Circular Array of Tapered Nylon Rod Antennas: A Computational Study
|
|
- Candice Jemima Cain
- 5 years ago
- Views:
Transcription
1 tratioal Joural of Elctroics ad Commuicatio Egirig. SSN Volum 4, Numbr (2), pp.3-38 tratioal Rsarch Publicatio Hous Circular Array of Taprd Nylo Rod Atas: A Computatioal Study R.V. Satyaarayaa ad M.V.S. Prasad 2 Profssor of ECE, Sri Vkatswara Uivrsity Collg of Egirig, Tirupati-5752, A.P., dia 2 Asst. Profssor, Dpt. of ECE, R.V.R. & J.C. Collg of Egirig, Gutur-5229, A.P., dia v.s.raviutala@gmail.com, mvs_prasad67@yahoo.co.i Abstract this papr th computatioal studis wr prformd o circular arrays usig taprd Nylo (ε r =3) dilctric rod atas, of lgth () qual to 6λ ad tapr agl (θ ) qual to 2.5, as lmts ar prstd. Th objctiv of th computatioal study is to fid th optimum choic of umbr of lmts i th array. Th atas ar uiformly spacd aroud th circumfrc of a circl. Th umbr of radiatig lmts i th array is varid from 8 to 28, with a icras of 4 lmts. Th pricipal pla pattrs ar computd, usig th pricipl of pattr multiplicatio. For ach st of lmts, Half Powr Bam Width (HPBW), Sid ob vl (S), ad Dirctivity (D ) ar dtrmid. Th pricipl pla pattrs ad 3D pattrs ar prstd for th optimum choic of lmts. Kywords: Nylo rod ata, Circular array, Array factor, Dirctivity, Sid ob vl, Half Powr Bam Width. troductio a circular array, th radiatig lmts ar placd alog th circumfrc of a circl with uiform spacig. Ths arrays fid wid applicatios i radio dirctio fidig, air ad spac avigatio, radar ad soar systms []. Svral ivstigatios has b carrid out usig circular arrays usig with diffrt typs of radiatig lmts ad ar rportd i litratur [2]-[5]. A importat fatur of th circular array that is s i most of th applicatios is th scaig of th mai bam through 36 i th azimuthal pla (pla of th array). Howvr, by propr choic of th lmts, thir oritatio ad phas xcitatio it is possibl to obtai a mai bam i th dirctio of zith ad sca it ovr a small agl co, aroud th zith dirctio,
2 32 R.V. Satyaarayaa ad M.V.S. Prasad with a littl chag of ithr bam width or sid lob lvl. Th choic of Nylo rod ata of lgth 6λ ad tapr agl 2.5, is mad o th basis of th rsults of computatioal studis, carrid out o th radiatio pattrs of taprd Nylo rod atas, rportd i [6]. this papr, th rsults of computatioal studis of th radiatio pattrs, of a circular array of taprd Nylo dilctric rod atas ar prstd. Radiatio from Taprd Nylo rod ata Th radiatio from a dilctric rod ata maily dpds o th dilctric matrial usd to fabricat th ata, physical shap of th ata, ad th mthod of xcitatio of th ata. Th dilctric rod ata is xcitd i th hybrid HE mod. Th advatag of asymmtric HE mod is that it givs maximum radiatio i th axial dirctio ad it dos ot shows ay cut off bhavior. Th amplitud of sid lobs ad back lobs may b rducd, by taprig th dilctric rod ata, util th diamtr is rachd for which th wav impdac bcoms qual to that of fr spac impdac. Taprig th dilctric rod miimizs th stadig wav distributio causd by rflctio at th fr d of th rod ad th lctric fild distributio riss to maximum ar th mid poit of th lgth of th rod ad th falls off towards th fr d [7]. Th lctric filds radiatd by a taprd dilctric rod ata ar aalyzd by Aad Kumar ad Rajswari Chattrj usig th Schlkuoff s quivalc pricipl [8]. Th pricipl stats that th lctromagtic fild isid a surfac S, du to sourcs outsid th surfac ca b producd by sht lctric currts J ad sht magtic currts M ovr th surfac S giv by th followig quatios, J = H () M = E (2) whr is a uit ormal vctor dirctd outwards from S, E ad H ar th valus of E ad H o th surfac S. Th gomtry of taprd dilctric rod is show i Fig.. Followig th aalysis i [8], th lctric fild compots radiatd by a taprd dilctric rod ar giv by: 2 λ r A ad jxp(jβr) Eθ = j(/fε ) si + j(/2fε ) cos si2 2 j(λ/2)cosθ cos si2 3 jλcosθ si 4 + j2πη si θ si 6 π ((+ δlη ) + [(βl /β) + ηδl]cosθ) xp( jβll) si 7 π ((- δlη ) + [(βl /β) - ηδl]cosθ) xp(jβ ll) si 8 (3)
3 Circular Array of Taprd Nylo Rod Atas 33 2 λ r jxp(jβr) E A = j(/fε ) cosθ cos j(/2fε ) cosθ si si2 2 + j(λ/2)si si2 3 jλ cos 4 + j2π si θ cos + π ((+ δlη ) cosθ + [(βl /β) + ηδl]) xp(jβll) cos 7 + π ((- δlη ) cosθ + [(βl/β ) - ηδl]) xp(jβll) cos 8 5 (4) Z FREE END a l P (r, θ, ) θ R a ρ r z ' Mdium- θ P' (ρ, ', z) Mdium- Є 2 = Є o, a o O Y X FEED END Figur : Gomtry of taprd dilctric rod ata. whr A is th xcitatio costat for H mods ad 2 = xp (jβ z) δ rj (r) { si J ( ξ) + cos2[j ( ξ)/ ] }dz (5) o ξ J( ξ ) 2 = xp (jβ z) δ krj(r) 2 J ( ξ ) ξ dz (6) J( ξ) 3 = xp (jβ z) krj(r) 2 J ( ξ) dz (7) ξ
