Maxwell's Equations
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Role of Dielectric Materials in Electrical Engineering B D Bhagat
ISSN: 2319-5967 ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 2, Issue 5, September 2013 Role of Dielectric Materials in Electrical Engineering B D Bhagat Abstract- In India commercially industrial consumer consume more quantity of electrical energy which is inductive load has lagging power factor. Drawback is that more current and power required. Capacitor improves the power factor. Commercially manufactured capacitors typically used solid dielectric materials with high permittivity .The most obvious advantages to using such dielectric materials is that it prevents the conducting plates the charges are stored on from coming into direct electrical contact. I. INTRODUCTION Dielectric materials are those which are used in condensers to store electrical energy e.g. for power factor improvement in single phase motors, in tube lights etc. Dielectric materials are essentially insulating materials. The function of an insulating material is to obstruct the flow of electric current while the function of dielectric is to store electrical energy. Thus, insulating materials and dielectric materials differ in their function. A. Electric Field Strength in a Dielectric Thus electric field strength in a dielectric is defined as the potential drop per unit length measured in volts/m. Electric field strength is also called as electric force. If a potential difference of V volts is maintained across the two metal plates say A1 and A2, held l meters apart, then Electric field strength= E= volts/m. B. Electric Flux in Dielectric It is assumed that one line of electric flux comes out from a positive charge of one coulomb and enters a negative charge of one coulombs. -
Lecture 17 - Rectangular Waveguides/Photonic Crystals� and Radiative Recombination -Outline�
6.772/SMA5111 - Compound Semiconductors Lecture 17 - Rectangular Waveguides/Photonic Crystals� and Radiative Recombination -Outline� • Dielectric optics (continuing discussion in Lecture 16) Rectangular waveguides� Coupled rectangular waveguide structures Couplers, Filters, Switches • Photonic crystals History: Optical bandgaps and Eli Yablonovich, to the present One-dimensional photonic crystals� Distributed Bragg reflectors� Photonic fibers; perfect mirrors� Two-dimensional photonic crystals� Guided wave optics structures� Defect levels� Three-dimensional photonic crystals • Recombination Processes (preparation for LEDs and LDs) Radiative vs. non-radiative� Relative carrier lifetimes� C. G. Fonstad, 4/03 Lecture 17 - Slide 1 Absorption in semiconductors - indirect-gap band-to-band� •� The phonon modes involved indirect band gap absorption •� Dispersion curves for acoustic and optical phonons Approximate optical phonon energies for several semiconductors Ge: 37 meV (Swaminathan and Macrander) Si: 63 meV GaAs: 36 meV C. G. Fonstad, 4/03� Lecture 15 - Slide 2� Slab dielectric waveguides� •�Nature of TE-modes (E-field has only a y-component). For the j-th mode of the slab, the electric field is given by: - (b -w ) = j j z t E y, j X j (x)Re[ e ] In this equation: w: frequency/energy of the light pw = n = l 2 c o l o: free space wavelength� b j: propagation constant of the j-th mode Xj(x): mode profile normal to the slab. satisfies d 2 X j + 2 2- b 2 = 2 (ni ko j )X j 0 dx where:� ni: refractive index in region i� ko: propagation constant in free space = pl ko 2 o C. G. Fonstad, 4/03� Lecture 17 - Slide 3� Slab dielectric waveguides� •�In approaching a slab waveguide problem, we typically take the dimensions and indices in the various regions and the free space wavelength or frequency of the light as the "givens" and the unknown is b, the propagation constant in the slab. -
A Broad Bandwidth Suspended Membrane Waveguide to Thinfilm
