Appendices on the Accompanying CD

Size: px
Start display at page:

Download "Appendices on the Accompanying CD"

Transcription

1 APPENDIX 4B Andis n th Amanyg CD TANSFE FUNCTIONS IN CONTINUOUS CONDUCTION MODE (CCM In this st, w will driv th transfr funt v / d fr th thr nvrtrs ratg CCM 4B- Buk Cnvrtrs Frm Fig. 4-7, th small signal diagram fr a Buk nvrtr is shwn Fig. 4B-. Dfg th utut stag imdan s as th aralll mbat f th filtr aaitr and th lad rsistan, s r ( sc = = ( r s( r C sc (4B- In any ratial nvrtr, r, and thrfr, r. Makg us f this assumt Eq. 4B-, s (4B- sc s d sc r v Fig. 4B- Equivalnt iruit f avrag buk nvrtr. Dfg ff as th sum f th filtr dutr imdan s and th utut stag imdan s, s ff = r C s s C C (4B-3 Thrfr, th Fig. 4B- by vltag divis Andis CD 4-

2 v s = = d ff r C s s C C (4B-4 4B- Bst Cnvrtr Frm Fig. 4-7, th small signal diagram f a Bst nvrtr is shwn Fig. 4B-a. In this iruit, th d stady stat ratg t valus an b alulatd as fllws: I = (4B-5 Equatg th ut and th utut wr, I = I (4B-6 Substitutg Eq. 4B-5 t Eq. 4B-6, I = I I = = (4B-7 In Fig. 4B-a, th sub-iruit lft f th markd trmals an b rlad by its Nrtn quivalnt, as shwn Fig. Fig. 4B-b. Th sub-iruit lft f th transfrmr FIg. 4B-b an b transfrmd t th right, as shwn Fig. 4B-, whr = ( D s (4B-8 d di s v : D (a Andis CD 4-

3 d s s di v : D s (b s ( D d ( D s di s v ( s d ( D s s v (d Fig. 4B- Equivalnt iruit f avrag bst nvrtr. Th tw urrnt surs Fig. 4B- an b mbd and usg th Thvn s quivalnt, th quivalnt vltag Fig. 4B-d is v q s = d ( D (4B-9 Usg th quivalnt vltag Eq. 4B-9 and alyg th vltag divis th iruit f Fig. 4B-d, v s = d ( D r C s s C C (4B-0 4B-3 Buk-Bst Cnvrtr Frm Fig. 4-7, th small signal diagram f a Buk-Bst nvrtr is shwn Fig. 4B- 3a. First, w will alulat th valus f th ndd quantitis at th d stady stat ratg t. Andis CD 4-3

4 In a Buk-Bst nvrtr, I = (4B- D = (4B- D Equatg th ut and th utut wr, I and hn, I = I (4B-3 = (4B-4 S, I = I I, I = D ( D (4B-5 Cnsidrg th sub-iruit t th lft f th markd trmals Fig. 4B-3a and drawn Fig. 4B-3b, whr, i i = i (4B-6 = Di (4B-7 Eqs. 4B-6 and 4B-7 ar valid gnral nly if i = i = 0. Thrfr Fig. 4B-3b, v = d (4B-8 ( D Shrtg th trmals as shwn Fig. 4B-3, s In Fig. 4B-3, = = ( (4B-9 i i Di D i i = d (4B-0 ( D s Substitutg Eq. 4B-0 t Eq. 4B-9, d s s = (4B- i Andis CD 4-4

5 Frm Figs. 4B-3b and 4B-3, and Eqs. 4B-8 and 4B-, th Thvn imdan t th lft f th markd trmals Fig. 4B-3a is v Th = = s whr, (4B- is = ( D (4B-3 v Th = d (4B-4 ( D s d ( di v :D ut (a i i Dv d D s v : D (b i i s d D i s :D ( Fig. 4B-3 Equivalnt iruit f avrag buk-bst nvrtr. Andis CD 4-5

6 With this Thvn quivalnt, th iruit f Fig. 4B-3a, an b drawn as shwn Fig. 4B-4a. s d ( D di s v Fig. 4B-4a Equivalnt iruit f avrag buk-bst nvrtr (ntd. Th sub-iruit t th lft f th markd trmals an b rrsntd by its Nrtn quivalnt, as shwn Fig. 4B-4b. s d s di v s Fig. 4B-4b Equivalnt iruit f avrag buk-bst nvrtr (ntd. Cmbg th urrnt surs and rrsntg th sub-iruit Fig. 4B-4b by its Thvn quivalnt as shwn Fig. 4B-4, ( D (4B-5 vq = d sd s d sd ( D s v Fig. 4B-4 Equivalnt iruit f avrag buk-bst nvrtr (ntd. Hn, v sd d = ( D r C s s C C (4B-6 Andis CD 4-6

7 APPENDIX 4C DEIATION OF PAAMETES OF THE CONTOE TANSFE FUNCTIONS 4C- CONTOE TANSFE FUNCTION WITH ONE POE-EO PAI Th ntrllr transfr funt givn blw nsists f a l at th rig and a lr air t rvid has bst k s / G ( s = s s/ (4C-a T analy this transfr funt, th l at th rig an b mittd s w knw that 0 it trdus a has f 90, by dfg anthr transfr funt as fllws: ' s / G( s = k s / (4C-b whr φ = G ( s = tan tan (4C- ' 4C-- Frquny at whih φ bst Ours Th maximum angl φ bst rvidd by th ntrllr urs at th gmtri man f th r and l frqunis, as shwn blw. (This gmtri man frquny is mad t id with = whr is th rss vr frquny. T fd th frquny at whih φ bst urs, w will st th drivativ f th has angl t r: Thrfr, r, d 0 d φ = = Frm Eq. 4C-5, = 0 ( ( ( ( (4C-3 (4C-4 = 0 (4C-5 = (4C-6 Andis CD 4-7

