School of Electrical Engineering. Lecture 2: Wire Antennas

Size: px
Start display at page:

Download "School of Electrical Engineering. Lecture 2: Wire Antennas"

Transcription

1 School of lctical ngining Lctu : Wi Antnnas

2 Wi antnna It is an antnna which mak us of mtallic wis to poduc a adiation. KT School of lctical ngining

3 Dipol λ/ Th most common adiato: λ Dipol 3λ/ KT School of lctical ngining 3

4 Fding Balanc o unbalanc? - If w ty to fd a balanc antnna with unbalanc fding, th adiation pattn can b distotd and asymmtic. - Th unbalancd cunts can b liminatd using a balun (balancd to unbalancd tansfom) KT School of lctical ngining 4

5 Infinitsimal dipol It is an lctically small antnna. Its dimnsions a much small than th wavlngth (l<<λ, l λ/5). Cunt: I( z) I KT School of lctical ngining 5

6 Th magntic potntial is: wh R is: and thn: Infinitsimal dipol: Cunt KT School of lctical ngining 6 / / ' ') ', ', ( 4 ),, ( l l jk dl z y x I z y x A z y x jk l l z jk z l I a dz I a z y x A / / 4 ' 4 ),, ( ') ( I z I

7 Infinitsimal dipol: Filds (I) If w know th magntic potntial, w can obtain th Filds (,). A j j A ( And changing th coodinats to sphical: A) A A A sin cos cos cos sin sin sin cos sin cos cos A sin A A x y z KT School of lctical ngining 7

8 Infinitsimal dipol: Filds (II) W know that: A x A y So thn: A A A jk Il 4 Il 4 cos jk sin Rmmb that: A j j A ( A) j KT School of lctical ngining 8

9 Infinitsimal dipol: Filds (III) So, th magntic fild will b: A / sin A / A sin / sin A jki l sin 4 jk jk And th lctic fild will b: I ki j l cos l sin 4 jk jk jk ( k) jk KT School of lctical ngining 9

10 omwok To div th magntic fild fom th magntic potntial vcto fo an infinitsimal dipol: jki l sin 4 jk jk KT School of lctical ngining

11 Th pow is coming fom th Poynting vcto: Fo this paticula cas: Infinitsimal dipol: Radiatd pow KT School of lctical ngining W W W W W

12 Infinitsimal dipol: Radiatd pow Thn: W 8 sin j I l 3 k and: W jk I l cos sin 3 6 k So, th pow is: P S Wds W W sin dd W sin dd P 3 I l j 3 k KT School of lctical ngining

13 omwok Div th total pow fom th point vcto: P S Wds W W sin dd W sin dd P 3 I l j 3 k KT School of lctical ngining 3

14 Infinitsimal dipol: Radiatd pow P P tot _ ad ~ j W m ~ W Th tim-avag adiatd pow: P tot _ ad Il 3 Th tim-avag activ pow: ~ W m ~ W Il 3 k 3 KT School of lctical ngining 4

15 Infinitsimal dipol: Na Fild W hav: I jki l sin 4 ki j l cos l sin 4 jk jk jk jk jk ( k) jk Dominant lmnts k k Il sin 4 jk Il cos j 3 k Il sin j 3 4k jk jk KT School of lctical ngining 5

16 W hav: Infinitsimal dipol: Fa Fild I jki l sin 4 ki j l cos l sin 4 jk jk jk jk jk ( k) jk Dominant lmnts k k jkil sin 4 ki j l sin 4 jk jk TM Mod: tansvsal lctic and magntic KT School of lctical ngining 6

17 Impdanc: Fa fild W hav a plan wav: jkil sin 4 ki j l sin 4 jk TM Mod: tansvsal lctic and magntic jk Z wav Z wav KT School of lctical ngining 7

18 Dictivity: Infinitsimal dipol Th adiatd pow is: P ad sin j 3 8 I l k In fa fild, it is: 8 And th adiation intnsity is: P ad Il sin kil sin j 4 jk U kil kil sin Pad sin 8 4 KT School of lctical ngining 8

19 Dictivity: Infinitsimal dipol Th maximum adiation intnsity is: / U max 8 kil So, th dictivity is: D max U P max 4 tot _ ad Il 8 4 Il 3 3 KT School of lctical ngining 9

20 Infinitsimal dipol Simulatd sults: -fild Radiation Pattn KT School of lctical ngining

21 Dipol Lt s suppos th following cunt distibution in th dipol: zi I( x', y', z') zi sin k sin k l z' z' l l z' z' l l / l KT School of lctical ngining

22 Dipol Sinc th dipol is not infinitsimally small, w can t tak as distanc to th dipol. If w hav a dipol ointd in z axis. R z'cos KT School of lctical ngining

23 Dipol W calculatd bfo th fa filds fo a small dipol: Thn, th diffntial is: jki( x', y', z')sin 4R ki( x', y', z')sin j 4R jkr l jkr l d d jki( x', y', z')sin 4R ki( x', y', z')sin j 4R jkr dz' jkr dz' KT School of lctical ngining 3

24 Whn fa fild: thn: Dipol d jkr ki( x', y', z')sin jk jkz' cos j dz' 4 and th lctic fild is: R jk( z'cos ) jk jkz'cos d k j sin 4 jk l / l / I( x', y', z') jkz'cos dz' I j jk cos kl cos cos sin kl j I jk cos kl cos cos sin kl KT School of lctical ngining 4

25 omwok 3 Undstanding of: R jkr jk( z'cos ) jk jkz'cos Plot fo lag valus of th magnitud and phas of: ) ) jk R jk jkz'cos What is a lag valu of? (choos an abitay valu of angl and fquncy) KT School of lctical ngining 5

26 Dipol Radiatd pow: P ad R I 8 cos kl cos cos sin kl Radiation intnsity: U P ad I 8 cos kl cos cos sin kl KT School of lctical ngining 6

27 Whn l = λ/: Dictivity: Dipol λ/ KT School of lctical ngining 7 sin cos cos 8 sin cos cos cos 8 U I I.5 dbi.64 4 _ max max ad P tot U D _ sin cos cos 4 P d I ad tot 3 sin 8 U I

