College of Engineering Department of Electronics and Communication Engineering. Test 2 MODEL ANSWERS

Size: px
Start display at page:

Download "College of Engineering Department of Electronics and Communication Engineering. Test 2 MODEL ANSWERS"

Transcription

1 Nae: tudet Nube: ect: ectue: z at Fazea zlee Jehaa y Jaalud able Nube: llee f ee eatet f lectcs ad ucat ee est O N, Y 050 ubject de : B73 use tle : lectcs alyss & es ate : uust 05 e llwed : hu 5 utes stucts t the caddates:. te yu Nae ad tudet ube. cle ectue f yu sect.. te all yu aswes us e. O NO U N excet f the daa. 3. N UON.. YOU N ON H UON. NO: O NO ON H UON UN NU O O O. GOO U! uest Nube 3 tal as ae

2 B73 est uest [0 as] a he dffeetal alfe shw Fue has a a f blas as ut deces ad a a f blas cected as a acte lad. he ccut bas s 0.5, ad the tasst aaetes ae 00, ad 00. aw the acte lad ccut t clete the ccut Fue. [ as] Fd the e-ccut dffeetal-de ltae a, d. [8 as] alculate the alue f a lad esstace cected t the utut O f the dffeetalde ltae a d s t be educed t 5. [ as] swe f uest a Fue swe f uest a ae

3 B73 est ae 3 swe f uest a a 3 as: cect label 3 as: cect laceet a [] [] [] [] d a [] 50 [] [] d

4 B73 est b F the dffeetal alfe wth cascde acte lad Fue t s e that the ccut aaetes ae: 3, 3, ad. NO tasst aaetes ae: N 0.7, 30 µ, 00 ad λ 0. - ; ad the O tasst aaetes ae: -0.8, 35 µ, 00 ad λ Fd the dffeetal a d. [8 as] t s e that the c-de a, c f the ccut s alculate the c-de eject at, db. [ as] t s e that the ltae acss the cstat cuet suce, 0.. Fue shws whee the s. alculate the axu ad u utut ltae. tate ay assuts. [8 as] swe f uest b -- Fue ae

5 B73 est ae 5 swe f uest b b b [] [] [] μ [] [] [] μ 0.5 [] 5 3 d d λ λ [] l l [] db db c d

6 B73 est ae b [] [] [] μ 0.5 [] [] ax [] [] μ 0.5 [] ax N N

7 B73 est uest [30 as] he ccut Fue 3 shws a sle ult-stae BJ -a, csst f thee dffeet staes. t s e that f all tassts: 00, 500, 5, ad π 3. Fue 3 a b t s als e that 3 50 ad 0. F 7, the aly ltae s assued t be fte. alculate the sall sal ut edace at the cllect f 7,.e. 7 as dcated the Fue 3. [ as] alculate the sall-sal ltae a f the a stae, O3 O. Ge that: O3 O c7 b 7 [0 as] c etee the utut esstace f the alfe,. [8 as] ae 7

8 B73 est swe f uest a [] c π [] c 077 [] b 8 π c b b 3 c7 7 b7 7 b 3 [3, ] 7 π π [] c π 8 Z Z c c7 c [] c7 7 [] c.077 [] [] 0 ae 8

9 B73 est uest 3 [30 as] class- ette fllwe based wth a cstat cuet suce s shw Fue. ssue ccut aaetes f,, ad 50. he tasst aaetes ae 0, B 0.7, ad 0.7. he u cuet s t be 0. a etee the alue f that wll duce the axu ssble utut ltae sw. hat s the alue f? [ as] b F utut ltae O 0, fd the we dsed the tasst ad the we dsed the tasst. [ as] c etee the we ces effcecy η f a syetcal se-wae utut ltae wth a ea alue f 0. [ as] swe f uest 3 Fue ae 9

10 B73 est ae 0 swe f uest 3 8.% 00% calculated us we dsed tassts ad : s O.937% 00% calculated us we dsed ad : s ] [ 00% 3c b [] [] [] [] [] 0 [] [] 3a 3 3 O O B O η η η

11 B73 est ae B FOU FO NO BJ OF sal ;all ; ; B B e e B B α α π π N N λ sal ;all ] [ OF ; ] [ OF N ;?

6. Cascode Amplifiers and Cascode Current Mirrors

6. Cascode Amplifiers and Cascode Current Mirrors 6. Cascde plfes and Cascde Cuent Ms Seda & Sth Sec. 7 (MOS ptn (S&S 5 th Ed: Sec. 6 MOS ptn & ne fequency espnse ECE 0, Fall 0, F. Najabad Cascde aplfe s a ppula buldn blck f ICs Cascde Cnfuatn CG stae

More information

Exercises for Cascode Amplifiers. ECE 102, Fall 2012, F. Najmabadi

Exercises for Cascode Amplifiers. ECE 102, Fall 2012, F. Najmabadi Execises f Cascde plifies ECE 0, Fall 0, F. Najabadi F. Najabadi, ECE0, Fall 0 /6 Execise : Cpute assue and Eey Cascde stae inceases by uble Cascde Execise : Cpute all indicated s, s, and i s. ssue tansists

More information

ANALOG ELECTRONICS DR NORLAILI MOHD NOH

ANALOG ELECTRONICS DR NORLAILI MOHD NOH 24 ANALOG LTRONIS lass 5&6&7&8&9 DR NORLAILI MOHD NOH 3.3.3 n-ase cnfguatn V V Rc I π π g g R V /p sgnal appled t. O/p taken f. ted t ac gnd. The hybd-π del pdes an accuate epesentatn f the sall-sgnal

More information

Active Load. Reading S&S (5ed): Sec. 7.2 S&S (6ed): Sec. 8.2

Active Load. Reading S&S (5ed): Sec. 7.2 S&S (6ed): Sec. 8.2 cte La ean S&S (5e: Sec. 7. S&S (6e: Sec. 8. In nteate ccuts, t s ffcult t fabcate essts. Instea, aplfe cnfuatns typcally use acte las (.e. las ae w acte eces. Ths can be ne usn a cuent suce cnfuatn,.e.