8 whih shws that th has angl f th ntrllr transfr funt rahs its maximum at th gmtri-man frquny. 4C-- Drivg th r and Pl Frqunis Substitutg Eq. 4C-6 t Eq. 4C-, r, φ φ bst = tan tan (4C-7 bst = tan tan (4C-8 Nt that tan x = t x and π tan y t y =. Thrfr, Eq. 4C-8 φ π π bst = tan tan = tan (4C-9 W will df an trmdiat variabl, alld th K-fatr, as K bst = (4C-0 Slvg Eqs. 4C-9 and 4C-0 r, K bst K bst φbst π = tan 4 φbst = tan 45 (4C- (4C- 4C-- alig th Cntrllr Transfr Funt with a Sgl O-Am Th ntrllr transfr funt Eq. 4C- an b ralid by a sgl -am iruit as shwn blw. Andis CD 4-8

9 C * ( v v C v Figur 4-C Cntrllr imlmntat f G ( s, usg Eq. 4-C(a, by an -am. In Fig. 4C-, btag th ut-utut rlatshi and marg it with th transfr funt f Eq. 4C-, C k = = = C ( C C C CC (4C-3 Frm Eq. 4C-3, trms f C = C = C / = /( C (4C-4 ( k 4C- CONTOE TANSFE FUNCTION WITH TWO POE-EO PAIS Th ntrllr transfr funt givn blw nsists f a l at th rig and tw lr airs t rvid has bst k G ( s = s ( s / ( s / (4C-5 T analy this transfr funt, th l at th rig an b mittd s w knw that 0 it trdus a has f 90, by dfg anthr transfr funt as fllws: G ( s = k ' ( s / ( s / (4C-6 whr φ = G ( s = tan tan (4C-7 ' A drivat similar t st 4C- shws that th has aks at a frquny f that is th gmtri man f th l and r frqunis, similar t that st 4C-: Andis CD 4-9

10 = (4C-8 Nxt, w will us th trignmtri idntity that x y tan x tan y tan = xy (4C-9 and frm Eqs. 4C-7 and 4C-8, at frquny, th has bst is φ bst = G ( s = tan ' (4C-0 φ ( bst tan = (4C- Dfg K bst as K f bst = (4C- f and usg Eqs. 4C-0 and 4C-, 0 K bst = tan 45 φ 4 bst (4C-3 Th ntrllr transfr funt Eq. 4C-5 an b ralid by a sgl -am iruit as shwn blw. C 3 C 3 C ( v rr v Figur 4-C Cntrllr imlmntat f G ( s, usg Eq. 4-C5, by an -am. In Fig. 4C-, btag th ut-utut rlatshi and marg it with th transfr funt f Eq. 4C-5, trms f Andis CD 4-0

11 C = /( k C ( / = C = /( C = /( / C = /( (4C-4 Andis CD 4-

Lecture 26: Quadrature (90º) Hybrid.

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

More information

Even/Odd Mode Analysis of the Wilkinson Divider

Even/Odd Mode Analysis of the Wilkinson Divider //9 Wilkinn Dividr Evn and Odd Md Analyi.dc / Evn/Odd Md Analyi f th Wilkinn Dividr Cnidr a matchd Wilkinn pwr dividr, with a urc at prt : Prt Prt Prt T implify thi chmatic, w rmv th grund plan, which

More information

Chapter 2 Linear Waveshaping: High-pass Circuits

Chapter 2 Linear Waveshaping: High-pass Circuits Puls and Digital Circuits nkata Ra K., Rama Sudha K. and Manmadha Ra G. Chaptr 2 Linar Wavshaping: High-pass Circuits. A ramp shwn in Fig.2p. is applid t a high-pass circuit. Draw t scal th utput wavfrm

More information

Outline. Heat Exchangers. Heat Exchangers. Compact Heat Exchangers. Compact Heat Exchangers II. Heat Exchangers April 18, ME 375 Heat Transfer 1

Outline. Heat Exchangers. Heat Exchangers. Compact Heat Exchangers. Compact Heat Exchangers II. Heat Exchangers April 18, ME 375 Heat Transfer 1 Hat Exangr April 8, 007 Hat Exangr Larry artt Manial Engrg 375 Hat ranfr April 8, 007 Outl Bai ida f at xangr Ovrall at tranfr ffiint Lg-man tmpratur diffrn mtd Efftivn NU mtd ratial nidratin Hat Exangr

More information

Allowable bearing capacity and settlement Vertical stress increase in soil

Allowable bearing capacity and settlement Vertical stress increase in soil 5 Allwabl barg aaity and ttlmnt Vrtial tr ra il - du t nntratd lad: 3 5 r r x y - du t irularly ladd ara lad:. G t tabl 5..6 Fd / by dtrmg th trm: r/(/) /(/) 3- blw rtangular ladd ara: th t i at th rnr

More information

ELEC 372 LECTURE NOTES, WEEK 11 Dr. Amir G. Aghdam Concordia University

ELEC 372 LECTURE NOTES, WEEK 11 Dr. Amir G. Aghdam Concordia University ELEC 37 LECTURE NOTES, WEE Dr Amir Aghdam Cncrdia Univrity Part f th nt ar adaptd frm th matrial in th fllwing rfrnc: Mdrn Cntrl Sytm by Richard C Drf and Rbrt H Bihp, Prntic Hall Fdback Cntrl f Dynamic

