) ( ) The pole-zero matching method. European School of Antennas. Rigorous multiport network. Loss less two port network. Two port network.

Size: px
Start display at page:

Download ") ( ) The pole-zero matching method. European School of Antennas. Rigorous multiport network. Loss less two port network. Two port network."

Transcription

1 European School of Antennas Rigorous multiport networ The pole-ero matching metho Stefano aci Universit of Siena, Dept. Of nformation Engineering Via Roma 5, -53 Siena, tal ( ( ( FW, FW, ( ( ( FW, ( ( FW, Presente at the European school of Antennas Antenna Center of Ecellence April 9, 5 Contributors from Universit of Siena:,. Caiao, F. Caminita, A. Cucini,. Ettorre,. Nannetti = (, ; F SS Loss less two port networ S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 Two port networ Cut-off region of the higer orer moes in the κ iagram, H H H H (, ; = Q Q Q Q H H H H (, ; = p P P p p P P p F SS Dipole tpe Slot tpe = = ( j ( cot ( h = ( j ( cot ( h = - et = et = = c = (Light cone c = c c = S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 Light cone comment E E E E = c = (Light cone c = c c = ( H ( H (, ; = H o = Q Q o o Through the inverse of the o matri, incorporates the information from all the higher-orer - an -FWs associate with the iscontinuit. This implies that the information on the overall ispersion euation in the cut-off region of higher-orer moes (Fig. 5b can be obtaine irectl from. Outsie of this region, a moel with more ports nees to recover the ispersion properties. S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4

2 Diagonaliation Diagonaliation of the o matri α E E E E ( ( ( ( = ( ( = (, (, (, tan ( ij ( ij = (,, Rotation matri cosα sinα R ( α = sinα cosα ( ( ( cosα sinα (, ; cosα sinα = ( ( ( sin cos (, ; sin cos α α α α E E E E Unwrappe angle r = 4.5 α u [egrees] f [GH] 3 X Γ.7 X S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 Eigenvalue construction properties of the eigenvalues ( ( ( (, ; cosα sinα cosα sinα ( = (, ; ( ( sin cos α α sin cos α α (, (, (, (, ; tan ( ( α = α = (, i j Since, in the absence of losses, are purel reactive in the cutoff region of higher-orer moes (Fig. 5b; this implies a real value of α for an wavenumber (also when / c <. R The limit an, implies α an. Thus, the an transmission line networs are ecouple. et = ( ( ( ( ( ( α ( ( sin =, S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 Decoupling of an T lines in the principal planes Valiit region of the single moe assumption in the κ iagram 3 Decoupling between the an ports also occurs when the irection of wave propagation is along an plane of geometrical smmetr of the. The planes of smmetr efine the contour of the irreucible Brillouin region (BR. As a conseuence, the ominant an moes are ecouple along the segments of the BR contour which converge in the origin. E φ E E E E / = c / c / c / = / E E S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4

3 Foster s reactance theorem. Properties of (no losses Respects the properties of the LC riving point impeance function ii s an eros lie on the real w ais, are simple an alternate. iii A pole or a ero must be at w=. iv The poles are smmetricall isplace w.r.t the origin. m p (, ; ( (, ; ( = R( α R( α (, ; ( ( p ( ( Re DPOLES Lp=.4nH Cp=.45pF Ls=.39nH Cs=.7pF SLOTS L=.35 nh C=.79 pf L= 4.5 nh C=.77 pf L w D L = cm, W =.5 cm D =.cm t=,5 cm D w t L L = cm, W =.5 cm D =.cm t=,5 cm s( =,f Freuenc (GH (f, ero ero 7.7GH 34.GH pole ero pole ero 3.9GH pole Lp Ls Cs Cp C C L L S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 f S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 ( ( ( ( (, p p(,.. j C (, (, (,.. (,, = Rational approimation of the eigenvalues ( ( ( ( i (, p p(,.. j L (, (, (,.. (,, = Step : full wave analsis for plane wave incience Step : atching of poles an eros using the properties of (, ; Difficulties:. niviuation of poles an eros. Sufficient number of pole an eros to have goo accurac 3. Reconstruction of the pole an ero epenence on the wavenumber S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 Phase of Γ (= Phase of Γ (=. Sufficient number of pole an eros to have a goo accurac pol e pol e mm mm mm mm ero h=.95 mm 5 5 (a ero To investigate the range =(, ma one shoul inclue the pole-ero pair internal to W an one more pair ero-pole, the closest to ma. -9 ero S. aci - Universit of Siena (b - ACE Short course on artificial surfaces- Chalmers Universit-4 3. Reconstruction of the pole an ero ispersion iagram s an eros in - plane = 4.3 r h =.9 cm p (, (, j = Ap B j Cp j pj = Dp E j Fp j ( -X; (X-; Γ (, (, j = A B j j C j j = D E j j F j p ( κ, κ = G H κ L κ j (- Γ ( κ, κ = G H κ L κ j =. cm W =.cm L =. cm =.cm ( p p ( (, ( (,,, = jc (, ( (, ( (, To have information on the ispersion iagram of pole an eros, we nee few constant S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4