More information

ECEN474/704: (Analog) VLSI Circuit Design Spring 2018

ECEN474/704: (Analog) VLSI Circuit Design Spring 2018 EEN474/704: (Anal) LSI cut De S 08 Lectue 8: Fequency ene Sa Pale Anal & Mxed-Sal ente Texa A&M Unety Annunceent & Aenda HW Due Ma 6 ead aza hate 3 & 6 Annunceent & Aenda n-suce A Fequency ene Oen-cut

More information

Exercises for Frequency Response. ECE 102, Fall 2012, F. Najmabadi

Exercises for Frequency Response. ECE 102, Fall 2012, F. Najmabadi Eecses Fequency espnse EE 0, Fall 0, F. Najabad Eecse : Fnd the d-band an and the lwe cut- equency the aple belw. µ n (W/ 4 A/, t 0.5, λ 0, 0 µf, and µf Bth capacts ae lw- capacts. F. Najabad, EE0, Fall

More information

T-model: - + v o. v i. i o. v e. R i

T-model: - + v o. v i. i o. v e. R i T-mdel: e gm - V Rc e e e gme R R R 23 e e e gme R R The s/c tanscnductance: G m e m g gm e 0 The nput esstance: R e e e e The utput esstance: R R 0 /c unladed ltage gan, R a g R m e gmr e 0 m e g me e/e

More information

m = Mass flow rate The Lonely Electron Example 0a:

m = Mass flow rate The Lonely Electron Example 0a: The Lel Elect Exaple 0a: Mass flw ate l Liea velcit Hw fa ut f ptial eeg iteacti? Hge ucleus Bh --- 93: Uest the etu ccept. Liea etu istace eeg ( l ) l F ( tie ) ( tie ) + Like t use the peples ieas (if

More information

χ be any function of X and Y then

χ be any function of X and Y then We have show that whe we ae gve Y g(), the [ ] [ g() ] g() f () Y o all g ()() f d fo dscete case Ths ca be eteded to clude fuctos of ay ube of ado vaables. Fo eaple, suppose ad Y ae.v. wth jot desty fucto,

More information

6.012 Electronic Devices and Circuits Formula Sheet for Final Exam, Fall q = 1.6x10 19 Coul III IV V = x10 14 o. = 3.

6.012 Electronic Devices and Circuits Formula Sheet for Final Exam, Fall q = 1.6x10 19 Coul III IV V = x10 14 o. = 3. 6.0 Elctc Dvcs ad Ccuts ula Sht f al Exa, all 003 Paat Valus: Pdc Tabl: q.6x0 9 Cul III IV V 8.854 x0 4 /c,,s.7,,so 3.9 B C N 0 S /c, SO 3.5 x0 3 /c Al S P [S@R.T] 0 0 c 3 Ga G As /q 0.05 V ; ( /q) l0

More information

Exercises for Frequency Response. ECE 102, Winter 2011, F. Najmabadi

Exercises for Frequency Response. ECE 102, Winter 2011, F. Najmabadi Eercses r Frequency espnse EE 0, Wnter 0, F. Najabad Eercse : A Mdy the crcut belw t nclude a dnant ple at 00 Mz ( 00 Ω, k, k, / 00 Ω, λ 0, and nre nternal capactances the MOS. pute the dnant ple n the

More information

are positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures.

are positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures. Lectue 4 8. MRAC Desg fo Affe--Cotol MIMO Systes I ths secto, we cosde MRAC desg fo a class of ult-ut-ult-outut (MIMO) olea systes, whose lat dyacs ae lealy aaetezed, the ucetates satsfy the so-called

More information

ES 330 Electronics II Homework 04 (Fall 2017 Due Wednesday, September 27, 2017)

ES 330 Electronics II Homework 04 (Fall 2017 Due Wednesday, September 27, 2017) Pae1 Nae Solutons ES 330 Electroncs II Hoework 04 (Fall 2017 Due Wednesday, Septeer 27, 2017) Prole 1 onsder the FET aplfer of F. 7.10 for the case of t =0.4, kn = 5 A/ 2, GS =0.6, DD = 1.8 and RD = 10

More information

SUBSEQUENCE CHARACTERIZAT ION OF UNIFORM STATISTICAL CONVERGENCE OF DOUBLE SEQUENCE

SUBSEQUENCE CHARACTERIZAT ION OF UNIFORM STATISTICAL CONVERGENCE OF DOUBLE SEQUENCE Reseach ad Coucatos atheatcs ad atheatcal ceces Vol 9 Issue 7 Pages 37-5 IN 39-6939 Publshed Ole o Novebe 9 7 7 Jyot cadec Pess htt//yotacadecessog UBEQUENCE CHRCTERIZT ION OF UNIFOR TTITIC CONVERGENCE

More information

Spring Term 1 SPaG Mat 4

Spring Term 1 SPaG Mat 4 Spg Tem 1 SPG Mt Cmplete the tle g sux t ech u t mke jectve Nu Ajectve c e C u vete cmms t ths ect speech setece? Hw u cete tht lvel pctue? ske the cuus gl C u wte et ech these hmphe ws? Use ct t help

More information

Microelectronics Circuit Analysis and Design. ac Equivalent Circuit for Common Emitter. Common Emitter with Time-Varying Input

Microelectronics Circuit Analysis and Design. ac Equivalent Circuit for Common Emitter. Common Emitter with Time-Varying Input Micelectnics Cicuit Analysis and Design Dnald A. Neamen Chapte 6 Basic BJT Amplifies In this chapte, we will: Undestand the pinciple f a linea amplifie. Discuss and cmpae the thee basic tansist amplifie

