Tuning of High-Power Antenna Resonances by Appropriately Reactive Sources
|
|
- Alice Beryl Black
- 5 years ago
- Views:
Transcription
1 Senor and Simulation Note Note 50 Augut 005 Tuning of High-Power Antenna Reonance by Appropriately Reactive Source Carl E. Baum Univerity of New Mexico Department of Electrical and Computer Engineering Albuquerque New Mexico 873 Abtract In deigning mall high-power electromagnetic radiator (of the order of a half wavelength or o in ize) baed on witched reonant circuit, there are quetion concerning the control of the reonance frequencie. Thi paper explore ome technique for tuning thee frequencie baed on the reactive propertie of the ource.. Thi work wa ponored in part by the Air Force Office of Scientific Reearch.
2 . Introduction Begin with ome antenna with Z a( ) = Y a ( ) input impedance = Ω + jω = Laplace-tranform variable or complex frequency (.) ~ = two-ided Laplace tranform Let thi be driven, a in Fig.., by Z ( ) = Y ( ) = ource impedance (.) Thee two impedance are connected by a cloing witch which we model by V V w ( 0 ) = V 0 = charge voltage before witch cloure (.3) In time domain thi i a tep function. We hould remember that the witch doe not cloe in zero time [4], and that thi limit the performance at high frequencie. then the antenna current (at the input terminal) i jut If Z ( ) = 0 V I 0 a( ) = Y a( ) (.4) Thi typically exhibit reonant behavior at frequencie given by ( ) 0 az a a = (.5) Neglecting a = 0 the contribution of a pole i given in time domain by d t () 0 Re ( ) a Iaa t = V a Z a e u() t d (.6) = a Where the conjugate pole i now included.
3 + V w ( ) _ a ( ) Z ( ) Z Fig.. Antenna and Source 3
4 . General Conideration Now conider the influence of the ource impedance. Thi might be a imple capacitance C. However, at high frequencie Y ( ) may have more complex tructure [5]. Thi nonzero Z ( ) then combine with z ( ) to hift the reonance frequencie. a The ource impedance ha reonance given by ( ) = 0 Z (.) When combined with the antenna impedance we have new natural frequencie given by ( ) + ( ) = 0 Z a m Z m (.) Then (.6) i replaced for a ingle pole pair by d () = 0 Re ( ) + ( ) mt Iam t V m Za Z e u() t d = m (.3) So our approach i to ee how we might hift the antenna reonance in deirable direction. The factor d m Za Z d ( ) + ( ) = m (.4) can be ued (at leat for high-q reonance) a a caling factor for the trength of the reonance. 4
5 3. Ditributed Capacitive Source For preent purpoe we need a model for the ource impedance. Let u chooe an open-circuited tranmiion line a indicated in Fig. 3.. It might include a high-dielectric-contant medium with ε = εε r 0 (.4) With a tranit time t r, the capacitance (low frequency) i jut t C = r Zc Z c = characteritic impedance of tranmiion line (.5) The ource impedance i then t e r Z + ( ) = Zc = Z coth( ) t c t r (.6) e r with open-circuit reonance at ( t ) ( ω t ) inh r = 0, in r = 0 ωr t = nπ, n = 0,,, ω = n f = π tr (.7) i.e., multiple of a half wavelength. are It i intereting to ee at what frequencie the ource ha zero impedance (hort-circuit reonance). Thee ( t ) ( ω t ) coth r = 0, co r = 0 n + ω tr = π, n = 0,,, (.8) ω n + f = = π 4tr i.e., odd multiple of a quarter wavelength. One might chooe the ource then a having zero impedance at an antenna reonance o a to deliver a large voltage to the antenna. 5
6 t r tranit time ε Fig. 3. Tranmiion-Line Capacitive Source 6
7 4. Combination With Magnetic Antenna One type of electrically mall antenna i a loop of ome kind producing a magnetic-dipole moment. When operating in reonance condition there may be ome appreciable fraction of a wavelength acro the tructure [, ]. Let u model the antenna impedance (up to firt reonance of current) a Z a ( ) = + C a La L a low-frequency loop inductance (4.) Ca capacitive correction aociated with lead into loop and tray capacitance of loop tructure Note that thi neglect the radiation reitance. ource V 0 / a If the ource i modeled a a imple capacitance C, thi appear in erie with Z a when driven by the Z ( ) = Z a ( ) + = + C a + Cg La C = L = C a L + a a LaC (4.) The reonance i then at 0 = ω C mla a ω mlac ω C ω mla = mlac / / ωm = La[ Ca + C] = [ LaCa] + / C Ca (4.3) Compared to the antenna reonance [ C ] ω a = L a a (4.4) We ee that 7
8 ωm < ωa (4.5) With equality if C = 0 (or Z = C, ωm 0. ). The effect of C i to lower the reonance frequency. Note that for infinite At the ame time the trength of the reonance i changed with the factor d m Za Z d ( ) + ( ) = m = C C m + a + m a mla mla mc j = C ω C ω + a m + a + m ω ω ω C mla mla m j C = [ C + C ] [ C + C ] + + a a La a C La ωm C jl C = a + a C C + a + + a ωm C C C jl C = a + a ωm C / / j L C C = a + + a Ca Ca C / 3/ j L C C = a + Ca Ca Ca (4.6) So maller C decreae the reonant current (at the antenna port). A C (zero-impedance ource) thi reonance ha ωm 0, for which the antenna i zerowavelength long. Small C correpond to a quarter wavelength. Let u conider a higher reonance correponding to a half wavelength. 8