4 34 R.V. Satyaarayaa ad M.V.S. Prasad 2 J( ξ) 4 = xp (jβ z) krj(r) cos J ( ξ) cos2 ) dz (8) ξ rj (r) ( δη )J(r) J ( ) dz 5 = xp (jβ z) ξ (9) = xp (jβ z) δrj (r) + δ J(r) J ( ) dz m η () 6 ξ a 7 = R J (R) J ( ξ ) dρ () a 8 J ( ) [ 2J (R) RJ (R)] 2 ξ = J( ξ ) dρ (2) ξ with ξ = β o a si θ ad ξ = β o ρ si θ (3) - (), δ is th ratio of xcitatio costats for E ad H mods. Th valus of δ ad k may b computd, by rprstig thir variatio giv i Fig.2 of [8], by picwis liar modls as: δ =.7 for a/λ. (3) δ = (2.9 a/λ ) / 4 for a/λ. (4) ad k =.5 (5 a/λ ) for a/λ.2 (5) k =.2 (5 7 a/λ ) for a/λ.2 (6) δ is th valu of δ at z = i Fig.. Th H-pla pattr may b obtaid by sttig =, ad th E-pla pattr by sttig =9 i (3) ad (4). Array Factor of Circular Array Th circular array of isotropic radiators is show i Fig.2. Radius of th circl, ρ is ρ = Nλ / 2π (7) whr N is th umbr of lmts i th array ad λ is th wavlgth. Elmts ar placd at azimuthal agular itrvals of 2π / N. Th azimuthal agl of th th lmt is
5 Circular Array of Taprd Nylo Rod Atas 35 2π = (8) N Array factor, AF, of a circular array of N qually spacd lmts may b writt [] as N AF= = xp { j[ β ρ si θcos( - ) + α ]} (9) whr = amplitud xcitatio of th th lmt, ad α = phas xcitatio of th th lmt, β = 2π / λ is th phas costat. For uiform amplitud xcitatio of ach lmt = o, a costat. To dirct th maximum of th mai bam i th (θ o, o ) dirctio, α may b chos to b α = βρ si θcos( - ) (2) Fig.2, R = r ρcos( ψ ) (2) whr r is th distac from origi to poit P, ρ is radius of circl, ad ψ is th progrssiv phas btw th lmts i th array. Z P(r, θ, ) θ r a r R ρ ψ Y a ρ N- N 2 X Figur 2: Gomtry of circular array of N lmts.
6 36 R.V. Satyaarayaa ad M.V.S. Prasad Circular Array of Nylo Rod Atas Th taprd Nylo rod atas, with fd d diamtr qual to.25m ar usd as radiatig lmts i th array. Th lmts ar uiformly spacd with a ctr to ctr spacig of λ m btw th lmts. Th radius of th array to plac N umbr of lmts without ovrlappig is th giv by ρ =N λ /2π (22) with this radius th array factor ca b computd usig(9). Total fild, E, of th array ca b computd usig th pricipl of pattr multiplicatio as: E = E (Fild of Sigl lmt) Array Factor (23) Th compots of E radiatd by a sigl Nylo rod ata ar giv by (3) ad (4) ad th array factor is giv by (9). Th pricipl pla pattrs ar computd usig (23). Softwar has b implmtd i matlab to plot th radiatio pattrs. Rsults ad Discussio Circular array of taprd Nylo rod atas of lgth () qual to 6λ, ad tapr agl (θ ) qual to 2.5 is cosidrd, to comput th pricipal pla pattrs of th array at a frqucy of GHz or λ =.3m. Th lmts ar uiformly placd aroud th circumfrc of th circl. Th umbr of lmts is varid from 8 to 28 with a icras of 4. Th pricipal pla pattrs ar computd for ach st of lmts ad HPBW, S, ad D ar computd for ach st of lmts ad rsults ar prstd i Tabl-.Th Dirctivity may b computd usig Kraus s formula []: Dirctivity (D ) = 4253/ (θ E θ H ) (23) Whr θ E = HPBW i E-Pla (dgrs) θ H = HPBW i H-Pla (dgrs) From th rsults prstd i Tabl-, it may b obsrvd that, with icrasig umbr of lmts i th array th dirctivity as wll as sid lob lvl icras, ad it may also b obsrvd that N=6, may b cosidrd as a optimum choic, bcaus i this cas dirctivity is 3.52 db ad sid lob lvl is -9.9 db. all othr cass, v though dirctivity is high, th S is slightly highr compard with N=6 cas. Th 3D radiatio pattr for optimum choic is show i Fig. 3. Th pricipl pla pattrs for optimum choic of lmts ar show i Fig.4.
7 Circular Array of Taprd Nylo Rod Atas 37 Tabl : Variatio of HPBW, S, ad D w with umbr of lmts. S.No. Numbr of Elmts(N) Radius of th array i cm.27λ.9λ 2.54λ 3.8λ 3.8λ 4.45λ λ λ λ λ λ λ HPBW (Dg.) S (db) = =9 = = D (db) E = = Rad Figur 3: Fig 3D diatio pattr circular array of Nylo rod atas 3D Radiatio patt of array of Nylo rod atas. (a) (b) Figur 4: Pricipal Pla pattrs of circular array (N= =6). With a dirctivity of 3.52 db ad sid lob lvl of -9.9 db, this array may b a attractiv choic for radar applicatios.
