(8) Gain Stage and Simple Output Stage

Size: px
Start display at page:

Download "(8) Gain Stage and Simple Output Stage"

Transcription

1 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 ) ntoducton n tually all opeatonal amplfes (opamps), thee ae 3 stages: 1) Fst stage s nput Stage Dff-amp wth acte load to amplfy dffeence between nput sgnals 1 and 2. 2) Second stage s Gan Stage Dalngton pa to pode addtonal gan. 3) hd stage s Output Stage Emtte followe to mnmze loadng effect on output sgnal. 8.1) Dalngton Pa and Smple Emtte-Followe Output Fgue 11.4 shows a BJ dff-amp wth a 3-tanssto acte load, a Dalngton pa connected to the dff-amp output, and a smple emtte-followe output stage. Dff-pa tansstos ( 1 and 2 ) ae based wth a Wdla cuent souce at a bas cuent. Fo the dff-amp cuents to be balanced: O B5 ( 1 ) β + β (11.118) Fom the fgue, can be seen E C O 1+ β β 1+ ( ) ( (11.119) n ode fo O B5, eque that C Means that emtte esstos of 10 and 11 should hae same alue (.e. 2 3 ). 11 also acts as an acte load fo Dalngton pa gan stage. Fgue and 4 fom the smple emtte-followe output stage mnmzes loadng effects because ts output esstance s small. Lectue: D Jamaludn Bn Oma 8-1

2 EEEB23 Electoncs Analyss & Desgn deally: When dff-amp nput s a pue commonmode sgnal, the output o 0. he combnaton of and 11 allows dc leel to shft. By slghtly changng bas cuent C V EC and V CE11 can be aed such that o 0. hs small aaton n C wll not sgnfcantly change the balance between O and B5. 8.2) Dalngton Pa: nput mpedance he nput esstance of Dalngton pa ( and ) detemnes the loadng effect on basc dff-amp. he gan of Dalngton pa affects the oeall gan of the op-amp ccut, and the output esstance of the emtte followe detemnes any loadng effects on the output sgnal. Fgue 11.4(a) s the ac equalent ccut of the Dalngton pa, whee s the effecte esstance connected between collecto of and sgnal gound. Fgue 11.4(b) s the smple hybd- model of the Dalngton pa and tuned upsde down. 8.2) Dalngton Pa: nput mpedance (Cont) Fgue 11.4: he Dalngton pa s (a) ac equalent ccut, and (b) small-sgnal equalent ccut 8.2) Dalngton Pa: nput mpedance (Cont) Wtng a KVL equaton aound the B-E loop of and can obtan Vb + (11.120) Also V (11.121) π π ( 1 + π π g β π π he KCL equaton at node E s + gm o whee m π V π π (11.122(b)) 8.2) Dalngton Pa: nput mpedance (Cont) Substtute (11.122(b)) and (11.121) nto (11.120) to obtan V + (11.123) π C C he nput esstance s theefoe Vb π + π π π π (11.124) Assumng C, the hybd- paametes ae (11.125(a)) (11.125(b)) 8.2) Dalngton Pa: nput mpedance (Cont) Combnng (11.125(a)), (11.125(b)), and (11.124) yelds an expesson fo nput esstance, as follows: 2 + (11.12) Lectue: D Jamaludn Bn Oma 8-2

3 EEEB23 Electoncs Analyss & Desgn 8.3) Dalngton Pa: Voltage Gan o detemne small-sgnal oltage gan of the Dalngton pa, fom Fg 11.4(b) can be obtaned Voltage Gan: o3 c A o3 β ( β b ) ( ) V + β β β hus, A (11.130) 2 1 2V β Fom Fgue 11.4, can see that s the paallel combnaton of the esstance lookng nto collecto of 11 and the esstance lookng nto base of 8. esstance lookng nto collecto of 11 s whee c11 o 11 1 ' E π11 ' ( + g ) esstance lookng nto base of 8 s b8 π m11 E (11.131) (11.132) Snce c11 and b8 ae lage, then the effecte esstance s also lage. Example Objecte: Calculate the nput esstance and the small-sgnal oltage gan of a Dalngton pa. Consde the ccut shown n Fgue 11.4, wth paametes C 0.2 ma, C8 1 ma, 4 10 k, and k. Assume 100 fo all tansstos, and the Ealy oltage fo 11 s 100 V. Soluton: he nput esstance, gen by Equaton (11.12), s V ( ) 2 β (100)(0.02) 2. 3MΩ 0.2m he small-sgnal oltage gan s a functon of, whch n tun s a functon of c11 and b8. We can fnd that 11 V / (100)(0.02)/(0.2m) 13 k such that E 13k 0.2k 0.19 k Also and g m11 / V 0.2m/ ma/v o11 V A / 100/0.2m 500 k heefoe, c11 o11 (1 + g m11 E ) 1.2 M We can detemne that 8 V / C8 (100)(0.02)/(1m) 2. k hen b8 8 +(1+) 4 2.k+(101)(10k) 1.01 M Consequently, esstance s c11 b8 1.2M1.01M 0.51 M Fnally, fom Equaton (11.130), the small-sgnal oltage gan s A ( / 2V ) 2158 Lectue: D Jamaludn Bn Oma 8-3