9 5. Tranmiion-Line Model of Loop and Source Conider the cae that both loop antenna and ource are modeled a tranmiion line a indicated in Fig. 5.. Then we have for the antenna impedanace t e Z a( ) = Zch = Z tanh ( ) t ch t (5.) + e For a zero-impedance ource we have current reonance a ( t) ( ω t) inh a = 0, in a = 0 ωat = nπ, n = 0,, (5.) ωa n fa = = π t which are multiple of a half wavelength. A pecial imple cae ha Zc = Zch (5.3) with t now the tranit time of the ource part. Thi i effectively a ingle tranmiion line of tranit time, t + t. With one end horted and the other open, the firt quarter-wave reonance i at f m ω = m = π 4 [ t + t ] (5.4) Here we ee that hortening t raie f m, conitent with the previou reult with leened ource capacitance. Here we can alo ee that a the witch approache the right end of the tranmiion line, where the current in the natural mode i weaket, the trength of the reonance i alo decreaed. The more general cae ha the reonance condition mt mt e + e Zch + Z c = mt mt + e e 0 (5.5) 9
10 hort circuit Z ch t V + _ t w ( ) Z c open circuit Fig. 5. Tranmiion-Line Model of Loop and Source 0
11 Note that for mall Z c we have Zc 0 Zch m a = jωa (5.6) a in (5.). Another pecial cae ha t = t, for which we have mt Z mt e c e + + Z ch = 0 tanh Z ( ) c mt = Zch tan Zc ( ωmt ) = Zch ωmt arctan / Zc = Zch (5.7) With additional olution baed on the periodicity of tan. The general cae (5.5) i readily olved numerically for ω m t or ω m t a a function of Zc/ Z ch and t / t. By taking the derivative of Z a a in (5.) one can alo find a perturbation olution about ω a a in Section 4.
12 6. Combination With Electric Antenna Another type of electrically mall antenna i an electric dipole of ome kind, i.e., two eparate conductor driven by ome ource between them, produding an electric dipole moment. Operated in reonance condition there may be ome appreciable fraction of a wavelength acro the tructure [3]. Let u model the antenna impedance (up to firt reonance of current) a Z a( ) = + La Ca Ca low-frequency dipole capacitance (6.) La inductive correction aociated with lead into dipole and tray inductance of dipole tructure Again thi neglect the radiation reitance. Vg / a With the ource modeled a a capacitance C, thi appear in erie with Z a when driven by the ource Z ( ) = Z a( ) + = La + + (6.) C 5 Ca C The reonance i then at 0 ωm = ωmla + ωm Ca C / = + La Ca C (6.3) Compared to the antenna reonance at [ L C ] / ωa = a a (6.4) We ee that ωm > ωa (6.5)
13 with equality if C = (or Z = 0 ). The effect of C i to raie the reonance frequency. For large C, the reonance correpond to a quarter-wave reonance related to the ource (or half wave on the two dipole conductor). For mall C the reult of (6.3) i unrealitic in that phyically thi hould go to an open-circuit or half-wave reonance related to the ource. For thi cae another model i appropriate. The trength of the reonance i changed a d m Z a( ) + Z ( ) d = m = mla + C m a C / = j + La Ca C La / j = La + Ca C (6.6) So larger C increae the reonant current (at the antenna port). 3
14 7. Tranmiion-Line Model of Electric Antenna and Source Model the electric antenna and ource a tranmiion line a indicated in Fig. 7.. Note that thi i topologically different from the loop cae ince both end are open circuited. Now the antenna impedance i t + e Za Zch Z t ch t e ( ) = = coth ( ) (7.) For a zero-impedance ource we have current reonance at ( t) ( ω t) coh a = 0, co a = 0 n + ωat = π, n = 0,,, (7.) ωa n + fa = = π 4t which are odd multiple of a quarter wavelength. For the pecial cae of Zc = Zch (7.3) we have a half-wavelgneth reonant tranmiion line of tranit time t + t. Thi give the lowet-order reonance at f m ω = m = π [ t + ] (7.4) For mall t thi become a half wavelength on each antenna conductor. However, thi alo implie a mall energy from the ource. The more general cae ha the reonance condition mt mt + e + e Zch + Z c = mt mt e e 0 (7.5) 4
15 For mall Z c we have Zc 0 Zch m a = jωa (7.6) a in (7.). Another pecial cae ha t = t, for which we have Z inh( ) c mt + inh( mt) = 0 Zch inh( mt) = 0, inh( ωmt) = 0 nπ ωmt =, n = 0,,, ωm n fm = = π 4t (7.7) The firt nonzero reonance i then when each antenna conductor i a quarter-wavelength long. Note alo that mall Z c mean more tored energy in the ource, giving a larger reonance current. The general cae (7.5) i alo readily olved numerically. 5
16 open circuit Z ch t V + _ t w ( ) Z c open circuit Fig. 7. Tranmiion-Line Model of Electric Antenna and Source 6
17 8. Concluding Remark A we can ee, judiciou choice of the frequency dependence of the ource impedance can alter the reonance frequency and reonance trength of the antenna, whether of loop or electric-dipole type. Here we have choen ome imple form of the ource impedance for illutration. More elaborate form can alo be purued. 7
18 Reference. C. E. Baum, Compact, Low-Impedance Magnetic Antenna, Senor and Simulation Note 470, December 00.. C. E. Baum, Symmetry in Low-Impedance Magnetic Antenna, Senor and Simulation Note 497, March C. E. Baum, Compact Electric Antenna, Senor and Simulation Note 500, Augut J. M. Lehr, C. E. Baum, and W. D. Prather, Fundamental Phyical Conideration for Ultrafat Spark Gap Switching, Switching Note 8, June 997; pp. -0 in E. Heyman et al (ed.), Ultra-Wideband, Short-Pule Electromagnetic 4, Kluwer Academic/Plenum Publiher, C. E. Baum, High-Dielectric-Contant Material a High-Frequency Capacitor, Energy Storage and Diipation Note, November