4 3. Reconstruction of reflection coefficient phase 3. Reconstruction of the ispersion iagram, (,, E, (,, T E,,,, A / (, (,, E, E, cc,, E (,, = / CC ero 4 4 r =.,9 r =., S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 r =.,9 r =., CC ero i,, S. aci - Universit of Siena - ACE Short erocourse i on, artificial surfaces- Chalmers Universit-4 H Plane inc E Γ (, = Γ (, h r w = sin c l =.5mm =.54mm w=.35mm l=.39mm h=.75mm r =.,,,, 3. Reconstruction of the ispersion iagram A / (, (,, E, E, cc,, E (,, = / CC = 4 = 4 9 = 4 = = 9 = PC S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 r =.,9 r =., CC ero i,, S. aci - Universit of Siena - ACE Short erocourse i on, artificial surfaces- Chalmers Universit-4 Lea waves Printe ipoles LW LW r =.,9 mm 4 LW LW SW Light line Dielectric light line SW SW LW m( Re( 4 (bare slab (bare slab Μ 4 X Γ Γ or X Hbri moes or Γ S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4

5 Dipole tpe Dipole vs slot tpe r = S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4 S. aci - Universit of Siena - ACE Short course on artificial surfaces- Chalmers Universit-4

Chapter 2 Derivatives

Chapter 2 Derivatives Chapter Derivatives Section. An Intuitive Introuction to Derivatives Consier a function: Slope function: Derivative, f ' For each, the slope of f is the height of f ' Where f has a horizontal tangent line,

More information

Summary of the Class before Exam1

Summary of the Class before Exam1 uar o the lass beore Ea Builing a FEA Moel Ingreients o a FEA sotware pacage teps in builing a FEA oel Moeling consierations D pring/truss Eleents ingle D spring/truss eleent Global stiness atri; properties

More information

MEASUREMENT OF THE ANGLE φ 1 (β) AND B B MIXING (RECENT RESULTS FROM BaBar AND Belle) Kazuo Abe KEK, Tsukuba, Japan

MEASUREMENT OF THE ANGLE φ 1 (β) AND B B MIXING (RECENT RESULTS FROM BaBar AND Belle) Kazuo Abe KEK, Tsukuba, Japan Physics in Collision - Zeuthen, Germany, June 26-28, 23 MEASUREMENT OF THE ANGLE φ 1 (β) AND B B MIXING (RECENT RESULTS FROM BaBar AND Belle) Kazuo Abe KEK, Tsukuba, Japan 35-81 ABSTRACT Recent results

More information

Homework 7 Due 18 November at 6:00 pm

Homework 7 Due 18 November at 6:00 pm Homework 7 Due 18 November at 6:00 pm 1. Maxwell s Equations Quasi-statics o a An air core, N turn, cylinrical solenoi of length an raius a, carries a current I Io cos t. a. Using Ampere s Law, etermine

More information

Table of Common Derivatives By David Abraham

Table of Common Derivatives By David Abraham Prouct an Quotient Rules: Table of Common Derivatives By Davi Abraham [ f ( g( ] = [ f ( ] g( + f ( [ g( ] f ( = g( [ f ( ] g( g( f ( [ g( ] Trigonometric Functions: sin( = cos( cos( = sin( tan( = sec

More information

Symmetry and Group Theory

Symmetry and Group Theory 4 Smmetr and Group Theor 4 Smmetr and Group Theor 4 Smmetr and Group Theor 4 Smmetr and Group Theor Smmetr Operation and Smmetr Elements Smmetr Operation: A well-defined, non-translational moement of an

More information

Math 1720 Final Exam Review 1

Math 1720 Final Exam Review 1 Math 70 Final Eam Review Remember that you are require to evaluate this class by going to evaluate.unt.eu an filling out the survey before minight May 8. It will only take between 5 an 0 minutes, epening

More information

ECE Spring Prof. David R. Jackson ECE Dept. Notes 6

ECE Spring Prof. David R. Jackson ECE Dept. Notes 6 ECE 6341 Spring 2016 Prof. David R. Jackson ECE Dept. Notes 6 1 Leaky Modes v TM 1 Mode SW 1 v= utan u ε R 2 R kh 0 n1 r = ( ) 1 u Splitting point ISW f = f s f > f s We will examine the solutions as the

More information

Math 3A Midterm 1 Solutions

Math 3A Midterm 1 Solutions Math 3A Miterm Solutions Rea all of the following information before starting the exam: 0/0/00 Check your exam to make sure all pages are present. When you use a major theorem (like the inermeiate value

More information

18 EVEN MORE CALCULUS

18 EVEN MORE CALCULUS 8 EVEN MORE CALCULUS Chapter 8 Even More Calculus Objectives After stuing this chapter you shoul be able to ifferentiate an integrate basic trigonometric functions; unerstan how to calculate rates of change;

More information

Exercise 4 - Hydraulic Systems

Exercise 4 - Hydraulic Systems Exercise 4 - Hyraulic Systems 4.1 Hyraulic Systems Hyraulic systems are, in general, escribe by the Navier-Stokes equations as you might have learne in flui ynamics courses. In orer to simplify the moeling

More information

Separation of Variables

Separation of Variables Physics 342 Lecture 1 Separation of Variables Lecture 1 Physics 342 Quantum Mechanics I Monay, January 25th, 2010 There are three basic mathematical tools we nee, an then we can begin working on the physical

More information

Open Access An Exponential Reaching Law Sliding Mode Observer for PMSM in Rotating Frame

Open Access An Exponential Reaching Law Sliding Mode Observer for PMSM in Rotating Frame Sen Orers for Reprints to reprints@benthamscience.ae The Open Automation an Control Systems Journal, 25, 7, 599-66 599 Open Access An Exponential Reaching Law Sliing Moe Observer for PMSM in Rotating Frame

More information

fv = ikφ n (11.1) + fu n = y v n iσ iku n + gh n. (11.3) n

fv = ikφ n (11.1) + fu n = y v n iσ iku n + gh n. (11.3) n Chapter 11 Rossby waves Supplemental reaing: Pelosky 1 (1979), sections 3.1 3 11.1 Shallow water equations When consiering the general problem of linearize oscillations in a static, arbitrarily stratifie