8 38 R.V. Satyaarayaa ad M.V.S. Prasad ist Symbols Symbol Maig Uits f Frqucy Hrtz λ o Fr spac wav lgth Mtrs ε Prmittivity of mdium Farads pr mtr μ Prmability of mdium Hris pr mtr β o Phas shift costat of fr spac Radias β Phas costat of guidd wavs isid th dilctric rod ata Radias β Valu of β at z = i Fig. Radias η o Fr spac wav impdac Ohms η Wav impdac of lctric fild compot Ohms m η Wav impdac of magtic fild compot Ohms ρ Radius of circl i th array cm N Total umbr of lmts i th array ψ Progrssiv phas shift btw th lmts Dgrs a r Uit vctor i th dirctio of r cm a ρ Radial uit vctor i th dirctio of ρ cm x, y, z Rctagular coordiats ρ,, z Cylidrical coordiats r, θ, Sphrical coordiats Rfrcs [] Costati A. Balais, 22, Ata Thory Aalysis ad Dsig, 2 d ditio, Joh wily & Sos c., pp [2] Rody G. Vaugha, J. Bach Adrso ad M.H. aghor, 988, Circular array of outward slopig moopols for Vhicular Divrsity Atas, EEE Tras. Atas propagatio, Vol.36, No., pp [3] Roaold W.P. Kig, 989, Suprgai atas ad th Yagi ad circular arrays, EEE Tras. Atas propagatio, Vol.37, No.2, pp [4] Sog izhog, Maig, i Chogsh ad Wuqum, 28 simulatio ad aalysis of a microstrip circular array ata at 5 GHz, EEE Xplor, [5] Nav Kumar Saxa ad Dr. P.K.S. Pourush, 29, Circular array of Triagular patchs as filtr, EEE Xplor. [6] Dr. J. Subramayam ad M.V.S. Prasad, 29, Radiatio from taprd Nylo Rod Atas A Computatioal study. CFA Joural of Elctrical ad Elctroics Egirig, vol., issu o.3, pp [7] D.G. Kily, Dilctric Arials, st ditio, 953, Mathu & Co imitd, odo, pag 4. [8] Aad Kumar, R. Chattrj, 968, Radiatio from taprd Dilctric Rod Arials, SC Joural, vol.5, issu o.4, pp
ECE594I Notes set 6: Thermal Noise
C594I ots, M. odwll, copyrightd C594I Nots st 6: Thrmal Nois Mark odwll Uivrsity of Califoria, ata Barbara rodwll@c.ucsb.du 805-893-344, 805-893-36 fax frcs ad Citatios: C594I ots, M. odwll, copyrightd
More informationMONTGOMERY COLLEGE Department of Mathematics Rockville Campus. 6x dx a. b. cos 2x dx ( ) 7. arctan x dx e. cos 2x dx. 2 cos3x dx
MONTGOMERY COLLEGE Dpartmt of Mathmatics Rockvill Campus MATH 8 - REVIEW PROBLEMS. Stat whthr ach of th followig ca b itgratd by partial fractios (PF), itgratio by parts (PI), u-substitutio (U), or o of
More informationIdeal crystal : Regulary ordered point masses connected via harmonic springs
Statistical thrmodyamics of crystals Mooatomic crystal Idal crystal : Rgulary ordrd poit masss coctd via harmoic sprigs Itratomic itractios Rprstd by th lattic forc-costat quivalt atom positios miima o
More information1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
More informationBlackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?
All bodis at a tmpratur T mit ad absorb thrmal lctromagtic radiatio Blackbody radiatio I thrmal quilibrium, th powr mittd quals th powr absorbd How is blackbody radiatio absorbd ad mittd? 1 2 A blackbody
More informationDTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1
DTFT Proprtis Exampl - Dtrmi th DTFT Y of y α µ, α < Lt x α µ, α < W ca thrfor writ y x x From Tabl 3., th DTFT of x is giv by ω X ω α ω Copyright, S. K. Mitra Copyright, S. K. Mitra DTFT Proprtis DTFT
More informationAnalysis of the power losses in the three-phase high-current busducts
Computr Applicatios i Elctrical Egirig Vol. 3 5 Aalysis of th powr losss i th thr-phas high-currt busucts Tomasz Szczgiliak, Zygmut Piątk, Dariusz Kusiak Częstochowa Uivrsity of Tchology 4- Częstochowa,
More informationSession : Plasmas in Equilibrium
Sssio : Plasmas i Equilibrium Ioizatio ad Coductio i a High-prssur Plasma A ormal gas at T < 3000 K is a good lctrical isulator, bcaus thr ar almost o fr lctros i it. For prssurs > 0.1 atm, collisio amog
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More informationAntenna Engineering Lecture 8: Antenna Arrays
Atea Egieerig Lecture 8: Atea Arrays ELCN45 Sprig 211 Commuicatios ad Computer Egieerig Program Faculty of Egieerig Cairo Uiversity 2 Outlie 1 Array of Isotropic Radiators Array Cofiguratios The Space
More informationDiscrete Fourier Transform (DFT)
Discrt Fourir Trasorm DFT Major: All Egirig Majors Authors: Duc guy http://umricalmthods.g.us.du umrical Mthods or STEM udrgraduats 8/3/29 http://umricalmthods.g.us.du Discrt Fourir Trasorm Rcalld th xpotial
More information8(4 m0) ( θ ) ( ) Solutions for HW 8. Chapter 25. Conceptual Questions
