320 winter 07 cockrum

Cal i fornia State Polytechnic Universi ty, PomonarJonert-menf of Electr ical anci Computer Engineer ingvv| /u!

ECE 320 Linear Active Circuit DesignSpring Quarter 2OO7

Course Instructora\FF: ^^UI I IUE

Off ice PhoneOff ice Hours

Qutzzes (9)

Midterm Exam (6th week)

Final Exam

Total points Possible

R. H. Cockrum (rhcockrumGcsupomona. edu)

J J 'AV

909-869-25L0MW 10: 00am to 11: 4OamTu L2:00 to 12:50pm

Course Ti t le: ECE 320 Linear Act ive Circui t Design

course object ives: To study smaf l s ignal model ing andr laqianq r :F qinr-r le s1-acre and mrr ' l f i -sfaoe emnl i f iers-

' * f I9f g D LqYE qIIs ILLUI L! r uqYv

Course Textbook: Neamen or Jaeger any edi t ion

Prerequis i tes: Complet ion of ECE 220Co-requis i te: none

Course Grading:

Homework Assignments (9 assignments)

Homework is due one week af ter being handed out - Late

work wi I l have Points deducted.

Grading is done usinq a curve technique'

NO CELL PHONES IN CLASS ! Points may be deducted.

No make-up exams wi l l be given'

Last day to turn in Late assignments: March 1 '

2001 '

Final Exam: Wed., March L4, 2001, L:AOpm to 3:4Opm'

ECE 320 Outline

Week 1 Basic Facts About Amplifrers1. Waveforms2. Active versus Passive Devices: Definitions3. Smail Signal Analysis and Models4. Amplifiers:

a. Types:i. Classifications

ii. Configurationsb. Efficiency: DC to ACc. Design Parameters

i. Techniquesii. AmplifierParameters

iii. Transistor parameters

Weeks 2-5 Amplifier Design and Analysis5. Single Stage BJT Class A Design and Analysis6. Single Stage JFET Class A Design and Analysis7. Single Stage MOSFET Class A Design and Analysis

Week 6 Multiple Stage Amplifier Design and Analysis8. Multi-Stage Amplifiers-BJT/JFET/MOSFET

a. Capacitive Couplingb. Direct Coupling

Week 7 R.eal Operational Amplifiers9. Op Amps: Gain, Offsets, Noise, Bias Currents

Week 8 Feedback in Amplifiers10. Feedback Types: An Overview

Week 9 Effects of Capacitance in Amplifiers1 1. Capacitive Filtering: An Introduction

Week L0 Frequency Response of Amplifiers12. Frequency Response: An Introduction

a. Bode Plotsb. Domainsc. Filter Responsesd. Circuit Wirine Effects

Chapter x : From Neamen textbook.

Class notesClass notesChapters 4, 5, 6 &.7Class notes, 4,6 & 8

Class notes& 4Class notes& 6Class notes& 6

Class notes, 4, & 6

Chapter 9,13, & 14

Chapter 12

Chapter 7

Revised 3-28-2005

Some Design Considerations for Transistor Amplifiers

---------Transistor Family-----BJT JFET EM-MOSFET DM-MOSFET

Parameter

Operating Mode Enhancement Depletion Enhancement Depletion

Operator Current Voltage / Voltage Voltage

Noise Level High Low Low VerY Low

Power Levels Low to High Low to Moderate Low to Moderate Low to Moderate

Failure Cause Excessive Ie Forward Biased Gate Oxide Breakdown Oxide Breakdown

Switching Speed Low to High Low to High Low to Moderate Low to Moderater- . \ U,i i tu r. . i rr I t t l r t t- l t \ .

Input Impedance Low to Moderate Moderate to High Moderate to Very High High to,Very Hight ,,t

i a.' t,o tl ( ol\'

Cost Low to Moderate Moderate Low to Moderate Moderate to High

Availability Low to High Low to High Low to Moderate Very Low

- t^ l " ' .hot \ \ . , . \^ M,. l - - . . i - r L.-

l ,okctro^ t1 l '1 \ \ t$ h ' ' l . - top-;o t ' t l$

Ilr ri c" \

l4wlelvle!q

0.0001- 1 uf

Medium-

rtectrotytic_ lTe4elum - iP

0.1 - 43,000uf 0.0001- 160uf0.1pf-100uf Medium

MediumVery Low

fn o P J

l- t,tr

:b in if 1<

;a,g :.

i^ i.e

:+ 5 a-

)Ft< 5

-1 -i-

N I I{.

