ECE Spring Prof. David R. Jackson ECE Dept. Notes 16
|
|
- Betty Webb
- 5 years ago
- Views:
Transcription
1 ECE 6345 Spring 5 Prof. David R. Jackson ECE Dept. Notes 6
2 Overview In this set of notes we calculate the power radiated into space by the circular patch. This will lead to Q sp of the circular patch.
3 Radiated Power of Circular Patch From Notes we have: E E r ah k h Q J k a ( ) = FF θ, θφ, ( )cosφtanc( z ) ( θ) π ( sin θ) η E E r ah k h P J k a ( ) = ( ) Assumption: ( ) E a, φ = cosφ FF φ, θφ, ( )sinφtanc z ( θ) π inc ( o sin θ) η z where TM Q( θ ) = Γ ( θ ) ( TE Γ ) P( θ) cosθ ( θ) J ( ) inc x J ( ) x x 3
4 Radiated Power of Circular Patch (cont.) The power density in the far field from the Poynting vector is Sr ( r, θφ, ) = Eθ + E η = η φ E ( ah) tanc ( kz h)( π ) η ( ). cos sin ( ) sin ( sin ) ( ) φ J θ Qθ + φ Jinc o θ Pθ Next, use E ωµ kη = = 4π r 4π r 4
5 Radiated Power of Circular Patch (cont.) We then have Sr r h kzh 8η (, θφ, ) = ( ) tanc ( ) ( ) ( ) cos ( ) sin + sin ( ) sin The space-wave power is r φ Q θ J ko a θ φ P θ Jinc θ ππ/ Psp = Sr ( r,, ) r sin d d θφ θ θ φ Performing the φ integrals, Psp = π ( ) h 8 η π / ( ) ( ) ( ) tanc kzh sin θ Q( θ) J sin θ + P( θ) Jinc sinθ dθ 5
6 Radiated Power of Circular Patch (cont.) Define π / Ic = C( θ) dθ where ( ) ( ) ( ) C( θ) = sinθ tanc kzh Q( θ) J sin θ + P( θ) Jinc sinθ We then have π Psp = ( ) h Ic 8η Note: We will get a CAD formula for I c later. 6
7 Calculation of Q sp The Q formula is Q sp U ω S = P sp U S = U E = ε εr E V z dv 4 = εε rh Ez ds S π a = εε rh Ez ρdρdφ = π εε rh Ez ρdρ a E z The electric field is ( ) ( kρ ) ( ) J ρφ φ, = cos J ( ) E a, φ = cosφ z Note: 7
8 Calculation of Q sp (cont.) The stored energy is then a r J ( ) US = h J ( k ) d εε π ρ ρ ρ Denote a I = J ( kρ) ρdρ = ρ J ( kρ) + ρ J ( kρ) ( kρ ) a = J ( ) + J ( ) ( ) a 8
9 Calculation of Q sp (cont.) Recall that k = x a x =.848 so ( ) ( ) J J x = = Hence a I J x x = ( ) We then have a US εε rhπ = J ( x ) J ( x) x or U S a εε rhπ = x 9
10 Calculation of Q sp (cont.) The formula for Q sp then becomes Q sp = ω εε rhπ x π 8η a h Ic ( ) This may be simplified by using the following expressions to eliminate ω and k : k µε a = x r r ω µε µε a = x r r = ω = a x µε r r x µε µε r r
11 Calculation of Q sp (cont.) We then have Q sp = ( x ) ε r x kh Ic Note that Q sp is proportional to the substrate permittivity and inversely proportional to the substrate thickness.