28 Dipol λ/ Simulatd sults: Fa filds -fild Radiation Pattn KT School of lctical ngining 8

29 Plot (fo instanc in Matlab), th adiation pattn fo dipols of diffnt sizs: l=λ/5 l=λ/3 l=λ l=3λ/ l=λ omwok 4 Calculat numically th maximum dictivity fo ach cas. kl kl D max 4 max U U sin dd max U U sin d U U cos cos cos sin KT School of lctical ngining 9

30 Imag Thoy (I) Whn ou antnna is placd na to a lctic o magntic fild: lctic lctic Magntic Magntic h h σ= (lctic conducto) lctic lctic Magntic Magntic KT School of lctical ngining 3

31 Imag Thoy (II) Whn ou antnna is placd na to a lctic o magntic fild: lctic lctic Magntic Magntic h h σ m = (Magntic conducto) lctic lctic Magntic Magntic KT School of lctical ngining 3

32 Infinit pfct conducto W could gt a cohnt contibution fom a dipol and its gound plan to poduc a cohnt adiation. KT School of lctical ngining 3

33 Infinit pfct conducto Fo a singl infinitsimal dipol (fa fild): d kil sin j 4 jk With th Imag thoy: kil sin jrv 4 jk Fo a pfct conducto (σ= ): R v KT School of lctical ngining 33

34 Infinit pfct conducto Th contibutions will b summd: TOT TOT d z z and in fa fild, fo th amplituds: but not fo th phass:, hcos hcos KT School of lctical ngining 34

35 Infinit pfct conducto Th total fa fild (θ componnt): TOT TOT ki j ki j l sin 4 l sin 4 jk( hcos ) jk cos( khcos) jk( hcos ) Th dictivity is: D max 3 cos(kh) (kh) sin(kh) 3 (kh) KT School of lctical ngining 35

36 Infinit pfct conducto Dictivity vsus th distanc to th gound plan: KT School of lctical ngining 36

37 Infinit pfct conducto λ/4 distanc. Simulations of adiation pattn: KT School of lctical ngining 37

38 Infinit pfct conducto 5λ distanc. Simulations of adiation pattn: KT School of lctical ngining 38

39 Monopol A vy common antnna, bcaus it is quivalnt to a full λ/ dipol: KT School of lctical ngining 39

40 Monopol λ/4 lngth. Simulations: Radiation Pattn Fa filds KT School of lctical ngining 4

Acoustics and electroacoustics

Acoustics and electroacoustics coustics and lctoacoustics Chapt : Sound soucs and adiation ELEN78 - Chapt - 3 Quantitis units and smbols: f Hz : fqunc of an acoustical wav pu ton T s : piod = /f m : wavlngth= c/f Sound pssu a : pzt

More information

GUC (Dr. Hany Hammad) 11/2/2016

GUC (Dr. Hany Hammad) 11/2/2016 GUC (D. Han Hammad) //6 ctu # 7 Magntic Vct Ptntial. Radiatin fm an lmnta Dipl. Dictivit. Radiatin Rsistanc. Th ng Dipl Th half wavlngth Dipl Dictivit. Radiatin Rsistanc. Tavling wav antnna. Th lp antnna.

More information

1. Radiation from an infinitesimal dipole (current element).

1. Radiation from an infinitesimal dipole (current element). LECTURE 3: Radiation fom Infinitsimal (Elmntay) Soucs (Radiation fom an infinitsimal dipol. Duality in Maxwll s quations. Radiation fom an infinitsimal loop. Radiation zons.). Radiation fom an infinitsimal

More information

E F. and H v. or A r and F r are dual of each other.

E F. and H v. or A r and F r are dual of each other. A Duality Thom: Consid th following quations as an xampl = A = F μ ε H A E A = jωa j ωμε A + β A = μ J μ A x y, z = J, y, z 4π E F ( A = jω F j ( F j β H F ωμε F + β F = ε M jβ ε F x, y, z = M, y, z 4π

More information

Sources. My Friends, the above placed Intro was given at ANTENTOP to Antennas Lectures.

Sources. My Friends, the above placed Intro was given at ANTENTOP to Antennas Lectures. ANTENTOP- 01-008, # 010 Radiation fom Infinitsimal (Elmntay) Soucs Fl Youslf a Studnt! Da finds, I would lik to giv to you an intsting and liabl antnna thoy. Hous saching in th wb gav m lots thotical infomation

More information

Q Q N, V, e, Quantum Statistics for Ideal Gas and Black Body Radiation. The Canonical Ensemble

Q Q N, V, e, Quantum Statistics for Ideal Gas and Black Body Radiation. The Canonical Ensemble Quantum Statistics fo Idal Gas and Black Body Radiation Physics 436 Lctu #0 Th Canonical Ensmbl Ei Q Q N V p i 1 Q E i i Bos-Einstin Statistics Paticls with intg valu of spin... qi... q j...... q j...

More information

Hydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals

Hydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals Hydogn atom Engy lvls and wav functions Obital momntum, lcton spin and nucla spin Fin and hypfin intaction Hydogn obitals Hydogn atom A finmnt of th Rydbg constant: R ~ 109 737.3156841 cm -1 A hydogn mas

More information

Fourier transforms (Chapter 15) Fourier integrals are generalizations of Fourier series. The series representation

Fourier transforms (Chapter 15) Fourier integrals are generalizations of Fourier series. The series representation Pof. D. I. Nass Phys57 (T-3) Sptmb 8, 03 Foui_Tansf_phys57_T3 Foui tansfoms (Chapt 5) Foui intgals a gnalizations of Foui sis. Th sis psntation a0 nπx nπx f ( x) = + [ an cos + bn sin ] n = of a function

More information

Molecules and electronic, vibrational and rotational structure

Molecules and electronic, vibrational and rotational structure Molculs and ctonic, ational and otational stuctu Max on ob 954 obt Oppnhim Ghad Hzbg ob 97 Lctu ots Stuctu of Matt: toms and Molculs; W. Ubachs Hamiltonian fo a molcul h h H i m M i V i fs to ctons, to

More information

EE243 Advanced Electromagnetic Theory Lec # 22 Scattering and Diffraction. Reading: Jackson Chapter 10.1, 10.3, lite on both 10.2 and 10.