Solutios for HW 8 Captr 5 Cocptual Qustios 5.. θ dcrass. As t crystal is coprssd, t spacig d btw t plas of atos dcrass. For t first ordr diffractio =. T Bragg coditio is = d so as d dcrass, ust icras for
More informationTime : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
More informationNEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES
Digst Joural of Naomatrials ad Biostructurs Vol 4, No, March 009, p 67-76 NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES A IRANMANESH a*, O KHORMALI b, I NAJAFI KHALILSARAEE c, B SOLEIMANI
More informationReview Exercises. 1. Evaluate using the definition of the definite integral as a Riemann Sum. Does the answer represent an area? 2
MATHEMATIS --RE Itgral alculus Marti Huard Witr 9 Rviw Erciss. Evaluat usig th dfiitio of th dfiit itgral as a Rima Sum. Dos th aswr rprst a ara? a ( d b ( d c ( ( d d ( d. Fid f ( usig th Fudamtal Thorm
More informationNET/JRF, GATE, IIT JAM, JEST, TIFR
Istitut for NET/JRF, GATE, IIT JAM, JEST, TIFR ad GRE i PHYSICAL SCIENCES Mathmatical Physics JEST-6 Q. Giv th coditio φ, th solutio of th quatio ψ φ φ is giv by k. kφ kφ lφ kφ lφ (a) ψ (b) ψ kφ (c) ψ
More informationJournal of Engineering Science and Technology Review 6 (5) (2013) Research Article
Jst Joural of Egirig Scic ad Tchology Rviw 6 (5 (3 38-47 Rsarch Articl JOURAL OF Egirig Scic ad Tchology Rviw www.jstr.org Smart Bas Statio Ata Prformac for Cllular Radio Systm R.Ghayoula *,,, A.Smida,
More informationElectronic Supplementary Information
Elctroic Supplmtary Matrial (ESI) for Joural of Matrials Chmistry A. This joural is Th Royal Socity of Chmistry 2016 Elctroic Supplmtary Iformatio Photolctrochmical Watr Oxidatio usig a Bi 2 MoO 6 / MoO
More informationFormation of A Supergain Array and Its Application in Radar
Formatio of A Supergai Array ad ts Applicatio i Radar Tra Cao Quye, Do Trug Kie ad Bach Gia Duog. Research Ceter for Electroic ad Telecommuicatios, College of Techology (Coltech, Vietam atioal Uiversity,
More informationPeriodic Structures. Filter Design by the Image Parameter Method
Prioic Structurs a Filtr sig y th mag Paramtr Mtho ECE53: Microwav Circuit sig Pozar Chaptr 8, Sctios 8. & 8. Josh Ottos /4/ Microwav Filtrs (Chaptr Eight) microwav filtr is a two-port twork us to cotrol
More informationPart B: Transform Methods. Professor E. Ambikairajah UNSW, Australia
Part B: Trasform Mthods Chaptr 3: Discrt-Tim Fourir Trasform (DTFT) 3. Discrt Tim Fourir Trasform (DTFT) 3. Proprtis of DTFT 3.3 Discrt Fourir Trasform (DFT) 3.4 Paddig with Zros ad frqucy Rsolutio 3.5
More informationScattering Parameters. Scattering Parameters
Motivatio cattrig Paramtrs Difficult to implmt op ad short circuit coditios i high frqucis masurmts du to parasitic s ad Cs Pottial stability problms for activ dvics wh masurd i oopratig coditios Difficult
More informationWorksheet: Taylor Series, Lagrange Error Bound ilearnmath.net
Taylor s Thorm & Lagrag Error Bouds Actual Error This is th ral amout o rror, ot th rror boud (worst cas scario). It is th dirc btw th actual () ad th polyomial. Stps:. Plug -valu ito () to gt a valu.
More informationEAcos θ, where θ is the angle between the electric field and
8.4. Modl: Th lctric flux flows out of a closd surfac around a rgion of spac containing a nt positiv charg and into a closd surfac surrounding a nt ngativ charg. Visualiz: Plas rfr to Figur EX8.4. Lt A
More informationA Review of Complex Arithmetic
/0/005 Rviw of omplx Arithmti.do /9 A Rviw of omplx Arithmti A omplx valu has both a ral ad imagiary ompot: { } ad Im{ } a R b so that w a xprss this omplx valu as: whr. a + b Just as a ral valu a b xprssd
More informationDigital Signal Processing, Fall 2006
Digital Sigal Procssig, Fall 6 Lctur 9: Th Discrt Fourir Trasfor Zhg-Hua Ta Dpartt of Elctroic Systs Aalborg Uivrsity, Dar zt@o.aau.d Digital Sigal Procssig, I, Zhg-Hua Ta, 6 Cours at a glac MM Discrt-ti
More informationS- AND P-POLARIZED REFLECTIVITIES OF EXPLOSIVELY DRIVEN STRONGLY NON-IDEAL XENON PLASMA
S- AND P-POLARIZED REFLECTIVITIES OF EXPLOSIVELY DRIVEN STRONGLY NON-IDEAL XENON PLASMA Zaporozhts Yu.B.*, Mitsv V.B., Gryazov V.K., Riholz H., Röpk G. 3, Fortov V.E. 4 Istitut of Problms of Chmical Physics
More informationBlackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?
