses that carry water and the electric cables that carry electricity can bend and give ≥90° turns, and pipes can be splitted, reduced in size, and so forth. The same with optical fibers and the same with microwave plumbing. Microwave circulators make the
Multiple reflections on the inner metallic wall of a wave guide allow the propagation of microwaves long distances, A, a laboratory Q-Band cylindrical wave guide connected on the upper part to a rectangular portion of another wave guide and connected at the bottom, B, to a cylindrical resonant cavity.
Concentrate of the basic properties of some cylindrical cavities that sustain some E and H modes (patterns of standing waves). The blue dashed lines are
As a way of example, next we give some cylindrical frequency parameters and some standing wave patters (Table 3) allowed to propagate in these cavities for an air-filled circular cylindrical cavity resonator of radius a and length d. The resonant frequencies are
where the boundary condition at the lateral wall, r = a, imposes
Above we show just a few roots of
It is a fundamental quantity in the theory and evaluation of microwave cavities. The quality factor of the cavity is defined by
Q becomes an extremely useful parameter to measure the performance of a cavity and to make quantitative the losses in it when it is empty and/or when it is loaded with a material sample of interest. The higher the Q, the higher the quality of the metallic cavity as reservoir of electromagnetic energy. A cavity with a Q of 17,000, 33,000, or 100,000 will lose energy in a fraction of 1/17,000 or 1/33,000 or 1/100,000 of the initial energy content per cycle. So, these devices are really very good at storing microwave energy. Notice that the inverse of Q is a measure of those losses:
Q−1 = Energy loss (absorbed, dissipated) per cycle/2π (time-avarage of energy stored at resonant frequency).
Let’s call L the inverse of Q; L = Q−1. The theory of cavities finds that there are four types, and only four types, of energy losses: (a) by Joule effect on the conducting walls and just within the skin depth, Lσ, (b) by dielectric losses if a dielectric material,
The first example is microwave ferrites. Their name clearly indicates the main function they have and have been studied with microwaves since their very invention. Microwave ferrites are crucial elements in microwave measurement equipment itself and in a pleyade of different microwave devices [17]. Its ability to absorb greatly microwaves under very specific circumstances and do not absorb them under other set of circumstances makes these materials highly controllable, and that is what engineering requires [11].
As microwave device it is desirable to have wide yellow and green regions in Figure 15 for passive circulator and isolator operation [11, 24]. Ferrites absorb microwave energy in a resonant fashion and under nonresonant conditions, making these responses a very versatile and manageable material. It is very cheap and easy to fabricate [41].
A variety of ferrites with different sizes and fabrication procedures absorb energy in similar ways. (a) Profile of absorption contains four distinctive regions. Only one is resonant. (b) The usual representation of the absorption is the derivative of the microwave power with respect to magnetic field. (c) Many other ferrites collapse the yellow region, and the FMR region expands to lower and higher fields.