More information

5 Curl-free fields and electrostatic potential

5 Curl-free fields and electrostatic potential 5 Curl-fr filds and lctrstatic tntial Mathmaticall, w can gnrat a curl-fr vctr fild E(,, ) as E = ( V, V, V ), b taking th gradint f an scalar functin V (r) =V (,, ). Th gradint f V (,, ) is dfind t b

More information

( ) Differential Equations. Unit-7. Exact Differential Equations: M d x + N d y = 0. Verify the condition

( ) Differential Equations. Unit-7. Exact Differential Equations: M d x + N d y = 0. Verify the condition Diffrntial Equations Unit-7 Eat Diffrntial Equations: M d N d 0 Vrif th ondition M N Thn intgrat M d with rspt to as if wr onstants, thn intgrat th trms in N d whih do not ontain trms in and quat sum of

More information

VTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS

VTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS Diffrntial Equations Unit-7 Eat Diffrntial Equations: M d N d 0 Vrif th ondition M N Thn intgrat M d with rspt to as if wr onstants, thn intgrat th trms in N d whih do not ontain trms in and quat sum of

More information

Another Explanation of the Cosmological Redshift. April 6, 2010.

Another Explanation of the Cosmological Redshift. April 6, 2010. Anthr Explanatin f th Csmlgical Rdshift April 6, 010. Jsé Francisc García Juliá C/ Dr. Marc Mrncian, 65, 5. 4605 Valncia (Spain) E-mail: js.garcia@dival.s h lss f nrgy f th phtn with th tim by missin f

More information

LECTURE 5 Guassian Wave Packet

LECTURE 5 Guassian Wave Packet LECTURE 5 Guassian Wav Pact 1.5 Eampl f a guassian shap fr dscribing a wav pact Elctrn Pact ψ Guassian Assumptin Apprimatin ψ As w hav sn in QM th wav functin is ftn rprsntd as a Furir transfrm r sris.

More information

HOMEWORK FOR UNIT 5-2: COMBINING FORCES

HOMEWORK FOR UNIT 5-2: COMBINING FORCES Nam Dat Partnrs HOMEWORK OR UNIT 52: COMBINING ORCES Qustins 15 rfr t a ty ar whih an mv in ithr dirtin alng a hrizntal lin (th psitin axis). 0 Assum that fritin is s small that it an b ignrd. Skth th

More information

9.5 Complex variables

9.5 Complex variables 9.5 Cmpl varabls. Cnsdr th funtn u v f( ) whr ( ) ( ), f( ), fr ths funtn tw statmnts ar as fllws: Statmnt : f( ) satsf Cauh mann quatn at th rgn. Statmnt : f ( ) ds nt st Th rrt statmnt ar (A) nl (B)

More information

More Foundations. Undirected Graphs. Degree. A Theorem. Graphs, Products, & Relations

More Foundations. Undirected Graphs. Degree. A Theorem. Graphs, Products, & Relations Mr Funtins Grphs, Pruts, & Rltins Unirt Grphs An unirt grph is pir f 1. A st f ns 2. A st f gs (whr n g is st f tw ns*) Friy, Sptmr 2, 2011 Ring: Sipsr 0.2 ginning f 0.4; Stughtn 1.1.5 ({,,,,}, {{,}, {,},

More information

CHAPTER 9. Compressible Flow. Btu ft-lb lbm ft-lb c p = = ft-lb slug- R. slug- R. 1 k. p p. p v p v. = ρ ρ

CHAPTER 9. Compressible Flow. Btu ft-lb lbm ft-lb c p = = ft-lb slug- R. slug- R. 1 k. p p. p v p v. = ρ ρ CHPTER 9 Cmrssibl Flw 9 Bu f-lb lbm f-lb c 778 6 lbm- R Bu slug slug- R f-lb cv c R 6 76 96 96 slug- R Bu 7 lbm R f-lb slug- R Bu 778 f - lb slug lbm c 9 c cv + R c cv c + R r c R c R / ( ) 9 If s, Eq

More information

Derivation of Eigenvalue Matrix Equations

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

More information

Topic 5: Discrete-Time Fourier Transform (DTFT)

Topic 5: Discrete-Time Fourier Transform (DTFT) ELEC36: Signals And Systms Tpic 5: Discrt-Tim Furir Transfrm (DTFT) Dr. Aishy Amr Cncrdia Univrsity Elctrical and Cmputr Enginring DT Furir Transfrm Ovrviw f Furir mthds DT Furir Transfrm f Pridic Signals

More information

Modern Physics. Unit 5: Schrödinger s Equation and the Hydrogen Atom Lecture 5.6: Energy Eigenvalues of Schrödinger s Equation for the Hydrogen Atom

Modern Physics. Unit 5: Schrödinger s Equation and the Hydrogen Atom Lecture 5.6: Energy Eigenvalues of Schrödinger s Equation for the Hydrogen Atom Mdrn Physics Unit 5: Schrödingr s Equatin and th Hydrgn Atm Lctur 5.6: Enrgy Eignvalus f Schrödingr s Equatin fr th Hydrgn Atm Rn Rifnbrgr Prfssr f Physics Purdu Univrsity 1 Th allwd nrgis E cm frm th

More information

For more important questions visit :