EE243 Advanced Electromagnetic Theory Lec # 22 Scattering and Diffraction. Reading: Jackson Chapter 10.1, 10.3, lite on both 10.2 and 10. Appid M Fa 6, Nuuth Lctu # V //6 43 Advancd ctomagntic Thoy Lc # Scatting and Diffaction Scatting Fom Sma Obcts Scatting by Sma Dictic and Mtaic Sphs Coction of Scatts Sphica Wav xpansions Scaa Vcto Rading:

More information

The angle between L and the z-axis is found from

The angle between L and the z-axis is found from Poblm 6 This is not a ifficult poblm but it is a al pain to tansf it fom pap into Mathca I won't giv it to you on th quiz, but know how to o it fo th xam Poblm 6 S Figu 6 Th magnitu of L is L an th z-componnt

More information

Auxiliary Sources for the Near-to-Far-Field Transformation of Magnetic Near-Field Data

Auxiliary Sources for the Near-to-Far-Field Transformation of Magnetic Near-Field Data Auxiliay Soucs fo th Na-to-Fa-Fild Tansfomation of Magntic Na-Fild Data Vladimi Volski 1, Guy A. E. Vandnbosch 1, Davy Pissoot 1 ESAT-TELEMIC, KU Luvn, Luvn, Blgium, vladimi.volski@sat.kuluvn.b, guy.vandnbosch@sat.kuluvn.b

More information

= x. ˆ, eˆ. , eˆ. 5. Curvilinear Coordinates. See figures 2.11 and Cylindrical. Spherical

= x. ˆ, eˆ. , eˆ. 5. Curvilinear Coordinates. See figures 2.11 and Cylindrical. Spherical Mathmatics Riw Polm Rholog 5. Cuilina Coodinats Clindical Sphical,,,,,, φ,, φ S figus 2. and 2.2 Ths coodinat sstms a otho-nomal, but th a not constant (th a with position). This causs som non-intuiti

More information

Q Q N, V, e, Quantum Statistics for Ideal Gas. The Canonical Ensemble 10/12/2009. Physics 4362, Lecture #19. Dr. Peter Kroll

Q Q N, V, e, Quantum Statistics for Ideal Gas. The Canonical Ensemble 10/12/2009. Physics 4362, Lecture #19. Dr. Peter Kroll Quantum Statistics fo Idal Gas Physics 436 Lctu #9 D. Pt Koll Assistant Pofsso Dpatmnt of Chmisty & Biochmisty Univsity of Txas Alington Will psnt a lctu ntitld: Squzing Matt and Pdicting w Compounds:

More information

Physics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM

Physics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM Physics 0, Lctu 5 Today s Topics nnouncmnts: Homwok #3 on Wbssign by tonight Du (with Homwok #) on 9/4, 10 PM Rviw: (Ch. 5Pat I) Elctic Potntial Engy, Elctic Potntial Elctic Potntial (Ch. 5Pat II) Elctic

More information

Solid state physics. Lecture 3: chemical bonding. Prof. Dr. U. Pietsch

Solid state physics. Lecture 3: chemical bonding. Prof. Dr. U. Pietsch Solid stat physics Lctu 3: chmical bonding Pof. D. U. Pitsch Elcton chag dnsity distibution fom -ay diffaction data F kp ik dk h k l i Fi H p H; H hkl V a h k l Elctonic chag dnsity of silicon Valnc chag

More information

STATISTICAL MECHANICS OF DIATOMIC GASES

STATISTICAL MECHANICS OF DIATOMIC GASES Pof. D. I. ass Phys54 7 -Ma-8 Diatomic_Gas (Ashly H. Cat chapt 5) SAISICAL MECHAICS OF DIAOMIC GASES - Fo monatomic gas whos molculs hav th dgs of fdom of tanslatoy motion th intnal u 3 ngy and th spcific

More information

rect_patch_cavity.doc Page 1 of 12 Microstrip Antennas- Rectangular Patch Chapter 14 in Antenna Theory, Analysis and Design (4th Edition) by Balanis

rect_patch_cavity.doc Page 1 of 12 Microstrip Antennas- Rectangular Patch Chapter 14 in Antenna Theory, Analysis and Design (4th Edition) by Balanis ect_patch_cavit.doc Page 1 of 1 Micostip Antennas- Rectangula Patch Chapte 14 in Antenna Theo, Analsis and Design (4th dition) b Balanis Cavit model Micostip antennas esemble dielectic-loaded cavities

More information

ECE 222b Applied Electromagnetics Notes Set 5

ECE 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 information

SAFE HANDS & IIT-ian's PACE EDT-15 (JEE) SOLUTIONS

SAFE HANDS & IIT-ian's PACE EDT-15 (JEE) SOLUTIONS It is not possibl to find flu through biggr loop dirctly So w will find cofficint of mutual inductanc btwn two loops and thn find th flu through biggr loop Also rmmbr M = M ( ) ( ) EDT- (JEE) SOLUTIONS

More information

ELEC 351 Notes Set #18

ELEC 351 Notes Set #18 Assignmnt #8 Poblm 9. Poblm 9.7 Poblm 9. Poblm 9.3 Poblm 9.4 LC 35 Nots St #8 Antnns gin nd fficincy Antnns dipol ntnn Hlf wv dipol Fiis tnsmission qution Fiis tnsmission qution Do this ssignmnt by Novmb

More information

5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS

5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS 5.61 Fall 2007 Lctu #2 pag 1 Th DEMISE of CLASSICAL PHYSICS (a) Discovy of th Elcton In 1897 J.J. Thomson discovs th lcton and masus ( m ) (and inadvtntly invnts th cathod ay (TV) tub) Faaday (1860 s 1870

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLMNTARY INFORMATION. Dtmin th gat inducd bgap cai concntation. Th fild inducd bgap cai concntation in bilay gaphn a indpndntly vaid by contolling th both th top bottom displacmnt lctical filds D t