12 Calculation of Q sp (cont.) Summary (exact Q sp ) Q sp ( ) = x r x Ic kh ε π / ( θ) Ιc C dθ x =.848 ( ) ( ) ( ) C( θ) = sinθ tanc kzh Q( θ) J sin θ + P( θ) Jinc sinθ
13 The p Factor We can express the Q sp formula in terms of a p factor (which will eventually be approximated in closed form). Define: C ( ) C( ) θ θ a π / ( θ) Ι C dθ The term C ignores the patch array factor. Also, define: p I I c = π / π / C C ( θ) ( θ) dθ dθ The p term gives the ratio of the power radiated by the actual patch to the power radiated if we ignore the array factor, and collapse the magnetic current down to a single dipole. (See the end of the notes for a derivation of the equivalent dipole moment of the circular patch.) 3
14 Then we have Q sp The p Factor (cont.) ( ) = x r x p I kh ε Note that as x J inc ( x) J ( x) This allows us to express I in a simpler form without the Bessel functions: π / sin tanc Ι = θ ( k hn ( θ) ) P( θ) + Q( θ) dθ 4 4
15 The p Factor (cont.) For the p factor we have: p = π / ( ) ( ) ( ) + ( ) ( ) sinθ tanc khn ( θ) Qθ J sinθ Pθ Jinc sinθ dθ π / θ ( k hn θ ) P( θ) + Q( θ) dθ sin tanc ( ) 4 The term p depends on the patch radius a and the substrate parameters. (After making some approximations, it will depend only on the patch radius.) 5
16 Approximation for a Thin Substrate For a thin substrate, we have: ( k hn θ ) tanc ( ) so π / Ι sinθ P( θ) Q( θ) + dθ 4 p π / ( ) ( ) + ( ) ( ) sinθ Q θ J sinθ P θ Jinc sinθ dθ π / sinθ P( θ) + Q( θ) dθ 4 6
17 Approximation for a Thin Substrate (cont.) From Notes 9 we also have P( θ) = cos θ( Γ ( θ)) = Q TM ( θ) ( θ) TE = Γ = N ( k hn θ ) + j tan ( ) ε r ( θ)secθ cosθ µ r cosθ + j tan ( ) N( θ ) ( k hn θ ) For a thin substrate we then have P( θ) cosθ Q( θ ) 7
18 Approximation for a Thin Substrate (cont.) For the I term (the denominator of the p function) we then have: Ι π / sin θ 4 ( cos θ + ) dθ 4 π / ( ) = sinθ cos θ + dθ This yields I 4 3 8
19 Approximation for a Thin Substrate (cont.) The formula for the p function then becomes π / 3 p sinθ J ( sinθ) + cosθ Jinc ( sinθ) dθ 4 so that π / ( ) ( ) p 3 sinθ J sinθ + cos θ Jinc sinθ dθ The p factor now only depends only on the patch size. 9
20 Approximation for a Thin Substrate (cont.) Summary (approximate Q sp ) Q sp ( ) = x r x p I kh ε x =.848 I 4 3 π / ( ) ( ) p 3 sinθ J sinθ + cos θ Jinc sinθ dθ
21 Equivalent Dipole Moment of Circular Patch Consider an equivalent magnetic dipole that models the patch: y Patch a φ M s φ x h / λ M s φ = cosφ y As a the magnetic current sheet approaches an equivalent magnetic dipole. Equivalent dipole K x
22 Equivalent Dipole Moment of Circular Patch (cont.) The dipole moment of the equivalent magnetic dipole is calculated: π π s sφ S Kl = M yˆ ds = h M cosφa dφ = h cosφcosφadφ = ha π cos φadφ This yields Kl = πah
23 Equivalent Dipole Moment of Circular Patch (cont.) We can therefore physically interpret the p factor as follows: p = P patch rad dip rad P where patch P rad = power radiated by circular patch dip P rad = power radiated by magnetic dipole of equal moment ( Kl = πah ) 3
24 CAD Formula for p In the next set of notes we will obtain approximate closed-form CAD expression for p. 4
ECE Spring Prof. David R. Jackson ECE Dept. Notes 10
ECE 6345 Spring 215 Prof. David R. Jackson ECE Dept. Notes 1 1 Overview In this set of notes we derive the far-field pattern of a circular patch operating in the dominant TM 11 mode. We use the magnetic
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 13
ECE 635 Spring 15 Prof. David R. Jackson ECE Dept. Notes 13 1 Overview In this set of notes we perform the algebra necessary to evaluate the p factor in closed form (assuming a thin substrate) and to simplify
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 26
ECE 6345 Spring 05 Prof. David R. Jackson ECE Dept. Notes 6 Overview In this set of notes we use the spectral-domain method to find the mutual impedance between two rectangular patch ennas. z Geometry
More informationANTENNAS. Vector and Scalar Potentials. Maxwell's Equations. E = jωb. H = J + jωd. D = ρ (M3) B = 0 (M4) D = εe