More information

Ultra-thin Acoustic Metasurface-Based Schroeder Diffuser

Ultra-thin Acoustic Metasurface-Based Schroeder Diffuser Ultra-thin Acoustic Metasurface-Base Schroeer Diffuser Yifan Zhu, Xuong Fan, Bin Liang *, Jianchun Cheng *, an Yun Jing * Key Laboratory of Moern Acoustics, MOE, Institute of Acoustics, Department of Physics,

More information

Characterization of lead zirconate titanate piezoceramic using high frequency ultrasonic spectroscopy

Characterization of lead zirconate titanate piezoceramic using high frequency ultrasonic spectroscopy JOURNAL OF APPLIED PHYSICS VOLUME 85, NUMBER 1 15 JUNE 1999 Characterization of lea zirconate titanate piezoceramic using high frequency ultrasonic spectroscopy Haifeng Wang, Wenhua Jiang, a) an Wenwu

More information

AN INTRODUCTION TO AIRCRAFT WING FLUTTER Revision A

AN INTRODUCTION TO AIRCRAFT WING FLUTTER Revision A AN INTRODUCTION TO AIRCRAFT WIN FLUTTER Revision A By Tom Irvine Email: tomirvine@aol.com January 8, 000 Introuction Certain aircraft wings have experience violent oscillations uring high spee flight.

More information

Objective Mathematics

Objective Mathematics Chapter No - ( Area Bounded by Curves ). Normal at (, ) is given by : y y. f ( ) or f ( ). Area d ()() 7 Square units. Area (8)() 6 dy. ( ) d y c or f ( ) c f () c f ( ) As shown in figure, point P is

More information

Summary: Differentiation

Summary: Differentiation Techniques of Differentiation. Inverse Trigonometric functions The basic formulas (available in MF5 are: Summary: Differentiation ( sin ( cos The basic formula can be generalize as follows: Note: ( sin

More information

12 th Annual Johns Hopkins Math Tournament Saturday, February 19, 2011

12 th Annual Johns Hopkins Math Tournament Saturday, February 19, 2011 1 th Annual Johns Hopkins Math Tournament Saturay, February 19, 011 Geometry Subject Test 1. [105] Let D x,y enote the half-isk of raius 1 with its curve bounary externally tangent to the unit circle at

More information

Tutorial 1 Differentiation

Tutorial 1 Differentiation Tutorial 1 Differentiation What is Calculus? Calculus 微積分 Differential calculus Differentiation 微分 y lim 0 f f The relation of very small changes of ifferent quantities f f y y Integral calculus Integration

More information

A Quantitative Analysis of Coupling for a WPT System Including Dielectric/Magnetic Materials

A Quantitative Analysis of Coupling for a WPT System Including Dielectric/Magnetic Materials Progress In Electromagnetics Research Letters, Vol. 72, 127 134, 2018 A Quantitative Analysis of Coupling for a WPT System Incluing Dielectric/Magnetic Materials Yangjun Zhang *, Tatsuya Yoshiawa, an Taahiro

More information

arxiv:hep-ph/ v1 21 Jul 2000

arxiv:hep-ph/ v1 21 Jul 2000 ER/468/948 UR-169 arxiv:hep-ph/724v1 21 Jul 2 Abstract Electroweak Precision Physics at e + e Colliers with A. Denner 1, S. Dittmaier 2, M. Roth 3, an D. Wackeroth 4 1 Paul-Scherrer-Institut, CH-232 Villigen

More information

26.1 Metropolis method

26.1 Metropolis method CS880: Approximations Algorithms Scribe: Dave Anrzejewski Lecturer: Shuchi Chawla Topic: Metropolis metho, volume estimation Date: 4/26/07 The previous lecture iscusse they some of the key concepts of

More information

About the hand-in tasks. Vehicle Propulsion Systems Lecture 3. Outline. Energy System Overview. W2M Energy Paths. The Vehicle Motion Equation

About the hand-in tasks. Vehicle Propulsion Systems Lecture 3. Outline. Energy System Overview. W2M Energy Paths. The Vehicle Motion Equation About the han-in tasks Vehicle Propulsion Systems Lecture 3 Conventional Powertrains with Transmission Performance, Tools an Optimization Lars Eriksson Professor Vehicular Systems Linköping University

More information

Design A Robust Power System Stabilizer on SMIB Using Lyapunov Theory

Design A Robust Power System Stabilizer on SMIB Using Lyapunov Theory Design A Robust Power System Stabilizer on SMIB Using Lyapunov Theory Yin Li, Stuent Member, IEEE, Lingling Fan, Senior Member, IEEE Abstract This paper proposes a robust power system stabilizer (PSS)

More information

Dynamic Analysis of a Single MEMS Vibratory Gyroscope with Decoupling Connection between Driving Frame and Sensing Proof Mass

Dynamic Analysis of a Single MEMS Vibratory Gyroscope with Decoupling Connection between Driving Frame and Sensing Proof Mass International Journal of Applie Engineering Research ISSN 0973-456 Volume 3, Number 7 (08 pp. 5554-556 Dnamic Analsis of a Single MEMS Vibrator Groscope with Decoupling Connection between Driving Frame

More information

Harmonic Modelling of Thyristor Bridges using a Simplified Time Domain Method

Harmonic Modelling of Thyristor Bridges using a Simplified Time Domain Method 1 Harmonic Moelling of Thyristor Briges using a Simplifie Time Domain Metho P. W. Lehn, Senior Member IEEE, an G. Ebner Abstract The paper presents time omain methos for harmonic analysis of a 6-pulse