For more important questions visit : For mor important qustions visit : www4onocom CHAPTER 5 CONTINUITY AND DIFFERENTIATION POINTS TO REMEMBER A function f() is said to b continuous at = c iff lim f f c c i, lim f lim f f c c c f() is continuous

More information

Higher. Specimen NAB Assessment

Higher. Specimen NAB Assessment hsn.uk.net Higher Mathematics UNIT Specimen NAB Assessment HSN50 This dcument was prduced speciall fr the HSN.uk.net website, and we require that an cpies r derivative wrks attribute the wrk t Higher Still

More information

Frequency Response. Lecture #12 Chapter 10. BME 310 Biomedical Computing - J.Schesser

Frequency Response. Lecture #12 Chapter 10. BME 310 Biomedical Computing - J.Schesser Frquncy Rspns Lcur # Chapr BME 3 Bimdical Cmpuing - J.Schssr 99 Idal Filrs W wan sudy Hω funcins which prvid frquncy slciviy such as: Lw Pass High Pass Band Pass Hwvr, w will lk a idal filring, ha is,

More information

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall Staning Wav Intrfrnc btwn th incint & rflct wavs Staning wav A string with on n fix on a wall Incint: y, t) Y cos( t ) 1( Y 1 ( ) Y (St th incint wav s phas to b, i.., Y + ral & positiv.) Rflct: y, t)

More information

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas

More information

Southern Taiwan University

Southern Taiwan University Chaptr Ordinar Diffrntial Equations of th First Ordr and First Dgr Gnral form:., d +, d 0.a. f,.b I. Sparabl Diffrntial quations Form: d + d 0 C d d E 9 + 4 0 Solution: 9d + 4d 0 9 + 4 C E + d Solution:

More information

H NT Z N RT L 0 4 n f lt r h v d lt n r n, h p l," "Fl d nd fl d " ( n l d n l tr l t nt r t t n t nt t nt n fr n nl, th t l n r tr t nt. r d n f d rd n t th nd r nt r d t n th t th n r lth h v b n f

More information

6. Negative Feedback in Single- Transistor Circuits

6. Negative Feedback in Single- Transistor Circuits Lctur 8: Intrductin t lctrnic analg circuit 36--366 6. Ngativ Fdback in Singl- Tranitr ircuit ugn Paprn, 2008 Our aim i t tudy t ffct f ngativ fdback n t mall-ignal gain and t mall-ignal input and utput

More information

Multiple-Choice Test Introduction to Partial Differential Equations COMPLETE SOLUTION SET

Multiple-Choice Test Introduction to Partial Differential Equations COMPLETE SOLUTION SET Mltipl-Choic Tst Introdction to Partial Diffrntial Eqations COMPLETE SOLUTION SET 1. A partial diffrntial qation has (A on indpndnt variabl (B two or mor indpndnt variabls (C mor than on dpndnt variabl

More information

TURFGRASS DISEASE RESEARCH REPORT J. M. Vargas, Jr. and R. Detweiler Department of Botany and Plant Pathology Michigan State University

TURFGRASS DISEASE RESEARCH REPORT J. M. Vargas, Jr. and R. Detweiler Department of Botany and Plant Pathology Michigan State University I TURFGRASS DISEASE RESEARCH REPORT 9 J. M. Vrgs, Jr. n R. Dtwilr Dprtmnt f Btny n Plnt Pthlgy Mihign Stt Univrsity. Snw Ml Th 9 snw ml fungii vlutin trils wr nut t th Byn Highln Rsrt, Hrr Springs, Mihign

More information

:2;$-$(01*%<*=,-./-*=0;"%/;"-*

:2;$-$(01*%<*=,-./-*=0;%/;-* !"#$%'()%"*#%*+,-./-*+01.2(.*3+456789*!"#$%"'()'*+,-."/0.%+1'23"45'46'7.89:89'/' ;8-,"$4351415,8:+#9' Dr. Ptr T. Gallaghr Astrphyscs Rsarch Grup Trnty Cllg Dubln :2;$-$(01*%

More information

Chapter 7 Control Systems Design by the Root Locus Method

Chapter 7 Control Systems Design by the Root Locus Method haptr 7 ntrl Sytm Dgn by th t Lu Mthd 7. Intrdutn! Prfrman Spfatn: h rqurmnt mpd n th ntrl ytm ar plld ut a prfrman pfatn, whh gnrally rlat t auray, rlatv tablty, and pd f rpn.! Sytm mpnatn: Sttng th gan

More information

IV. First Law of Thermodynamics. Cooler. IV. First Law of Thermodynamics

IV. First Law of Thermodynamics. Cooler. IV. First Law of Thermodynamics D. Applcatons to stady flow dvcs. Hat xchangrs - xampl: Clkr coolr for cmnt kln Scondary ar 50 C, 57,000 lbm/h Clkr? C, 5 ton/h Coolr Clkr 400 C, 5 ton/h Scondary ar 0 C, 57,000 lbm/h a. Assumptons. changs

More information

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c.