MAE140 Linear Circuits Fall 2012 Final, December 13th
MAE40 Linear Circuit Fall 202 Final, December 3th Intruction. Thi exam i open book. You may ue whatever written material you chooe, including your cla note and textbook. You may ue a hand calculator with
More informationQuestion 1 Equivalent Circuits
MAE 40 inear ircuit Fall 2007 Final Intruction ) Thi exam i open book You may ue whatever written material you chooe, including your cla note and textbook You may ue a hand calculator with no communication
More informationSIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005.
SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2005. Initial Condition Source 0 V battery witch flip at t 0 find i 3 (t) Component value:
More informationLecture 12 - Non-isolated DC-DC Buck Converter
ecture 12 - Non-iolated DC-DC Buck Converter Step-Down or Buck converter deliver DC power from a higher voltage DC level ( d ) to a lower load voltage o. d o ene ref + o v c Controller Figure 12.1 The
More informationFUNDAMENTALS OF POWER SYSTEMS
1 FUNDAMENTALS OF POWER SYSTEMS 1 Chapter FUNDAMENTALS OF POWER SYSTEMS INTRODUCTION The three baic element of electrical engineering are reitor, inductor and capacitor. The reitor conume ohmic or diipative
More informationBogoliubov Transformation in Classical Mechanics
Bogoliubov Tranformation in Claical Mechanic Canonical Tranformation Suppoe we have a et of complex canonical variable, {a j }, and would like to conider another et of variable, {b }, b b ({a j }). How
More informationLecture 10 Filtering: Applied Concepts
Lecture Filtering: Applied Concept In the previou two lecture, you have learned about finite-impule-repone (FIR) and infinite-impule-repone (IIR) filter. In thee lecture, we introduced the concept of filtering
More informationIntroduction to Laplace Transform Techniques in Circuit Analysis
Unit 6 Introduction to Laplace Tranform Technique in Circuit Analyi In thi unit we conider the application of Laplace Tranform to circuit analyi. A relevant dicuion of the one-ided Laplace tranform i found
More informationNonlinear Single-Particle Dynamics in High Energy Accelerators
Nonlinear Single-Particle Dynamic in High Energy Accelerator Part 6: Canonical Perturbation Theory Nonlinear Single-Particle Dynamic in High Energy Accelerator Thi coure conit of eight lecture: 1. Introduction
More informationChapter 17 Amplifier Frequency Response
hapter 7 Amplifier Frequency epone Microelectronic ircuit Deign ichard. Jaeger Travi N. Blalock 8/0/0 hap 7- hapter Goal eview tranfer function analyi and dominant-pole approximation of amplifier tranfer
More informationSocial Studies 201 Notes for March 18, 2005
1 Social Studie 201 Note for March 18, 2005 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the
More informationNo-load And Blocked Rotor Test On An Induction Machine
No-load And Blocked Rotor Tet On An Induction Machine Aim To etimate magnetization and leakage impedance parameter of induction machine uing no-load and blocked rotor tet Theory An induction machine in
More informationCombined Electric and Magnetic Dipoles for Mesoband Radiation
Sensor and Simulation Notes Note 53 0 August 007 Combined Electric and Magnetic Dipoles for Mesoband Radiation Carl E. Baum University of New Mexico Department of Electrical and Computer Engineering Albuquerque
More informationLecture 6: Resonance II. Announcements
EES 5 Spring 4, Lecture 6 Lecture 6: Reonance II EES 5 Spring 4, Lecture 6 Announcement The lab tart thi week You mut how up for lab to tay enrolled in the coure. The firt lab i available on the web ite,
More informationSERIES COMPENSATION: VOLTAGE COMPENSATION USING DVR (Lectures 41-48)
Chapter 5 SERIES COMPENSATION: VOLTAGE COMPENSATION USING DVR (Lecture 41-48) 5.1 Introduction Power ytem hould enure good quality of electric power upply, which mean voltage and current waveform hould
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder Cloed-loop buck converter example: Section 9.5.4 In ECEN 5797, we ued the CCM mall ignal model to
More informationSocial Studies 201 Notes for November 14, 2003
1 Social Studie 201 Note for November 14, 2003 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the
More informationLiquid cooling
SKiiPPACK no. 3 4 [ 1- exp (-t/ τ )] + [( P + P )/P ] R [ 1- exp (-t/ τ )] Z tha tot3 = R ν ν tot1 tot tot3 thaa-3 aa 3 ν= 1 3.3.6. Liquid cooling The following table contain the characteritic R ν and
More informationPulsed Magnet Crimping
Puled Magnet Crimping Fred Niell 4/5/00 1 Magnetic Crimping Magnetoforming i a metal fabrication technique that ha been in ue for everal decade. A large capacitor bank i ued to tore energy that i ued to
More informationonline learning Unit Workbook 4 RLC Transients
online learning Pearon BTC Higher National in lectrical and lectronic ngineering (QCF) Unit 5: lectrical & lectronic Principle Unit Workbook 4 in a erie of 4 for thi unit Learning Outcome: RLC Tranient
More informationNOTE: The items d) and e) of Question 4 gave you bonus marks.