ANTENNAS Vector and Scalar Potentials Maxwell's Equations E = jωb H = J + jωd D = ρ B = (M) (M) (M3) (M4) D = εe B= µh For a linear, homogeneous, isotropic medium µ and ε are contant. Since B =, there
More informationNotes 19 Gradient and Laplacian
ECE 3318 Applied Electricity and Magnetism Spring 218 Prof. David R. Jackson Dept. of ECE Notes 19 Gradient and Laplacian 1 Gradient Φ ( x, y, z) =scalar function Φ Φ Φ grad Φ xˆ + yˆ + zˆ x y z We can
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 33
C 6345 Spring 2015 Prof. David R. Jackson C Dept. Notes 33 1 Overview In this set of notes we eamine the FSS problem in more detail, using the periodic spectral-domain Green s function. 2 FSS Geometry
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 7
ECE 6341 Spring 216 Prof. David R. Jackson ECE Dept. Notes 7 1 Two-ayer Stripline Structure h 2 h 1 ε, µ r2 r2 ε, µ r1 r1 Goal: Derive a transcendental equation for the wavenumber k of the TM modes of
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 1
ECE 6341 Spring 16 Prof. David R. Jackson ECE Dept. Notes 1 1 Fields in a Source-Free Region Sources Source-free homogeneous region ( ε, µ ) ( EH, ) Note: For a lossy region, we replace ε ε c ( / ) εc
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 41
ECE 634 Sprng 6 Prof. Davd R. Jackson ECE Dept. Notes 4 Patch Antenna In ths set of notes we do the followng: Fnd the feld E produced by the patch current on the nterface Fnd the feld E z nsde the substrate
More informationChapter 4 Reflection and Transmission of Waves
4-1 Chapter 4 Reflection and Transmission of Waves ECE 3317 Dr. Stuart Long www.bridgat.com www.ranamok.com Boundary Conditions 4- -The convention is that is the outward pointing normal at the boundary
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 9
ECE 6341 Spring 2016 Prof. David R. Jackson ECE Dept. Notes 9 1 Circular Waveguide The waveguide is homogeneously filled, so we have independent TE and TM modes. a ε r A TM mode: ψ ρφ,, ( ) Jυ( kρρ) sin(
More information3.4-7 First check to see if the loop is indeed electromagnetically small. Ie sinθ ˆφ H* = 2. ˆrr 2 sinθ dθ dφ =
ECE 54/4 Spring 17 Assignment.4-7 First check to see if the loop is indeed electromagnetically small f 1 MHz c 1 8 m/s b.5 m λ = c f m b m Yup. (a) You are welcome to use equation (-5), but I don t like
More informationIntegrals in cylindrical, spherical coordinates (Sect. 15.7)
Integrals in clindrical, spherical coordinates (Sect. 15.7 Integration in spherical coordinates. Review: Clindrical coordinates. Spherical coordinates in space. Triple integral in spherical coordinates.
More informationLinear Wire Antennas. EE-4382/ Antenna Engineering
EE-4382/5306 - Antenna Engineering Outline Introduction Infinitesimal Dipole Small Dipole Finite Length Dipole Half-Wave Dipole Ground Effect Constantine A. Balanis, Antenna Theory: Analysis and Design
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 37
ECE 6341 Spring 16 Prof. David R. Jacson ECE Dept. Notes 37 1 Line Source on a Grounded Slab y ε r E jω A z µ I 1 A 1 e e d y ( ) + TE j y j z 4 j +Γ y 1/ 1/ ( ) ( ) y y1 1 There are branch points only
More informationFields of a Dipole Near a Layered Substrate
Appendix C Fields of a Dipole Near a Layered Substrate µ z θ µ 1 ε 1 µ 2 ε 2 µ 3 ε 3 d z o x,y Figure C.1: An electric dipole with moment µ is located at r o = (,, z o ) near a layered substrate. The fields
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 32
ECE 6345 Spring 215 Prof. David R. Jackson ECE Dept. Notes 32 1 Overview In this set of notes we extend the spectral-domain method to analyze infinite periodic structures. Two typical examples of infinite
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 6
ECE 6341 Spring 2016 Prof. David R. Jackson ECE Dept. Notes 6 1 Leaky Modes v TM 1 Mode SW 1 v= utan u ε R 2 R kh 0 n1 r = ( ) 1 u Splitting point ISW f = f s f > f s We will examine the solutions as the