4 EEEB23 Electoncs Analyss & Desgn 8.4) Emtte Followe: Output esstance Fom Fgue 11.4, the output esstance of the emtte followe 8 s o 4 + Z π 8 (11.133) whee Z s the equalent mpedance, o esstance, n the base of 8. n ths case, Z c11 c, whee c s esstance lookng nto the collecto of 8.4) Emtte Followe: Output esstance (Cont) Example Objecte: Calculate the output esstance of the ccut n Fgue Consde the same ccut and tanssto paametes descbed n Example Assume the Ealy oltage of s 100 V. he facto (1+) n the denomnato makes output esstance of the emtte followe nomally small. 8.4) Emtte Followe: Output esstance (Cont) Example (Cont) Soluton: Fom Example 11.13, we hae that c M and 8 2. k. 8.5) Oeall Gan of the Op-amp ccut nput stage: Dff-amp wth acte load A V Gan stage: Dalngton pa A V We can detemne that c V A / 100/0.2m 500 k hen, Z c11 c 1.2M500k 358 k heefoe o π 8 + Z 2.k + 358k 10k ( 101) 4 2.3k Output stage: Emtte-followe A V3 1 Oeall Gan: A V (A V1 ).(A V2 ).(A V3 ) s the typcal alue fo low-fequency, open-loop gan of the op-amp ccuts Lage ccuts Fgue 11.4 Lectue: D Jamaludn Bn Oma 8-4

5 EEEB23 Electoncs Analyss & Desgn 8.2) Dalngton Pa: nput mpedance and Voltage Gan (Cont) Fgue 11.4: he Dalngton pa s (a) ac equalent ccut, and (b) small-sgnal equalent ccut Lectue: D Jamaludn Bn Oma 8-5

9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor

9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor Mcoelectoncs Ccut Analyss and Desgn Donald A. Neamen Chapte 5 The pola Juncton Tanssto In ths chapte, we wll: Dscuss the physcal stuctue and opeaton of the bpola juncton tanssto. Undestand the dc analyss

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

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

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010 FE REVEW OPERATONAL AMPLFERS (OP-AMPS)( ) 1 The Op-amp 2 An op-amp has two nputs and one output. Note the op-amp below. The termnal labeled l wth the (-) sgn s the nvertng nput and the nput labeled wth

More information

Amplifier Constant Gain and Noise

Amplifier Constant Gain and Noise Amplfe Constant Gan and ose by Manfed Thumm and Wene Wesbeck Foschungszentum Kalsuhe n de Helmholtz - Gemenschaft Unvestät Kalsuhe (TH) Reseach Unvesty founded 85 Ccles of Constant Gan (I) If s taken to

More information

Week 11: Differential Amplifiers

Week 11: Differential Amplifiers ELE 0A Electronc rcuts Week : Dfferental Amplfers Lecture - Large sgnal analyss Topcs to coer A analyss Half-crcut analyss eadng Assgnment: hap 5.-5.8 of Jaeger and Blalock or hap 7. - 7.3, of Sedra and

More information

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS) FE EIEW OPEATIONAL AMPLIFIES (OPAMPS) 1 The Opamp An opamp has two nputs and one output. Note the opamp below. The termnal labeled wth the () sgn s the nvertng nput and the nput labeled wth the () sgn

More information

Physics Exam II Chapters 25-29

Physics Exam II Chapters 25-29 Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do

More information

55:141 Advanced Circuit Techniques Two-Port Theory

55:141 Advanced Circuit Techniques Two-Port Theory 55:4 Adanced Crcut Technques Two-Port Theory Materal: Lecture Notes A. Kruger 55:4: Adanced Crcut Technques The Unersty of Iowa, 03 Two-Port Theory, Slde What Are Two-Ports? Basc dea: replace a complex

More information

55:041 Electronic Circuits

55:041 Electronic Circuits 55:04 Electronc Crcuts Feedback & Stablty Sectons of Chapter 2. Kruger Feedback & Stablty Confguraton of Feedback mplfer Negate feedback β s the feedback transfer functon S o S S o o S S o f S S S S fb

More information

55:141 Advanced Circuit Techniques Two-Port Theory

55:141 Advanced Circuit Techniques Two-Port Theory 55:4 Adanced Crcut Technques Two-Port Theory Materal: Lecture Notes A. Kruger 55:4: Adanced Crcut Technques The Unersty of Iowa, 205 Two-Port Theory, Slde Two-Port Networks Note, the BJT s all are hghly

More information

Selected Student Solutions for Chapter 2

Selected Student Solutions for Chapter 2 /3/003 Assessment Prolems Selected Student Solutons for Chapter. Frst note that we know the current through all elements n the crcut except the 6 kw resstor (the current n the three elements to the left

More information

Celso José Faria de Araújo, M.Sc.