More information

Microelectronics Circuit Analysis and Design. NMOS Common-Source Circuit. NMOS Common-Source Circuit 10/15/2013. In this chapter, we will:

Microelectronics Circuit Analysis and Design. NMOS Common-Source Circuit. NMOS Common-Source Circuit 10/15/2013. In this chapter, we will: Mcrelectrncs Crcut Analyss and Desn Dnald A. Neaen Chapter 4 Basc FET Aplfers In ths chapter, we wll: Inestate a snle-transstr crcut that can aplfy a sall, te-aryn nput snal Deelp sall-snal dels that are

More information

β A Constant-G m Biasing

β A Constant-G m Biasing p 2002 EE 532 Anal IC Des II Pae 73 Cnsan-G Bas ecall ha us a PTAT cuen efeence (see p f p. 66 he nes) bas a bpla anss pes cnsan anscnucance e epeaue (an als epenen f supply lae an pcess). Hw h we achee

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

6. Introduction to Transistor Amplifiers: Concepts and Small-Signal Model

6. Introduction to Transistor Amplifiers: Concepts and Small-Signal Model 6. ntoucton to anssto mples: oncepts an Small-Sgnal Moel Lectue notes: Sec. 5 Sea & Smth 6 th E: Sec. 5.4, 5.6 & 6.3-6.4 Sea & Smth 5 th E: Sec. 4.4, 4.6 & 5.3-5.4 EE 65, Wnte203, F. Najmaba Founaton o

More information

Chapter 3 Applications of resistive circuits

Chapter 3 Applications of resistive circuits Chapte 3 pplcat f ete ccut 3. (ptal) eal uce mel, maxmum pwe tafe 3. mplfe mel ltage amplfe mel, cuet amplfe mel 3.3 Op-amp lea mel, etg p-amp, etg p-amp, ummg a ffeece p-amp 3.4-3.5 (ptal) teal p-amp

More information

Is current gain generally significant in FET amplifiers? Why or why not? Substitute each capacitor with a

Is current gain generally significant in FET amplifiers? Why or why not? Substitute each capacitor with a FET Sall Snal Mdband Mdel Ntatn: C arables and quanttes are enerally desnated wth an uppercase subscrpt. AC arables and quanttes are enerally desnated wth a lwercase subscrpt. Phasr ntatn wll be used when

More information

Physics 1501 Lecture 19

Physics 1501 Lecture 19 Physcs 1501 ectue 19 Physcs 1501: ectue 19 Today s Agenda Announceents HW#7: due Oct. 1 Mdte 1: aveage 45 % Topcs otatonal Kneatcs otatonal Enegy Moents of Ineta Physcs 1501: ectue 19, Pg 1 Suay (wth copason

More information

(8) Gain Stage and Simple Output Stage

(8) Gain Stage and Simple Output Stage EEEB23 Electoncs Analyss & Desgn (8) Gan Stage and Smple Output Stage Leanng Outcome Able to: Analyze an example of a gan stage and output stage of a multstage amplfe. efeence: Neamen, Chapte 11 8.0) ntoducton

More information

VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles.

VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles. Seeth Edto CHPTER 4 VECTOR MECHNICS FOR ENINEERS: DYNMICS Fedad P. ee E. Russell Johsto, J. Systems of Patcles Lectue Notes: J. Walt Ole Texas Tech Uesty 003 The Mcaw-Hll Compaes, Ic. ll ghts eseed. Seeth

More information

Signal Circuit and Transistor Small-Signal Model

Signal Circuit and Transistor Small-Signal Model Snal cut an anto Sall-Snal Mol Lctu not: Sc. 5 Sa & Sth 6 th E: Sc. 5.5 & 6.7 Sa & Sth 5 th E: Sc. 4.6 & 5.6 F. Najaba EE65 Wnt 0 anto pl lopnt Ba & Snal Ba Snal only Ba Snal - Ba? MOS... : : S... MOS...

More information

/ / MET Day 000 NC1^ INRTL MNVR I E E PRE SLEEP K PRE SLEEP R E

/ / MET Day 000 NC1^ INRTL MNVR I E E PRE SLEEP K PRE SLEEP R E 05//0 5:26:04 09/6/0 (259) 6 7 8 9 20 2 22 2 09/7 0 02 0 000/00 0 02 0 04 05 06 07 08 09 0 2 ay 000 ^ 0 X Y / / / / ( %/ ) 2 /0 2 ( ) ^ 4 / Y/ 2 4 5 6 7 8 9 2 X ^ X % 2 // 09/7/0 (260) ay 000 02 05//0

More information

THE EQUIVALENCE OF GRAM-SCHMIDT AND QR FACTORIZATION (page 227) Gram-Schmidt provides another way to compute a QR decomposition: n

THE EQUIVALENCE OF GRAM-SCHMIDT AND QR FACTORIZATION (page 227) Gram-Schmidt provides another way to compute a QR decomposition: n HE EQUIVAENCE OF GRA-SCHID AND QR FACORIZAION (page 7 Ga-Schdt podes anothe way to copute a QR decoposton: n gen ectos,, K, R, Ga-Schdt detenes scalas j such that o + + + [ ] [ ] hs s a QR factozaton of

More information

Chapter 2: Descriptive Statistics

Chapter 2: Descriptive Statistics Chapte : Decptve Stattc Peequte: Chapte. Revew of Uvaate Stattc The cetal teecy of a oe o le yetc tbuto of a et of teval, o hghe, cale coe, ofte uaze by the athetc ea, whch efe a We ca ue the ea to ceate