More information

A Comparison between a Conventional Power System Stabilizer (PSS) and Novel PSS Based on Feedback Linearization Technique

A Comparison between a Conventional Power System Stabilizer (PSS) and Novel PSS Based on Feedback Linearization Technique J. Basic. Appl. Sci. Res., ()9-99,, TextRoa Publication ISSN 9-434 Journal of Basic an Applie Scientific Research www.textroa.com A Comparison between a Conventional Power System Stabilizer (PSS) an Novel

More information

ABDELSHAFY, OTHMAN, OSHMARIN, AL-MUTAWA, CAPOLINO: EPD IN CTLS UC IRVINE, SEP 2018

ABDELSHAFY, OTHMAN, OSHMARIN, AL-MUTAWA, CAPOLINO: EPD IN CTLS UC IRVINE, SEP 2018 arxiv: [physics.app-ph] 13 SEP 2018 ABDELSHAFY, OTHMAN, OSHMARIN, AL-MUTAWA, CAPOLINO: EPD IN CTLS UC IRVINE, SEP 2018 Exceptional Points of Degeneracy in Perioically- Couple Waveguies an the Interplay

More information

ensembles When working with density operators, we can use this connection to define a generalized Bloch vector: v x Tr x, v y Tr y

ensembles When working with density operators, we can use this connection to define a generalized Bloch vector: v x Tr x, v y Tr y Ph195a lecture notes, 1/3/01 Density operators for spin- 1 ensembles So far in our iscussion of spin- 1 systems, we have restricte our attention to the case of pure states an Hamiltonian evolution. Toay

More information

MAT 111 Practice Test 2

MAT 111 Practice Test 2 MAT 111 Practice Test 2 Solutions Spring 2010 1 1. 10 points) Fin the equation of the tangent line to 2 + 2y = 1+ 2 y 2 at the point 1, 1). The equation is y y 0 = y 0) So all we nee is y/. Differentiating

More information

Space-time Linear Dispersion Using Coordinate Interleaving

Space-time Linear Dispersion Using Coordinate Interleaving Space-time Linear Dispersion Using Coorinate Interleaving Jinsong Wu an Steven D Blostein Department of Electrical an Computer Engineering Queen s University, Kingston, Ontario, Canaa, K7L3N6 Email: wujs@ieeeorg

More information

Chapter 4. Electrostatics of Macroscopic Media

Chapter 4. Electrostatics of Macroscopic Media Chapter 4. Electrostatics of Macroscopic Meia 4.1 Multipole Expansion Approximate potentials at large istances 3 x' x' (x') x x' x x Fig 4.1 We consier the potential in the far-fiel region (see Fig. 4.1

More information

Math Implicit Differentiation. We have discovered (and proved) formulas for finding derivatives of functions like

Math Implicit Differentiation. We have discovered (and proved) formulas for finding derivatives of functions like Math 400 3.5 Implicit Differentiation Name We have iscovere (an prove) formulas for fining erivatives of functions like f x x 3x 4x. 3 This amounts to fining y for 3 y x 3x 4x. Notice that in this case,

More information

Linear and quadratic approximation

Linear and quadratic approximation Linear an quaratic approximation November 11, 2013 Definition: Suppose f is a function that is ifferentiable on an interval I containing the point a. The linear approximation to f at a is the linear function

More information

ME 101: Engineering Mechanics

ME 101: Engineering Mechanics ME 0: Engineering Mechanics Rajib Kumar Bhattacharja Department of Civil Engineering ndian nstitute of Technolog Guwahati M Block : Room No 005 : Tel: 8 www.iitg.ernet.in/rkbc Area Moments of nertia Parallel

More information

Quantum Mechanics in Three Dimensions

Quantum Mechanics in Three Dimensions Physics 342 Lecture 20 Quantum Mechanics in Three Dimensions Lecture 20 Physics 342 Quantum Mechanics I Monay, March 24th, 2008 We begin our spherical solutions with the simplest possible case zero potential.

More information

With the Chain Rule. y x 2 1. and. with respect to second axle. dy du du dx. Rate of change of first axle. with respect to third axle

With the Chain Rule. y x 2 1. and. with respect to second axle. dy du du dx. Rate of change of first axle. with respect to third axle 0 CHAPTER Differentiation Section The Chain Rule Fin the erivative of a composite function using the Chain Rule Fin the erivative of a function using the General Power Rule Simplif the erivative of a function

More information

System Modeling of MEMS Gyroscopes

System Modeling of MEMS Gyroscopes Proceeings of the 5th Meiterranean Conference on Control & Automation, Jul 7-9, 7, Athens - Greece T-7 Sstem Moeling of MEMS Groscopes Ramar Rashe an H. Momeni* * Tarbiat Moares Universit, Facult of Engineering,

More information

Shape functions in 1D

Shape functions in 1D MAE 44 & CIV 44 Introuction to Finite Elements Reaing assignment: ecture notes, ogan.,. Summary: Prof. Suvranu De Shape functions in D inear shape functions in D Quaratic an higher orer shape functions

More information

Implicit Differentiation

Implicit Differentiation Implicit Differentiation Thus far, the functions we have been concerne with have been efine explicitly. A function is efine explicitly if the output is given irectly in terms of the input. For instance,

More information

Outcome of this lecture

Outcome of this lecture Outcome of this lecture At the en of this lecture you will be able to: List the ifferent parts of a synchronous machine Explain the operation principles of the machine Use the equivalent circuit moel of

More information

Optimization of Geometries by Energy Minimization

Optimization of Geometries by Energy Minimization Optimization of Geometries by Energy Minimization by Tracy P. Hamilton Department of Chemistry University of Alabama at Birmingham Birmingham, AL 3594-140 hamilton@uab.eu Copyright Tracy P. Hamilton, 1997.