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c. MA56 utorial Solutions Qustion a Intgrating fator is ln p p in gnral, multipl b p So b ln p p sin his kin is all a Brnoulli quation -- st Sin w fin Y, Y Y, Y Y p Qustion Dfin v / hn our quation is v μ

More information

Impedance Transformation and Parameter Relations

Impedance Transformation and Parameter Relations 8/1/18 Cours nstructor Dr. Raymond C. Rumpf Offic: A 337 Phon: (915) 747 6958 E Mail: rcrumpf@utp.du EE 4347 Applid Elctromagntics Topic 4 mpdanc Transformation and Paramtr Rlations mpdanc Ths Transformation

More information

Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK

Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal

More information

are given in the table below. t (hours)

are given in the table below. t (hours) CALCULUS WORKSHEET ON INTEGRATION WITH DATA Work th following on notbook papr. Giv dcimal answrs corrct to thr dcimal placs.. A tank contains gallons of oil at tim t = hours. Oil is bing pumpd into th

More information

Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Thomas Whitham Sith Form Pur Mathmatics Cor rvision gui Pag Algbra Moulus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv blow th ais in th ais. f () f () f

More information

SUMMER 17 EXAMINATION

SUMMER 17 EXAMINATION (ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: Important Instructions to aminrs: ) Th answrs should b amind by ky words and not as word-to-word as givn in th modl answr schm. ) Th modl answr

More information

Math 102. Rumbos Spring Solutions to Assignment #8. Solution: The matrix, A, corresponding to the system in (1) is

Math 102. Rumbos Spring Solutions to Assignment #8. Solution: The matrix, A, corresponding to the system in (1) is Math 12. Rumbos Spring 218 1 Solutions to Assignmnt #8 1. Construct a fundamntal matrix for th systm { ẋ 2y ẏ x + y. (1 Solution: Th matrix, A, corrsponding to th systm in (1 is 2 A. (2 1 1 Th charactristic

More information

A distributed device model for phonon-cooled HEB mixers predicting IV characteristics, gain, noise and IF bandwidth

A distributed device model for phonon-cooled HEB mixers predicting IV characteristics, gain, noise and IF bandwidth distributd dvi modl for honon-oold HEB mirs rditing V haratristis, gain, nois and F bandwidth. Khosroanah *, H. Mrkl *, S. Yngvsson #,. dam, S. hrdnihnko *, E. Kollbrg * * halmrs Univrsity of hnology,

More information

More on FT. Lecture 10 4CT.5 3CT.3-5,7,8. BME 333 Biomedical Signals and Systems - J.Schesser

More on FT. Lecture 10 4CT.5 3CT.3-5,7,8. BME 333 Biomedical Signals and Systems - J.Schesser Mr n FT Lcur 4CT.5 3CT.3-5,7,8 BME 333 Bimdicl Signls nd Sysms - J.Schssr 43 Highr Ordr Diffrniin d y d x, m b Y b X N n M m N M n n n m m n m n d m d n m Y n d f n [ n ] F d M m bm m X N n n n n n m p

More information

Chapter 6: Polarization and Crystal Optics

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

More information

Richard s Transformations

Richard s Transformations 4/27/25 Rihard Tranfrmatin.d /7 Rihard Tranfrmatin Reall the put impedane f hrt-iruited and peniruited tranmiin le tub. j tan β, β t β, β Nte that the put impedane are purely reatie jut like lumped element!

More information

Prelim Examination 2011 / 2012 (Assessing Units 1 & 2) MATHEMATICS. Advanced Higher Grade. Time allowed - 2 hours

Prelim Examination 2011 / 2012 (Assessing Units 1 & 2) MATHEMATICS. Advanced Higher Grade. Time allowed - 2 hours Prlim Eamination / (Assssing Units & ) MATHEMATICS Advancd Highr Grad Tim allowd - hours Rad Carfull. Calculators ma b usd in this papr.. Candidats should answr all qustions. Full crdit will onl b givn

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

More information

120~~60 o D 12~0 1500~30O, 15~30 150~30. ..,u 270,,,, ~"~"-4-~qno 240 2~o 300 v 240 ~70O 300

120~~60 o D 12~0 1500~30O, 15~30 150~30. ..,u 270,,,, ~~-4-~qno 240 2~o 300 v 240 ~70O 300 1 Find th plar crdinats that d nt dscrib th pint in th givn graph. (-2, 30 ) C (2,30 ) B (-2,210 ) D (-2,-150 ) Find th quatin rprsntd in th givn graph. F 0=3 H 0=2~ G r=3 J r=2 0 :.1 2 3 ~ 300 2"~ 2,

More information

Lecture 16: Bipolar Junction Transistors. Large Signal Models.

Lecture 16: Bipolar Junction Transistors. Large Signal Models. Whits, EE 322 Ltur 16 Pag 1 of 8 Ltur 16: Bipolar Juntion Transistors. Larg Signal Modls. Transistors prform ky funtions in most ltroni iruits. This is rtainly tru in RF iruits, inluding th NorCal 40A.

More information

Washington State University

Washington 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 information

a 1and x is any real number.

a 1and x is any real number. Calcls Nots Eponnts an Logarithms Eponntial Fnction: Has th form y a, whr a 0, a an is any ral nmbr. Graph y, Graph y ln y y Th Natral Bas (Elr s nmbr): An irrational nmbr, symboliz by th lttr, appars

More information

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw

More information

Vr Vr

Vr Vr F rt l Pr nt t r : xt rn l ppl t n : Pr nt rv nd PD RDT V t : t t : p bl ( ll R lt: 00.00 L n : n L t pd t : 0 6 20 8 :06: 6 pt (p bl Vr.2 8.0 20 8.0. 6 TH N PD PPL T N N RL http : h b. x v t h. p V l

More information

Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms

Chapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms Chapter 5 1 Chapter Summary Mathematical Inductin Strng Inductin Recursive Definitins Structural Inductin Recursive Algrithms Sectin 5.1 3 Sectin Summary Mathematical Inductin Examples f Prf by Mathematical