Celso José Faria de Araújo, M.Sc. Celso José Faa de Aaújo, M.c. he deal dode: (a) dode ccut symbol; (b) - chaactestc; (c) equalent ccut n the eese decton; (d) equalent ccut n the fowad decton. odes (a) Rectfe ccut. (b) nput waefom. (c)

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

55:041 Electronic Circuits

55:041 Electronic Circuits 55:04 Electronc Crcuts Feedback & Stablty Sectons of Chapter 2. Kruger Feedback & Stablty Confguraton of Feedback mplfer S o S ε S o ( S β S ) o Negate feedback S S o + β β s the feedback transfer functon

More information

VI. Transistor Amplifiers

VI. Transistor Amplifiers VI. Transstor Amplfers 6. Introducton In ths secton we wll use the transstor small-sgnal model to analyze and desgn transstor amplfers. There are two ssues that we need to dscuss frst: ) What are the mportant

More information

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment

More information

College of Engineering Department of Electronics and Communication Engineering. Test 1 With Model Answer

College of Engineering Department of Electronics and Communication Engineering. Test 1 With Model Answer Name: Student D Number: Secton Number: 01/0/03/04 A/B Lecturer: Dr Jamaludn/ Dr Jehana Ermy/ Dr Azn Wat Table Number: College of Engneerng Department of Electroncs and Communcaton Engneerng Test 1 Wth

More information

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment

More information

CHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation:

CHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation: HPT 3 xercses 3. The emtter current s gen by the Shockley equaton: S exp VT For operaton wth, we hae exp >> S >>, and we can wrte VT S exp VT Solng for, we hae 3. 0 6ln 78.4 mv 0 0.784 5 4.86 V VT ln 4

More information

Electrical Engineering Department Network Lab.

Electrical Engineering Department Network Lab. Electrcal Engneerng Department Network Lab. Objecte: - Experment on -port Network: Negate Impedance Conerter To fnd the frequency response of a smple Negate Impedance Conerter Theory: Negate Impedance

More information

1 S = G R R = G. Enzo Paterno

1 S = G R R = G. Enzo Paterno ECET esistie Circuits esistie Circuits: - Ohm s Law - Kirchhoff s Laws - Single-Loop Circuits - Single-Node Pair Circuits - Series Circuits - Parallel Circuits - Series-Parallel Circuits Enzo Paterno ECET

More information

MAE140 - Linear Circuits - Winter 16 Final, March 16, 2016

MAE140 - Linear Circuits - Winter 16 Final, March 16, 2016 ME140 - Lnear rcuts - Wnter 16 Fnal, March 16, 2016 Instructons () The exam s open book. You may use your class notes and textbook. You may use a hand calculator wth no communcaton capabltes. () You have

More information

Graphical Analysis of a BJT Amplifier

Graphical Analysis of a BJT Amplifier 4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 1/18 Graphcal Analyss of a BJT Amplfer onsder agan ths smple BJT amplfer: ( t) = + ( t) O O o B + We note that for ths amplfer, the output oltage s

More information

19 The Born-Oppenheimer Approximation

19 The Born-Oppenheimer Approximation 9 The Bon-Oppenheme Appoxmaton The full nonelatvstc Hamltonan fo a molecule s gven by (n a.u.) Ĥ = A M A A A, Z A + A + >j j (883) Lets ewte the Hamltonan to emphasze the goal as Ĥ = + A A A, >j j M A

More information

Chapter 13 - Universal Gravitation

Chapter 13 - Universal Gravitation Chapte 3 - Unesal Gataton In Chapte 5 we studed Newton s thee laws of moton. In addton to these laws, Newton fomulated the law of unesal gataton. Ths law states that two masses ae attacted by a foce gen

More information

If there are k binding constraints at x then re-label these constraints so that they are the first k constraints.

If there are k binding constraints at x then re-label these constraints so that they are the first k constraints. Mathematcal Foundatons -1- Constaned Optmzaton Constaned Optmzaton Ma{ f ( ) X} whee X {, h ( ), 1,, m} Necessay condtons fo to be a soluton to ths mamzaton poblem Mathematcally, f ag Ma{ f ( ) X}, then

More information

Introduction of Two Port Network Negative Feedback (Uni lateral Case) Feedback Topology Analysis of feedback applications

Introduction of Two Port Network Negative Feedback (Uni lateral Case) Feedback Topology Analysis of feedback applications Lectue Feedback mple ntductn w Pt Netwk Negatve Feedback Un lateal Case Feedback plg nalss eedback applcatns Clse Lp Gan nput/output esstances e:83h 3 Feedback w-pt Netwk z-paametes Open-Ccut mpedance

More information

COLLEGE OF ENGINEERING PUTRAJAYA CAMPUS FINAL EXAMINATION SPECIAL SEMESTER 2013 / 2014

COLLEGE OF ENGINEERING PUTRAJAYA CAMPUS FINAL EXAMINATION SPECIAL SEMESTER 2013 / 2014 OLLEGE OF ENGNEENG PUTAJAYA AMPUS FNAL EXAMNATON SPEAL SEMESTE 03 / 04 POGAMME SUBJET ODE SUBJET : Bachelor of Electrcal & Electroncs Engneerng (Honours) Bachelor of Electrcal Power Engneerng (Honours)

More information

6.01: Introduction to EECS 1 Week 6 October 15, 2009

6.01: Introduction to EECS 1 Week 6 October 15, 2009 6.0: ntroducton to EECS Week 6 October 5, 2009 6.0: ntroducton to EECS Crcuts The Crcut Abstracton Crcuts represent systems as connectons of component through whch currents (through arables) flow and across

More information

Formulation of Circuit Equations

Formulation of Circuit Equations ECE 570 Sesson 2 IC 752E Computer Aded Engneerng for Integrated Crcuts Formulaton of Crcut Equatons Bascs of crcut modelng 1. Notaton 2. Crcut elements 3. Krchoff laws 4. ableau formulaton 5. Modfed nodal