More information

ANALOG ELECTRONICS 1 DR NORLAILI MOHD NOH

ANALOG ELECTRONICS 1 DR NORLAILI MOHD NOH 24 ANALOG LTRONIS TUTORIAL DR NORLAILI MOHD NOH . 0 8kΩ Gen, Y β β 00 T F 26, 00 0.7 (a)deterne the dc ltages at the 3 X ternals f the JT (,, ). 0kΩ Z (b) Deterne g,r π and r? (c) Deterne the ltage gan

More information

H STO RY OF TH E SA NT

H STO RY OF TH E SA NT O RY OF E N G L R R VER ritten for the entennial of th e Foundin g of t lair oun t y on ay 8 82 Y EEL N E JEN K RP O N! R ENJ F ] jun E 3 1 92! Ph in t ed b y h e t l a i r R ep u b l i c a n O 4 1922

More information

ECEN474/704: (Analog) VLSI Circuit Design Spring 2016

ECEN474/704: (Analog) VLSI Circuit Design Spring 2016 EEN7/70: (nal) VS icuit Desin Spin 06 ectue 0: Siple OT Sa Pale nal & Mixed-Sinal ente Texas &M Uniesity nnunceents H is due tday H is due Ma 0 Exa is n p 9:0-0:5PM (0 exta inutes) lsed bk w/ ne standad

More information

Consider two masses m 1 at x = x 1 and m 2 at x 2.

Consider two masses m 1 at x = x 1 and m 2 at x 2. Chapte 09 Syste of Patcles Cete of ass: The cete of ass of a body o a syste of bodes s the pot that oes as f all of the ass ae cocetated thee ad all exteal foces ae appled thee. Note that HRW uses co but

More information

Today. The geometry of homogeneous and nonhomogeneous matrix equations. Solving nonhomogeneous equations. Method of undetermined coefficients

Today. The geometry of homogeneous and nonhomogeneous matrix equations. Solving nonhomogeneous equations. Method of undetermined coefficients Today The geometry of homogeneous and nonhomogeneous matrix equations Solving nonhomogeneous equations Method of undetermined coefficients 1 Second order, linear, constant coeff, nonhomogeneous (3.5) Our

More information

THIS PAGE DECLASSIFIED IAW E

THIS PAGE DECLASSIFIED IAW E THS PAGE DECLASSFED AW E0 2958 BL K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW E0 2958 B L K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW EO 2958 THS PAGE DECLASSFED AW EO 2958 THS

More information

THIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.

THIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings. T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson

More information

VIII Dynamics of Systems of Particles

VIII Dynamics of Systems of Particles VIII Dyacs of Systes of Patcles Cete of ass: Cete of ass Lea oetu of a Syste Agula oetu of a syste Ketc & Potetal Eegy of a Syste oto of Two Iteactg Bodes: The Reduced ass Collsos: o Elastc Collsos R whee:

More information

Optical Remote Sensing with DIfferential Absorption Lidar (DIAL)

Optical Remote Sensing with DIfferential Absorption Lidar (DIAL) Optcal emote esg wth DIffeetal Absopt Lda DIAL Pat : Theoy hstoph eff IE Uvesty of oloado & OAA/EL/D/Atmosphec emote esg oup http://www.esl.oaa.gov/csd/goups/csd3/ uest lectue fo AE-659 Lda emote esg U

More information

Parts Manual. EPIC II Critical Care Bed REF 2031

Parts Manual. EPIC II Critical Care Bed REF 2031 EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4

More information

Charged particle motion in magnetic field

Charged particle motion in magnetic field Chaged paticle otion in agnetic field Paticle otion in cued agnetic fieldlines We diide the equation of otion into a elocity coponent along the agnetic field and pependicula to the agnetic field. Suppose

More information

Question 1. Typical Cellular System. Some geometry TELE4353. About cellular system. About cellular system (2)

Question 1. Typical Cellular System. Some geometry TELE4353. About cellular system. About cellular system (2) TELE4353 Moble a atellte Commucato ystems Tutoal 1 (week 3-4 4 Questo 1 ove that fo a hexagoal geomety, the co-chael euse ato s gve by: Q (3 N Whee N + j + j 1/ 1 Typcal Cellula ystem j cells up cells

More information

Scratch Ticket Game Closing Analysis SUMMARY REPORT

Scratch Ticket Game Closing Analysis SUMMARY REPORT TEXAS LTTERY SS Sctch Ticket Ge lsing Anlysis SUARY REPRT Sctch Ticket nftin Dte pleted 6/ 29/216 Ge# 1737 nfied Pcks 13, 431 Ge e Hit$ 5, Active Pcks 7, 752 untity Pinted 1, 279,3 ehuse Pcks 13 Pice Pint

More information

I. Exponential Function

I. Exponential Function MATH & STAT Ch. Eoetil Fuctios JCCSS I. Eoetil Fuctio A. Defiitio f () =, whee ( > 0 ) d is the bse d the ideedet vible is the eoet. [ = 1 4 4 4L 4 ] ties (Resf () = is owe fuctio i which the bse is the

More information

FYSE400 ANALOG ELECTRONICS

FYSE400 ANALOG ELECTRONICS YSE400 ANALOG ELECTONCS LECTUE 3 Bipolar Sub Circuits 1 BPOLA SUB CCUTS Bipolar Current Sinks and -Sources Transistor operates in forwardactive region. < < sat CE CN max CE < < + BN CN BN max CE N N N

More information

Consider the simple circuit of Figure 1 in which a load impedance of r is connected to a voltage source. The no load voltage of r

Consider the simple circuit of Figure 1 in which a load impedance of r is connected to a voltage source. The no load voltage of r 1 Intductin t Pe Unit Calculatins Cnside the simple cicuit f Figue 1 in which a lad impedance f L 60 + j70 Ω 9. 49 Ω is cnnected t a vltage suce. The n lad vltage f the suce is E 1000 0. The intenal esistance