More information

XV Quantum Electrodynamics

XV Quantum Electrodynamics XV Qnt lctrdynics Fynn Rls fr QD An xl: Sry: iht Sts f Fynn Tchnis Fr rfrnc s: Hlzn&Mrtin s 86,8,9 Intrdctin t Prticl Physics ctr XV Cntnts R. Or Srin 005 Fynn rls sin 0 ty dl sin sin htn xtrnl lin in

More information

EE 119 Homework 6 Solution

EE 119 Homework 6 Solution EE 9 Hmwrk 6 Slutin Prr: J Bkr TA: Xi Lu Slutin: (a) Th angular magniicatin a tlcp i m / th cal lngth th bjctiv ln i m 4 45 80cm (b) Th clar aprtur th xit pupil i 35 mm Th ditanc btwn th bjctiv ln and

More information

Numerical methods, Mixed exercise 10

Numerical methods, Mixed exercise 10 Numrial mthos, Mi ris a f ( ) 6 f ( ) 6 6 6 a = 6, b = f ( ) So. 6 b n a n 6 7.67... 6.99....67... 6.68....99... 6.667....68... To.p., th valus ar =.68, =.99, =.68, =.67. f (.6).6 6.6... f (.6).6 6.6.7...

More information

BASIC DIRECT-CURRENT MEASUREMENTS

BASIC DIRECT-CURRENT MEASUREMENTS Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard

More information

The ZCS Boost Converter

The ZCS Boost Converter EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman The ZCS Bs Cnverer The bs-quasi-resnan nverer wih an M-ype swih as shwn Fig. 6.(a, wih is equivalen irui shwn Fig. 6.(b. (a (b Fig 6. (a ZCS bs

More information

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin

More information

Differentiation of Exponential Functions

Differentiation of Exponential Functions Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of

More information

CONSTRUCTING STATECHART DIAGRAMS

CONSTRUCTING STATECHART DIAGRAMS CONSTRUCTING STATECHART DIAGRAMS The fllwing checklist shws the necessary steps fr cnstructing the statechart diagrams f a class. Subsequently, we will explain the individual steps further. Checklist 4.6

More information

,. *â â > V>V. â ND * 828.

,. *â â > V>V. â ND * 828. BL D,. *â â > V>V Z V L. XX. J N R â J N, 828. LL BL D, D NB R H â ND T. D LL, TR ND, L ND N. * 828. n r t d n 20 2 2 0 : 0 T http: hdl.h ndl.n t 202 dp. 0 02802 68 Th N : l nd r.. N > R, L X. Fn r f,

More information

Einstein Equations for Tetrad Fields

Einstein Equations for Tetrad Fields Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for

More information

Solution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers:

Solution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers: APPM 6 Final 5 pts) Spring 4. 6 pts total) Th following parts ar not rlatd, justify your answrs: a) Considr th curv rprsntd by th paramtric quations, t and y t + for t. i) 6 pts) Writ down th corrsponding

More information

MSLC Math 151 WI09 Exam 2 Review Solutions

MSLC Math 151 WI09 Exam 2 Review Solutions Eam Rviw Solutions. Comput th following rivativs using th iffrntiation ruls: a.) cot cot cot csc cot cos 5 cos 5 cos 5 cos 5 sin 5 5 b.) c.) sin( ) sin( ) y sin( ) ln( y) ln( ) ln( y) sin( ) ln( ) y y

More information

Acid Base Reactions. Acid Base Reactions. Acid Base Reactions. Chemical Reactions and Equations. Chemical Reactions and Equations

Acid Base Reactions. Acid Base Reactions. Acid Base Reactions. Chemical Reactions and Equations. Chemical Reactions and Equations Chmial Ratins and Equatins Hwitt/Lyns/Suhki/Yh Cnptual Intgratd Sin During a hmial ratin, n r mr nw mpunds ar frmd as a rsult f th rarrangmnt f atms. Chaptr 13 CHEMICAL REACTIONS Ratants Prduts Chmial

More information

NAME: ANSWER KEY DATE: PERIOD. DIRECTIONS: MULTIPLE CHOICE. Choose the letter of the correct answer.

NAME: ANSWER KEY DATE: PERIOD. DIRECTIONS: MULTIPLE CHOICE. Choose the letter of the correct answer. R A T T L E R S S L U G S NAME: ANSWER KEY DATE: PERIOD PREAP PHYSICS REIEW TWO KINEMATICS / GRAPHING FORM A DIRECTIONS: MULTIPLE CHOICE. Chs h r f h rr answr. Us h fgur bw answr qusns 1 and 2. 0 10 20

More information

Math 656 Midterm Examination March 27, 2015 Prof. Victor Matveev

Math 656 Midterm Examination March 27, 2015 Prof. Victor Matveev Math 656 Mdtrm Examnatn March 7, 05 Prf. Vctr Matvv ) (4pts) Fnd all vals f n plar r artsan frm, and plt thm as pnts n th cmplx plan: (a) Snc n-th rt has xactly n vals, thr wll b xactly =6 vals, lyng n

More information

1973 AP Calculus AB: Section I

1973 AP Calculus AB: Section I 97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=

More information

y = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b)

y = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b) 4. y = y = + 5. Find th quation of th tangnt lin for th function y = ( + ) 3 whn = 0. solution: First not that whn = 0, y = (1 + 1) 3 = 8, so th lin gos through (0, 8) and thrfor its y-intrcpt is 8. y

More information

PLEASURE TEST SERIES (XI) - 07 By O.P. Gupta (For stuffs on Math, click at theopgupta.com)

PLEASURE TEST SERIES (XI) - 07 By O.P. Gupta (For stuffs on Math, click at theopgupta.com) A Cmpilatin By : OP Gupta (WhatsApp @ +9-9650 50 80) Fr mre stuffs n Maths, please visit : wwwtheopguptacm Time Allwed : 80 Minutes Max Marks : 00 SECTION A Questin numbers 0 t 0 carry mark each x x 5

More information

PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n

PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n R P RT F TH PR D NT N N TR T F R N V R T F NN T V D 0 0 : R PR P R JT..P.. D 2 PR L 8 8 J PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D.. 20 00 D r r. Pr d nt: n J n r f th r d t r v th

More information

ECE-320: Linear Control Systems Homework 1. 1) For the following transfer functions, determine both the impulse response and the unit step response.