More information

Mid Year Examination F.4 Mathematics Module 1 (Calculus & Statistics) Suggested Solutions

Mid Year Examination F.4 Mathematics Module 1 (Calculus & Statistics) Suggested Solutions Mid Ya Eamination 3 F. Matmatics Modul (Calculus & Statistics) Suggstd Solutions Ma pp-: 3 maks - Ma pp- fo ac qustion: mak. - Sam typ of pp- would not b countd twic fom wol pap. - In any cas, no pp maks

More information

International Journal of Scientific & Engineering Research, Volume 7, Issue 9, September ISSN

International Journal of Scientific & Engineering Research, Volume 7, Issue 9, September ISSN Intnational Jounal of cintific & Engining Rsach, Volum 7, Issu 9, ptmb-016 08 Analysis and Dsign of Pocklingotn s Equation fo any Abitay ufac fo Radiation Pavn Kuma Malik [1], Haish Pathasathy [], M P

More information

Physics 111. Lecture 38 (Walker: ) Phase Change Latent Heat. May 6, The Three Basic Phases of Matter. Solid Liquid Gas

Physics 111. Lecture 38 (Walker: ) Phase Change Latent Heat. May 6, The Three Basic Phases of Matter. Solid Liquid Gas Physics 111 Lctu 38 (Walk: 17.4-5) Phas Chang May 6, 2009 Lctu 38 1/26 Th Th Basic Phass of Matt Solid Liquid Gas Squnc of incasing molcul motion (and ngy) Lctu 38 2/26 If a liquid is put into a sald contain

More information

Effect of Ground Conductivity on Radiation Pattern of a Dipole Antenna

Effect of Ground Conductivity on Radiation Pattern of a Dipole Antenna Intnationa Jouna of Coput and ctica ngining, Vo., No. 3, August 9 793-863 ffct of Gound Conductivity on Radiation Pattn of a Dipo Antnna Md. Shahidu Isa, Md. Shohidu Isa, S. Mb, I, Md. Shah Aa Abst This

More information

Diffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28

Diffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28 Chapt 10 Phys 3 Lctu 8 Dffacton Dffacton: gnal Fsnl vs. Faunhof dffacton Sval cohnt oscllatos Sngl-slt dffacton Dffacton Gmald, 1600s: dffacto, dvaton of lght fom lna popagaton Dffacton s a consqunc of

More information

Lecture 2: Frequency domain analysis, Phasors. Announcements

Lecture 2: Frequency domain analysis, Phasors. Announcements EECS 5 SPRING 24, ctu ctu 2: Fquncy domain analyi, Phao EECS 5 Fall 24, ctu 2 Announcmnt Th cou wb it i http://int.c.bkly.du/~5 Today dicuion ction will mt Th Wdnday dicuion ction will mo to Tuday, 5:-6:,

More information

Lossy Transmission Lines. EELE 461/561 Digital System Design. Module #7 Lossy Lines. Lossy Transmission Lines. Lossy Transmission Lines

Lossy Transmission Lines. EELE 461/561 Digital System Design. Module #7 Lossy Lines. Lossy Transmission Lines. Lossy Transmission Lines Topics EEE 46/56 Digital Systm Dsign. Skin Ect. Dilctic oss Modul #7 ossy ins ossy ins - Whn w divd Tlgaphs Equations, w mad an assumption that th was no loss in th quivalnt cicuit modl i.., =, = - This

More information

GAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL

GAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL GAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL Ioannis Iaklis Haanas * and Michal Hany# * Dpatmnt of Physics and Astonomy, Yok Univsity 34 A Pti Scinc Building Noth Yok, Ontaio, M3J-P3,

More information

Diffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28

Diffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28 Chapt 10 Phys 3 Lctu 8 Dffacton Dffacton: gnal Fsnl vs. Faunhof dffacton Sval cohnt oscllatos Sngl-slt dffacton Dffacton Gmald, 1600s: dffacto, dvaton of lght fom lna popagaton Dffacton s a consqunc of

More information

FREQUENCY DETECTION METHOD BASED ON RECURSIVE DFT ALGORITHM

FREQUENCY DETECTION METHOD BASED ON RECURSIVE DFT ALGORITHM FREQUECY DETECTIO METHOD BAED O RECURIE ALGORITHM Katsuyasu akano*, Yutaka Ota*, Hioyuki Ukai*, Koichi akamua*, and Hidki Fujita** *Dpt. of ystms Managmnt and Engining, agoya Institut of Tchnology, Gokiso-cho,

More information

PH672 WINTER Problem Set #1. Hint: The tight-binding band function for an fcc crystal is [ ] (a) The tight-binding Hamiltonian (8.

PH672 WINTER Problem Set #1. Hint: The tight-binding band function for an fcc crystal is [ ] (a) The tight-binding Hamiltonian (8. PH67 WINTER 5 Poblm St # Mad, hapt, poblm # 6 Hint: Th tight-binding band function fo an fcc cstal is ( U t cos( a / cos( a / cos( a / cos( a / cos( a / cos( a / ε [ ] (a Th tight-binding Hamiltonian (85

More information

Definition1: The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.

Definition1: The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. Dirctivity or Dirctiv Gain. 1 Dfinition1: Dirctivity Th ratio of th radiation intnsity in a givn dirction from th antnna to th radiation intnsity avragd ovr all dirctions. Dfinition2: Th avg U is obtaind

More information

Extinction Ratio and Power Penalty

Extinction Ratio and Power Penalty Application Not: HFAN-.. Rv.; 4/8 Extinction Ratio and ow nalty AVALABLE Backgound Extinction atio is an impotant paamt includd in th spcifications of most fib-optic tanscivs. h pupos of this application

More information

Shor s Algorithm. Motivation. Why build a classical computer? Why build a quantum computer? Quantum Algorithms. Overview. Shor s factoring algorithm

Shor s Algorithm. Motivation. Why build a classical computer? Why build a quantum computer? Quantum Algorithms. Overview. Shor s factoring algorithm Motivation Sho s Algoith It appas that th univs in which w liv is govnd by quantu chanics Quantu infoation thoy givs us a nw avnu to study & tst quantu chanics Why do w want to build a quantu coput? Pt