A Broad Bandwidth Suspended Membrane Waveguide to Thinfilm Microstrip Transition J. W. Kooi California Institute of Technology, 320-47, Pasadena, CA 91125, USA. C. K. Walker University of Arizona, Dept. of Astronomy. J. Hesler University of Virginia, Dept. of Electrical Engineering. Abstract Excellent progress in the development of Submillimeter-wave SIS and HEB mixers has been demonstrated in recent years. At frequencies below 800 GHz these mixers are typically implemented using waveguide techniques, while above 800 GHz quasi-optical (open structure) methods are often used. In many instances though, the use of waveguide components offers certain advantages. For example, broadband corrugated feed-horns with well defined on axis Gaussian beam patterns. Over the years a number of waveguide to microstrip transitions have been proposed. Most of which are implemented in reduced height waveguide with RF bandwidth less than 35%. Unfortunately reducing the height makes machining of mixer components at terahertz frequencies rather difficult. It also increases RF loss as the current density in the waveguide goes up, and surface finish is degraded. An additional disadvantage of existing high frequency waveguide mixers is the way the active device (SIS, HEB, Schottky diode) is mounted in the waveguide. Traditionally the junction, and its supporting substrate, is mounted in a narrow channel across the guide. This structure forms a partially filled dielectric waveguide, whose dimensions must kept small to prevent energy from leaking out the channel. At frequencies approaching or exceeding a terahertz this mounting scheme becomes impractical. Because of these issues, quasi-optical mixers are typically used at these small wavelength. In this paper, we propose the use of suspended silicon (Si) and silicon nitride (Si3N4) membranes with silicon micro-machined backshort and feedhorn blocks. -
A Survey on Microstrip Patch Antenna Using Metamaterial Anisha Susan Thomas1, Prof
ISSN (Print) : 2320 – 3765 ISSN (Online): 2278 – 8875 International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering (An ISO 3297: 2007 Certified Organization) Vol. 2, Issue 12, December 2013 A Survey on Microstrip Patch Antenna using Metamaterial Anisha Susan Thomas1, Prof. A K Prakash2 PG Student [Wireless Technology], Dept of ECE, Toc H Institute of Science and Technology, Cochin, Kerala, India 1 Professor, Dept of ECE, Toc H Institute of Science and Technology, Cochin, Kerala, India 2 ABSTRACT: Microstrip patch antennas are used for mobile phone applications due to their small size, low cost, ease of production etc. The MSA has proved to be an excellent radiator for many applications because of its several advantages, but it also has some disadvantages. Lower gain and narrow bandwidth are the major drawbacks of a patch antenna. In this paper, a survey on the existing solutions for the same which are developed through several years and an evolving technology metamaterial is presented. Metamaterials are artificial materials characterized by parameters generally not found in nature, but can be engineered. They differ from other materials due to the property of having negative permeability as well as permittivity. Metamaterial structure consists of Split Ring Resonators (SRRs) to produce negative permeability and thin wire elements to generate negative permittivity. Performance parameters especially bandwidth, of patch antennas which are usually considered as narrowband antennas can be improved using metamaterial. Metamaterials are also the basis of further miniaturization of microwave antennas. Keywords: Microstrip antenna, Metamaterial, Split Ring Resonator, Miniaturization, Narrowband antennas. I. INTRODUCTION Although the field of antenna engineering has a history of over 80 years it still remains as described in [1] “…. -
RF Coils, Helical Resonators and Voltage Magnification by Coherent Spatial Modes
TELSIKS 2001, University of Nis, Yugoslavia (September 19-21, 2001) and MICROWAVE REVIEW 1 RF Coils, Helical Resonators and Voltage Magnification by Coherent Spatial Modes K.L. Corum* and J.F. Corum** “Is there, I ask, can there be, a more interesting study than that of alternating currents.” Nikola Tesla, (Life Fellow, and 1892 Vice President of the AIEE)1 Abstract – By modeling a wire-wound coil as an anisotropically II. CYLINDRICAL HELICES conducting cylindrical boundary, one may start from Maxwell’s equations and deduce the structure’s resonant behavior. Not A. Problem Formulation only can the propagation factor and characteristic impedance be determined for such a helically disposed surface waveguide, but also its resonances, “self-capacitance” (so-called), and its voltage A uniform helix is described by its radius (r = a), its pitch magnification by standing waves. Further, the Tesla coil passes (or turn-to-turn wire spacing "s"), and its