All bodis at a tmpratur T mit ad absorb thrmal lctromagtic radiatio Blackbody radiatio I thrmal quilibrium, th powr mittd quals th powr absorbd How is blackbody radiatio absorbd ad mittd? 1 2 A blackbody
More informationFigure 2-18 Thevenin Equivalent Circuit of a Noisy Resistor
.8 NOISE.8. Th Nyquist Nois Thorm W ow wat to tur our atttio to ois. W will start with th basic dfiitio of ois as usd i radar thory ad th discuss ois figur. Th typ of ois of itrst i radar thory is trmd
More informationTriple Play: From De Morgan to Stirling To Euler to Maclaurin to Stirling
Tripl Play: From D Morga to Stirlig To Eulr to Maclauri to Stirlig Augustus D Morga (186-1871) was a sigificat Victoria Mathmaticia who mad cotributios to Mathmatics History, Mathmatical Rcratios, Mathmatical
More informationEE 232 Lightwave Devices Lecture 3: Basic Semiconductor Physics and Optical Processes. Optical Properties of Semiconductors
3 Lightwav Dvics Lctur 3: Basic Smicoductor Physics ad Optical Procsss Istructor: Mig C. Wu Uivrsity of Califoria, Brly lctrical girig ad Computr Scics Dpt. 3 Lctur 3- Optical Proprtis of Smicoductors
More informationBipolar Junction Transistors
ipolar Juctio Trasistors ipolar juctio trasistors (JT) ar activ 3-trmial dvics with aras of applicatios: amplifirs, switch tc. high-powr circuits high-spd logic circuits for high-spd computrs. JT structur:
More informationz 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z
Sris Expasio of Rciprocal of Gamma Fuctio. Fuctios with Itgrs as Roots Fuctio f with gativ itgrs as roots ca b dscribd as follows. f() Howvr, this ifiit product divrgs. That is, such a fuctio caot xist
More informationMILLIKAN OIL DROP EXPERIMENT
11 Oct 18 Millika.1 MILLIKAN OIL DROP EXPERIMENT This xprimt is dsigd to show th quatizatio of lctric charg ad allow dtrmiatio of th lmtary charg,. As i Millika s origial xprimt, oil drops ar sprayd ito
More informationChapter 11.00C Physical Problem for Fast Fourier Transform Civil Engineering
haptr. Physical Problm for Fast Fourir Trasform ivil Egirig Itroductio I this chaptr, applicatios of FFT algorithms [-5] for solvig ral-lif problms such as computig th dyamical (displacmt rspos [6-7] of
More informationOn the approximation of the constant of Napier
Stud. Uiv. Babş-Bolyai Math. 560, No., 609 64 O th approximatio of th costat of Napir Adri Vrscu Abstract. Startig from som oldr idas of [] ad [6], w show w facts cocrig th approximatio of th costat of
More informationDiscrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform. Discrete Fourier Transform
Discrt Fourir Trasform Dfiitio - T simplst rlatio btw a lt- squc x dfid for ω ad its DTFT X ( ) is ω obtaid by uiformly sampli X ( ) o t ω-axis btw ω < at ω From t dfiitio of t DTFT w tus av X X( ω ) ω
More informationThe Interplay between l-max, l-min, p-max and p-min Stable Distributions
DOI: 0.545/mjis.05.4006 Th Itrplay btw lma lmi pma ad pmi Stabl Distributios S Ravi ad TS Mavitha Dpartmt of Studis i Statistics Uivrsity of Mysor Maasagagotri Mysuru 570006 Idia. Email:ravi@statistics.uimysor.ac.i
More informationcoulombs or esu charge. It s mass is about 1/1837 times the mass of hydrogen atom. Thus mass of electron is
1 ATOMIC STRUCTURE Fudamtal Particls: Mai Fudamtal Particl : (a) Elctro: It is a fudamtal particl of a atom which carris a uit gativ charg. It was discovrd by J.J. Thomso (1897) from th studis carrid out
More informationElectromagnetic radiation and steady states of hydrogen atom
Elctromagtic radiatio ad stady stats of hydrog atom Jiaomig Luo Egirig Rsarch Ctr i Biomatrials, Sichua Uivrsity, 9# Wagjiag Road, Chgdu, Chia, 610064 Abstract. Elctromagtic phoma i hydrog atom ar cotrolld
More informationElitist Genetic Algorithm Performance on the Uniform Circular Antenna Array Pattern Synthesis Problem
Fatih YAMA, Asım Egm YILMAZ Akara Uivrsity Elitist Gtic Algorithm Prformac o th Uiform Circular Ata Array Pattr Sythsis Problm Abstract. I this papr, th impacts of litism rat o th Gtic Algorithm (GA) prformac
More informationDefinition1: 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 informationFolding of Hyperbolic Manifolds
It. J. Cotmp. Math. Scics, Vol. 7, 0, o. 6, 79-799 Foldig of Hyprbolic Maifolds H. I. Attiya Basic Scic Dpartmt, Collg of Idustrial Educatio BANE - SUEF Uivrsity, Egypt hala_attiya005@yahoo.com Abstract
More informationMixed Mode Oscillations as a Mechanism for Pseudo-Plateau Bursting
Mixd Mod Oscillatios as a Mchaism for Psudo-Platau Burstig Richard Brtram Dpartmt of Mathmatics Florida Stat Uivrsity Tallahass, FL Collaborators ad Support Thodor Vo Marti Wchslbrgr Joël Tabak Uivrsity
More informationEE243 Advanced Electromagnetic Theory Lec # 23 Scattering and Diffraction. Reading: Jackson Chapter , lite
Applid M Fall 6, Nuruthr Lctur #3 Vr /5/6 43 Advancd lctromagntic Thory Lc # 3 cattring and Diffraction calar Diffraction Thory Vctor Diffraction Thory Babint and Othr Principls Optical Thorm ading: Jackson
More informationSolid State Device Fundamentals
8 Biasd - Juctio Solid Stat Dvic Fudamtals 8. Biasd - Juctio ENS 345 Lctur Cours by Aladr M. Zaitsv aladr.zaitsv@csi.cuy.du Tl: 718 98 81 4N101b Dartmt of Egirig Scic ad Physics Biasig uiolar smicoductor
More informationLECTURE 13 Filling the bands. Occupancy of Available Energy Levels
LUR 3 illig th bads Occupacy o Availabl rgy Lvls W hav dtrmid ad a dsity o stats. W also d a way o dtrmiig i a stat is illd or ot at a giv tmpratur. h distributio o th rgis o a larg umbr o particls ad
More information15/03/1439. Lectures on Signals & systems Engineering
Lcturs o Sigals & syms Egirig Dsigd ad Prd by Dr. Ayma Elshawy Elsfy Dpt. of Syms & Computr Eg. Al-Azhar Uivrsity Email : aymalshawy@yahoo.com A sigal ca b rprd as a liar combiatio of basic sigals. Th
More informationDiscrete Fourier Transform. Nuno Vasconcelos UCSD
Discrt Fourir Trasform uo Vascoclos UCSD Liar Shift Ivariat (LSI) systms o of th most importat cocpts i liar systms thory is that of a LSI systm Dfiitio: a systm T that maps [ ito y[ is LSI if ad oly if
More informationA Strain-based Non-linear Elastic Model for Geomaterials
A Strai-basd No-liar Elastic Modl for Gomatrials ANDREW HEATH Dpartmt of Architctur ad Civil Egirig Uivrsity of Bath Bath, BA2 7AY UNITED KINGDOM A.Hath@bath.ac.uk http://www.bath.ac.uk/ac Abstract: -
More informationBohr type models of the atom give a totally incorrect picture of the atom and are of only historical significance.