What is microwave energy absorption in a resonant fashion? The phenomenon is really ferromagnetic resonance (FMR). What is the role of microwaves in the ferromagnetic resonance phenomenon? A brief description follows; the most common measurements of the ferrite absorption performance or profile are carried out in equipment as the one shown in Figure 13. In addition to the microwave excitation of the ferrite inside the cavity, an extra static magnetic field, H0, is applied to the ferrite through the magnet poles of the electromagnet also shown in Figure 13a. This is why the cavity is seen located at the center of the magnet poles. This field serves to simplify the magnetic structure of domains of the ferrite, and when 250 mT (2500 Oersters) or more are applied, the domain structure has disappeared, and the material becomes magnetically saturated, and the whole sample has the magnetization value Ms, and this Ms as a whole interacts with the microwave magnetic field and absorbs its energy greatly in the form of ћω = gβH0, in which ћω is the energy of a quantum of the microwave field and the right side gβH0 is the magnetic energy splitting of two consecutive magnetic energy levels. This is the well-known Zemann effect, where β = ћe/2me is Bohr magneton and g is the spectroscopic factor (for ferromagnets and ferrimagnets g is close to 2.00 but always larger). To have ћω = gβH0 means that a stimulated transition between two contiguous energy levels, ∆E = gβH0, is taking place and the energy is provided by photons, hν, with v exactly in the microwave region, of the magnetic component of the microwaves. This is called the resonance condition; it is fully quantum and was discovered without knowing what it was in 1946 by R. Griffiths [34] and explained fully 1 year later by Kittel [32]. When this absorption fullfils the Kittel condition, hν = gβH0, it is resonant absorption of energy (no more, no less, just exactly the energy content in a microwave photon hν), meaning that resonant absorption of microwave (photon) energy is performed by the magnetization of a ferromagnetic specimen. When the atomic magnetic moments or uncoupled electron spins are not governed by the strong magnetic exchange interactions, they do not behave collectively, as a unit, and they behave individually. Such is the case of paramagnetic substances. Each atomic magnetic moment,
When the microwave experimental setup is as described but the equality hν = gβH0 is not fullfiled and absorption of microwaves is still registered, then we have a nonresonant absorption of microwaves, and other dissipative process dynamics are taking place. For example, domain walls can be made to oscillate with an external field, and the motion is dissipative, or some conduction “currents” can be operating. So, the same equipment and experimental setup can measure resonant and nonresonant absorption of microwaves. Measurements of this kind, carried out in equipment as in Figure 13a on ferrites fabricated with different methods and with different compositions [41], give very frequent absorption profiles as the ones shown in Figure 15. This contains nonresonant and resonant absorption of microwaves. This kind of absorption profile has been known for many years. Here we want to demonstrate that resonant and nonresonant absorption of microwaves coexists in just one measurement that is capturing different microscopic absorption mechanisms at different values of H0. The information obtained this way is very rich. For passive microwave circulators and isolators, it is highly convenient that the regions below resonance (B/R, yellow) and above resonance (A/R, green) be as wide as possible since no absorption is demanded. The widening of these yellow and green regions is a continuous search by modifying ferrite fabrication parameters and continuously measuring this kind of microwave absorption. Yet, many ferrites do the contrary and absorb in all regions of H0. On the other hand, the maximum possible absorption is required in order to sensing it from a distance. In a sense a kind of sink is desirable, like an antenna that works by absorbing greatly microwaves. Much the same way radar works. In order to develop potential applications as the one illustrated in Figure 3, “sensors” that absorb greatly microwaves in preferred directions are required. Some promising materials are Fe79B10Si11 glass-covered amorphous-conducting magnetic microwires (simply FeBSi wires) because they have shown great capacity to absorb microwaves at X-band in an anisotropic fashion [42]. The proposed application in Figure 3 demands a great global absorption of microwaves in order to detect reflected microwaves from implanted magnetic microwires (glass-covered for them to be biologically inert) in patients that have undergone some kind of orthopedic surgery at the level of knee, shoulder, vertebra, hip, and so on. The microwires are implanted with some specific orientation, and as recovery develops and bone grows, or fractures heal, the microwires would move when pushed by the new processes taking place. Those changes are expected to be informative to the surgeons. The idea of the detection is quite similar as how radar detects moving or static “objects” at a distance. The same idea is used in how the laser gun works detecting a speeding vehicle. A good level of reflected, or perturbed. microwave “signal” coming back to the transducer is required. In laboratory models, FeBSi wires have shown great microwave absorption at some particular orientations. Experiments are carried out with the wires inside microwave cavities in equipment as the one shown in Figure 13. Conditions are established for FMR absorption because it is the maximum possible; hence in addition to the X-band microwaves fed to the resonant cavity, an extra static magnetic field is also applied. The physical interactions are as described for ferrites, except that these are amorphous and no long-range order exists and the strong crystalline anisotropy does not exist and Hint that goes in Heff is different from the Hint present in ferrites. A typical absorption profile is shown in Figure 16. Here the quantity of interest is the integral of the absorption curve since it gives directly the total microwave power absorbed by the sample. The higher the integral, the better in order to use it as sensor-detector of microwaves. The total absorption resulted in a fast-increasing monotonic function of power. The Abs% grows to over 1000% for P = 180 mW. The measured absorption for the military material “mu” is shown for comparison; it does not show such effect. This is a kind of amplification effect [42].