ECE-320: Linear Control Systems Homework 1. 1) For the following transfer functions, determine both the impulse response and the unit step response. Due: Mnday Marh 4, 6 at the beginning f la ECE-: Linear Cntrl Sytem Hmewrk ) Fr the fllwing tranfer funtin, determine bth the imule rene and the unit te rene. Srambled Anwer: H ( ) H ( ) ( )( ) ( )( )

More information

D t r l f r th n t d t t pr p r d b th t ff f th l t tt n N tr t n nd H n N d, n t d t t n t. n t d t t. h n t n :.. vt. Pr nt. ff.,. http://hdl.handle.net/2027/uiug.30112023368936 P bl D n, l d t z d

More information

Analysis of the Output Ripple of the DC DC Boost Charger for Li-Ion Batteries

Analysis of the Output Ripple of the DC DC Boost Charger for Li-Ion Batteries Jurnal f Pwr Elctrnics, Vl. 4, N., pp. 35-4, January 4 35 JPE 4--4 http://dx.di.rg/.63/ JPE.4.4..35 ISSN(Print: 598-9 / ISSN(nlin: 93-478 Analysis f th utput ippl f th Bst hargr fr i-in Battris Van-Sang

More information

1997 AP Calculus AB: Section I, Part A

1997 AP Calculus AB: Section I, Part A 997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs for which f () is a ral numbr.. (4 6 ) d= 4 6 6

More information

Types of Communication

Types of Communication Tps f Cmmunicatin Analg: cntinuus ariabls with nis {rrr 0} 0 (imprfct) Digital: dcisins, discrt chics, quantizd, nis {rrr} 0 (usuall prfct) Mssag S, S, r S M Mdulatr (t) channl; adds nis and distrtin M-ar

More information

Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Thomas Whitham Sith Form Pur Mathmatics Unit C Algbra Trigonomtr Gomtr Calculus Vctor gomtr Pag Algbra Molus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv

More information

Vowel package manual

Vowel package manual Vwl pckg mnl FUKUI R Grdt Schl f Hmnts nd Sclgy Unvrsty f Tky 28 ctbr 2001 1 Drwng vwl dgrms 1.1 Th vwl nvrnmnt Th gnrl frmt f th vwl nvrnmnt s s fllws. [ptn(,ptn,)] cmmnds fr npttng vwls ptns nd cmmnds

More information

Humanistic, and Particularly Classical, Studies as a Preparation for the Law

Humanistic, and Particularly Classical, Studies as a Preparation for the Law University of Michigan Law School University of Michigan Law School Scholarship Repository Articles Faculty Scholarship 1907 Humanistic, and Particularly Classical, Studies as a Preparation for the Law

More information

Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 3 Kinematics in Two Dimensions; Vectors Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs

More information

Coupled Pendulums. Two normal modes.

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

More information

Name: Date: AP Physics 1 Per. Vector Addition Practice. 1. F1 and F2 are vectors shown below (N is a unit of force, it stands for Newton, not north)

Name: Date: AP Physics 1 Per. Vector Addition Practice. 1. F1 and F2 are vectors shown below (N is a unit of force, it stands for Newton, not north) ame: Date: AP Phsics 1 Per. Vectr Additin Practice 1. F1 and F are ectrs shwn belw ( is a unit f frce, it stands fr ewtn, nt nrth) F1 = 500 F = 300 40 50 a) Add the ectrs F1 and F: F1+F = 1. Add graphicall

More information

Linear-Phase FIR Transfer Functions. Functions. Functions. Functions. Functions. Functions. Let

Linear-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 information

SOLUTIONS SET 1 MATHEMATICS CLASS X

SOLUTIONS SET 1 MATHEMATICS CLASS X Tp Careers & Yu SOLUTIONS SET MTHEMTICS CLSS X. 84 7 Prime factrs f 84 are, and 7.. Sum f zeres 5 + 4 Prduct f zeres 5 4 0 Required plynmial x ( )x + ( 0) x + x 0. Given equatin is x + y 0 Fr x, y L.H.S

More information

Abstract Interpretation: concrete and abstract semantics

Abstract Interpretation: concrete and abstract semantics Abstract Intrprtation: concrt and abstract smantics Concrt smantics W considr a vry tiny languag that manags arithmtic oprations on intgrs valus. Th (concrt) smantics of th languags cab b dfind by th funzcion

More information

ECE 3600 Lumped-Parameter Transmission Line Models b

ECE 3600 Lumped-Parameter Transmission Line Models b Lumpd-Paramtr Transmission Lin Modls b Lon-th Lins: ovr 40 (50 mils) (ovr 00 mi in som tts) Nd: Units lin th:, d stik to th sam unit th for all paramtrs mils ma also b usd Rsistan pr unit th: r Units ndutan

More information

. This is made to keep the kinetic energy at outlet a minimum.