More informationECE 6340 Intermediate EM Waves. Fall Prof. David R. Jackson Dept. of ECE. Notes 17
ECE 634 Intermediate EM Waves Fall 16 Prof. David R. Jacson Dept. of ECE Notes 17 1 General Plane Waves General form of plane wave: E( xz,, ) = Eψ ( xz,, ) where ψ ( xz,, ) = e j( xx+ + zz) The wavenumber
More information( z) ( ) ( )( ) ω ω. Wave equation. Transmission line formulas. = v. Helmholtz equation. Exponential Equation. Trig Formulas = Γ. cos sin 1 1+Γ = VSWR
Wave equation 1 u tu v u(, t f ( vt + g( + vt Helmholt equation U + ku jk U Ae + Be + jk Eponential Equation γ e + e + γ + γ Trig Formulas sin( + y sin cos y+ sin y cos cos( + y cos cos y sin sin y + cos
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 15
ECE 6341 Spring 216 Prof. David R. Jackson ECE Dept. Notes 15 1 Arbitrary Line Current TM : A (, ) Introduce Fourier Transform: I I + ( k ) jk = I e d x y 1 I = I ( k ) jk e dk 2π 2 Arbitrary Line Current
More informationCBE 6333, R. Levicky 1. Orthogonal Curvilinear Coordinates
CBE 6333, R. Levicky 1 Orthogonal Curvilinear Coordinates Introduction. Rectangular Cartesian coordinates are convenient when solving problems in which the geometry of a problem is well described by the
More information1-2 Vector and scalar potentials
1-2 Vector and scalar potentials z a f a r q a q J y x f Maxwell's equations μ (1) ε (2) ρ (3) (4) - Derivation of E and H field by source current J Approach 1 : take (1) and plug into (2) μ ε μ μ (5)
More informationNotes 24 Image Theory
ECE 3318 Applied Electricity and Magnetism Spring 218 Prof. David R. Jackson Dept. of ECE Notes 24 Image Teory 1 Uniqueness Teorem S ρ v ( yz),, ( given) Given: Φ=ΦB 2 ρv Φ= ε Φ=Φ B on boundary Inside
More informationAperture Antennas 1 Introduction
1 Introduction Very often, we have antennas in aperture forms, for example, the antennas shown below: Pyramidal horn antenna Conical horn antenna 1 Paraboloidal antenna Slot antenna Analysis Method for.1
More informationNotes 3 Review of Vector Calculus
ECE 3317 Applied Electromagnetic Waves Prof. David R. Jackson Fall 2018 A ˆ Notes 3 Review of Vector Calculus y ya ˆ y x xa V = x y ˆ x Adapted from notes by Prof. Stuart A. Long 1 Overview Here we present
More informationGeneral Properties of Planar Leaky-Wave Antennas
European School of Antennas High-frequency techniques and Travelling-wave antennas General Properties of Planar Leaky-Wave Antennas Giampiero Lovat La Sapienza University of Rome Roma, 24th February 2005
More informationLECTURE 18: Horn Antennas (Rectangular horn antennas. Circular apertures.)
LCTUR 18: Horn Antennas (Rectangular horn antennas. Circular apertures.) 1 Rectangular Horn Antennas Horn antennas are popular in the microwave bands (above 1 GHz). Horns provide high gain, low VSWR (with
More informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 Before Starting All of your grades should now be posted
More informationr,t r R Z j ³ 0 1 4π² 0 r,t) = 4π
5.4 Lienard-Wiechert Potential and Consequent Fields 5.4.1 Potential and Fields (chapter 10) Lienard-Wiechert potential In the previous section, we studied the radiation from an electric dipole, a λ/2
More informationGeneral review: - a) Dot Product
General review: - a) Dot Product If θ is the angle between the vectors a and b, then a b = a b cos θ NOTE: Two vectors a and b are orthogonal, if and only if a b = 0. Properties of the Dot Product If a,
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 5
ECE 6345 Sping 15 Pof. David R. Jackson ECE Dept. Notes 5 1 Oveview This set of notes discusses impoved models of the pobe inductance of a coaxially-fed patch (accuate fo thicke substates). A paallel-plate
More informationMIDSUMMER EXAMINATIONS 2001
No. of Pages: 7 No. of Questions: 10 MIDSUMMER EXAMINATIONS 2001 Subject PHYSICS, PHYSICS WITH ASTROPHYSICS, PHYSICS WITH SPACE SCIENCE & TECHNOLOGY, PHYSICS WITH MEDICAL PHYSICS Title of Paper MODULE
More informationxy 2 e 2z dx dy dz = 8 3 (1 e 4 ) = 2.62 mc. 12 x2 y 3 e 2z 2 m 2 m 2 m Figure P4.1: Cube of Problem 4.1.