MAE 40 Linear ircuit Summer 2007 Final Solution NOTE: The item d) and e) of Quetion 4 gave you bonu mark. Quetion [Equivalent irciut] [4 mark] Find the equivalent impedance between terminal A and B in
More informationLecture 23 Date:
Lecture 3 Date: 4.4.16 Plane Wave in Free Space and Good Conductor Power and Poynting Vector Wave Propagation in Loy Dielectric Wave propagating in z-direction and having only x-component i given by: E
More informationChapter 13. Root Locus Introduction
Chapter 13 Root Locu 13.1 Introduction In the previou chapter we had a glimpe of controller deign iue through ome imple example. Obviouly when we have higher order ytem, uch imple deign technique will
More information55:041 Electronic Circuits
55:04 Electronic ircuit Frequency epone hapter 7 A. Kruger Frequency epone- ee page 4-5 of the Prologue in the text Important eview co Thi lead to the concept of phaor we encountered in ircuit In Linear
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder ZOH: Sampled Data Sytem Example v T Sampler v* H Zero-order hold H v o e = 1 T 1 v *( ) = v( jkω
More informationLaplace Transformation
Univerity of Technology Electromechanical Department Energy Branch Advance Mathematic Laplace Tranformation nd Cla Lecture 6 Page of 7 Laplace Tranformation Definition Suppoe that f(t) i a piecewie continuou
More informationChapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog
Chapter Sampling and Quantization.1 Analog and Digital Signal In order to invetigate ampling and quantization, the difference between analog and digital ignal mut be undertood. Analog ignal conit of continuou
More informationDesign of Digital Filters
Deign of Digital Filter Paley-Wiener Theorem [ ] ( ) If h n i a caual energy ignal, then ln H e dω< B where B i a finite upper bound. One implication of the Paley-Wiener theorem i that a tranfer function
More informationinto a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get
Lecture 25 Introduction to Some Matlab c2d Code in Relation to Sampled Sytem here are many way to convert a continuou time function, { h( t) ; t [0, )} into a dicrete time function { h ( k) ; k {0,,, }}
More informationEE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject
EE 508 Lecture 6 Filter Tranformation Lowpa to Bandpa Lowpa to Highpa Lowpa to Band-reject Review from Lat Time Theorem: If the perimeter variation and contact reitance are neglected, the tandard deviation
More informationBasic parts of an AC motor : rotor, stator, The stator and the rotor are electrical
INDUCTION MOTO 1 CONSTUCTION Baic part of an AC motor : rotor, tator, encloure The tator and the rotor are electrical circuit that perform a electromagnet. CONSTUCTION (tator) The tator - tationary part
More informationEE/ME/AE324: Dynamical Systems. Chapter 8: Transfer Function Analysis
EE/ME/AE34: Dynamical Sytem Chapter 8: Tranfer Function Analyi The Sytem Tranfer Function Conider the ytem decribed by the nth-order I/O eqn.: ( n) ( n 1) ( m) y + a y + + a y = b u + + bu n 1 0 m 0 Taking
More informationDigital Control System
Digital Control Sytem - A D D A Micro ADC DAC Proceor Correction Element Proce Clock Meaurement A: Analog D: Digital Continuou Controller and Digital Control Rt - c Plant yt Continuou Controller Digital
More informationGNSS Solutions: What is the carrier phase measurement? How is it generated in GNSS receivers? Simply put, the carrier phase
GNSS Solution: Carrier phae and it meaurement for GNSS GNSS Solution i a regular column featuring quetion and anwer about technical apect of GNSS. Reader are invited to end their quetion to the columnit,
More informationChapter 4. The Laplace Transform Method
Chapter 4. The Laplace Tranform Method The Laplace Tranform i a tranformation, meaning that it change a function into a new function. Actually, it i a linear tranformation, becaue it convert a linear combination