VISUAL PHYSICS ONLIN BOHR MODL OF TH ATOM Bhr typ mdls f th atm giv a ttally icrrct pictur f th atm ad ar f ly histrical sigificac. Fig.. Bhr s platary mdl f th atm. Hwvr, th Bhr mdls wr a imprtat stp
More informationChapter 4 - The Fourier Series
M. J. Robrts - 8/8/4 Chaptr 4 - Th Fourir Sris Slctd Solutios (I this solutio maual, th symbol,, is usd for priodic covolutio bcaus th prfrrd symbol which appars i th txt is ot i th fot slctio of th word
More informationChapter 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(Reference: sections in Silberberg 5 th ed.)
ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists
More informationAPPENDIX: STATISTICAL TOOLS
I. Nots o radom samplig Why do you d to sampl radomly? APPENDI: STATISTICAL TOOLS I ordr to masur som valu o a populatio of orgaisms, you usually caot masur all orgaisms, so you sampl a subst of th populatio.
More informationNarayana IIT Academy
INDIA Sc: LT-IIT-SPARK Dat: 9--8 6_P Max.Mars: 86 KEY SHEET PHYSIS A 5 D 6 7 A,B 8 B,D 9 A,B A,,D A,B, A,B B, A,B 5 A 6 D 7 8 A HEMISTRY 9 A B D B B 5 A,B,,D 6 A,,D 7 B,,D 8 A,B,,D 9 A,B, A,B, A,B,,D A,B,
More informationJoule-Lenz Energy of Quantum Electron Transitions Compared with the Electromagnetic Emission of Energy
Joural of Modr Physics, 06, 7, 440-448 Publishd Oli August 06 i SciRs http://wwwscirporg/joural/jmp http://dxdoiorg/0436/jmp0673 Joul-Lz Ergy of Quatum Elctro Trasitios Compard with th Elctromagtic Emissio
More information2.29 Numerical Fluid Mechanics Spring 2015 Lecture 12
REVIEW Lctur 11: Numrical Fluid Mchaics Sprig 2015 Lctur 12 Fiit Diffrcs basd Polyomial approximatios Obtai polyomial (i gral u-qually spacd), th diffrtiat as dd Nwto s itrpolatig polyomial formulas Triagular
More informationProbability & Statistics,
Probability & Statistics, BITS Pilai K K Birla Goa Campus Dr. Jajati Kshari Sahoo Dpartmt of Mathmatics BITS Pilai, K K Birla Goa Campus Poisso Distributio Poisso Distributio: A radom variabl X is said
More information1973 AP Calculus BC: Section I
97 AP Calculus BC: Scio I 9 Mius No Calculaor No: I his amiaio, l dos h aural logarihm of (ha is, logarihm o h bas ).. If f ( ) =, h f ( ) = ( ). ( ) + d = 7 6. If f( ) = +, h h s of valus for which f
More informationPartition Functions and Ideal Gases
Partitio Fuctios ad Idal Gass PFIG- You v lard about partitio fuctios ad som uss ow w ll xplor tm i mor dpt usig idal moatomic diatomic ad polyatomic gass! for w start rmmbr: Q( N ( N! N Wat ar N ad? W
More informationLinear-Phase FIR Transfer Functions. Functions. Functions. Functions. Functions. Functions. Let
It is impossibl to dsign an IIR transfr function with an xact linar-phas It is always possibl to dsign an FIR transfr function with an xact linar-phas rspons W now dvlop th forms of th linarphas FIR transfr
More informationJournal of Modern Applied Statistical Methods
Joural of Modr Applid Statistical Mthods Volum Issu Articl 6 --03 O Som Proprtis of a Htrogous Trasfr Fuctio Ivolvig Symmtric Saturatd Liar (SATLINS) with Hyprbolic Tagt (TANH) Trasfr Fuctios Christophr
More informationELECTROMAGNETIC FIELD COUPLING TO ARBITRARY WIRE CONFIGURATIONS BURIED IN A LOSSY GROUND: A REVIEW OF ANTENNA MODEL AND TRANSMISSION LINE APPROACH
D. Poljak t al., It. J. Comp. Mth. ad Exp. Ma., Vol., No. (3) 4 63 ELECTROMAGNETIC FIELD COUPLING TO ARBITRARY WIRE CONFIGURATIONS BURIED IN A LOSSY GROUND: A REVIEW OF ANTENNA MODEL AND TRANSMISSION LINE
More informationDivision of Mechanics Lund University MULTIBODY DYNAMICS. Examination Name (write in block letters):.