More information

19 Eigenvalues, Eigenvectors, Ordinary Differential Equations, and Control

19 Eigenvalues, Eigenvectors, Ordinary Differential Equations, and Control 19 Eigenvalues, Eigenvectors, Orinary Differential Equations, an Control This section introuces eigenvalues an eigenvectors of a matrix, an iscusses the role of the eigenvalues in etermining the behavior

More information

Transactions on Engineering Sciences vol 5, 1994 WIT Press, ISSN

Transactions on Engineering Sciences vol 5, 1994 WIT Press,   ISSN Generalize heat conuction transfer functions in two imensional linear systems of assigne geometry F. Marcotullio & A. Ponticiello Dipartimento i Energetica- Universit i L 'Aquila Monteluco i Roio - 67100

More information

IPMSM Inductances Calculation Using FEA

IPMSM Inductances Calculation Using FEA X International Symposium on Inustrial Electronics INDEL 24, Banja Luka, November 68, 24 IPMSM Inuctances Calculation Using FEA Dejan G. Jerkan, Marko A. Gecić an Darko P. Marčetić Department for Power,

More information

An inductance lookup table application for analysis of reluctance stepper motor model

An inductance lookup table application for analysis of reluctance stepper motor model ARCHIVES OF ELECTRICAL ENGINEERING VOL. 60(), pp. 5- (0) DOI 0.478/ v07-0-000-y An inuctance lookup table application for analysis of reluctance stepper motor moel JAKUB BERNAT, JAKUB KOŁOTA, SŁAWOMIR

More information

CALCULATION OF 2D-THERMOMAGNETIC CURRENT AND ITS FLUCTUATIONS USING THE METHOD OF EFFECTIVE HAMILTONIAN. R. G. Aghayeva

CALCULATION OF 2D-THERMOMAGNETIC CURRENT AND ITS FLUCTUATIONS USING THE METHOD OF EFFECTIVE HAMILTONIAN. R. G. Aghayeva CALCULATION OF D-THERMOMAGNETIC CURRENT AND ITS FLUCTUATIONS USING THE METHOD OF EFFECTIVE HAMILTONIAN H. M. Abullaev Institute of Phsics, National Acaem of Sciences of Azerbaijan, H. Javi ave. 33, Baku,

More information

Computed Tomography Notes, Part 1. The equation that governs the image intensity in projection imaging is:

Computed Tomography Notes, Part 1. The equation that governs the image intensity in projection imaging is: Noll 6 CT Notes : Page Compute Tomograph Notes Part Challenges with Projection X-ra Sstems The equation that governs the image intensit in projection imaging is: z I I ep μ z Projection -ra sstems are

More information

12.11 Laplace s Equation in Cylindrical and

12.11 Laplace s Equation in Cylindrical and SEC. 2. Laplace s Equation in Cylinrical an Spherical Coorinates. Potential 593 2. Laplace s Equation in Cylinrical an Spherical Coorinates. Potential One of the most important PDEs in physics an engineering

More information

The derivative of a constant function is 0. That is,

The derivative of a constant function is 0. That is, NOTES 3: DIFFERENTIATION RULES Name: Date: Perio: LESSON 3. DERIVATIVE OF POLYNOMIALS AND EXPONENTIAL FUNCTIONS Eample : Prove f ( ) 6 is not ifferentiable at 4. Practice Problems: Fin f '( ) using the

More information

SYNCHRONOUS SEQUENTIAL CIRCUITS

SYNCHRONOUS SEQUENTIAL CIRCUITS CHAPTER SYNCHRONOUS SEUENTIAL CIRCUITS Registers an counters, two very common synchronous sequential circuits, are introuce in this chapter. Register is a igital circuit for storing information. Contents

More information

Consider for simplicity a 3rd-order IIR filter with a transfer function. where

Consider for simplicity a 3rd-order IIR filter with a transfer function. where Basic IIR Digital Filter The causal IIR igital filters we are concerne with in this course are characterie by a real rational transfer function of or, equivalently by a constant coefficient ifference equation

More information

Negative Refraction by a Multilayered Mushroom-type Metamaterial

Negative Refraction by a Multilayered Mushroom-type Metamaterial 29 IEEE AP-S International Smposium June 5, 29, Charleston, South Carolina Negative Refraction b a Multilaered Mushroom-tpe Metamaterial Mário G. Silveirinha, Department of Electrical Engineering, Universit

More information

www.onlineeamhelp.com www.onlineeamhelp.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June question paper for the guidance of teachers FURTHER MATHEMATICS

More information

Basic IIR Digital Filter Structures

Basic IIR Digital Filter Structures Basic IIR Digital Filter Structures The causal IIR igital filters we are concerne with in this course are characterie by a real rational transfer function of or, equivalently by a constant coefficient

More information

Exam 2 Review Solutions

Exam 2 Review Solutions Exam Review Solutions 1. True or False, an explain: (a) There exists a function f with continuous secon partial erivatives such that f x (x, y) = x + y f y = x y False. If the function has continuous secon

More information

Do not open your test until instructed to do so!