More information

8 - GRAVITATION Page 1

8 - GRAVITATION Page 1 8 GAVITATION Pag 1 Intoduction Ptolmy, in scond cntuy, gav gocntic thoy of plantay motion in which th Eath is considd stationay at th cnt of th univs and all th stas and th plants including th Sun volving

More information

EE 5337 Computational Electromagnetics (CEM) Method of Lines

EE 5337 Computational Electromagnetics (CEM) Method of Lines 11/30/017 Instucto D. Ramon Rumpf (915) 747 6958 cumpf@utp.u 5337 Computational lctomagntics (CM) Lctu #4 Mto of Lins Lctu 4 Ts nots ma contain copigt matial obtain un fai us uls. Distibution of ts matials

More information

PHYS 272H Spring 2011 FINAL FORM B. Duration: 2 hours

PHYS 272H Spring 2011 FINAL FORM B. Duration: 2 hours PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish.

More information

PHYS 272H Spring 2011 FINAL FORM A. Duration: 2 hours

PHYS 272H Spring 2011 FINAL FORM A. Duration: 2 hours PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish.

More information

4.4 Linear Dielectrics F

4.4 Linear Dielectrics F 4.4 Lina Dilctics F stal F stal θ magntic dipol imag dipol supconducto 4.4.1 Suscptiility, mitivility, Dilctic Constant I is not too stong, th polaization is popotional to th ild. χ (sinc D, D is lctic

More information

Estimation of a Random Variable

Estimation of a Random Variable Estimation of a andom Vaiabl Obsv and stimat. ˆ is an stimat of. ζ : outcom Estimation ul ˆ Sampl Spac Eampl: : Pson s Hight, : Wight. : Ailin Company s Stock Pic, : Cud Oil Pic. Cost of Estimation Eo

More information

Mutual impedance between linear elements: The induced EMF method. Persa Kyritsi September 29th, 2005 FRB7, A1-104

Mutual impedance between linear elements: The induced EMF method. Persa Kyritsi September 29th, 2005 FRB7, A1-104 Mutual impedance between linea elements: The induced EMF method Septembe 9th, 5 FRB7, A-4 Outline Septembe 9, 5 Reminde: self impedance nduced EMF method Nea-field of a dipole Self impedance vs. Mutual

More information

Electromagnetic scattering. Graduate Course Electrical Engineering (Communications) 1 st Semester, Sharif University of Technology

Electromagnetic scattering. Graduate Course Electrical Engineering (Communications) 1 st Semester, Sharif University of Technology Elctromagntic scattring Graduat Cours Elctrical Enginring (Communications) 1 st Smstr, 1388-1389 Sharif Univrsity of Tchnology Contnts of lctur 8 Contnts of lctur 8: Scattring from small dilctric objcts

More information

Introduction to Arrays

Introduction to Arrays Intoduction to Aays Page 1 Intoduction to Aays The antennas we have studied so fa have vey low diectivity / gain. While this is good fo boadcast applications (whee we want unifom coveage), thee ae cases

More information

Aakash. For Class XII Studying / Passed Students. Physics, Chemistry & Mathematics

Aakash. For Class XII Studying / Passed Students. Physics, Chemistry & Mathematics Aakash A UNIQUE PPRTUNITY T HELP YU FULFIL YUR DREAMS Fo Class XII Studying / Passd Studnts Physics, Chmisty & Mathmatics Rgistd ffic: Aakash Tow, 8, Pusa Road, Nw Dlhi-0005. Ph.: (0) 4763456 Fax: (0)

More information

BASIC ANTENNA PARAMETERS AND WIRE ANTENNAS

BASIC ANTENNA PARAMETERS AND WIRE ANTENNAS Naval Postgraduat School Distanc Larning Antnnas & Propagation LCTUR NOTS VOLUM II BASIC ANTNNA PARAMTRS AND WIR ANTNNAS by Profssor David Jnn λ kˆ H PROPAGATION DIRCTION ANTNNA (vr 1.3) Antnnas: Introductory

More information

Coupled Pendulums. Two normal modes.

Coupled Pendulums. Two normal modes. Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron

More information

Collisionless Hall-MHD Modeling Near a Magnetic Null. D. J. Strozzi J. J. Ramos MIT Plasma Science and Fusion Center

Collisionless Hall-MHD Modeling Near a Magnetic Null. D. J. Strozzi J. J. Ramos MIT Plasma Science and Fusion Center Collisionlss Hall-MHD Modling Na a Magntic Null D. J. Stoi J. J. Ramos MIT Plasma Scinc and Fusion Cnt Collisionlss Magntic Rconnction Magntic connction fs to changs in th stuctu of magntic filds, bought

More information

Brushless Doubly-Fed Induction Machines: Torque Ripple

Brushless Doubly-Fed Induction Machines: Torque Ripple Bushlss Doubly-Fd Induction Machins: Toqu Rippl Tim. D. Stous, Xuzhou Wang, Hn Polind, Snio Mmb, IEEE, and J. A. (Bam Fia, Fllow, IEEE Abstact-- Th Bushlss DFIM without its bush-ga and slip-ings loos pomising

More information

II.3. DETERMINATION OF THE ELECTRON SPECIFIC CHARGE BY MEANS OF THE MAGNETRON METHOD

II.3. DETERMINATION OF THE ELECTRON SPECIFIC CHARGE BY MEANS OF THE MAGNETRON METHOD II.3. DETEMINTION OF THE ELETON SPEIFI HGE Y MENS OF THE MGNETON METHOD. Wok pupos Th wok pupos is to dtin th atio btwn th absolut alu of th lcton chag and its ass, /, using a dic calld agnton. In this

More information

Basic Interconnects at High Frequencies (Part 1)

Basic Interconnects at High Frequencies (Part 1) Basic Intcnncts at High Fquncis (Pat ) Outlin Tw-wi cabls and caxial cabls Stiplin Stiplin gmty and fild distibutin Chaactizing stiplins Micstip lin Micstip gmty and fild distibutin Chaactizing micstip