More informationBASIC INDUCTION MOTOR CONCEPTS
INDUCTION MOTOS An induction motor ha the ame phyical tator a a ynchronou machine, with a different rotor contruction. There are two different type of induction motor rotor which can be placed inide the
More informationEE C128 / ME C134 Problem Set 1 Solution (Fall 2010) Wenjie Chen and Jansen Sheng, UC Berkeley
EE C28 / ME C34 Problem Set Solution (Fall 200) Wenjie Chen and Janen Sheng, UC Berkeley. (0 pt) BIBO tability The ytem h(t) = co(t)u(t) i not BIBO table. What i the region of convergence for H()? A bounded
More informationBehavioral Modeling of Transmission Line Channels via Linear Transformations
Behavioral Modeling of Tranmiion Line Channel via Linear Tranformation Albert Vareljian albertv@ieeeorg Member, IEEE, Canada Abtract An approach baed on the linear tranformation of network port variable
More informationSIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. R 4 := 100 kohm
SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2003. Cacaded Op Amp [DC&L, problem 4.29] An ideal op amp ha an output impedance of zero,
More informationAdvanced D-Partitioning Analysis and its Comparison with the Kharitonov s Theorem Assessment
Journal of Multidiciplinary Engineering Science and Technology (JMEST) ISSN: 59- Vol. Iue, January - 5 Advanced D-Partitioning Analyi and it Comparion with the haritonov Theorem Aement amen M. Yanev Profeor,
More informationRELIABILITY OF REPAIRABLE k out of n: F SYSTEM HAVING DISCRETE REPAIR AND FAILURE TIMES DISTRIBUTIONS
www.arpapre.com/volume/vol29iue1/ijrras_29_1_01.pdf RELIABILITY OF REPAIRABLE k out of n: F SYSTEM HAVING DISCRETE REPAIR AND FAILURE TIMES DISTRIBUTIONS Sevcan Demir Atalay 1,* & Özge Elmataş Gültekin
More informationLecture #9 Continuous time filter
Lecture #9 Continuou time filter Oliver Faut December 5, 2006 Content Review. Motivation......................................... 2 2 Filter pecification 2 2. Low pa..........................................
More informationCHAPTER 13 FILTERS AND TUNED AMPLIFIERS
HAPTE FILTES AND TUNED AMPLIFIES hapter Outline. Filter Traniion, Type and Specification. The Filter Tranfer Function. Butterworth and hebyhev Filter. Firt Order and Second Order Filter Function.5 The
More informationTHE EXPERIMENTAL PERFORMANCE OF A NONLINEAR DYNAMIC VIBRATION ABSORBER
Proceeding of IMAC XXXI Conference & Expoition on Structural Dynamic February -4 Garden Grove CA USA THE EXPERIMENTAL PERFORMANCE OF A NONLINEAR DYNAMIC VIBRATION ABSORBER Yung-Sheng Hu Neil S Ferguon
More informationECEN620: Network Theory Broadband Circuit Design Fall 2018
ECEN60: Network Theory Broadband Circuit Deign Fall 08 Lecture 6: Loop Filter Circuit Sam Palermo Analog & Mixed-Signal Center Texa A&M Univerity Announcement HW i due Oct Require tranitor-level deign
More informationECE Linear Circuit Analysis II
ECE 202 - Linear Circuit Analyi II Final Exam Solution December 9, 2008 Solution Breaking F into partial fraction, F 2 9 9 + + 35 9 ft δt + [ + 35e 9t ]ut A 9 Hence 3 i the correct anwer. Solution 2 ft
More information7.2 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 281
72 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 28 and i 2 Show how Euler formula (page 33) can then be ued to deduce the reult a ( a) 2 b 2 {e at co bt} {e at in bt} b ( a) 2 b 2 5 Under what condition
More informationMechanics. Free rotational oscillations. LD Physics Leaflets P Measuring with a hand-held stop-clock. Oscillations Torsion pendulum
Mechanic Ocillation Torion pendulum LD Phyic Leaflet P.5.. Free rotational ocillation Meauring with a hand-held top-clock Object of the experiment g Meauring the amplitude of rotational ocillation a function
More information15 Problem 1. 3 a Draw the equivalent circuit diagram of the synchronous machine. 2 b What is the expected synchronous speed of the machine?