More information

Central limit theorem for functions of weakly dependent variables

Central limit theorem for functions of weakly dependent variables Int. Statistical Inst.: Poc. 58th Wold Statistical Congess, 2011, Dublin (Session CPS058 p.5362 Cental liit theoe fo functions of weakly dependent vaiables Jensen, Jens Ledet Aahus Univesity, Depatent

More information

LECTURE 14. m 1 m 2 b) Based on the second law of Newton Figure 1 similarly F21 m2 c) Based on the third law of Newton F 12

LECTURE 14. m 1 m 2 b) Based on the second law of Newton Figure 1 similarly F21 m2 c) Based on the third law of Newton F 12 CTU 4 ] NWTON W O GVITY -The gavity law i foulated fo two point paticle with ae and at a ditance between the. Hee ae the fou tep that bing to univeal law of gavitation dicoveed by NWTON. a Baed on expeiental

More information

FARADAY'S LAW dt

FARADAY'S LAW dt FAADAY'S LAW 31.1 Faaday's Law of Induction In the peious chapte we leaned that electic cuent poduces agnetic field. Afte this ipotant discoey, scientists wondeed: if electic cuent poduces agnetic field,

More information

Plane Trusses Trusses

Plane Trusses Trusses TRUSSES Plane Trusses Trusses- It is a system of uniform bars or members (of various circular section, angle section, channel section etc.) joined together at their ends by riveting or welding and constructed

More information

Module Title: Business Mathematics and Statistics 2

Module Title: Business Mathematics and Statistics 2 CORK INSTITUTE OF TECHNOLOGY INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ Semeste Eamatos 009/00 Module Ttle: Busess Mathematcs ad Statstcs Module Code: STAT 6003 School: School of Busess ogamme Ttle: Bachelo of

More information

Consumer theory. A. The preference ordering B. The feasible set C. The consumption decision. A. The preference ordering. Consumption bundle

Consumer theory. A. The preference ordering B. The feasible set C. The consumption decision. A. The preference ordering. Consumption bundle Thomas Soesso Mcoecoomcs Lecte Cosme theoy A. The efeece odeg B. The feasble set C. The cosmto decso A. The efeece odeg Cosmto bdle x ( 2 x, x,... x ) x Assmtos: Comleteess 2 Tastvty 3 Reflexvty 4 No-satato

More information

Transistors. Lesson #10 Chapter 4. BME 372 Electronics I J.Schesser

Transistors. Lesson #10 Chapter 4. BME 372 Electronics I J.Schesser Tanssts essn #10 Chapte 4 BM 372 lectncs 154 Hmewk Ps. 4.40, 4.42, 4.43, 4.45, 4.46, 4.51, 4.53, 4.54, 4.56 BM 372 lectncs 155 Hmewk Answes #20 Ps. 4.40 See fgue 4.33 BM 372 lectncs 156 Ps. 4.42 Hmewk

More information

Ch. 3: Forward and Inverse Kinematics

Ch. 3: Forward and Inverse Kinematics Ch. : Fowa an Invee Knemat Reap: The Denavt-Hatenbeg (DH) Conventon Repeentng eah nvual homogeneou tanfomaton a the pout of fou ba tanfomaton: pout of fou ba tanfomaton: x a x z z a a a Rot Tan Tan Rot

More information

K owi g yourself is the begi i g of all wisdo.

K owi g yourself is the begi i g of all wisdo. I t odu tio K owi g yourself is the begi i g of all wisdo. A istotle Why You Need Insight Whe is the last ti e ou a e e e taki g ti e to thi k a out ou life, ou alues, ou d ea s o ou pu pose i ei g o this

More information

The Second Law implies:

The Second Law implies: e Send Law ilie: ) Heat Engine η W in H H L H L H, H H ) Ablute eerature H H L L Sale, L L W ) Fr a yle H H L L H 4) Fr an Ideal Ga Cyle H H L L L δ reerible ree d Claiu Inequality δ eerible Cyle fr a

More information

Th e E u r o p e a n M ig r a t io n N e t w o r k ( E M N )

Th e E u r o p e a n M ig r a t io n N e t w o r k ( E M N ) Th e E u r o p e a n M ig r a t io n N e t w o r k ( E M N ) H E.R E T h em at ic W o r k sh o p an d Fin al C o n fer en ce 1 0-1 2 Ju n e, R agu sa, It aly D avid R eisen zein IO M V ien n a Foto: Monika

More information

Exercises for Differential Amplifiers. ECE 102, Fall 2012, F. Najmabadi

Exercises for Differential Amplifiers. ECE 102, Fall 2012, F. Najmabadi Execises f iffeential mplifies ECE 0, Fall 0, F. Najmabai Execise : Cmpute,, an G if m, 00 Ω, O, an ientical Q &Q with µ n C x 8 m, t, λ 0. F G 0 an B F G. epeat the execise f λ 0. -. This execise shws

More information

Optical Remote Sensing with DIfferential Absorption Lidar (DIAL)

Optical Remote Sensing with DIfferential Absorption Lidar (DIAL) Optcal emote esg wth DIffeetal Absopt Lda DIAL Pat : Theoy hstoph eff IE Uvesty of oloado & OAA/EL/D/Atmosphec emote esg Goup http://www.esl.oaa.gov/csd/goups/csd3/ Guest lectue fo AE-659 Lda emote esg

More information

c i l l is I D. a ^ ;5 3? i "0 > D N) NO o w

c i l l is I D. a ^ ;5 3? i 0 > D N) NO o w ;t::0 V>_;t/? t l> ! ( ; ~ - g : _! ;0 :0 :..4-4... "! " _ Z!! d) -~ Q 7 g! S a- ; -l!s D. : 2 (5 :g- g : 5 D? ;! -0?lg:? :$; ;

More information

Principles of multiple scattering in the atmosphere. Radiative transfer equation with scattering for solar radiation in a plane-parallel atmosphere.