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat

More information

Analysis and Design of Basic Interconnects (Part 1)

Analysis and Design of Basic Interconnects (Part 1) Analysis and Dsign f Basic Intcnncts (Pat ) Outlin Tw-wi lins and caxial lins Stiplin Stiplin gmty and fild distibutin Chaactizing stiplins Micstip lin Micstip gmty and fild distibutin Chaactizing micstip

More information

DIELECTRICS MICROSCOPIC VIEW

DIELECTRICS MICROSCOPIC VIEW HYS22 M_ DILCTRICS MICROSCOIC VIW DILCTRIC MATRIALS Th tm dilctic coms fom th Gk dia lctic, wh dia mans though, thus dilctic matials a thos in which a stady lctic fild can st up without causing an appcial

More information

Lecture 3.2: Cosets. Matthew Macauley. Department of Mathematical Sciences Clemson University

Lecture 3.2: Cosets. Matthew Macauley. Department of Mathematical Sciences Clemson University Lctu 3.2: Costs Matthw Macauly Dpatmnt o Mathmatical Scincs Clmson Univsity http://www.math.clmson.du/~macaul/ Math 4120, Modn Algba M. Macauly (Clmson) Lctu 3.2: Costs Math 4120, Modn Algba 1 / 11 Ovviw

More information

ALLEN. è ø = MB = = (1) 3 J (2) 3 J (3) 2 3 J (4) 3J (1) (2) Ans. 4 (3) (4) W = MB(cosq 1 cos q 2 ) = MB (cos 0 cos 60 ) = MB.

ALLEN. è ø = MB = = (1) 3 J (2) 3 J (3) 2 3 J (4) 3J (1) (2) Ans. 4 (3) (4) W = MB(cosq 1 cos q 2 ) = MB (cos 0 cos 60 ) = MB. at to Succss LLEN EE INSTITUTE KT (JSTHN) HYSIS 6. magntic ndl suspndd paalll to a magntic fild quis J of wok to tun it toug 60. T toqu ndd to mata t ndl tis position will b : () J () J () J J q 0 M M

More information

STRIPLINES. A stripline is a planar type transmission line which is well suited for microwave integrated circuitry and photolithographic fabrication.

STRIPLINES. A stripline is a planar type transmission line which is well suited for microwave integrated circuitry and photolithographic fabrication. STIPLINES A tiplin i a plana typ tanmiion lin hih i ll uitd fo mioav intgatd iuity and photolithogaphi faiation. It i uually ontutd y thing th nt onduto of idth, on a utat of thikn and thn oving ith anoth

More information

6.Optical and electronic properties of Low

6.Optical and electronic properties of Low 6.Optical and lctonic poptis of Low dinsional atials (I). Concpt of Engy Band. Bonding foation in H Molculs Lina cobination of atoic obital (LCAO) Schoding quation:(- i VionV) E find a,a s.t. E is in a

More information

Free carriers in materials

Free carriers in materials Lctu / F cais in matials Mtals n ~ cm -3 Smiconductos n ~ 8... 9 cm -3 Insulatos n < 8 cm -3 φ isolatd atoms a >> a B a B.59-8 cm 3 ϕ ( Zq) q atom spacing a Lctu / "Two atoms two lvls" φ a T splitting

More information

Overview. 1 Recall: continuous-time Markov chains. 2 Transient distribution. 3 Uniformization. 4 Strong and weak bisimulation

Overview. 1 Recall: continuous-time Markov chains. 2 Transient distribution. 3 Uniformization. 4 Strong and weak bisimulation Rcall: continuous-tim Makov chains Modling and Vification of Pobabilistic Systms Joost-Pit Katon Lhstuhl fü Infomatik 2 Softwa Modling and Vification Goup http://movs.wth-aachn.d/taching/ws-89/movp8/ Dcmb

More information

As the matrix of operator B is Hermitian so its eigenvalues must be real. It only remains to diagonalize the minor M 11 of matrix B.

As the matrix of operator B is Hermitian so its eigenvalues must be real. It only remains to diagonalize the minor M 11 of matrix B. 7636S ADVANCED QUANTUM MECHANICS Solutions Spring. Considr a thr dimnsional kt spac. If a crtain st of orthonormal kts, say, and 3 ar usd as th bas kts, thn th oprators A and B ar rprsntd by a b A a and

More information

UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r.

UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r. UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM Solution (TEST SERIES ST PAPER) Dat: No 5. Lt a b th adius of cicl, dscibd by th aticl P in fig. if, a th ola coodinats of P, thn acos Diffntial

More information

u 3 = u 3 (x 1, x 2, x 3 )

u 3 = u 3 (x 1, x 2, x 3 ) Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.

More information

Linear Wire Antennas. EE-4382/ Antenna Engineering

Linear 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 information

Phys 402: Nonlinear Spectroscopy: SHG and Raman Scattering

Phys 402: Nonlinear Spectroscopy: SHG and Raman Scattering Rquirmnts: Polariation of Elctromagntic Wavs Phys : Nonlinar Spctroscopy: SHG and Scattring Gnral considration of polariation How Polarirs work Rprsntation of Polariation: Jons Formalism Polariation of

More information

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim. MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function

More information

College Prep Physics I Multiple Choice Practice Final #2 Solutions Northville High School Mr. Palmer, Physics Teacher. Name: Hour: Score: /zero

College Prep Physics I Multiple Choice Practice Final #2 Solutions Northville High School Mr. Palmer, Physics Teacher. Name: Hour: Score: /zero Collg Pp Phsics Multipl Choic Pactic inal # Solutions Nothvill High School M. Palm, Phsics Tach Nam: Hou: Sco: /zo You inal Exam will hav 40 multipl choic qustions woth 5 points ach.. How is cunt actd

More information

Chapter 6: Polarization and Crystal Optics

Chapter 6: Polarization and Crystal Optics Chaptr 6: Polarization and Crystal Optics * P6-1. Cascadd Wav Rtardrs. Show that two cascadd quartr-wav rtardrs with paralll fast axs ar quivalnt to a half-wav rtardr. What is th rsult if th fast axs ar

More information

CBSE-XII-2013 EXAMINATION (MATHEMATICS) The value of determinant of skew symmetric matrix of odd order is always equal to zero.