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

Electrical Circuits 2.1 INTRODUCTION CHAPTER

Electrical Circuits 2.1 INTRODUCTION CHAPTER CHAPTE Electrcal Crcuts. INTODUCTION In ths chapter, we brefly revew the three types of basc passve electrcal elements: resstor, nductor and capactor. esstance Elements: Ohm s Law: The voltage drop across

More information

EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING

EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING TaChang Chen Unersty of Washngton, Bothell Sprng 2010 EE215 1 WEEK 8 FIRST ORDER CIRCUIT RESPONSE May 21 st, 2010 EE215 2 1 QUESTIONS TO ANSWER Frst order crcuts

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

Energy Storage Elements: Capacitors and Inductors

Energy Storage Elements: Capacitors and Inductors CHAPTER 6 Energy Storage Elements: Capactors and Inductors To ths pont n our study of electronc crcuts, tme has not been mportant. The analyss and desgns we hae performed so far hae been statc, and all

More information

Transfer Characteristic

Transfer Characteristic Eeld-Effect Transstors (FETs 3.3 The CMS Common-Source Amplfer Transfer Characterstc Electronc Crcuts, Dept. of Elec. Eng., The Chnese Unersty of Hong Kong, Prof. K.-L. Wu Lesson 8&9 Eeld-Effect Transstors

More information

Test 1 phy What mass of a material with density ρ is required to make a hollow spherical shell having inner radius r i and outer radius r o?

Test 1 phy What mass of a material with density ρ is required to make a hollow spherical shell having inner radius r i and outer radius r o? Test 1 phy 0 1. a) What s the pupose of measuement? b) Wte all fou condtons, whch must be satsfed by a scala poduct. (Use dffeent symbols to dstngush opeatons on ectos fom opeatons on numbes.) c) What

More information

G = G 1 + G 2 + G 3 G 2 +G 3 G1 G2 G3. Network (a) Network (b) Network (c) Network (d)

G = G 1 + G 2 + G 3 G 2 +G 3 G1 G2 G3. Network (a) Network (b) Network (c) Network (d) Massachusetts Insttute of Technology Department of Electrcal Engneerng and Computer Scence 6.002 í Electronc Crcuts Homework 2 Soluton Handout F98023 Exercse 21: Determne the conductance of each network

More information

Physics Exam 3

Physics Exam 3 Physcs 114 1 Exam 3 The numbe of ponts fo each secton s noted n backets, []. Choose a total of 35 ponts that wll be gaded that s you may dop (not answe) a total of 5 ponts. Clealy mak on the cove of you

More information

V V. This calculation is repeated now for each current I.

V V. This calculation is repeated now for each current I. Page1 Page2 The power supply oltage V = +5 olts and the load resstor R = 1 k. For the range of collector bas currents, I = 0.5 ma, 1 ma, 2.5 ma, 4 ma and 4.5 ma, determne the correspondng collector-to-emtter

More information

Copyright 2004 by Oxford University Press, Inc.

Copyright 2004 by Oxford University Press, Inc. JT as an Amplfer &a Swtch, Large Sgnal Operaton, Graphcal Analyss, JT at D, asng JT, Small Sgnal Operaton Model, Hybrd P-Model, TModel. Lecture # 7 1 Drecton of urrent Flow & Operaton for Amplfer Applcaton

More information

CIRCUITS 1 DEVELOP TOOLS FOR THE ANALYSIS AND DESIGN OF BASIC LINEAR ELECTRIC CIRCUITS

CIRCUITS 1 DEVELOP TOOLS FOR THE ANALYSIS AND DESIGN OF BASIC LINEAR ELECTRIC CIRCUITS CCUTS DEELOP TOOLS FO THE ANALYSS AND DESGN OF BASC LNEA ELECTC CCUTS ESSTE CCUTS Here we introduce the basic concepts and laws that are fundamental to circuit analysis LEANNG GOALS OHM S LAW - DEFNES

More information

55:041 Electronic Circuits

55:041 Electronic Circuits 55:041 Electonic icuits BJT eview Sections in hapte 5 & 6 in Textbook A. Kuge BJT eview, Page- 1 npn Output Family of uves A. Kuge BJT eview, Page- 2 npn BJT dc Equivalent evese biased Fowad biased i B

More information

MAE140 - Linear Circuits - Winter 16 Midterm, February 5

MAE140 - Linear Circuits - Winter 16 Midterm, February 5 Instructons ME140 - Lnear Crcuts - Wnter 16 Mdterm, February 5 () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator

More information

Energy in Closed Systems

Energy in Closed Systems Enegy n Closed Systems Anamta Palt palt.anamta@gmal.com Abstact The wtng ndcates a beakdown of the classcal laws. We consde consevaton of enegy wth a many body system n elaton to the nvese squae law and

More information

A. Thicknesses and Densities

A. Thicknesses and Densities 10 Lab0 The Eath s Shells A. Thcknesses and Denstes Any theoy of the nteo of the Eath must be consstent wth the fact that ts aggegate densty s 5.5 g/cm (ecall we calculated ths densty last tme). In othe