Principles of multiple scattering in the atmosphere. Radiative transfer equation with scattering for solar radiation in a plane-parallel atmosphere. Lectue 7 incipes of utipe scatteing in the atosphee. Raiative tansfe equation with scatteing fo soa aiation in a pane-paae atosphee. Objectives:. Concepts of the iect an iffuse scattee soa aiation.. Souce

More information

Introduction to Money & Banking Lecture notes 3/2012. Matti Estola

Introduction to Money & Banking Lecture notes 3/2012. Matti Estola Intoduction to Mone & Banking Lectue notes 3/22 Matti Estola Inteest and pesent value calculation Tansfoation equations between inteest ates Inteest calculation Inteest ate (/t is the ate of etun of an

More information

A B CDE F B FD D A C AF DC A F

A B CDE F B FD D A C AF DC A F International Journal of Arts & Sciences, CD-ROM. ISSN: 1944-6934 :: 4(20):121 131 (2011) Copyright c 2011 by InternationalJournal.org A B CDE F B FD D A C A BC D EF C CE C A D ABC DEF B B C A E E C A

More information

ROOT-LOCUS ANALYSIS. Lecture 11: Root Locus Plot. Consider a general feedback control system with a variable gain K. Y ( s ) ( ) K

ROOT-LOCUS ANALYSIS. Lecture 11: Root Locus Plot. Consider a general feedback control system with a variable gain K. Y ( s ) ( ) K ROOT-LOCUS ANALYSIS Coder a geeral feedback cotrol yte wth a varable ga. R( Y( G( + H( Root-Locu a plot of the loc of the pole of the cloed-loop trafer fucto whe oe of the yte paraeter ( vared. Root locu

More information

MOSFET Internal Capacitances

MOSFET Internal Capacitances ead MOSFET Iteral aactace S&S (5ed): Sec. 4.8, 4.9, 6.4, 6.6 S&S (6ed): Sec. 9., 9.., 9.3., 9.4-9.5 The curret-voltae relatoh we have dcued thu far for the MOSFET cature the ehavor at low ad oderate frequece.

More information

NONDIFFERENTIABLE MATHEMATICAL PROGRAMS. OPTIMALITY AND HIGHER-ORDER DUALITY RESULTS

NONDIFFERENTIABLE MATHEMATICAL PROGRAMS. OPTIMALITY AND HIGHER-ORDER DUALITY RESULTS HE PUBLISHING HOUSE PROCEEDINGS OF HE ROMANIAN ACADEMY, See A, OF HE ROMANIAN ACADEMY Volue 9, Nube 3/8,. NONDIFFERENIABLE MAHEMAICAL PROGRAMS. OPIMALIY AND HIGHER-ORDER DUALIY RESULS Vale PREDA Uvety

More information

Chapter 8. Linear Momentum, Impulse, and Collisions

Chapter 8. Linear Momentum, Impulse, and Collisions Chapte 8 Lnea oentu, Ipulse, and Collsons 8. Lnea oentu and Ipulse The lnea oentu p of a patcle of ass ovng wth velocty v s defned as: p " v ote that p s a vecto that ponts n the sae decton as the velocty

More information

Lecture 2 Feedback Amplifier

Lecture 2 Feedback Amplifier Lectue Feedback mple ntductn w-pt Netwk Negatve Feedback Un-lateal Case Feedback plg nalss eedback applcatns Clse-Lp Gan nput/output esstances e:83hkn 3 Feedback mples w-pt Netwk z-paametes Open-Ccut mpedance

More information

ˆ SSE SSE q SST R SST R q R R q R R q

ˆ SSE SSE q SST R SST R q R R q R R q Bll Evas Spg 06 Sggested Aswes, Poblem Set 5 ECON 3033. a) The R meases the facto of the vaato Y eplaed by the model. I ths case, R =SSM/SST. Yo ae gve that SSM = 3.059 bt ot SST. Howeve, ote that SST=SSM+SSE

More information

( ) H α iff α Pure and Impure Altruism C H,H S,T. Find the utility payoff matrix of PD if subjects all have utility u C D

( ) H α iff α Pure and Impure Altruism C H,H S,T. Find the utility payoff matrix of PD if subjects all have utility u C D .8. Pure ad pure Altrus u x x x, ~ u P Altrus H,H S,T T,S L,L T H L S Fd the utlty payoff atrx of P f subects all have utlty u Altrus. (sol,, (, H ( T H S T, T S S, S T L (, L( Whe wll (, stll be the oly

More information

Department of Mathematics UNIVERSITY OF OSLO. FORMULAS FOR STK4040 (version 1, September 12th, 2011) A - Vectors and matrices

Department of Mathematics UNIVERSITY OF OSLO. FORMULAS FOR STK4040 (version 1, September 12th, 2011) A - Vectors and matrices Deartet of Matheatcs UNIVERSITY OF OSLO FORMULAS FOR STK4040 (verso Seteber th 0) A - Vectors ad atrces A) For a x atrx A ad a x atrx B we have ( AB) BA A) For osgular square atrces A ad B we have ( )

More information

2 c!? c!? c!? 9 D 5)e 99 9) 3 3P 2D % 5 s. r c!? z 3. s -2. sl P. s4 C? er a. se 2 " 59. " ee flh. - cfe. 5 te. cn " s9 5.

2 c!? c!? c!? 9 D 5)e 99 9) 3 3P 2D % 5 s. r c!? z 3. s -2. sl P. s4 C? er a. se 2  59.  ee flh. - cfe. 5 te. cn  s9 5. 5, 2 3-2 JI ee JI 4 2 3 5 c!? P 2 c!? 3 JI S- e, e 3L c!? =! - s- 5 9 9 a I. s9 5 5 te 3 3 " 59 t$ 3 cn " -1 " ee flh s4 C? er a - cfe 5 s 9 5 ge E z 3 r c!? sl P ee 3 3P 2D 2 9 D 5)e se 2 2 % 5-3 s -2

More information

Noise in electronic components.