Problem 4.1 A cube m on a side is located in the first octant in a Cartesian coordinate system, with one of its corners at the origin. Find the total charge contained in the cube if the charge density
More informationHandout 6: Rotational motion and moment of inertia. Angular velocity and angular acceleration
1 Handout 6: Rotational motion and moment of inertia Angular velocity and angular acceleration In Figure 1, a particle b is rotating about an axis along a circular path with radius r. The radius sweeps
More informationScattering cross-section (µm 2 )
Supplementary Figures Scattering cross-section (µm 2 ).16.14.12.1.8.6.4.2 Total scattering Electric dipole, a E (1,1) Magnetic dipole, a M (1,1) Magnetic quardupole, a M (2,1). 44 48 52 56 Wavelength (nm)
More informationMULTIVARIABLE INTEGRATION
MULTIVARIABLE INTEGRATION (SPHERICAL POLAR COORDINATES) Question 1 a) Determine with the aid of a diagram an expression for the volume element in r, θ, ϕ. spherical polar coordinates, ( ) [You may not
More informationECE 6340 Intermediate EM Waves. Fall 2016 Prof. David R. Jackson Dept. of ECE. Notes 18
C 6340 Intermediate M Waves Fall 206 Prof. David R. Jacson Dept. of C Notes 8 T - Plane Waves φˆ θˆ T φˆ θˆ A homogeneous plane wave is shown for simplicit (but the principle is general). 2 Arbitrar Polariation:
More informationECE 6340 Intermediate EM Waves. Fall Prof. David R. Jackson Dept. of ECE. Notes 22
ECE 634 Intemediate EM Waves Fall 6 Pof. David R. Jackson Dept. of ECE Notes Radiation z Infinitesimal dipole: I l y kl
More informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 efore Starting All of your grades should now be posted
More informationECE 6340 Intermediate EM Waves. Fall Prof. David R. Jackson Dept. of ECE. Notes 7
ECE 634 Intermediate EM Waves Fall 16 Prof. David R. Jackson Dept. of ECE Notes 7 1 TEM Transmission Line conductors 4 parameters C capacitance/length [F/m] L inductance/length [H/m] R resistance/length
More informationBasics of Electromagnetics Maxwell s Equations (Part - I)
Basics of Electromagnetics Maxwell s Equations (Part - I) Soln. 1. C A. dl = C. d S [GATE 1994: 1 Mark] A. dl = A. da using Stoke s Theorem = S A. ds 2. The electric field strength at distant point, P,
More informationElectromagnetic Field Theory (EMT)
Electromagnetic Field Theory (EMT) Lecture # 9 1) Coulomb s Law and Field Intensity 2) Electric Fields Due to Continuous Charge Distributions Line Charge Surface Charge Volume Charge Coulomb's Law Coulomb's
More informationIII. Spherical Waves and Radiation
III. Spherical Waves and Radiation Antennas radiate spherical waves into free space Receiving antennas, reciprocity, path gain and path loss Noise as a limit to reception Ray model for antennas above a
More informationECE Spring Prof. David R. Jackson ECE Dept.
ECE 634 Spring 26 Prof. David R. Jacson ECE Dept. Notes Notes 42 43 Sommerfeld Problem In this set of notes we use SDI theory to solve the classical "Sommerfeld problem" of a vertical dipole over an semi-infinite
More informationPhys 4322 Final Exam - Solution May 12, 2015
Phys 4322 Final Exam - Solution May 12, 2015 You may NOT use any book or notes other than that supplied with this test. You will have 3 hours to finish. DO YOUR OWN WORK. Express your answers clearly and
More informationEM Waves. From previous Lecture. This Lecture More on EM waves EM spectrum Polarization. Displacement currents Maxwell s equations EM Waves
EM Waves This Lecture More on EM waves EM spectrum Polarization From previous Lecture Displacement currents Maxwell s equations EM Waves 1 Reminders on waves Traveling waves on a string along x obey the
More informationModern Physics. Unit 6: Hydrogen Atom - Radiation Lecture 6.3: Vector Model of Angular Momentum
Modern Physics Unit 6: Hydrogen Atom - Radiation ecture 6.3: Vector Model of Angular Momentum Ron Reifenberger Professor of Physics Purdue University 1 Summary of Important Points from ast ecture The magnitude
More informationLinear Wire Antennas
Linear Wire Antennas Ranga Rodrigo August 4, 010 Lecture notes are fully based on Balanis?. Some diagrams and text are directly from the books. Contents 1 Infinitesimal Dipole 1 Small Dipole 7 3 Finite-Length
More informationBasics of Wave Propagation
Basics of Wave Propagation S. R. Zinka zinka@hyderabad.bits-pilani.ac.in Department of Electrical & Electronics Engineering BITS Pilani, Hyderbad Campus May 7, 2015 Outline 1 Time Harmonic Fields 2 Helmholtz
More informationPlane Waves Part II. 1. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when
Plane Waves Part II. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when (a) The angle of incidence is equal to the Brewster angle with E field perpendicular
More informationAnalytic Trigonometry. Copyright Cengage Learning. All rights reserved.