More information

EE C245 ME C218 Introduction to MEMS Design

EE C245 ME C218 Introduction to MEMS Design EE C45 ME C8 Introducton to MEM Desgn Fall 7 Prof. Clark T.C. Nguyen Dept. of Electrcal Engneerng & Computer cences Unersty of Calforna at Berkeley Berkeley, C 947 Dscusson: eew of Op mps EE C45: Introducton

More information

ELG 2135 ELECTRONICS I SECOND CHAPTER: OPERATIONAL AMPLIFIERS

ELG 2135 ELECTRONICS I SECOND CHAPTER: OPERATIONAL AMPLIFIERS ELG 35 ELECTONICS I SECOND CHAPTE: OPEATIONAL AMPLIFIES Sesson Wnter 003 Dr. M. YAGOUB Second Chapter: Operatonal amplfers II - _ After reewng the basc aspects of amplfers, we wll ntroduce a crcut representng

More information

Rotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1

Rotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1 Rotatonal Knematcs Rgd Object about a Fxed Axs Westen HS AP Physcs 1 Leanng Objectes What we know Unfom Ccula Moton q s Centpetal Acceleaton : Centpetal Foce: Non-unfom a F c c m F F F t m ma t What we

More information

Electrical Circuits II (ECE233b)

Electrical Circuits II (ECE233b) Electrcal Crcuts (ECE33b SteadyState Power Analyss Anests Dounas The Unersty of Western Ontaro Faculty of Engneerng Scence SteadyState Power Analyss (t AC crcut: The steady state oltage and current can

More information

MAE140 - Linear Circuits - Fall 13 Midterm, October 31

MAE140 - Linear Circuits - Fall 13 Midterm, October 31 Instructons ME140 - Lnear Crcuts - Fall 13 Mdterm, October 31 () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator

More information

Lecture 5: Operational Amplifiers and Op Amp Circuits

Lecture 5: Operational Amplifiers and Op Amp Circuits Lecture 5: peratonal mplers and p mp Crcuts Gu-Yeon We Dson o Engneerng and ppled Scences Harard Unersty guyeon@eecs.harard.edu We erew eadng S&S: Chapter Supplemental eadng Background rmed wth our crcut

More information

I = α I I. Bipolar Junction Transistors (BJTs) 2.15 The Emitter-Coupled Pair. By using KVL: V

I = α I I. Bipolar Junction Transistors (BJTs) 2.15 The Emitter-Coupled Pair. By using KVL: V Bpolar Juncton ransstors (BJs).5 he Emtter-oupled Par By usng KL: + + 0 Wth the transstors based n the forward-acte mode, the reerse saturaton current of the collector-base juncton s neglgble. / α F ES

More information

BASIC ELECTRICAL CIRCUITS AND ANALYSIS. Ref: Horowitz, P, & W. Hill, The Art of Electronics, 2nd. ed., Cambridge (1989).

BASIC ELECTRICAL CIRCUITS AND ANALYSIS. Ref: Horowitz, P, & W. Hill, The Art of Electronics, 2nd. ed., Cambridge (1989). BASC ELECTCAL CCUTS AND ANALYSS ef: Horowitz, P, & W. Hill, The Art of Electronics, nd. ed., Cambridge (989). CHAGE - symbol C, unit is coulomb; coulomb 6.45 0 8 electrons CUENT - symbol or i, unit is

More information

3. A Review of Some Existing AW (BT, CT) Algorithms

3. A Review of Some Existing AW (BT, CT) Algorithms 3. A Revew of Some Exstng AW (BT, CT) Algothms In ths secton, some typcal ant-wndp algothms wll be descbed. As the soltons fo bmpless and condtoned tansfe ae smla to those fo ant-wndp, the pesented algothms

More information

Scalars and Vectors Scalar

Scalars and Vectors Scalar Scalas and ectos Scala A phscal quantt that s completel chaacteed b a eal numbe (o b ts numecal value) s called a scala. In othe wods a scala possesses onl a magntude. Mass denst volume tempeatue tme eneg

More information

Chapter 6. Operational Amplifier. inputs can be defined as the average of the sum of the two signals.

Chapter 6. Operational Amplifier.  inputs can be defined as the average of the sum of the two signals. 6 Operatonal mpler Chapter 6 Operatonal mpler CC Symbol: nput nput Output EE () Non-nvertng termnal, () nvertng termnal nput mpedance : Few mega (ery hgh), Output mpedance : Less than (ery low) Derental

More information

I. INTRODUCTION. There are two other circuit elements that we will use and are special cases of the above elements. They are:

I. INTRODUCTION. There are two other circuit elements that we will use and are special cases of the above elements. They are: I. INTRODUCTION 1.1 Crcut Theory Fundamentals In ths course we study crcuts wth non-lnear elements or deces (dodes and transstors). We wll use crcut theory tools to analyze these crcuts. Snce some of tools

More information

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Kinematics of Rigid Bodies in Three Dimensions. Seventh Edition CHAPTER

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Kinematics of Rigid Bodies in Three Dimensions. Seventh Edition CHAPTER Edton CAPTER 8 VECTOR MECANCS FOR ENGNEERS: DYNAMCS Fednand P. Bee E. Russell Johnston, J. Lectue Notes: J. Walt Ole Teas Tech Unvest Knematcs of Rgd Bodes n Thee Dmensons 003 The McGaw-ll Companes, nc.