Do not open your test until instructed to do so! Fifth Annual Columbus State Calculus Contest-Precalculus Test Sponsored by The Columbus State University Department of Mathematics April 1 th, 017 ************************* The Columbus State University

More information

The derivative of a constant function is 0. That is,

The derivative of a constant function is 0. That is, NOTES : DIFFERENTIATION RULES Name: LESSON. DERIVATIVE OF POLYNOMIALS AND EXPONENTIAL FUNCTIONS Date: Perio: Mrs. Nguyen s Initial: Eample : Prove f ( ) 4 is not ifferentiable at. Practice Problems: Fin

More information

XI. Influence of Terrain and Vegetation

XI. Influence of Terrain and Vegetation XI. Influence of Terrain and Vegetation Terrain Diffraction over bare, wedge shaped hills Diffraction of wedge shaped hills with houses Diffraction over rounded hills with houses Vegetation Effective propagation

More information

Optimal LQR Control of Structures using Linear Modal Model

Optimal LQR Control of Structures using Linear Modal Model Optimal LQR Control of Structures using Linear Moal Moel I. Halperin,2, G. Agranovich an Y. Ribakov 2 Department of Electrical an Electronics Engineering 2 Department of Civil Engineering Faculty of Engineering,

More information

Quantum mechanical approaches to the virial

Quantum mechanical approaches to the virial Quantum mechanical approaches to the virial S.LeBohec Department of Physics an Astronomy, University of Utah, Salt Lae City, UT 84112, USA Date: June 30 th 2015 In this note, we approach the virial from

More information

Implementation of Finite Difference Frequency Domain

Implementation of Finite Difference Frequency Domain Instructor Dr. Ramon Rumpf (915) 747 6958 rcrumpf@utep.eu EE 5337 Computational Electromagnetics (CEM) Lecture #14 Implementation of Finite Difference Frequenc Domain Lecture 14 These notes ma contain

More information

TMA 4195 Matematisk modellering Exam Tuesday December 16, :00 13:00 Problems and solution with additional comments

TMA 4195 Matematisk modellering Exam Tuesday December 16, :00 13:00 Problems and solution with additional comments Problem F U L W D g m 3 2 s 2 0 0 0 0 2 kg 0 0 0 0 0 0 Table : Dimension matrix TMA 495 Matematisk moellering Exam Tuesay December 6, 2008 09:00 3:00 Problems an solution with aitional comments The necessary

More information

The Chain Rule. y x 2 1 y sin x. and. Rate of change of first axle. with respect to second axle. dy du. du dx. Rate of change of first axle

The Chain Rule. y x 2 1 y sin x. and. Rate of change of first axle. with respect to second axle. dy du. du dx. Rate of change of first axle . The Chain Rule 9. The Chain Rule Fin the erivative of a composite function using the Chain Rule. Fin the erivative of a function using the General Power Rule. Simplif the erivative of a function using

More information

Article Coupling Mechanism Analysis and Fabrication of Triaxial Gyroscopes in Monolithic MIMU

Article Coupling Mechanism Analysis and Fabrication of Triaxial Gyroscopes in Monolithic MIMU Article Coupling Mechanism Analsis an Fabrication of Triaial Groscopes in Monolithic MIMU Dunhu Xia * an Lei Xu Ke Laborator of Micro-Inertial Instrument an Avance Navigation Technolog, Ministr of Eucation,

More information

SELF-ERECTING, ROTARY MOTION INVERTED PENDULUM Quanser Consulting Inc.

SELF-ERECTING, ROTARY MOTION INVERTED PENDULUM Quanser Consulting Inc. SELF-ERECTING, ROTARY MOTION INVERTED PENDULUM Quanser Consulting Inc. 1.0 SYSTEM DESCRIPTION The sel-erecting rotary motion inverte penulum consists of a rotary servo motor system (SRV-02) which rives

More information

Optical wire-grid polarizers at oblique angles of incidence

Optical wire-grid polarizers at oblique angles of incidence JOURNAL OF APPLIED PHYSICS VOLUME 93, NUMBER 8 15 APRIL 003 Optical wire-gri polarizers at oblique angles of incience X. J. Yu an H. S. Kwok a) Center for Display Research, Department of Electrical an

More information

1 Introuction In the past few years there has been renewe interest in the nerson impurity moel. This moel was originally propose by nerson [2], for a

1 Introuction In the past few years there has been renewe interest in the nerson impurity moel. This moel was originally propose by nerson [2], for a Theory of the nerson impurity moel: The Schrieer{Wol transformation re{examine Stefan K. Kehrein 1 an nreas Mielke 2 Institut fur Theoretische Physik, uprecht{karls{universitat, D{69120 Heielberg, F..

More information

SUCCEEDING IN THE VCE 2017 UNIT 3 SPECIALIST MATHEMATICS STUDENT SOLUTIONS

SUCCEEDING IN THE VCE 2017 UNIT 3 SPECIALIST MATHEMATICS STUDENT SOLUTIONS SUCCEEDING IN THE VCE 07 UNIT SPECIALIST MATHEMATICS STUDENT SOLUTIONS FOR ERRORS AND UPDATES, PLEASE VISIT WWW.TSFX.COM.AU/VCE-UPDATES QUESTION (a) 0 0 0 9 (b) 7 0 0 0 0 0 i The School For Ecellence 07

More information

Optimal design and modeling of tactile resistive and capacitive sensors interfaces used in modern mechatronics

Optimal design and modeling of tactile resistive and capacitive sensors interfaces used in modern mechatronics ROMANIAN JOURNAL OF INFORMATION SCIENCE AND TECHNOLOGY Volume 20, Number 4, 2017, 400 414 Optimal esign an moeling of tactile resistive an capacitive sensors interfaces use in moern mechatronics Anghel