Exam Electrical Machine and Drive (ET4117) 6 November 009 from 9.00 to 1.00. Thi exam conit of 4 problem on 4 page. Page 5 can be ued to anwer problem quetion b. The number before a quetion indicate how
More informationProperties of Z-transform Transform 1 Linearity a
Midterm 3 (Fall 6 of EEG:. Thi midterm conit of eight ingle-ided page. The firt three page contain variou table followed by FOUR eam quetion and one etra workheet. You can tear out any page but make ure
More informationFinding the location of switched capacitor banks in distribution systems based on wavelet transform
UPEC00 3t Aug - 3rd Sept 00 Finding the location of witched capacitor bank in ditribution ytem baed on wavelet tranform Bahram nohad Shahid Chamran Univerity in Ahvaz bahramnohad@yahoo.com Mehrdad keramatzadeh
More informationECE382/ME482 Spring 2004 Homework 4 Solution November 14,
ECE382/ME482 Spring 2004 Homework 4 Solution November 14, 2005 1 Solution to HW4 AP4.3 Intead of a contant or tep reference input, we are given, in thi problem, a more complicated reference path, r(t)
More informationEE105 - Fall 2005 Microelectronic Devices and Circuits
EE5 - Fall 5 Microelectronic Device and ircuit Lecture 9 Second-Order ircuit Amplifier Frequency Repone Announcement Homework 8 due tomorrow noon Lab 7 next week Reading: hapter.,.3. Lecture Material Lat
More informationME 375 FINAL EXAM SOLUTIONS Friday December 17, 2004
ME 375 FINAL EXAM SOLUTIONS Friday December 7, 004 Diviion Adam 0:30 / Yao :30 (circle one) Name Intruction () Thi i a cloed book eamination, but you are allowed three 8.5 crib heet. () You have two hour
More informationReliability Analysis of Embedded System with Different Modes of Failure Emphasizing Reboot Delay
International Journal of Applied Science and Engineering 3., 4: 449-47 Reliability Analyi of Embedded Sytem with Different Mode of Failure Emphaizing Reboot Delay Deepak Kumar* and S. B. Singh Department
More informationThe Influence of Landau Damping on Multi Bunch Instabilities
Univerität Dortmund The Influence of Landau Damping on Multi Bunch Intabilitie A Baic Coure on Landau Damping + A Few Implication Prof. Dr. Thoma Wei Department of Phyic / Dortmund Univerity Riezlern,
More informationMoment of Inertia of an Equilateral Triangle with Pivot at one Vertex
oment of nertia of an Equilateral Triangle with Pivot at one Vertex There are two wa (at leat) to derive the expreion f an equilateral triangle that i rotated about one vertex, and ll how ou both here.
More informationMarch 18, 2014 Academic Year 2013/14
POLITONG - SHANGHAI BASIC AUTOMATIC CONTROL Exam grade March 8, 4 Academic Year 3/4 NAME (Pinyin/Italian)... STUDENT ID Ue only thee page (including the back) for anwer. Do not ue additional heet. Ue of
More informationA Constraint Propagation Algorithm for Determining the Stability Margin. The paper addresses the stability margin assessment for linear systems
A Contraint Propagation Algorithm for Determining the Stability Margin of Linear Parameter Circuit and Sytem Lubomir Kolev and Simona Filipova-Petrakieva Abtract The paper addree the tability margin aement
More informationThe Influence of the Load Condition upon the Radial Distribution of Electromagnetic Vibration and Noise in a Three-Phase Squirrel-Cage Induction Motor
The Influence of the Load Condition upon the Radial Ditribution of Electromagnetic Vibration and Noie in a Three-Phae Squirrel-Cage Induction Motor Yuta Sato 1, Iao Hirotuka 1, Kazuo Tuboi 1, Maanori Nakamura
More informationDelhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:
Serial : LS_N_A_Network Theory_098 Delhi Noida Bhopal Hyderabad Jaipur Lucknow ndore Pune Bhubanewar Kolkata Patna Web: E-mail: info@madeeay.in Ph: 0-4546 CLASS TEST 08-9 NSTRUMENTATON ENGNEERNG Subject
More informationDelhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:
Serial : LS_B_EC_Network Theory_0098 CLASS TEST (GATE) Delhi Noida Bhopal Hyderabad Jaipur Lucknow ndore Pune Bhubanewar Kolkata Patna Web: E-mail: info@madeeay.in Ph: 0-4546 CLASS TEST 08-9 ELECTRONCS
More informationReflection and transmission of obliquely incident graphene plasmons by discontinuities in
Home Search Collection Journal About Contact u My IOPcience Reflection and tranmiion of obliquely incident graphene plamon by dicontinuitie in urface conductivity: obervation of the Brewter-like effect
More informationFinite Element Analysis of a Fiber Bragg Grating Accelerometer for Performance Optimization
Finite Element Analyi of a Fiber Bragg Grating Accelerometer for Performance Optimization N. Baumallick*, P. Biwa, K. Dagupta and S. Bandyopadhyay Fiber Optic Laboratory, Central Gla and Ceramic Reearch
More informationChapter 7. Root Locus Analysis
Chapter 7 Root Locu Analyi jw + KGH ( ) GH ( ) - K 0 z O 4 p 2 p 3 p Root Locu Analyi The root of the cloed-loop characteritic equation define the ytem characteritic repone. Their location in the complex
More informationLecture 17: Analytic Functions and Integrals (See Chapter 14 in Boas)
Lecture 7: Analytic Function and Integral (See Chapter 4 in Boa) Thi i a good point to take a brief detour and expand on our previou dicuion of complex variable and complex function of complex variable.
More informationON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION. Xiaoqun Wang
Proceeding of the 2008 Winter Simulation Conference S. J. Maon, R. R. Hill, L. Mönch, O. Roe, T. Jefferon, J. W. Fowler ed. ON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION Xiaoqun Wang
More informationControl Systems Analysis and Design by the Root-Locus Method
6 Control Sytem Analyi and Deign by the Root-Locu Method 6 1 INTRODUCTION The baic characteritic of the tranient repone of a cloed-loop ytem i cloely related to the location of the cloed-loop pole. If
More informationBasics of a Quartz Crystal Microbalance
Baic of a Quartz Crytal Microbalance Introduction Thi document provide an introduction to the quartz crytal microbalance (QCM) which i an intrument that allow a uer to monitor mall ma change on an electrode.