pitch angle ψ, to a conventional lumped element inductor as the helix is which is the angle that the tangent to the helix makes with a electrically shortened. plane perpendicular to the axis of the structure (z). Geometrically, ψ = cot-1(2πa/s). The wave equation is not Keywords – coil, helix, surface wave, resonator, inductor, Tesla. separable in helical coordinates and there exists no rigorous 3 solution of Maxwell's equations for the solenoidal helix. I. INTRODUCTION However, at radio frequencies a wire-wound helix with many turns per free-space wavelength (e.g., a Tesla coil) One of the more significant challenges in electrical may be modeled as an idealized anisotropically conducting cylindrical surface that conducts only in the helical science is that of constricting a great deal of insulated conductor into a compact spatial volume and determining direction. -
Lecture 26 Dielectric Slab Waveguides
Lecture 26 Dielectric Slab Waveguides In this lecture you will learn: • Dielectric slab waveguides •TE and TM guided modes in dielectric slab waveguides ECE 303 – Fall 2005 – Farhan Rana – Cornell University TE Guided Modes in Parallel-Plate Metal Waveguides r E()rr = yˆ E sin()k x e− j kz z x>0 o x x Ei Ei r r Ey k E r k i r kr i H Hi i z ε µo Hr r r ki = −kx xˆ + kzzˆ kr = kx xˆ + kzzˆ Guided TE modes are TE-waves bouncing back and fourth between two metal plates and propagating in the z-direction ! The x-component of the wavevector can have only discrete values – its quantized m π k = where : m = 1, 2, 3, x d KK ECE 303 – Fall 2005 – Farhan Rana – Cornell University 1 Dielectric Waveguides - I Consider TE-wave undergoing total internal reflection: E i x ε1 µo r k E r i r kr H θ θ i i i z r H r ki = −kx xˆ + kzzˆ r kr = kx xˆ + kzzˆ Evanescent wave ε2 µo ε1 > ε2 r E()rr = yˆ E e− j ()−kx x +kz z + yˆ ΓE e− j (k x x +kz z) 2 2 2 x>0 i i kz + kx = ω µo ε1 Γ = 1 when θi > θc When θ i > θ c : kx = − jα x r E()rr = yˆ T E e− j kz z e−α x x 2 2 2 x<0 i kz − α x = ω µo ε2 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Dielectric Waveguides - II x ε2 µo Evanescent wave cladding Ei E ε1 µo r i r k E r k i r kr i core Hi θi θi Hi ε1 > ε2 z Hr cladding Evanescent wave ε2 µo One can have a guided wave that is bouncing between two dielectric interfaces due to total internal reflection and moving in the z-direction ECE 303 – Fall 2005 – Farhan Rana – Cornell University 2 Dielectric Slab Waveguides W 2d Assumption: W >> d x cladding y core -
Electrodynamics of Topological Insulators
Electrodynamics of Topological Insulators Author: Michael Sammon Advisor: Professor Harsh Mathur Department of Physics Case Western Reserve University Cleveland, OH 44106-7079 May 2, 2014 0.1 Abstract Topological insulators are new metamaterials that have an insulating interior, but a conductive surface. The specific nature of this conducting surface causes a mixing of the electric and magnetic fields around these materials. This project, investigates this effect to deepen our understanding of the electrodynamics of topological insulators. The first part of the project focuses on the fields that arise when a current carrying wire is brought near a topological insulator slab and a cylindrical topological insulator. In both problems, the method of images was able to be used. The result were image electric and magnetic currents. These magnetic currents provide the manifestation of an effect predicted by Edward Witten for Axion particles. Though the physics is extremely different, the overall result is the same in which fields that seem to be generated by magnetic currents exist. The second part of the project begins an analysis of a topological insulator in constant electric and magnetic fields. It was found that both fields generate electric and magnetic dipole like responses from the topological insulator, however the electric field response within the material that arise from the applied fields align in opposite directions. Further investigation into the effect this has, as well as the overall force that the topological insulator experiences in these fields will be investigated this summer. 1 List of Figures 0.4.1 Dyon1 fields of a point charge near a Topological Insulator . -
High Gain Slotted Waveguide Antenna Based on Beam Focusing Using Electrically Split Ring Resonator Metasurface Employing Negative Refractive Index Medium