Noise in electronic components. No lto opot5098, JDS No lto opot Th PN juto Th ut thouh a PN juto ha fou opot t: two ffuo ut (hol fo th paa to th aa a lto th oppot to) a thal at oty ha a (hol fo th aa to th paa a lto th oppot to, laka

More information

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN

More information

dm dt = 1 V The number of moles in any volume is M = CV, where C = concentration in M/L V = liters. dcv v

dm dt = 1 V The number of moles in any volume is M = CV, where C = concentration in M/L V = liters. dcv v Mg: Pcess Aalyss: Reac ae s defed as whee eac ae elcy lue M les ( ccea) e. dm he ube f les ay lue s M, whee ccea M/L les. he he eac ae beces f a hgeeus eac, ( ) d Usually s csa aqueus eeal pcesses eac,

More information

c- : r - C ' ',. A a \ V

c- : r - C ' ',. A a \ V HS PAGE DECLASSFED AW EO 2958 c C \ V A A a HS PAGE DECLASSFED AW EO 2958 HS PAGE DECLASSFED AW EO 2958 = N! [! D!! * J!! [ c 9 c 6 j C v C! ( «! Y y Y ^ L! J ( ) J! J ~ n + ~ L a Y C + J " J 7 = [ " S!

More information

SI Appendix Model Flow Chart of Dog-Human Rabies Transmission

SI Appendix Model Flow Chart of Dog-Human Rabies Transmission Appenx Moel Flow Cat of Dog-Huan abes Tanssson Aea epenent enstes of te og an uan populatons wee assue an ntal alues calculate by usng a suface fo te stuy aea of Djaéna of 700 k 2. Te ntal nube of expose

More information

1 Random Variable. Why Random Variable? Discrete Random Variable. Discrete Random Variable. Discrete Distributions - 1 DD1-1

1 Random Variable. Why Random Variable? Discrete Random Variable. Discrete Random Variable. Discrete Distributions - 1 DD1-1 Rando Vaiable Pobability Distibutions and Pobability Densities Definition: If S is a saple space with a pobability easue and is a eal-valued function defined ove the eleents of S, then is called a ando

More information

Probability Distribution (Probability Model) Chapter 2 Discrete Distributions. Discrete Random Variable. Random Variable. Why Random Variable?

Probability Distribution (Probability Model) Chapter 2 Discrete Distributions. Discrete Random Variable. Random Variable. Why Random Variable? Discete Distibutions - Chapte Discete Distibutions Pobability Distibution (Pobability Model) If a balanced coin is tossed, Head and Tail ae equally likely to occu, P(Head) = = / and P(Tail) = = /. Rando

More information

A New Result On A,p n,δ k -Summabilty

A New Result On A,p n,δ k -Summabilty OSR Joual of Matheatics (OSR-JM) e-ssn: 2278-5728, p-ssn:239-765x. Volue 0, ssue Ve. V. (Feb. 204), PP 56-62 www.iosjouals.og A New Result O A,p,δ -Suabilty Ripeda Kua &Aditya Kua Raghuashi Depatet of

More information

AN ALGORITHM FOR CALCULATING THE CYCLETIME AND GREENTIMES FOR A SIGNALIZED INTERSECTION

AN ALGORITHM FOR CALCULATING THE CYCLETIME AND GREENTIMES FOR A SIGNALIZED INTERSECTION AN AGORITHM OR CACUATING THE CYCETIME AND GREENTIMES OR A SIGNAIZED INTERSECTION Henk Taale 1. Intoducton o a snalzed ntesecton wth a fedte contol state the cclete and eentes ae the vaables that nfluence

More information

Objectives. Learning Outcome. 7.1 Centre of Gravity (C.G.) 7. Statics. Determine the C.G of a lamina (Experimental method)

Objectives. Learning Outcome. 7.1 Centre of Gravity (C.G.) 7. Statics. Determine the C.G of a lamina (Experimental method) Ojectves 7 Statcs 7. Cete of Gavty 7. Equlum of patcles 7.3 Equlum of g oes y Lew Sau oh Leag Outcome (a) efe cete of gavty () state the coto whch the cete of mass s the cete of gavty (c) state the coto

More information

Variability, Randomness and Little s Law

Variability, Randomness and Little s Law Vaalty, Randomness and Lttle s Law Geoge Leopoulos Lttle s Law Assumptons Any system (poducton system) n whch enttes (pats) ave, spend some tme (pocessng tme + watng) and eventually depat Defntons = (long-un

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

Week 9: Multivibrators, MOSFET Amplifiers

Week 9: Multivibrators, MOSFET Amplifiers ELE 2110A Electronc Crcuts Week 9: Multbrators, MOSFET Aplfers Lecture 09-1 Multbrators Topcs to coer Snle-stae MOSFET aplfers Coon-source aplfer Coon-dran aplfer Coon-ate aplfer eadn Assnent: Chap 14.1-14.5

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

TEXAS LOTTERY COMMISSION Scratch Ticket Game Closing Analysis SUMMARY REPORT Scratch Ticket Information Date Completed 9/20/2017

TEXAS LOTTERY COMMISSION Scratch Ticket Game Closing Analysis SUMMARY REPORT Scratch Ticket Information Date Completed 9/20/2017 TES LTTERY CISSI Scch Ticke Ge Clsing nlysis SURY REPRT Scch Ticke Infin Clee 9/2/217 Ge # 183 Cnfie Pcks 5,26 Ge e illy nk Glen Ticke cive Pcks,33 Quniy Pine 9,676,3 ehuse Pcks,233 Pice Pin 1 Reune Pcks