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

Designing Information Devices and Systems II Spring 2018 J. Roychowdhury and M. Maharbiz Discussion 3A

Designing Information Devices and Systems II Spring 2018 J. Roychowdhury and M. Maharbiz Discussion 3A EECS 16B Desgnng Informaton Devces and Systems II Sprng 018 J. Roychowdhury and M. Maharbz Dscusson 3A 1 Phasors We consder snusodal voltages and currents of a specfc form: where, Voltage vt) = V 0 cosωt

More information

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

College of Engineering Department of Electronics and Communication Engineering. Test 2 Name: Student D Number: Secton Number: 01/0/03/04 A/B Lecturer: Dr Jamaludn/ Dr Azn Wat/ Dr Jehana Ermy/ Prof Md Zan Table Number: ollege of Engneerng Department of Electroncs and ommuncaton Engneerng

More information

Driving your LED s. LED Driver. The question then is: how do we use this square wave to turn on and turn off the LED?

Driving your LED s. LED Driver. The question then is: how do we use this square wave to turn on and turn off the LED? 0//00 rng your LE.doc / rng your LE s As we hae preously learned, n optcal communcaton crcuts, a dgtal sgnal wth a frequency n the tens or hundreds of khz s used to ampltude modulate (on and off) the emssons

More information

Optimization Methods: Linear Programming- Revised Simplex Method. Module 3 Lecture Notes 5. Revised Simplex Method, Duality and Sensitivity analysis

Optimization Methods: Linear Programming- Revised Simplex Method. Module 3 Lecture Notes 5. Revised Simplex Method, Duality and Sensitivity analysis Optmzaton Meods: Lnea Pogammng- Revsed Smple Meod Module Lectue Notes Revsed Smple Meod, Dualty and Senstvty analyss Intoducton In e pevous class, e smple meod was dscussed whee e smple tableau at each

More information

Lecture 10: Small Signal Device Parameters

Lecture 10: Small Signal Device Parameters Lecture 0: Small Sgnal Dece Parameters 06009 Lecture 9, Hgh Speed Deces 06 Lecture : Ballstc FETs Lu: 0, 394 06009 Lecture 9, Hgh Speed Deces 06 Large Sgnal / Small Sgnal e I E c I C The electrcal sgnal

More information

Diode. Current HmAL Voltage HVL Simplified equivalent circuit. V γ. Reverse bias. Forward bias. Designation: Symbol:

Diode. Current HmAL Voltage HVL Simplified equivalent circuit. V γ. Reverse bias. Forward bias. Designation: Symbol: Dode Materal: Desgnaton: Symbol: Poste Current flow: ptype ntype Anode Cathode Smplfed equalent crcut Ideal dode Current HmAL 0 8 6 4 2 Smplfed model 0.5.5 2 V γ eal dode Voltage HVL V γ closed open V

More information

Multistage Median Ranked Set Sampling for Estimating the Population Median

Multistage Median Ranked Set Sampling for Estimating the Population Median Jounal of Mathematcs and Statstcs 3 (: 58-64 007 ISSN 549-3644 007 Scence Publcatons Multstage Medan Ranked Set Samplng fo Estmatng the Populaton Medan Abdul Azz Jeman Ame Al-Oma and Kamaulzaman Ibahm

More information

ELCT 503: Semiconductors. Fall 2014

ELCT 503: Semiconductors. Fall 2014 EL503 Semconductors Fall 2014 Lecture 09: BJ rcut Analyss Dr. Hassan Mostafa د. حسن مصطفى hmostafa@aucegypt.edu EL 503: Semconductors ntroducton npn transstor pnp transstor EL 503: Semconductors ntroducton

More information

COMPLEMENTARY ENERGY METHOD FOR CURVED COMPOSITE BEAMS

COMPLEMENTARY ENERGY METHOD FOR CURVED COMPOSITE BEAMS ultscence - XXX. mcocd Intenatonal ultdscplnay Scentfc Confeence Unvesty of skolc Hungay - pl 06 ISBN 978-963-358-3- COPLEENTRY ENERGY ETHOD FOR CURVED COPOSITE BES Ákos József Lengyel István Ecsed ssstant

More information

FEEDBACK AMPLIFIERS. v i or v s v 0

FEEDBACK AMPLIFIERS. v i or v s v 0 FEEDBCK MPLIFIERS Feedback n mplers FEEDBCK IS THE PROCESS OF FEEDING FRCTION OF OUTPUT ENERGY (VOLTGE OR CURRENT) BCK TO THE INPUT CIRCUIT. THE CIRCUIT EMPLOYED FOR THIS PURPOSE IS CLLED FEEDBCK NETWORK.