Analytic Trigonometry Copyright Cengage Learning. All rights reserved. 7.1 Trigonometric Identities Copyright Cengage Learning. All rights reserved. Objectives Simplifying Trigonometric Expressions Proving
More informationCLASS XII CBSE MATHEMATICS INTEGRALS
Using Partial Fractions LSS XII SE MTHEMTIS INTEGRLS () cos ( sin)(sin ) () ns: log sin sin () () (SE 8) tan (sin ) c Let sin t cos ( t)( t ) t ( )( ) cosθ (sin θ)(5 cos θ) t,,, t (SE 8 OMP) dθ (SE 7)
More informationAdvanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell
Advanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell 9.2 The Blackbody as the Ideal Radiator A material that absorbs 100 percent of the energy incident on it from all directions
More information( ) = x( u, v) i + y( u, v) j + z( u, v) k
Math 8 ection 16.6 urface Integrals The relationship between surface integrals and surface area is much the same as the relationship between line integrals and arc length. uppose f is a function of three
More informationFundamental Concepts of Particle Accelerators III : High-Energy Beam Dynamics (2) Koji TAKATA KEK. Accelerator Course, Sokendai. Second Term, JFY2012
.... Fundamental Concepts of Particle Accelerators III : High-Energy Beam Dynamics (2) Koji TAKATA KEK koji.takata@kek.jp http://research.kek.jp/people/takata/home.html Accelerator Course, Sokendai Second
More informationECE 6341 Spring 2016 HW 2
ECE 6341 Spring 216 HW 2 Assigned problems: 1-6 9-11 13-15 1) Assume that a TEN models a layered structure where the direction (the direction perpendicular to the layers) is the direction that the transmission
More informationCylindrical Radiation and Scattering
Cylindrical Radiation and Daniel S. Weile Department of Electrical and Computer Engineering University of Delaware ELEG 648 Radiation and in Cylindrical Coordinates Outline Cylindrical Radiation 1 Cylindrical
More informationECE 3318 Applied Electricity and Magnetism. Spring Prof. David R. Jackson Dept. of ECE. Notes 25 Capacitance
EE 3318 pplied Electricity and Magnetism Spring 218 Prof. David R. Jackson Dept. of EE Notes 25 apacitance 1 apacitance apacitor [F] + V - +Q ++++++++++++++++++ - - - - - - - - - - - - - - - - - Q ε r
More informationPropagation of EM Waves in material media
Propagation of EM Waves in material media S.M.Lea 09 Wave propagation As usual, we start with Maxwell s equations with no free charges: D =0 B =0 E = B t H = D t + j If we now assume that each field has
More informationCyclotron, final. The cyclotron s operation is based on the fact that T is independent of the speed of the particles and of the radius of their path
Cyclotron, final The cyclotron s operation is based on the fact that T is independent of the speed of the particles and of the radius of their path K 1 qbr 2 2m 2 = mv = 2 2 2 When the energy of the ions
More informationExam 3: Tuesday, April 18, 5:00-6:00 PM
Exam 3: Tuesday, April 18, 5:-6: PM Test rooms: Instructor Sections Room Dr. Hale F, H 14 Physics Dr. Kurter, N 15 CH Dr. Madison K, M 199 Toomey Dr. Parris J, L -1 ertelsmeyer Mr. Upshaw A, C, E, G G-3
More informationAntenna Theory Exam No. 1 October 9, 2000
ntenna Theory Exa No. 1 October 9, 000 Solve the following 4 probles. Each proble is 0% of the grade. To receive full credit, you ust show all work. If you need to assue anything, state your assuptions
More informationECE 6340 Intermediate EM Waves. Fall 2016 Prof. David R. Jackson Dept. of ECE. Notes 15
ECE 634 Intermediate EM Waves Fall 6 Prof. David R. Jackson Dept. of ECE Notes 5 Attenuation Formula Waveguiding system (WG or TL): S z Waveguiding system Exyz (,, ) = E( xye, ) = E( xye, ) e γz jβz αz
More informationElectrodynamics Exam Solutions
Electrodynamics Exam Solutions Name: FS 215 Prof. C. Anastasiou Student number: Exercise 1 2 3 4 Total Max. points 15 15 15 15 6 Points Visum 1 Visum 2 The exam lasts 18 minutes. Start every new exercise
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 25
ECE 6345 Sprng 2015 Prof. Davd R. Jackson ECE Dept. Notes 25 1 Overvew In ths set of notes we use the spectral-doman method to fnd the nput mpedance of a rectangular patch antenna. Ths method uses the
More informationECE 222b Applied Electromagnetics Notes Set 5
ECE b Applied Electomagnetics Notes Set 5 Instucto: Pof. Vitaliy Lomakin Depatment of Electical and Compute Engineeing Univesity of Califonia, San Diego 1 Auxiliay Potential Functions (1) Auxiliay Potential