More information

1. Linear second-order circuits

1. Linear second-order circuits ear eco-orer crcut Sere R crcut Dyamc crcut cotag two capactor or two uctor or oe uctor a oe capactor are calle the eco orer crcut At frt we coer a pecal cla of the eco-orer crcut, amely a ere coecto of

More information

Lecture 6 & 7. Shuanglin Shao. September 16th and 18th, 2013

Lecture 6 & 7. Shuanglin Shao. September 16th and 18th, 2013 Lecture 6 & 7 Shuanglin Shao September 16th and 18th, 2013 1 Elementary matrices 2 Equivalence Theorem 3 A method of inverting matrices Def An n n matrice is called an elementary matrix if it can be obtained

More information

Copyright Birkin Cars (Pty) Ltd

Copyright Birkin Cars (Pty) Ltd e f u:- 5: K360 98AA RADIATOR 5: K360 053AA SEAT MOUNTING GROU 5:3 K360 06A WIER MOTOR GROU 5:4 K360 0A HANDRAKE 5:5 K360 0A ENTRE ONSOE 5:6 K360 05AA RO AGE 5:7 K360 48AA SARE WHEE RADE 5:8 K360 78AA

More information

2. Elementary Linear Algebra Problems

2. Elementary Linear Algebra Problems . Eleety e lge Pole. BS: B e lge Suoute (Pog pge wth PCK) Su of veto opoet:. Coputto y f- poe: () () () (3) N 3 4 5 3 6 4 7 8 Full y tee Depth te tep log()n Veto updte the f- poe wth N : ) ( ) ( ) ( )

More information

Lecture 24: Observability and Constructibility

Lecture 24: Observability and Constructibility ectue 24: Obsevability ad Costuctibility 7 Obsevability ad Costuctibility Motivatio: State feedback laws deped o a kowledge of the cuet state. I some systems, xt () ca be measued diectly, e.g., positio

More information

A New I 1 -Based Hyperelastic Model for Rubber Elastic Materials

A New I 1 -Based Hyperelastic Model for Rubber Elastic Materials A New I -Based Hypeelastic Model fo Rubbe Elastic Mateials Osca Lopez-Paies SES Octobe -4, Evanston, IL Neo-Hookean odel W ìï ï ( I - ) = ( if l + l + l - ) lll = = í ï + othewise ïî (*). Matheatical siplicity

More information

3.2 Subspace. Definition: If S is a non-empty subset of a vector space V, and S satisfies the following conditions: (i).

3.2 Subspace. Definition: If S is a non-empty subset of a vector space V, and S satisfies the following conditions: (i). . ubspace Given a vector spacev, it is possible to form another vector space by taking a subset of V and using the same operations (addition and multiplication) of V. For a set to be a vector space, it

More information

ME306 Dynamics, Spring HW1 Solution Key. AB, where θ is the angle between the vectors A and B, the proof

ME306 Dynamics, Spring HW1 Solution Key. AB, where θ is the angle between the vectors A and B, the proof ME6 Dnms, Spng HW Slutn Ke - Pve, gemetll.e. usng wngs sethes n nltll.e. usng equtns n nequltes, tht V then V. Nte: qunttes n l tpee e vets n n egul tpee e sls. Slutn: Let, Then V V V We wnt t pve tht:

More information

Lesson Ten. What role does energy play in chemical reactions? Grade 8. Science. 90 minutes ENGLISH LANGUAGE ARTS

Lesson Ten. What role does energy play in chemical reactions? Grade 8. Science. 90 minutes ENGLISH LANGUAGE ARTS Lesson Ten What role does energy play in chemical reactions? Science Asking Questions, Developing Models, Investigating, Analyzing Data and Obtaining, Evaluating, and Communicating Information ENGLISH

More information

Revision of Lecture Eight

Revision of Lecture Eight Revision of Lectue Eight Baseband equivalent system and equiements of optimal tansmit and eceive filteing: (1) achieve zeo ISI, and () maximise the eceive SNR Thee detection schemes: Theshold detection

More information

11. Ideal Gas Mixture

11. Ideal Gas Mixture . Ideal Ga xture. Geeral oderato ad xture of Ideal Gae For a geeral xture of N opoet, ea a pure ubtae [kg ] te a for ea opoet. [kol ] te uber of ole for ea opoet. e al a ( ) [kg ] N e al uber of ole (

More information

Week 2: First Order Semi-Linear PDEs

Week 2: First Order Semi-Linear PDEs Week 2: First Order Semi-Linear PDEs Introction We want to find a formal solution to the first order semilinear PDEs of the form a(, y)u + b(, y)u y = c(, y, u). Using a change of variables corresponding

More information

Example. Addition, subtraction, and multiplication in Z are binary operations; division in Z is not ( Z).

Example. Addition, subtraction, and multiplication in Z are binary operations; division in Z is not ( Z). CHAPTER 2 Groups Definition (Binary Operation). Let G be a set. A binary operation on G is a function that assigns each ordered pair of elements of G an element of G. Note. This condition of assigning

More information

xfyy.sny E gyef Lars g 8 2 s Zs yr Yao x ao X Axe B X'lo AtB tair z2schhyescosh's 2C scoshyesukh 8 gosh E si Eire 3AtB o X g o I

xfyy.sny E gyef Lars g 8 2 s Zs yr Yao x ao X Axe B X'lo AtB tair z2schhyescosh's 2C scoshyesukh 8 gosh E si Eire 3AtB o X g o I Math 418, Fall 2018, Midterm Prf. Sherman Name nstructins: This is a 50 minute exam. Fr credit yu must shw all relevant wrk n each prblem. Yu may nt use any calculatrs, phnes, bks, ntes, etc. There are

More information