FMR absorption of microwaves by glass-coated amorphous-conducting ferromagnetic microwires. (a) First derivative of absorption intensity as function of delivered microwave power and (b) the total absorption is a fast-increasing function of power. The Abs% grows to over 1000% for P = 180 mW. The measured absorption for the military material “mu” is shown for comparison, it does not show such effect [
In, yet, another application, the cavity microwave magnetic field near an extra inserted conducting perturbation is greatly enhanced. Nanomagnets and micromagnets could require for their study an enhancement of the fields they experience inside a resonant cavity. This could be achieved by introducing an extra conductor (wire) in the cavity in order to expose its free electrons to the microwave electric field in the cavity. Induced currents in the conductor, of the same frequency of the microwaves, would produce an extra magnetic field H+ in some small regions, γ, very close to the extra wires, w+. Placing a micron- or nano-sized sample, η, in region γ of increased field Hincr = H0 + Hint + H+ could produce an amplified ferromagnetic resonance absorption, since now ћω = gβH0 is fulfilled as before, but more microwave effective power is absorbed by a micro- or nano-magnetic material with a not so large total magnetic moment, M, placed at the γ region. This was proven experimentally by R. Rodbell in 1952 [39, 40] more than half a century ago; we consider it a classic of deep understanding of electrodynamics in cavities and a good example of how to use them in novel ways. Present-day microwave experiments of these kinds can be performed on ferromagnetic resonance equipment that looks like the one shown in Figure 13.
One interesting result obtained by Rodbell is that the microwave magnetic field strength near the surface of a conducting rod may be easily made to exceed the maximum magnetic field strength existing in the unperturbed cavity at the same incident power level. This would appear to be a useful means of effectively coupling microwave energy into a magnetic specimen. The experiment described by Rodbell is the measurement of the relative intensity of the microwave magnetic resonance absorption of an
The results indicate that the electric field “drives” the absorption; that is, the microwave electric field is locally perturbed and gives rise to a locally large magnetic field. Further confirmation is found in curve (c) of Figure 17 which displays the result of an experiment in which a copper wire of the same size as in (b) is coated directly (no intervening quartz capillary) with approximately the same amount of the ferrite (MnFe2O4) powder. The increased absorption, here relative to (b), is interpreted to be the result of the larger microwave magnetic field that occurs closer to the perturbing conductor.
The intensity of the ferromagnetic resonance measured for a sample of MnFe2O powder as it depends upon position of the sample in a rectangular TE011 X-band microwave cavity. The incident power is 50 mW. (a) FMR with the ferrite alone, (b) ferrite near a cooper wire, (c) ferrite powder glued to the copper wire. The FMR absorption increase amplification is more than 1000X.
An overview of the universality of the microwaves in the universe and in the modern technology world was given. Maxwell’s equations are placed in the center of the electrodynamics universe and in particular in all the technological applications that were mentioned: microwaves in open spaces as in radar, Wi-Fi, guided microwaves, and microwaves in closed resonant cavities with very good conducting walls. Solutions of Maxwell’s equations are given in tables, and the phenomena of reflection, refraction, and absorption are shown to be universal. The Snell and Fresnel reflection and refraction equations are given. The fundamental physics of propagation is given, and the main features of electromagnetism in resonant cavities were described. Real waveguides and cavities and microwave equipment were presented, and general ideas of their use for research were also given. Few applications of absorption measurements under ferromagnetic resonance and nonresonant conditions for ferrites, amorphous microwires, and conductors with magnetism were given.
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