Division of Mchanics Lund Univrsity MULTIBODY DYNMICS Examination 7033 Nam (writ in block lttrs):. Id.-numbr: Writtn xamination with fiv tasks. Plas chck that all tasks ar includd. clan copy of th solutions
More informationDIELECTRIC AND MAGNETIC PROPERTIES OF MATERIALS
DILCTRIC AD MAGTIC PROPRTIS OF MATRIALS Dilctric Proprtis: Dilctric matrial Dilctric constant Polarization of dilctric matrials, Typs of Polarization (Polarizability). quation of intrnal filds in liquid
More informationIterative Methods of Order Four for Solving Nonlinear Equations
Itrativ Mods of Ordr Four for Solvig Noliar Equatios V.B. Kumar,Vatti, Shouri Domii ad Mouia,V Dpartmt of Egirig Mamatis, Formr Studt of Chmial Egirig Adhra Uivrsity Collg of Egirig A, Adhra Uivrsity Visakhapatam
More informationHadamard Exponential Hankel Matrix, Its Eigenvalues and Some Norms
Math Sci Ltt Vol No 8-87 (0) adamard Exotial al Matrix, Its Eigvalus ad Som Norms İ ad M bula Mathmatical Scics Lttrs Itratioal Joural @ 0 NSP Natural Scics Publishig Cor Dartmt of Mathmatics, aculty of
More informationUNIT 2: MATHEMATICAL ENVIRONMENT
UNIT : MATHEMATICAL ENVIRONMENT. Itroductio This uit itroducs som basic mathmatical cocpts ad rlats thm to th otatio usd i th cours. Wh ou hav workd through this uit ou should: apprciat that a mathmatical
More informationElectromagnetics Research Group A THEORETICAL MODEL OF A LOSSY DIELECTRIC SLAB FOR THE CHARACTERIZATION OF RADAR SYSTEM PERFORMANCE SPECIFICATIONS
Elctromagntics Rsarch Group THEORETICL MODEL OF LOSSY DIELECTRIC SLB FOR THE CHRCTERIZTION OF RDR SYSTEM PERFORMNCE SPECIFICTIONS G.L. Charvat, Prof. Edward J. Rothwll Michigan Stat Univrsit 1 Ovrviw of
More information0WAVE PROPAGATION IN MATERIAL SPACE
0WAVE PROPAGATION IN MATERIAL SPACE All forms of EM nrgy shar thr fundamntal charactristics: 1) thy all tral at high locity 2) In traling, thy assum th proprtis of was 3) Thy radiat outward from a sourc
More informationPhysics 2D Lecture Slides Lecture 14: Feb 3 rd 2004
Bria Wcht, th TA is back! Pl. giv all rgrad rqusts to him Quiz 4 is This Friday Physics D Lctur Slids Lctur 14: Fb 3 rd 004 Vivk Sharma UCSD Physics Whr ar th lctros isid th atom? Early Thought: Plum puddig
More informationThey must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei.
37 1 How may utros ar i a uclus of th uclid l? 20 37 54 2 crtai lmt has svral isotops. Which statmt about ths isotops is corrct? Thy must hav diffrt umbrs of lctros orbitig thir ucli. Thy must hav th sam
More informationDesign and Analysis of Broadside Arrays of Uniformly Spaced Linear Elements
Volum 156 No 6, Dcmbr 16 Dsign and Analysis of Broadsid Arrays of Uniformly Spacd Linar Elmnts Raji A. Abimbola Dpt. of Elctrical and Elctronics Enginring Fdral Univrsity of Agricultur, Abokuta, Nigria
More informationln x = n e = 20 (nearest integer)
H JC Prlim Solutios 6 a + b y a + b / / dy a b 3/ d dy a b at, d Giv quatio of ormal at is y dy ad y wh. d a b () (,) is o th curv a+ b () y.9958 Qustio Solvig () ad (), w hav a, b. Qustio d.77 d d d.77
More informationKey words Non-uniform; specific energy; critical; gradually-varied steady flow; water surface profiles
Chaptr NON-UNIFORM FLOW 4.. Itroductio 4.. Gradually-varid stady 4.3. Typs of watr surfac profils 4.4. Drawig watr surfac profils Summary Likig up with Chaptr, dalig with uiform i op chals, it may b otd
More informationPHYS ,Fall 05, Term Exam #1, Oct., 12, 2005
PHYS1444-,Fall 5, Trm Exam #1, Oct., 1, 5 Nam: Kys 1. circular ring of charg of raius an a total charg Q lis in th x-y plan with its cntr at th origin. small positiv tst charg q is plac at th origin. What
More informationChapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series
Chatr Ifiit Sris Pag of Sctio F Itgral Tst Chatr : Ifiit Sris By th d of this sctio you will b abl to valuat imror itgrals tst a sris for covrgc by alyig th itgral tst aly th itgral tst to rov th -sris
More informationWashington State University
he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us
More informationWhy is a E&M nature of light not sufficient to explain experiments?