More informationSECTION x2 x > 0, t > 0, (8.19a)
SECTION 8.5 433 8.5 Application of aplace Tranform to Partial Differential Equation In Section 8.2 and 8.3 we illutrated the effective ue of aplace tranform in olving ordinary differential equation. The
More informationSolving Differential Equations by the Laplace Transform and by Numerical Methods
36CH_PHCalter_TechMath_95099 3//007 :8 PM Page Solving Differential Equation by the Laplace Tranform and by Numerical Method OBJECTIVES When you have completed thi chapter, you hould be able to: Find the
More informationRECURSIVE LEAST SQUARES HARMONIC IDENTIFICATION IN ACTIVE POWER FILTERS. A. El Zawawi, K. H. Youssef, and O. A. Sebakhy
RECURSIVE LEAST SQUARES HARMONIC IDENTIFICATION IN ACTIVE POWER FILTERS A. El Zawawi, K. H. Youef, and O. A. Sebakhy Department of Electrical Engineering, Alexandria Univerity, Alexandria 21544, Egypt.P.O.
More informationLECTURE 22. Collective effects in multi-particle beams: Parasitic Losses. Longitudinal impedances in accelerators (continued)
LECTURE Collective effect in multi-particle beam: Longitudinal impedance in accelerator Tranvere impedance in accelerator Paraitic Loe /7/0 USPAS Lecture Longitudinal impedance in accelerator (continued)
More informationAnnex-A: RTTOV9 Cloud validation
RTTOV-91 Science and Validation Plan Annex-A: RTTOV9 Cloud validation Author O Embury C J Merchant The Univerity of Edinburgh Intitute for Atmo. & Environ. Science Crew Building King Building Edinburgh
More informationIII.9. THE HYSTERESIS CYCLE OF FERROELECTRIC SUBSTANCES
III.9. THE HYSTERESIS CYCLE OF FERROELECTRIC SBSTANCES. Work purpoe The analyi of the behaviour of a ferroelectric ubtance placed in an eternal electric field; the dependence of the electrical polariation
More informationEECS2200 Electric Circuits. RLC Circuit Natural and Step Responses
5--4 EECS Electric Circuit Chapter 6 R Circuit Natural and Step Repone Objective Determine the repone form of the circuit Natural repone parallel R circuit Natural repone erie R circuit Step repone of
More informationEE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject
EE 508 Lecture 6 Filter Tranformation Lowpa to Bandpa Lowpa to Highpa Lowpa to Band-reject Review from Lat Time Theorem: If the perimeter variation and contact reitance are neglected, the tandard deviation
More informationEmittance limitations due to collective effects for the TOTEM beams
LHC Project ote 45 June 0, 004 Elia.Metral@cern.ch Andre.Verdier@cern.ch Emittance limitation due to collective effect for the TOTEM beam E. Métral and A. Verdier, AB-ABP, CER Keyword: TOTEM, collective
More informationImproving Power System Transient Stability with Static Synchronous Series Compensator
American Journal of Applied Science 8 (1): 77-81, 2011 ISSN 1546-9239 2010 Science Pulication Improving Power Sytem Tranient Staility with Static Synchronou Serie Compenator Prechanon Kumkratug Diviion
More informationGain and Phase Margins Based Delay Dependent Stability Analysis of Two- Area LFC System with Communication Delays
Gain and Phae Margin Baed Delay Dependent Stability Analyi of Two- Area LFC Sytem with Communication Delay Şahin Sönmez and Saffet Ayaun Department of Electrical Engineering, Niğde Ömer Halidemir Univerity,
More informationCoherent Resonance of Saturated Absorption in Spectroscopy of Counterpropagating Waves
Journal of Modern Phyic,,, 8-5 doi:.6/jmp..5b Publihed Online May (http://www.cirp.org/journal/jmp Coherent Reonance of Saturated Aborption in Spectrocopy of Counterpropagating Wave A. A. Chernenko, E.