More information

13 Definite integrals

13 Definite integrals 3 Definite integrals Read: Boas h. 4. 3. Laurent series: Def.: Laurent series (LS). If f() is analytic in a region R, then converges in R, with a n = πi f() = a n ( ) n + n= n= f() ; b ( ) n+ n = πi b

More information

10.7. DIFFERENTIATION 7 (Inverse hyperbolic functions) A.J.Hobson

10.7. DIFFERENTIATION 7 (Inverse hyperbolic functions) A.J.Hobson JUST THE MATHS SLIDES NUMBER 0.7 DIFFERENTIATION 7 (Inverse hyperbolic functions) by A.J.Hobson 0.7. Summary of results 0.7.2 The erivative of an inverse hyperbolic sine 0.7.3 The erivative of an inverse

More information

Core Mathematics C3 Advanced Level

Core Mathematics C3 Advanced Level Paper Reference(s) 666/0 Edecel GCE Core Mathematics C Advanced Level Wednesda 0 Januar 00 Afternoon Time: hour 0 minutes Materials required for eamination Mathematical Formulae (Pink or Green) Items included

More information

LQG FLUTTER CONTROL OF WIND TUNNEL MODEL USING PIEZO-CERAMIC ACTUATOR

LQG FLUTTER CONTROL OF WIND TUNNEL MODEL USING PIEZO-CERAMIC ACTUATOR 5 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES LQG FLUTTER CONTROL OF WIND TUNNEL MODEL USING PIEZO-CERAMIC ACTUATOR Tatsunori Kaneko* an Yasuto Asano* * Department of Mechanical Engineering,

More information

AQA Core 3 Revision booklet

AQA Core 3 Revision booklet AQA Core Revision booklet Name:... Tutor group:... AQA - Core Ke ates Core eam: 0 th June 0 am Term ates: Term : Mona September 0 Fria 5 October 0 Term : Mona Februar 0 Fria April 0 Term : Mona November

More information

Robust discrete time control Design of robust discrete time controllers

Robust discrete time control Design of robust discrete time controllers obust iscrete time control Design of robust iscrete time controllers I.D.Lanau course on robust iscrete time control, part II Outline ole placement tracking an regulation Tracking an regulation with inepenent

More information

ECE 422 Power System Operations & Planning 7 Transient Stability

ECE 422 Power System Operations & Planning 7 Transient Stability ECE 4 Power System Operations & Planning 7 Transient Stability Spring 5 Instructor: Kai Sun References Saaat s Chapter.5 ~. EPRI Tutorial s Chapter 7 Kunur s Chapter 3 Transient Stability The ability of

More information

Design of all-pole microwave filters. Giuseppe Macchiarella Polytechnic of Milan, Italy Electronic and Information Department

Design of all-pole microwave filters. Giuseppe Macchiarella Polytechnic of Milan, Italy Electronic and Information Department Design of all-pole microwave filters Giuseppe Macchiarella Polytechnic of Milan, Italy Electronic and Information Department In-line filters with all-equal resonators R L eq, f L eq, f L eq, f L eq, f

More information

arxiv: v3 [quant-ph] 25 Sep 2012

arxiv: v3 [quant-ph] 25 Sep 2012 Three-Level Laser Dynamics with the Atoms Pumpe by Electron Bombarment arxiv:115.1438v3 [quant-ph] 25 Sep 212 Fesseha Kassahun Department of Physics, Ais Ababa University, P. O. Box 33761, Ais Ababa, Ethiopia

More information

THE ACCURATE ELEMENT METHOD: A NEW PARADIGM FOR NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

THE ACCURATE ELEMENT METHOD: A NEW PARADIGM FOR NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS THE PUBISHING HOUSE PROCEEDINGS O THE ROMANIAN ACADEMY, Series A, O THE ROMANIAN ACADEMY Volume, Number /, pp. 6 THE ACCURATE EEMENT METHOD: A NEW PARADIGM OR NUMERICA SOUTION O ORDINARY DIERENTIA EQUATIONS

More information

CE 579: STRUCTRAL STABILITY AND DESIGN

CE 579: STRUCTRAL STABILITY AND DESIGN 8/5/4 CE 579: STRUCTRA STABIITY AND DESIGN Amit H. Varma rofessor School of Civil Engineering urue Universit h. No. (765) 496 349 Email: ahvarma@purue.eu Chapter. Introuction to Structural Stabilit OUTINE

More information

State Space Analysis of Power System Stability Enhancement with Used the STATCOM

State Space Analysis of Power System Stability Enhancement with Used the STATCOM tate pace Analysis of Power ystem tability Enhancement with Use the ACOM M. Mahavian () - G. hahgholian () () Department of Electrical Engineering, Islamic Aza University, Naein Branch, Esfahan, Iran ()

More information

Simple Relations between a Uniaxial Medium and an Isotropic Medium

Simple Relations between a Uniaxial Medium and an Isotropic Medium Progress In Electromagnetics Research B, Vol. 6, 79 93, 214 Simple Relations between a Uniaial Meium an an Isotropic Meium Saffet G. Şen * Abstract In this article, in a simple wa, simple relations are

More information

Homework 2 Solutions EM, Mixture Models, PCA, Dualitys

Homework 2 Solutions EM, Mixture Models, PCA, Dualitys Homewor Solutions EM, Mixture Moels, PCA, Dualitys CMU 0-75: Machine Learning Fall 05 http://www.cs.cmu.eu/~bapoczos/classes/ml075_05fall/ OUT: Oct 5, 05 DUE: Oct 9, 05, 0:0 AM An EM algorithm for a Mixture