More informationECE 107: Electromagnetism
ECE 107: Electromagnetism Set 7: Dynamic fields Instructor: Prof. Vitaliy Lomakin Department of Electrical and Computer Engineering University of California, San Diego, CA 92093 1 Maxwell s equations Maxwell
More informationDifferential Equations: Homework 8
Differential Equations: Homework 8 Alvin Lin January 08 - May 08 Section.6 Exercise Find a general solution to the differential equation using the method of variation of parameters. y + y = tan(t) r +
More informationModule I: Electromagnetic waves
Module I: Electromagnetic waves Lecture 9: EM radiation Amol Dighe Outline 1 Electric and magnetic fields: radiation components 2 Energy carried by radiation 3 Radiation from antennas Coming up... 1 Electric
More informationNotes 18 Faraday s Law
EE 3318 Applied Electricity and Magnetism Spring 2018 Prof. David R. Jackson Dept. of EE Notes 18 Faraday s Law 1 Example (cont.) Find curl of E from a static point charge q y E q = rˆ 2 4πε0r x ( E sinθ
More informationElectromagnetic Waves. Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)
PH 222-3A Spring 2007 Electromagnetic Waves Lecture 22 Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 33 Electromagnetic Waves Today s information age is based almost
More informationD. S. Weile Radiation
Radiation Daniel S. Weile Department of Electrical and Computer Engineering University of Delaware ELEG 648 Radiation Outline Outline Maxwell Redux Maxwell s Equation s are: 1 E = jωb = jωµh 2 H = J +
More informationBohr & Wheeler Fission Theory Calculation 4 March 2009
Bohr & Wheeler Fission Theory Calculation 4 March 9 () Introduction The goal here is to reproduce the calculation of the limiting Z /A against spontaneous fission Z A lim a S. (.) a C as first done by
More informationSolutions: Homework 5
Ex. 5.1: Capacitor Solutions: Homework 5 (a) Consider a parallel plate capacitor with large circular plates, radius a, a distance d apart, with a d. Choose cylindrical coordinates (r,φ,z) and let the z
More informationPhysics Lecture 07
Physics 2113 Jonathan Dowling Physics 2113 Lecture 07 Electric Fields III Charles-Augustin de Coulomb (1736-1806) Electric Charges and Fields First: Given Electric Charges, We Calculate the Electric Field
More informationMechanics Physics 151
Mechanics Phsics 151 Lecture 8 Rigid Bod Motion (Chapter 4) What We Did Last Time! Discussed scattering problem! Foundation for all experimental phsics! Defined and calculated cross sections! Differential
More informationPHY492: Nuclear & Particle Physics. Lecture 3 Homework 1 Nuclear Phenomenology
PHY49: Nuclear & Particle Physics Lecture 3 Homework 1 Nuclear Phenomenology Measuring cross sections in thin targets beam particles/s n beam m T = ρts mass of target n moles = m T A n nuclei = n moles
More information2nd Year Electromagnetism 2012:.Exam Practice
2nd Year Electromagnetism 2012:.Exam Practice These are sample questions of the type of question that will be set in the exam. They haven t been checked the way exam questions are checked so there may
More informationPHYS General Physics for Engineering II FIRST MIDTERM
Çankaya University Department of Mathematics and Computer Sciences 2010-2011 Spring Semester PHYS 112 - General Physics for Engineering II FIRST MIDTERM 1) Two fixed particles of charges q 1 = 1.0µC and
More informationToday in Physics 218: electromagnetic waves in linear media
Today in Physics 218: electromagnetic waves in linear media Their energy and momentum Their reflectance and transmission, for normal incidence Their polarization Sunrise over Victoria Falls, Zambezi River
More informationPHYS 5012 Radiation Physics and Dosimetry
PHYS 5012 Radiation Physics and Dosimetry Tuesday 12 March 2013 What are the dominant photon interactions? (cont.) Compton scattering, photoelectric absorption and pair production are the three main energy
More informationChapter 33. Electromagnetic Waves
Chapter 33 Electromagnetic Waves Today s information age is based almost entirely on the physics of electromagnetic waves. The connection between electric and magnetic fields to produce light is own of
More informationLow Emittance Machines
Advanced Accelerator Physics Course RHUL, Egham, UK September 2017 Low Emittance Machines Part 1: Beam Dynamics with Synchrotron Radiation Andy Wolski The Cockcroft Institute, and the University of Liverpool,