More informationControl of Delayed Integrating Processes Using Two Feedback Controllers R MS Approach
Proceeding of the 7th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING (ICOSSSE '8) Control of Delayed Integrating Procee Uing Two Feedback Controller R MS Approach LIBOR
More informationTheoretical study of the dual harmonic system and its application on the CSNS/RCS
Theoretical tudy of the dual harmonic ytem and it application on the CSNS/RCS Yao-Shuo Yuan, Na Wang, Shou-Yan Xu, Yue Yuan, and Sheng Wang Dongguan branch, Intitute of High Energy Phyic, CAS, Guangdong
More informationEELE 3332 Electromagnetic II Chapter 10
EELE 333 Electromagnetic II Chapter 10 Electromagnetic Wave Propagation Ilamic Univerity of Gaza Electrical Engineering Department Dr. Talal Skaik 01 1 Electromagnetic wave propagation A changing magnetic
More informationGATE SOLVED PAPER - EC
0 ONE MARK Q. Conider a delta connection of reitor and it equivalent tar connection a hown below. If all element of the delta connection are caled by a factor k, k > 0, the element of the correponding
More informationSingular perturbation theory
Singular perturbation theory Marc R. Rouel June 21, 2004 1 Introduction When we apply the teady-tate approximation (SSA) in chemical kinetic, we typically argue that ome of the intermediate are highly
More informationPOWER SYSTEM SMALL SIGNAL STABILITY ANALYSIS BASED ON TEST SIGNAL
POWE YEM MALL INAL ABILIY ANALYI BAE ON E INAL Zheng Xu, Wei hao, Changchun Zhou Zheang Univerity, Hangzhou, 37 PChina Email: hvdc@ceezueducn Abtract - In thi paper, a method baed on ome tet ignal (et
More informationClustering Methods without Given Number of Clusters
Clutering Method without Given Number of Cluter Peng Xu, Fei Liu Introduction A we now, mean method i a very effective algorithm of clutering. It mot powerful feature i the calability and implicity. However,
More informationECE-202 FINAL December 13, 2016 CIRCLE YOUR DIVISION
ECE-202 Final, Fall 16 1 ECE-202 FINAL December 13, 2016 Name: (Pleae print clearly.) Student Email: CIRCLE YOUR DIVISION DeCarlo- 8:30-9:30 Talavage-9:30-10:30 2021 2022 INSTRUCTIONS There are 35 multiple
More informationRefinements to the Model of a Single Woodwind Instrument Tonehole
Proceeding of 20th International Sympoium on Muic Acoutic (Aociated Meeting of the International Congre on Acoutic) 25-31 Augut 2010, Sydney and Katoomba, Autralia Refinement to the Model of a Single Woodwind
More information5.5 Application of Frequency Response: Signal Filters
44 Dynamic Sytem Second order lowpa filter having tranfer function H()=H ()H () u H () H () y Firt order lowpa filter Figure 5.5: Contruction of a econd order low-pa filter by combining two firt order
More informationA PLC BASED MIMO PID CONTROLLER FOR MULTIVARIABLE INDUSTRIAL PROCESSES
ABCM Sympoium Serie in Mechatronic - Vol. 3 - pp.87-96 Copyright c 8 by ABCM A PLC BASE MIMO PI CONOLLE FO MULIVAIABLE INUSIAL POCESSES Joé Maria Galvez, jmgalvez@ufmg.br epartment of Mechanical Engineering
More informationME 375 FINAL EXAM Wednesday, May 6, 2009
ME 375 FINAL EXAM Wedneday, May 6, 9 Diviion Meckl :3 / Adam :3 (circle one) Name_ Intruction () Thi i a cloed book examination, but you are allowed three ingle-ided 8.5 crib heet. A calculator i NOT allowed.
More informationSupplementary Figures
Supplementary Figure Supplementary Figure S1: Extraction of the SOF. The tandard deviation of meaured V xy at aturated tate (between 2.4 ka/m and 12 ka/m), V 2 d Vxy( H, j, hm ) Vxy( H, j, hm ) 2. The
More informationS.E. Sem. III [EXTC] Circuits and Transmission Lines
S.E. Sem. III [EXTC] Circuit and Tranmiion Line Time : Hr.] Prelim Quetion Paper Solution [Mark : 80 Q.(a) Tet whether P() = 5 4 45 60 44 48 i Hurwitz polynomial. (A) P() = 5 4 45 60 44 48 5 45 44 4 60
More informationDigital Control System
Digital Control Sytem Summary # he -tranform play an important role in digital control and dicrete ignal proceing. he -tranform i defined a F () f(k) k () A. Example Conider the following equence: f(k)
More informationThermal Resistance Measurements and Thermal Transient Analysis of Power Chip Slug-Up and Slug-Down Mounted on HDI Substrate
Intl Journal of Microcircuit and Electronic Packaging Thermal Reitance Meaurement and Thermal Tranient Analyi of Power Chip Slug-Up and Slug-Down Mounted on HDI Subtrate Claudio Sartori Magneti Marelli
More informationc n b n 0. c k 0 x b n < 1 b k b n = 0. } of integers between 0 and b 1 such that x = b k. b k c k c k
1. Exitence Let x (0, 1). Define c k inductively. Suppoe c 1,..., c k 1 are already defined. We let c k be the leat integer uch that x k An eay proof by induction give that and for all k. Therefore c n
More informationSMALL-SIGNAL STABILITY ASSESSMENT OF THE EUROPEAN POWER SYSTEM BASED ON ADVANCED NEURAL NETWORK METHOD
SMALL-SIGNAL STABILITY ASSESSMENT OF THE EUROPEAN POWER SYSTEM BASED ON ADVANCED NEURAL NETWORK METHOD S.P. Teeuwen, I. Erlich U. Bachmann Univerity of Duiburg, Germany Department of Electrical Power Sytem
More informationChapter 2 Homework Solution P2.2-1, 2, 5 P2.4-1, 3, 5, 6, 7 P2.5-1, 3, 5 P2.6-2, 5 P2.7-1, 4 P2.8-1 P2.9-1
Chapter Homework Solution P.-1,, 5 P.4-1, 3, 5, 6, 7 P.5-1, 3, 5 P.6-, 5 P.7-1, 4 P.8-1 P.9-1 P.-1 An element ha oltage and current i a hown in Figure P.-1a. Value of the current i and correponding oltage
More information