Progress In Electromagnetics Research C, Vol. 79, 115–126, 2017 High Gain Slotted Waveguide Antenna Based on Beam Focusing Using Electrically Split Ring Resonator Metasurface Employing Negative Refractive Index Medium Adel A. A. Abdelrehim and Hooshang Ghafouri-Shiraz* Abstract—In this paper, a new high performance slotted waveguide antenna incorporated with negative refractive index metamaterial structure is proposed, designed and experimentally demonstrated. The metamaterial structure is constructed from a multilayer two-directional structure of electrically split ring resonator which exhibits negative refractive index in direction of the radiated wave propagation when it is placed in front of the slotted waveguide antenna. As a result, the radiation beams of the slotted waveguide antenna are focused in both E and H planes, and hence the directivity and the gain are improved, while the beam area is reduced. The proposed antenna and the metamaterial structure operating at 10 GHz are designed, optimized and numerically simulated by using CST software. The effective parameters of the eSRR structure are extracted by Nicolson Ross Weir (NRW) algorithm from the s-parameters. For experimental verification, a proposed antenna operating at 10 GHz is fabricated using both wet etching microwave integrated circuit technique (for the metamaterial structure) and milling technique (for the slotted waveguide antenna). The measurements are carried out in an anechoic chamber. The measured results show that the E plane gain of the proposed slotted waveguide antenna is improved from 6.5 dB to 11 dB as compared to the conventional slotted waveguide antenna. Also, the E plane beamwidth is reduced from 94.1 degrees to about 50 degrees. -
The Self-Resonance and Self-Capacitance of Solenoid Coils: Applicable Theory, Models and Calculation Methods
1 The self-resonance and self-capacitance of solenoid coils: applicable theory, models and calculation methods. By David W Knight1 Version2 1.00, 4th May 2016. DOI: 10.13140/RG.2.1.1472.0887 Abstract The data on which Medhurst's semi-empirical self-capacitance formula is based are re-analysed in a way that takes the permittivity of the coil-former into account. The updated formula is compared with theories attributing self-capacitance to the capacitance between adjacent turns, and also with transmission-line theories. The inter-turn capacitance approach is found to have no predictive power. Transmission-line behaviour is corroborated by measurements using an induction loop and a receiving antenna, and by visualising the electric field using a gas discharge tube. In-circuit solenoid self-capacitance determinations show long-coil asymptotic behaviour corresponding to a wave propagating along the helical conductor with a phase-velocity governed by the local refractive index (i.e., v = c if the medium is air). This is consistent with measurements of transformer phase error vs. frequency, which indicate a constant time delay. These observations are at odds with the fact that a long solenoid in free space will exhibit helical propagation with a frequency-dependent phase velocity > c. The implication is that unmodified helical-waveguide theories are not appropriate for the prediction of self-capacitance, but they remain applicable in principle to open- circuit systems, such as Tesla coils, helical resonators and loaded vertical antennas, despite poor agreement with actual measurements. A semi-empirical method is given for predicting the first self- resonance frequencies of free coils by treating the coil as a helical transmission-line terminated by its own axial-field and fringe-field capacitances. -
Ec6503 - Transmission Lines and Waveguides Transmission Lines and Waveguides Unit I - Transmission Line Theory 1