CBSE-XII-2013 EXAMINATION (MATHEMATICS) The value of determinant of skew symmetric matrix of odd order is always equal to zero. CBSE-XII- EXAMINATION (MATHEMATICS) Cod : 6/ Gnal Instuctions : (i) All qustions a compulso. (ii) Th qustion pap consists of 9 qustions dividd into th sctions A, B and C. Sction A compiss of qustions of

More information

Photon Energy (Particle Like)

Photon Energy (Particle Like) L8 Potovoltaic Lctu : Caactitic of Sunligt. Todd J. Kai tjkai@c.montana.du patmnt of lctical and Comput ngining Montana Stat Univity - Bozman Wav Paticl uality Ligt bav a bot a wav and a paticl Wav Popti

More information

STiCM. Select / Special Topics in Classical Mechanics. STiCM Lecture 11: Unit 3 Physical Quantities scalars, vectors. P. C.

STiCM. Select / Special Topics in Classical Mechanics. STiCM Lecture 11: Unit 3 Physical Quantities scalars, vectors. P. C. STiCM Slct / Spcial Topics in Classical Mchanics P. C. Dshmukh Dpatmnt of Phsics Indian Institut of Tchnolog Madas Chnnai 600036 pcd@phsics.iitm.ac.in STiCM Lctu 11: Unit 3 Phsical Quantitis scalas, vctos.

More information

Radiation Equilibrium, Inertia Moments, and the Nucleus Radius in the Electron-Proton Atom

Radiation Equilibrium, Inertia Moments, and the Nucleus Radius in the Electron-Proton Atom 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Radiation Equilibiu, Intia onts, and th Nuclus Radius in th Elcton-Poton Ato H. Vic Dannon vic@gaug-institut.og Novb, 13 Rvisd July, 14 Abstact

More information

CDS 101/110: Lecture 7.1 Loop Analysis of Feedback Systems

CDS 101/110: Lecture 7.1 Loop Analysis of Feedback Systems CDS 11/11: Lctu 7.1 Loop Analysis of Fdback Systms Novmb 7 216 Goals: Intoduc concpt of loop analysis Show how to comput closd loop stability fom opn loop poptis Dscib th Nyquist stability cition fo stability

More information

ANTENNAS. Vector and Scalar Potentials. Maxwell's Equations. D = εe. For a linear, homogeneous, isotropic medium µ and ε are contant.

ANTENNAS. Vector and Scalar Potentials. Maxwell's Equations. D = εe. For a linear, homogeneous, isotropic medium µ and ε are contant. ANTNNAS Vecto and Scala Potentials Maxwell's quations jωb J + jωd D ρ B (M) (M) (M3) (M4) D ε B Fo a linea, homogeneous, isotopic medium and ε ae contant. Since B, thee exists a vecto A such that B A and

More information

Propagation of Light About Rapidly Rotating Neutron Stars. Sheldon Campbell University of Alberta

Propagation of Light About Rapidly Rotating Neutron Stars. Sheldon Campbell University of Alberta Ppagatin f Light Abut Rapily Rtating Nutn Stas Shln Campbll Univsity f Albta Mtivatin Tlscps a nw pcis nugh t tct thmal spcta fm cmpact stas. What flux is masu by an bsv lking at a apily tating lativistic

More information

Galaxy Photometry. Recalling the relationship between flux and luminosity, Flux = brightness becomes

Galaxy Photometry. Recalling the relationship between flux and luminosity, Flux = brightness becomes Galaxy Photomty Fo galaxis, w masu a sufac flux, that is, th couts i ach pixl. Though calibatio, this is covtd to flux dsity i Jaskys ( Jy -6 W/m/Hz). Fo a galaxy at som distac, d, a pixl of sid D subtds

More information

Study on the Classification and Stability of Industry-University- Research Symbiosis Phenomenon: Based on the Logistic Model

Study on the Classification and Stability of Industry-University- Research Symbiosis Phenomenon: Based on the Logistic Model Jounal of Emging Tnds in Economics and Managmnt Scincs (JETEMS 3 (1: 116-1 Scholalink sach Institut Jounals, 1 (ISS: 141-74 Jounal jtms.scholalinksach.og of Emging Tnds Economics and Managmnt Scincs (JETEMS

More information

Derivation of Eigenvalue Matrix Equations

Derivation of Eigenvalue Matrix Equations Drivation of Eignvalu Matrix Equations h scalar wav quations ar φ φ η + ( k + 0ξ η β ) φ 0 x y x pq ε r r whr for E mod E, 1, y pq φ φ x 1 1 ε r nr (4 36) for E mod H,, 1 x η η ξ ξ n [ N ] { } i i i 1

More information

ROLE OF FLUCTUATIONAL ELECTRODYNAMICS IN NEAR-FIELD RADIATIVE HEAT TRANSFER

ROLE OF FLUCTUATIONAL ELECTRODYNAMICS IN NEAR-FIELD RADIATIVE HEAT TRANSFER ROLE OF FLUCTUATIONAL ELECTRODYNAMICS IN NEAR-FIELD RADIATIE HEAT TRANSFER Mathiu Fancou and M. Pina Mngüç Radiativ Tansf Laboatoy, Dpatmnt of Mchanical Engining Univsity of Kntucky, Lington, KY 456-53,

More information

A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m.

A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m. 1. Young s doubl-slit xprint undrlis th instrunt landing syst at ost airports and is usd to guid aircraft to saf landings whn th visibility is poor. Suppos that a pilot is trying to align hr plan with

More information

Theoretical Study of Electromagnetic Wave Propagation: Gaussian Bean Method

Theoretical Study of Electromagnetic Wave Propagation: Gaussian Bean Method Applid Mathmatics, 3, 4, 466-47 http://d.doi.og/.436/am.3.498 Publishd Onlin Octob 3 (http://www.scip.og/jounal/am) Thotical Study of Elctomagntic Wav Popagation: Gaussian Ban Mthod E. I. Ugwu, J. E. Ekp,

More information

Physics 240: Worksheet 15 Name

Physics 240: Worksheet 15 Name Physics 40: Woksht 15 Nam Each of ths poblms inol physics in an acclatd fam of fnc Althouh you mind wants to ty to foc you to wok ths poblms insid th acclatd fnc fam (i.. th so-calld "won way" by som popl),

More information

Lecture 26: Quadrature (90º) Hybrid.