. This is made to keep the kinetic energy at outlet a minimum. Runnr Francis Turbin Th shap th blads a Francis runnr is cmplx. Th xact shap dpnds n its spciic spd. It is bvius rm th quatin spciic spd (Eq.5.8) that highr spciic spd mans lwr had. This rquirs that th

More information

COMPUTATIONAL NUCLEAR THERMAL HYDRAULICS

COMPUTATIONAL NUCLEAR THERMAL HYDRAULICS COMPUTTIONL NUCLER THERML HYDRULICS Cho, Hyoung Kyu Dpartmnt of Nuclar Enginring Soul National Univrsity CHPTER4. THE FINITE VOLUME METHOD FOR DIFFUSION PROBLEMS 2 Tabl of Contnts Chaptr 1 Chaptr 2 Chaptr

More information

Hydrogen Atom and One Electron Ions

Hydrogen Atom and One Electron Ions Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial

More information

n

n p l p bl t n t t f Fl r d, D p rt nt f N t r l R r, D v n f nt r r R r, B r f l. n.24 80 T ll h, Fl. : Fl r d D p rt nt f N t r l R r, B r f l, 86. http://hdl.handle.net/2027/mdp.39015007497111 r t v n

More information

Department of Civil Engineering & Applied Mechanics McGill University, Montreal, Quebec Canada

Department of Civil Engineering & Applied Mechanics McGill University, Montreal, Quebec Canada Department f Ciil ngeerg Applied Mechanics McGill Uniersity, Mntreal, Quebec Canada CI 90 THRMODYNAMICS HAT TRANSFR Assignment #4 SOLUTIONS. A 68-kg man whse aerage bdy temperature is 9 C drks L f cld

More information

N J of oscillators in the three lowest quantum

N J of oscillators in the three lowest quantum . a) Calculat th fractinal numbr f scillatrs in th thr lwst quantum stats (j,,,) fr fr and Sl: ( ) ( ) ( ) ( ) ( ).6.98. fr usth sam apprach fr fr j fr frm q. b) .) a) Fr a systm f lcalizd distinguishabl

More information

ZVS Boost Converter. (a) (b) Fig 6.29 (a) Quasi-resonant boost converter with M-type switch. (b) Equivalent circuit.

ZVS Boost Converter. (a) (b) Fig 6.29 (a) Quasi-resonant boost converter with M-type switch. (b) Equivalent circuit. EEL6246 Pwer Electrnics II Chapter 6 Lecture 6 Dr. Sam Abdel-Rahman ZVS Bst Cnverter The quasi-resnant bst cnverter by using the M-type switch as shwn in Fig. 6.29(a) with its simplified circuit shwn in

More information

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables.

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables. Chaptr Functions o Two Variabls Applid Calculus 61 Sction : Calculus o Functions o Two Variabls Now that ou hav som amiliarit with unctions o two variabls it s tim to start appling calculus to hlp us solv

More information

The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function

The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function A gnraliation of th frquncy rsons function Th convolution sum scrition of an LTI iscrt-tim systm with an imuls rsons h[n] is givn by h y [ n] [ ] x[ n ] Taing th -transforms of both sis w gt n n h n n

More information

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

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

More information

LEARNING : At the end of the lesson, students should be able to: OUTCOMES a) state trigonometric ratios of sin,cos, tan, cosec, sec and cot

LEARNING : At the end of the lesson, students should be able to: OUTCOMES a) state trigonometric ratios of sin,cos, tan, cosec, sec and cot Mathematics DM 05 Tpic : Trignmetric Functins LECTURE OF 5 TOPIC :.0 TRIGONOMETRIC FUNCTIONS SUBTOPIC :. Trignmetric Ratis and Identities LEARNING : At the end f the lessn, students shuld be able t: OUTCOMES

More information

Copyright Paul Tobin 63

Copyright Paul Tobin 63 DT, Kevin t. lectric Circuit Thery DT87/ Tw-Prt netwrk parameters ummary We have seen previusly that a tw-prt netwrk has a pair f input terminals and a pair f utput terminals figure. These circuits were

More information

Lecture 27: The 180º Hybrid.

Lecture 27: The 180º Hybrid. Whits, EE 48/58 Lctur 7 Pag f 0 Lctur 7: Th 80º Hybrid. Th scnd rciprcal dirctinal cuplr w will discuss is th 80º hybrid. As th nam implis, th utputs frm such a dvic can b 80º ut f phas. Thr ar tw primary

More information

Equil. Properties of Reacting Gas Mixtures. So far have looked at Statistical Mechanics results for a single (pure) perfect gas

Equil. Properties of Reacting Gas Mixtures. So far have looked at Statistical Mechanics results for a single (pure) perfect gas Shool of roa Engnrng Equl. Prort of Ratng Ga Mxtur So far hav lookd at Stattal Mhan rult for a ngl (ur) rft ga hown how to gt ga rort (,, h, v,,, ) from artton funton () For nonratng rft ga mxtur, gt mxtur

More information

10.5 Linear Viscoelasticity and the Laplace Transform

10.5 Linear Viscoelasticity and the Laplace Transform Scn.5.5 Lnar Vclacy and h Lalac ranfrm h Lalac ranfrm vry uful n cnrucng and analyng lnar vclac mdl..5. h Lalac ranfrm h frmula fr h Lalac ranfrm f h drvav f a funcn : L f f L f f f f f c..5. whr h ranfrm

More information