EC6503 - TRANSMISSION LINES AND WAVEGUIDES TRANSMISSION LINES AND WAVEGUIDES UNIT I - TRANSMISSION LINE THEORY 1. Define – Characteristic Impedance [M/J–2006, N/D–2006] Characteristic impedance is defined as the impedance of a transmission line measured at the sending end. It is given by 푍 푍0 = √ ⁄푌 where Z = R + jωL is the series impedance Y = G + jωC is the shunt admittance 2. State the line parameters of a transmission line. The line parameters of a transmission line are resistance, inductance, capacitance and conductance. Resistance (R) is defined as the loop resistance per unit length of the transmission line. Its unit is ohms/km. Inductance (L) is defined as the loop inductance per unit length of the transmission line. Its unit is Henries/km. Capacitance (C) is defined as the shunt capacitance per unit length between the two transmission lines. Its unit is Farad/km. Conductance (G) is defined as the shunt conductance per unit length between the two transmission lines. Its unit is mhos/km. 3. What are the secondary constants of a line? The secondary constants of a line are 푍 i. Characteristic impedance, 푍0 = √ ⁄푌 ii. Propagation constant, γ = α + jβ 4. Why the line parameters are called distributed elements? The line parameters R, L, C and G are distributed over the entire length of the transmission line. Hence they are called distributed parameters. They are also called primary constants. The infinite line, wavelength, velocity, propagation & Distortion line, the telephone cable 5. What is an infinite line? [M/J–2012, A/M–2004] An infinite line is a line where length is infinite. -
Modulation of Crystal and Electronic Structures in Topological Insulators by Rare-Earth Doping
Modulation of crystal and electronic structures in topological insulators by rare-earth doping Zengji Yue*, Weiyao Zhao, David Cortie, Zhi Li, Guangsai Yang and Xiaolin Wang* 1. Institute for Superconducting & Electronic Materials, Australian Institute of Innovative Materials, University of Wollongong, Wollongong, NSW 2500, Australia 2. ARC Centre for Future Low-Energy Electronics Technologies (FLEET), University of Wollongong, Wollongong, NSW 2500, Australia Email: [email protected]; [email protected]; Abstract We study magnetotransport in a rare-earth-doped topological insulator, Sm0.1Sb1.9Te3 single crystals, under magnetic fields up to 14 T. It is found that that the crystals exhibit Shubnikov– de Haas (SdH) oscillations in their magneto-transport behaviour at low temperatures and high magnetic fields. The SdH oscillations result from the mixed contributions of bulk and surface states. We also investigate the SdH oscillations in different orientations of the magnetic field, which reveals a three-dimensional Fermi surface topology. By fitting the oscillatory resistance with the Lifshitz-Kosevich theory, we draw a Landau-level fan diagram that displays the expected nontrivial phase. In addition, the density functional theory calculations shows that Sm doping changes the crystal structure and electronic structure compared with pure Sb2Te3. This work demonstrates that rare earth doping is an effective way to manipulate the Fermi surface of topological insulators. Our results hold potential for the realization of exotic topological effects -
Frequency Response
EE105 – Fall 2015 Microelectronic Devices and Circuits Frequency Response Prof. Ming C. Wu [email protected] 511 Sutardja Dai Hall (SDH) Amplifier Frequency Response: Lower and Upper Cutoff Frequency • Midband gain Amid and upper and lower cutoff frequencies ωH and ω L that define bandwidth of an amplifier are often of more interest than the complete transferfunction • Coupling and bypass capacitors(~ F) determineω L • Transistor (and stray) capacitances(~ pF) determineω H Lower Cutoff Frequency (ωL) Approximation: Short-Circuit Time Constant (SCTC) Method 1. Identify all coupling and bypass capacitors 2. Pick one capacitor ( ) at a time, replace all others with short circuits 3. Replace independent voltage source withshort , and independent current source withopen 4. Calculate the resistance ( ) in parallel with 5. Calculate the time constant, 6. Repeat this for each of n the capacitor 7. The low cut-off frequency can be approximated by n 1 ωL ≅ ∑ i=1 RiSCi Note: this is an approximation. The real low cut-off is slightly lower Lower Cutoff Frequency (ωL) Using SCTC Method for CS Amplifier SCTC Method: 1 n 1 fL ≅ ∑ 2π i=1 RiSCi For the Common-Source Amplifier: 1 # 1 1 1 & fL ≅ % + + ( 2π $ R1SC1 R2SC2 R3SC3 ' Lower Cutoff Frequency (ωL) Using SCTC Method for CS Amplifier Using the SCTC method: For C2 : = + = + 1 " 1 1 1 % R3S R3 (RD RiD ) R3 (RD ro ) fL ≅ $ + + ' 2π # R1SC1 R2SC2 R3SC3 & For C1: R1S = RI +(RG RiG ) = RI + RG For C3 : 1 R2S = RS RiS = RS gm Design: How Do We Choose the Coupling and Bypass Capacitor Values? • Since the impedance of a capacitor increases with decreasing frequency, coupling/bypass capacitors reduce amplifier gain at low frequencies.