More information

Linearity. If kx is applied to the element, the output must be ky. kx ky. 2. additivity property. x 1 y 1, x 2 y 2

Linearity. If kx is applied to the element, the output must be ky. kx ky. 2. additivity property. x 1 y 1, x 2 y 2 Lnearty An element s sad to be lnear f t satsfes homogenety (scalng) property and addte (superposton) property. 1. homogenety property Let x be the nput and y be the output of an element. x y If kx s appled

More information

I. INTRODUCTION. 1.1 Circuit Theory Fundamentals

I. INTRODUCTION. 1.1 Circuit Theory Fundamentals I. INTRODUCTION 1.1 Crcut Theory Fundamentals Crcut theory s an approxmaton to Maxwell s electromagnetc equatons n order to smplfy analyss of complcated crcuts. A crcut s made of seeral elements (boxes

More information

Detection and Estimation Theory

Detection and Estimation Theory ESE 54 Detecton and Etmaton Theoy Joeph A. O Sullvan Samuel C. Sach Pofeo Electonc Sytem and Sgnal Reeach Laboatoy Electcal and Sytem Engneeng Wahngton Unvety 411 Jolley Hall 314-935-4173 (Lnda anwe) jao@wutl.edu

More information

II. PASSIVE FILTERS. H(j ω) Pass. Stop

II. PASSIVE FILTERS. H(j ω) Pass. Stop II. PASSIE FILTES Frequency-selectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called pass band). The ampltude of sgnals outsde ths range of frequences

More information

ECSE Linearity Superposition Principle Superposition Example Dependent Sources. 10 kω. 30 V 5 ma. 6 kω. 2 kω

ECSE Linearity Superposition Principle Superposition Example Dependent Sources. 10 kω. 30 V 5 ma. 6 kω. 2 kω S-00 Lnearty Superposton Prncple Superposton xample Dependent Sources Lecture 4. sawyes@rp.edu www.rp.edu/~sawyes 0 kω 6 kω 8 V 0 V 5 ma 4 Nodes Voltage Sources Ref Unknown Node Voltage, kω If hae multple

More information

Capítulo. Three Dimensions

Capítulo. Three Dimensions Capítulo Knematcs of Rgd Bodes n Thee Dmensons Mecánca Contents ntoducton Rgd Bod Angula Momentum n Thee Dmensons Pncple of mpulse and Momentum Knetc Eneg Sample Poblem 8. Sample Poblem 8. Moton of a Rgd

More information

Distinct 8-QAM+ Perfect Arrays Fanxin Zeng 1, a, Zhenyu Zhang 2,1, b, Linjie Qian 1, c

Distinct 8-QAM+ Perfect Arrays Fanxin Zeng 1, a, Zhenyu Zhang 2,1, b, Linjie Qian 1, c nd Intenatonal Confeence on Electcal Compute Engneeng and Electoncs (ICECEE 15) Dstnct 8-QAM+ Pefect Aays Fanxn Zeng 1 a Zhenyu Zhang 1 b Lnje Qan 1 c 1 Chongqng Key Laboatoy of Emegency Communcaton Chongqng

More information

Set of square-integrable function 2 L : function space F

Set of square-integrable function 2 L : function space F Set of squae-ntegable functon L : functon space F Motvaton: In ou pevous dscussons we have seen that fo fee patcles wave equatons (Helmholt o Schödnge) can be expessed n tems of egenvalue equatons. H E,

More information

3.5 Rectifier Circuits

3.5 Rectifier Circuits 9/24/2004 3_5 Rectfer Crcuts empty.doc 1/2 3.5 Rectfer Crcuts A. Juncton ode 2-Port Networks - ( t ) Juncton ode Crcut ( t ) H: The Transfer Functon of ode Crcuts Q: A: H: teps for fndng a Juncton ode

More information

III. Electromechanical Energy Conversion

III. Electromechanical Energy Conversion . Electoancal Enegy Coneson Schematc epesentaton o an toancal enegy coneson ece coppe losses coe losses (el losses) ancal losses Deental enegy nput om tcal souce: W V t Rt e t t W net ancal enegy output

More information

Coupling Element and Coupled circuits. Coupled inductor Ideal transformer Controlled sources

Coupling Element and Coupled circuits. Coupled inductor Ideal transformer Controlled sources Couplng Element and Coupled crcuts Coupled nductor Ideal transformer Controlled sources Couplng Element and Coupled crcuts Coupled elements hae more that one branch and branch oltages or branch currents

More information

ELECTRONICS. EE 42/100 Lecture 4: Resistive Networks and Nodal Analysis. Rev B 1/25/2012 (9:49PM) Prof. Ali M. Niknejad

ELECTRONICS. EE 42/100 Lecture 4: Resistive Networks and Nodal Analysis. Rev B 1/25/2012 (9:49PM) Prof. Ali M. Niknejad A. M. Nknejad Unversty of Calforna, Berkeley EE 100 / 42 Lecture 4 p. 1/14 EE 42/100 Lecture 4: Resstve Networks and Nodal Analyss ELECTRONICS Rev B 1/25/2012 (9:49PM) Prof. Al M. Nknejad Unversty of Calforna,

More information

Two Port Characterizations

Two Port Characterizations lectronc Crcuts Two Port Characterzatons Contents Input and output resstances Two port networks Models Prof. C.K. Tse: -port networks Impedances and loadng effects Voltage amplfers R s R out smaller 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

Physics 2A Chapter 11 - Universal Gravitation Fall 2017

Physics 2A Chapter 11 - Universal Gravitation Fall 2017 Physcs A Chapte - Unvesal Gavtaton Fall 07 hese notes ae ve pages. A quck summay: he text boxes n the notes contan the esults that wll compse the toolbox o Chapte. hee ae thee sectons: the law o gavtaton,