More informationCompton Storage Rings
Compton Polarimetry @ Storage Rings Wolfgang Hillert ELectron Stretcher Accelerator Physics Institute of Bonn University Møller-Polarimeter Compton-Polarimeter Mott-Polarimeter Compton Scattering Differential
More informationTheoretical study of two-element array of equilateral triangular patch microstrip antenna on ferrite substrate
PRAMANA c Indian Academy of Sciences Vol. 65, No. 3 journal of September 2005 physics pp. 501 512 Theoretical study of two-element array of equilateral triangular patch microstrip antenna on ferrite substrate
More informationWave Phenomena Physics 15c. Lecture 17 EM Waves in Matter
Wave Phenomena Physics 15c Lecture 17 EM Waves in Matter What We Did Last Time Reviewed reflection and refraction Total internal reflection is more subtle than it looks Imaginary waves extend a few beyond
More informationUNIT-I INTRODUCTION TO COORDINATE SYSTEMS AND VECTOR ALGEBRA
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : EMF(16EE214) Sem: II-B.Tech & II-Sem Course & Branch: B.Tech - EEE Year
More informationES.182A Topic 44 Notes Jeremy Orloff
E.182A Topic 44 Notes Jeremy Orloff 44 urface integrals and flux Note: Much of these notes are taken directly from the upplementary Notes V8, V9 by Arthur Mattuck. urface integrals are another natural
More informationA Quantum Mechanical Model for the Vibration and Rotation of Molecules. Rigid Rotor
A Quantum Mechanical Model for the Vibration and Rotation of Molecules Harmonic Oscillator Rigid Rotor Degrees of Freedom Translation: quantum mechanical model is particle in box or free particle. A molecule
More informationNotes 7 Analytic Continuation
ECE 6382 Fall 27 David R. Jackson Notes 7 Analtic Continuation Notes are from D. R. Wilton, Dept. of ECE Analtic Continuation of Functions We define analtic continuation as the process of continuing a
More informationElectromagnetism Phys 3230 Exam 2005
Electromagnetism Phys Exam 5 All four questions in Phys should be addressed. If one is not certain in maths, one should try to present explanations in words. 1. Maxwell s equations (5% from 1 given for
More informationCoordinates 2D and 3D Gauss & Stokes Theorems
Coordinates 2 and 3 Gauss & Stokes Theorems Yi-Zen Chu 1 2 imensions In 2 dimensions, we may use Cartesian coordinates r = (x, y) and the associated infinitesimal area We may also employ polar coordinates
More information4. Integrated Photonics. (or optoelectronics on a flatland)
4. Integrated Photonics (or optoelectronics on a flatland) 1 x Benefits of integration in Electronics: Are we experiencing a similar transformation in Photonics? Mach-Zehnder modulator made from Indium
More informationand in each case give the range of values of x for which the expansion is valid.
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω Mathematics is indeed dangerous in that it absorbs students to such a degree that it dulls their senses to everything else P Kraft Further Maths A (MFPD)
More information1 Fundamentals of laser energy absorption
1 Fundamentals of laser energy absorption 1.1 Classical electromagnetic-theory concepts 1.1.1 Electric and magnetic properties of materials Electric and magnetic fields can exert forces directly on atoms
More informationProblem Set #1 Chapter 21 10, 22, 24, 43, 47, 63; Chapter 22 7, 10, 36. Chapter 21 Problems
Problem Set #1 Chapter 1 10,, 4, 43, 47, 63; Chapter 7, 10, 36 Chapter 1 Problems 10. (a) T T m g m g (b) Before the charge is added, the cork balls are hanging verticall, so the tension is T 1 mg (0.10
More informationMATH 162. FINAL EXAM ANSWERS December 17, 2006
MATH 6 FINAL EXAM ANSWERS December 7, 6 Part A. ( points) Find the volume of the solid obtained by rotating about the y-axis the region under the curve y x, for / x. Using the shell method, the radius
More informationQualifying Exam. Aug Part II. Please use blank paper for your work do not write on problems sheets!
Qualifying Exam Aug. 2015 Part II Please use blank paper for your work do not write on problems sheets! Solve only one problem from each of the four sections Mechanics, Quantum Mechanics, Statistical Physics
More informationTime-harmonic form Phasor form. =0 (1.11d)
Chapter 2 Wave in an Unbounded Medium Maxwell s Equations Time-harmonic form Phasor form (Real quantity) (complex quantity) B E = Eˆ = jωbˆ (1.11 a) t D= ρ Dˆ = ρ (1.11 b) D H = J + Hˆ = Jˆ+ jωdˆ ( 1.11
More information