Lecture 26: Quadrature (90º) Hybrid. Whits, EE 48/58 Lctur 26 Pag f Lctur 26: Quadratur (9º) Hybrid. Back in Lctur 23, w bgan ur discussin f dividrs and cuplrs by cnsidring imprtant gnral prprtis f thrand fur-prt ntwrks. This was fllwd by

More information

Lecture Outline. Skin Depth Power Flow 8/7/2018. EE 4347 Applied Electromagnetics. Topic 3e

Lecture Outline. Skin Depth Power Flow 8/7/2018. EE 4347 Applied Electromagnetics. Topic 3e 8/7/018 Cours Instructor Dr. Raymond C. Rumpf Offic: A 337 Phon: (915) 747 6958 E Mail: rcrumpf@utp.du EE 4347 Applid Elctromagntics Topic 3 Skin Dpth & Powr Flow Skin Dpth Ths & Powr nots Flow may contain

More information

Calculation of electromotive force induced by the slot harmonics and parameters of the linear generator

Calculation of electromotive force induced by the slot harmonics and parameters of the linear generator Calculation of lctromotiv forc inducd by th lot harmonic and paramtr of th linar gnrator (*)Hui-juan IU (**)Yi-huang ZHANG (*)School of Elctrical Enginring, Bijing Jiaotong Univrity, Bijing,China 8++58483,

More information

1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by:

1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by: Elctromagntic Induction. Lorntz forc on moving charg Point charg moving at vlocity v, F qv B () For a sction of lctric currnt I in a thin wir dl is Idl, th forc is df Idl B () Elctromotiv forc f s any

More information

ECE 2210 / 00 Phasor Examples

ECE 2210 / 00 Phasor Examples EE 0 / 00 Phasor Exampls. Add th sinusoidal voltags v ( t ) 4.5. cos( t 30. and v ( t ) 3.. cos( t 5. v ( t) using phasor notation, draw a phasor diagram of th thr phasors, thn convrt back to tim domain

More information

Partial Fraction Expansion

Partial Fraction Expansion Paial Facion Expanion Whn ying o find h inv Laplac anfom o inv z anfom i i hlpfl o b abl o bak a complicad aio of wo polynomial ino fom ha a on h Laplac Tanfom o z anfom abl. W will illa h ing Laplac anfom.

More information

Section 11.6: Directional Derivatives and the Gradient Vector

Section 11.6: Directional Derivatives and the Gradient Vector Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # -4 p. 799 # 4-5 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th

More information

ELECTRON-MUON SCATTERING

ELECTRON-MUON SCATTERING ELECTRON-MUON SCATTERING ABSTRACT Th lctron charg is considrd to b distributd or xtndd in spac. Th diffrntial of th lctron charg is st qual to a function of lctron charg coordinats multiplid by a four-dimnsional

More information

ECE 344 Microwave Fundamentals

ECE 344 Microwave Fundamentals ECE 44 Microwav Fundamntals Lctur 08: Powr Dividrs and Couplrs Part Prpard By Dr. hrif Hkal 4/0/08 Microwav Dvics 4/0/08 Microwav Dvics 4/0/08 Powr Dividrs and Couplrs Powr dividrs, combinrs and dirctional

More information

CHAPTER 5 CIRCULAR MOTION

CHAPTER 5 CIRCULAR MOTION CHAPTER 5 CIRCULAR MOTION and GRAVITATION 5.1 CENTRIPETAL FORCE It is known that if a paticl mos with constant spd in a cicula path of adius, it acquis a cntiptal acclation du to th chang in th diction

More information

Chapter Six Free Electron Fermi Gas

Chapter Six Free Electron Fermi Gas Chapt Six Elcton mi Gas What dtmins if th cystal will b a mtal, an insulato, o a smiconducto? E Band stuctus of solids mpty stats filld stats mpty stats filld stats E g mpty stats filld stats E g Conduction

More information

3/19/2018. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105

3/19/2018. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 PHY 7 Eletodynamis 9-9:5 A WF Olin 5 Plan fo Letue 4: Complete eading of Chap. 9 & A. Supeposition of adiation B. Satteed adiation PHY 7 Sping 8 -- Letue 4 PHY 7 Sping 8 -- Letue 4 Eletomagneti waves fom

More information

SCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER. J. C. Sprott

SCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER. J. C. Sprott SCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER J. C. Sprott PLP 821 Novmbr 1979 Plasma Studis Univrsity of Wisconsin Ths PLP Rports ar informal and prliminary and as such may contain rrors not yt

More information

11: Echo formation and spatial encoding

11: Echo formation and spatial encoding 11: Echo formation and spatial ncoding 1. What maks th magntic rsonanc signal spatiall dpndnt? 2. How is th position of an R signal idntifid? Slic slction 3. What is cho formation and how is it achivd?

More information

ELECTROMAGNETIC INDUCTION CHAPTER - 38

ELECTROMAGNETIC INDUCTION CHAPTER - 38 . (a) CTOMAGNTIC INDUCTION CHAPT - 38 3 3.dl MT I M I T 3 (b) BI T MI T M I T (c) d / MI T M I T. at + bt + c s / t Volt (a) a t t Sc b t Volt c [] Wbr (b) d [a., b.4, c.6, t s] at + b. +.4. volt 3. (a)

More information

Sinusoidal Response Notes

Sinusoidal Response Notes ECE 30 Sinusoidal Rspons Nots For BIBO Systms AStolp /29/3 Th sinusoidal rspons of a systm is th output whn th input is a sinusoidal (which starts at tim 0) Systm Sinusoidal Rspons stp input H( s) output

More information