More information

Ch. 3. The Smith Chart

Ch. 3. The Smith Chart Ch. 3. The Smth Chat d d = l L j L e j l Mappng of the eflecton coeffcent n the comple doman IFI548: RF ketse, teo og desgn Sven-Ek Haman Insttutt fo Infomatkk Insttutt fo Infomatkk IFI548: RF ketse, teo

More information

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

The Decibel and its Usage

The Decibel and its Usage The Decbel and ts Usage Consder a two-stage amlfer system, as shown n Fg.. Each amlfer rodes an ncrease of the sgnal ower. Ths effect s referred to as the ower gan,, of the amlfer. Ths means that the sgnal

More information

Design of Analog Integrated Circuits

Design of Analog Integrated Circuits Desgn f Analg Integrated Crcuts I. Amplfers Desgn f Analg Integrated Crcuts Fall 2012, Dr. Guxng Wang 1 Oerew Basc MOS amplfer structures Cmmn-Surce Amplfer Surce Fllwer Cmmn-Gate Amplfer Desgn f Analg

More information

ANALOG ELECTRONICS I. Transistor Amplifiers DR NORLAILI MOHD NOH

ANALOG ELECTRONICS I. Transistor Amplifiers DR NORLAILI MOHD NOH 241 ANALO LTRONI I Lectures 2&3 ngle Transstor Amplfers R NORLAILI MOH NOH 3.3 Basc ngle-transstor Amplfer tages 3 dfferent confguratons : 1. ommon-emtter ommon-source Ib B R I d I c o R o gnal appled

More information

4 Recursive Linear Predictor

4 Recursive Linear Predictor 4 Recusve Lnea Pedcto The man objectve of ths chapte s to desgn a lnea pedcto wthout havng a po knowledge about the coelaton popetes of the nput sgnal. In the conventonal lnea pedcto the known coelaton

More information

Groupoid and Topological Quotient Group

Groupoid and Topological Quotient Group lobal Jounal of Pue and Appled Mathematcs SSN 0973-768 Volume 3 Numbe 7 07 pp 373-39 Reseach nda Publcatons http://wwwpublcatoncom oupod and Topolocal Quotent oup Mohammad Qasm Manna Depatment of Mathematcs

More information

P 365. r r r )...(1 365

P 365. r r r )...(1 365 SCIENCE WORLD JOURNAL VOL (NO4) 008 www.scecncewoldounal.og ISSN 597-64 SHORT COMMUNICATION ANALYSING THE APPROXIMATION MODEL TO BIRTHDAY PROBLEM *CHOJI, D.N. & DEME, A.C. Depatment of Mathematcs Unvesty

More information

Advanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017)

Advanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017) Advanced rcuts Topcs - Part by Dr. olton (Fall 07) Part : Some thngs you should already know from Physcs 0 and 45 These are all thngs that you should have learned n Physcs 0 and/or 45. Ths secton s organzed

More information

PHYS 705: Classical Mechanics. Derivation of Lagrange Equations from D Alembert s Principle

PHYS 705: Classical Mechanics. Derivation of Lagrange Equations from D Alembert s Principle 1 PHYS 705: Classcal Mechancs Devaton of Lagange Equatons fom D Alembet s Pncple 2 D Alembet s Pncple Followng a smla agument fo the vtual dsplacement to be consstent wth constants,.e, (no vtual wok fo

More information

Chapter 2 Problem Solutions 2.1 R v = Peak diode current i d (max) = R 1 K 0.6 I 0 I 0

Chapter 2 Problem Solutions 2.1 R v = Peak diode current i d (max) = R 1 K 0.6 I 0 I 0 Chapter Problem Solutons. K γ.6, r f Ω For v, v.6 r + f ( 9.4) +. v 9..6 9.. v v v v v T ln and S v T ln S v v.3 8snωt (a) vs 3.33snωt 6 3.33 Peak dode current d (max) (b) P v s (max) 3.3 (c) T o π vo(

More information

Complex Numbers, Signals, and Circuits

Complex Numbers, Signals, and Circuits Complex Numbers, Sgnals, and Crcuts 3 August, 009 Complex Numbers: a Revew Suppose we have a complex number z = x jy. To convert to polar form, we need to know the magntude of z and the phase of z. z =

More information

(b) i(t) for t 0. (c) υ 1 (t) and υ 2 (t) for t 0. Solution: υ 2 (0 ) = I 0 R 1 = = 10 V. υ 1 (0 ) = 0. (Given).

(b) i(t) for t 0. (c) υ 1 (t) and υ 2 (t) for t 0. Solution: υ 2 (0 ) = I 0 R 1 = = 10 V. υ 1 (0 ) = 0. (Given). Problem 5.37 Pror to t =, capactor C 1 n the crcut of Fg. P5.37 was uncharged. For I = 5 ma, R 1 = 2 kω, = 5 kω, C 1 = 3 µf, and C 2 = 6 µf, determne: (a) The equvalent crcut nvolvng the capactors for

More information

Department of Electrical and Computer Engineering FEEDBACK AMPLIFIERS

Department of Electrical and Computer Engineering FEEDBACK AMPLIFIERS Department o Electrcal and Computer Engneerng UNIT I EII FEEDBCK MPLIFIES porton the output sgnal s ed back to the nput o the ampler s called Feedback mpler. Feedback Concept: block dagram o an ampler

More information