More information

GATE PHYSICS-PH 2019 SECTION : GENERAL APTITUDE

GATE PHYSICS-PH 2019 SECTION : GENERAL APTITUDE 1 GAT PHYSICS-PH 19 SCTION : GNRAL APTITUD 1. The fishermen, the floo victims owe lives, were reware by the government. whom to which to whom that. Until Iran came along, Inia ha never been in kabai. efeate

More information

arxiv: v2 [cond-mat.stat-mech] 30 Aug 2010

arxiv: v2 [cond-mat.stat-mech] 30 Aug 2010 Experimental Examination of the Effect of Short ay Trajectories in Two-port Wave-Chaotic Scattering Systems arxiv:16.34v2 [con-mat.stat-mech 3 Aug 21 Jen-HaoYeh 1, JamesA. Hart 1,2, ElliottBrashaw 2, ThomasM.

More information

Capacity Analysis of MIMO Systems with Unknown Channel State Information

Capacity Analysis of MIMO Systems with Unknown Channel State Information Capacity Analysis of MIMO Systems with Unknown Channel State Information Jun Zheng an Bhaskar D. Rao Dept. of Electrical an Computer Engineering University of California at San Diego e-mail: juzheng@ucs.eu,

More information

Math 2163, Practice Exam II, Solution

Math 2163, Practice Exam II, Solution Math 63, Practice Exam II, Solution. (a) f =< f s, f t >=< s e t, s e t >, an v v = , so D v f(, ) =< ()e, e > =< 4, 4 > = 4. (b) f =< xy 3, 3x y 4y 3 > an v =< cos π, sin π >=, so

More information

Theorem (Change of Variables Theorem):

Theorem (Change of Variables Theorem): Avance Higher Notes (Unit ) Prereqisites: Integrating (a + b) n, sin (a + b) an cos (a + b); erivatives of tan, sec, cosec, cot, e an ln ; sm/ifference rles; areas ner an between crves. Maths Applications:

More information

Stopband Prediction with Dispersion Diagram for Electromagnetic Bandgap Structures in Printed Circuit Boards

Stopband Prediction with Dispersion Diagram for Electromagnetic Bandgap Structures in Printed Circuit Boards Stopband Prediction with Dispersion Diagram for Electromagnetic Bandgap Structures in Printed Circuit Boards Yoshitaka Toota Department of Communication Network Engineering kaama Universit kaama 7 53 Japan

More information

ECE 451 Advanced Microwave Measurements. TL Characterization

ECE 451 Advanced Microwave Measurements. TL Characterization ECE 451 Advanced Microwave Measurements TL Characterization Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jesa@illinois.edu ECE 451 Jose Schutt-Aine 1 Maxwell s Equations

More information

A Path Planning Method Using Cubic Spiral with Curvature Constraint

A Path Planning Method Using Cubic Spiral with Curvature Constraint A Path Planning Metho Using Cubic Spiral with Curvature Constraint Tzu-Chen Liang an Jing-Sin Liu Institute of Information Science 0, Acaemia Sinica, Nankang, Taipei 5, Taiwan, R.O.C., Email: hartree@iis.sinica.eu.tw

More information

VIBRATION CONTROL AND FULL-SCALE MEASUREMENT OF A STEEL TV TOWER WITH A DAMPER DEVICE OF PTTMD

VIBRATION CONTROL AND FULL-SCALE MEASUREMENT OF A STEEL TV TOWER WITH A DAMPER DEVICE OF PTTMD 13 th Worl Conference on Earthquake Engineering Vancouver, B.C., Canaa August 1-6, 24 Paper No. 1439 VIBRATION CONTROL AND FULL-SCALE MEASUREMENT OF A STEEL TV TOWER WITH A DAMPER DEVICE OF PTTMD Renle

More information

Entanglement is not very useful for estimating multiple phases

Entanglement is not very useful for estimating multiple phases PHYSICAL REVIEW A 70, 032310 (2004) Entanglement is not very useful for estimating multiple phases Manuel A. Ballester* Department of Mathematics, University of Utrecht, Box 80010, 3508 TA Utrecht, The

More information

Ogive Nose Cones. David Stribling NAR Sr

Ogive Nose Cones. David Stribling NAR Sr Ogive Nose ones Davi Stribling NA 80 Sr The ogive nose cone is probably one of the most common shapes use in moel rocketry. It exhibits very goo rag characteristics for general moel rocketry use. If you

More information

Further Differentiation and Applications

Further Differentiation and Applications Avance Higher Notes (Unit ) Prerequisites: Inverse function property; prouct, quotient an chain rules; inflexion points. Maths Applications: Concavity; ifferentiability. Real-Worl Applications: Particle

More information

Chapter 6. Additional Topics in Trigonometry. 6.6 Vectors. Copyright 2014, 2010, 2007 Pearson Education, Inc.

Chapter 6. Additional Topics in Trigonometry. 6.6 Vectors. Copyright 2014, 2010, 2007 Pearson Education, Inc. Chapter 6 Additional Topics in Trigonometry 6.6 Vectors Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Obectives: Use magnitude and direction to show vectors are equal. Visualize scalar multiplication,

More information

This section outlines the methodology used to calculate the wave load and wave wind load values.

This section outlines the methodology used to calculate the wave load and wave wind load values. COMPUTERS AND STRUCTURES, INC., JUNE 2014 AUTOMATIC WAVE LOADS TECHNICAL NOTE CALCULATION O WAVE LOAD VALUES This section outlines the methoology use to calculate the wave loa an wave win loa values. Overview

More information