1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt
More informationECE 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 informationWarped, Chirp Z-Transform: Radar Signal Processing
arped, Chirp Z-Trasform: Radar Sigal Processig by Garimella Ramamurthy Report o: IIIT/TR// Cetre for Commuicatios Iteratioal Istitute of Iformatio Techology Hyderabad - 5 3, IDIA Jauary ARPED, CHIRP Z
More informationOutline. Ionizing Radiation. Introduction. Ionizing radiation
Outli Ioizig Radiatio Chaptr F.A. Attix, Itroductio to Radiological Physics ad Radiatio Dosimtry Radiological physics ad radiatio dosimtry Typs ad sourcs of ioizig radiatio Dscriptio of ioizig radiatio
More informationVII. Quantum Entanglement
VII. Quantum Entanglmnt Quantum ntanglmnt is a uniqu stat of quantum suprposition. It has bn studid mainly from a scintific intrst as an vidnc of quantum mchanics. Rcntly, it is also bing studid as a basic
More informationChapter At each point (x, y) on the curve, y satisfies the condition
Chaptr 6. At ach poit (, y) o th curv, y satisfis th coditio d y 6; th li y = 5 is tagt to th curv at th poit whr =. I Erciss -6, valuat th itgral ivolvig si ad cosi.. cos si. si 5 cos 5. si cos 5. cos
More informationSTIRLING'S 1 FORMULA AND ITS APPLICATION
MAT-KOL (Baja Luka) XXIV ()(08) 57-64 http://wwwimviblorg/dmbl/dmblhtm DOI: 075/МК80057A ISSN 0354-6969 (o) ISSN 986-588 (o) STIRLING'S FORMULA AND ITS APPLICATION Šfkt Arslaagić Sarajvo B&H Abstract:
More informationNetwork Congestion Games
Ntwork Congstion Gams Assistant Profssor Tas A&M Univrsity Collg Station, TX TX Dallas Collg Station Austin Houston Bst rout dpnds on othrs Ntwork Congstion Gams Travl tim incrass with congstion Highway
More information5.1 The Nuclear Atom
Sav My Exams! Th Hom of Rvisio For mor awsom GSE ad lvl rsourcs, visit us at www.savmyxams.co.uk/ 5.1 Th Nuclar tom Qustio Papr Lvl IGSE Subjct Physics (0625) Exam oard Topic Sub Topic ooklt ambridg Itratioal
More informationPart 7: Capacitance And Capacitors
Part 7: apacitanc And apacitors 7. Elctric harg And Elctric Filds onsidr a pair of flat, conducting plats, arrangd paralll to ach othr (as in figur 7.) and sparatd by an insulator, which may simply b air.
More informationHigh-frequency Incremental Techniques for Scattering and Diffraction. ALBERTO TOCCAFONDI Dept. of Information Engineering University of Siena - Italy
High-frqucy Icrmtal Tchiqus for Scattrig ad Diffractio ALBERTO TOCCAFONDI Dpt. of Iformatio Egirig Uivrsity of Sia - Italy Sia, Fbruary 23, 2005 SUMMARY Backgroud Basic trmiology GTD vrsus PTD Basic cocpts
More informationArray Antennas - Analysis
S. R. Zika zika@vit.ac.i School of Electroics Egieerig Vellore Istitute of Techology July 24, 2013 Outlie 1 Itroductio 2 Liear Arrays 3 Plaar Array 4 Liear Arrays - Examples 5 Plaar Arrays - Examples Outlie
More informationIndian Institute of Information Technology, Allahabad. End Semester Examination - Tentative Marking Scheme
Idia Istitute of Iformatio Techology, Allahabad Ed Semester Examiatio - Tetative Markig Scheme Course Name: Mathematics-I Course Code: SMAT3C MM: 75 Program: B.Tech st year (IT+ECE) ate of Exam:..7 ( st
More informationChapter 4 Network Analysis
Chaptr 4 Ntwork Aalysis 4. troductio Th KL ad KCL i circuit i thory ar o logr valid. Us th Maxwll s quatios to solv all microwav circuits:? Fild Problm EH, (ctors Circuit Problm, (calars (Equivalt quatitis
More information2. Laser physics - basics
. Lasr physics - basics Spontanous and stimulatd procsss Einstin A and B cofficints Rat quation analysis Gain saturation What is a lasr? LASER: Light Amplification by Stimulatd Emission of Radiation "light"
More informationAn Introduction to Asymptotic Expansions
A Itroductio to Asmptotic Expasios R. Shaar Subramaia Asmptotic xpasios ar usd i aalsis to dscrib th bhavior of a fuctio i a limitig situatio. Wh a fuctio ( x, dpds o a small paramtr, ad th solutio of
More informationFourier Series: main points
BIOEN 3 Lcur 6 Fourir rasforms Novmbr 9, Fourir Sris: mai pois Ifii sum of sis, cosis, or boh + a a cos( + b si( All frqucis ar igr mulipls of a fudamal frqucy, o F.S. ca rprs ay priodic fucio ha w ca
More informationTotal Prime Graph. Abstract: We introduce a new type of labeling known as Total Prime Labeling. Graphs which admit a Total Prime labeling are
Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu. 5 Total Prm Graph M.Rav (a) Ramasubramaa 1, R.Kala 1 Dpt.of Mathmatcs, Sr Shakth Isttut of Egrg & Tchology, Combator 641 06. Dpt. of Mathmatcs,
More informationReliability of time dependent stress-strength system for various distributions
IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,
More informationA Novel Approach to Recovering Depth from Defocus
Ssors & Trasducrs 03 by IFSA http://www.ssorsportal.com A Novl Approach to Rcovrig Dpth from Dfocus H Zhipa Liu Zhzhog Wu Qiufg ad Fu Lifag Collg of Egirig Northast Agricultural Uivrsity 50030 Harbi Chia
More informationElectromagnetic 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