'-P i,

; JI 7t

il ----

-,"4 ,} e>

> f .i

7 2 <- s

rB r+.i

6,5 i> 's 2

.- c d

1lli j

G' c6 l+

): raP c

l\ I t I t I I i I I

TN fn 6) 0

€5 z,e

Q-h (^

-i t e o- f ,

I I I--

1-s- l/

' t\ l> l- I --

t/ IG t\

t€ It It \{ t\ {'^.

l e s-a

IO ,T,-

\t/ IO -r

2 F r1 o I

\ - rl

- t! ts

. I rl I t-

rl 4 o trl^

Cal.ifornj-a State PoJ-ytechnic University, Pomona.EJ-ectrical- and Computer Engineering Department

ECE 320Homework #1

Device Problems

1. For a s i l icon (Si) smal l s ignal t ransistor operat ing at 300Kwith a base to emit ter junct ion diode reverse saturat ioncurrent of 1 nanoAmpere and a measured vol tage across the base-amit- far - ' ,nct ion of 0.75 vol ts, f ind the current f lowinqthrough t .he ;unct ion. Show answer in mi l l iAmperes.

2. For a germanium (Ge) smal l s ignal d iode operat ing at 300K witha reverse saturat ion current of 0.1 nanoAmpere and a measured.rrnl t - :aa i - ross the diode of 0.35 vol ts, f ind the currentf lowing through the diode. Show answer in mi l l iAmperes.

Transistor Biasing Configuration

3. A bipolar junct ion s i l icon (Si) t ransistor is used in a conmonemit ter (CE) conf igurat ion wi th an emit ter resistor (R") . I f thetransistor has a F:50, the col lector resistor (R.) is 10Kohms, the emit ter resistor (R") is 100 ohms, and che base biasraqiql-nr 1Rs) is 50K ohms, f ind the current in the base ( Ie) ,\col lector ( Ic) and emit ter ( Is) c i rcui t paths.

Circuit Models

4. For the t ransistor c i rcui t descr ibed in problem 3, drawthe ac smal l s ignal hybr id c l rcuj- t model. Assume hi" :1.1 Kohms, hr" = 2.5 x 10-4, and ho" = 25 microAmperes per vol t .

CaliforniaStatePolytechnicUniversity'Pomonan.putt**t of Electrical and Computer Engineering

ECE 320 Quiz #1 rg

Determine the value of Vsp for the transistor shown beiow'Ie: 1 PA.-7

xo = r.(e il-ot- r )-+lo

6Esl@nu Dtoog gooAfloN

5o: I * ,o-9 o

&s = zl.a mVn1=z

.7/ t ,

l i"8:

\_, i ,

L;. / ,t , ( t , t

nt ) ./ / / ,; t ' tJ

c,. z{ l

it, - .), , t31 ,

'lfr FJ o

Y) :' r

cf- ;'4

,2 i e.7

[.J o,/

"/ ? 3

.P tz 2

6- a, d^

-lilf,

I I J 3-I

l= lr l" l- l^ to l; la \-

* c vl

:- 4-) o

cr< ;-

"p Fl< I

.F n o

lt d d

o o 3 .>

o J (4c I

- vt c.

.J -, P

q- xl( 4,, F (

Caiifomia State Polyechnic University, PomonaDepartment of Electrical and Computer Engineering

ECE 320 Quiz#2

Name: 1ot"^ Al lu fv,+

Draw the hybrid-Il model for the following circuit. Label ali components in the model.

t--- Vc"

f' C )l(

fl <-.

lF I' tl g

l"I l\

-t-,|,

:l 'Ifr

(o a (' \- -ilN t-

\lo IJ

5 I4 t- I-@

It tF lv

t2c '-T

I tT J c

-- l4*1

cal i fornia state Polytechnic universi ty, Pomona'

Electr ical and Computer Engineer ing Department

ECE 320 Homework #2

Draw the dc schematic mod.el , the hybr id, and the hybr id-pi smal l

s ignalacmodelforeachofthefol lowingconf igurat ions:

1. Common emit ter , sel f -b iased' grounded emit ter '

2.Commonemit ter ,sel f -b iased,withemj-t terresistor.3. Common emit ter , sel f -b iased, beta- ind'ependent, grounded

emit ter ' .4.Commonemit ter ,sel f_biased,beta- independent,wi th

emit ter resistor '5. Common col lector, sel f -b iased' col lector grounded'

6.Commoncol lector,sel f -b iased,withcol lectorresistor.-1. common cor lector, se1.f-biased, beta- independent, col lector

grounded 'B. Common col lector, sel f -b iased' , beta- independent, wi th

col lector resistor

Derive the equat ions for vol tage and current gain and rnput and

Output resisCance for e.ach circui t '

-T- I I C)

q t'.<

-T- I ! I 5

--]- I l o

J 0 f t f> a t- ,

,s r 3.

!t- a f? "+

s { €- lf I

r L. J

T} Ff (' e -J o

fl {-7

^a-l\|

F pe fn

s 7 J ?

f r I I

^l ^lV

€ l-e

l€ t-P

.r\- ii l-

lr l. ln l.- c : F

--l )-

I !:--

Cal i fornia State Polytechnic Universi ty, Pomona.Electr i -cal and Computer Engineer ing Department

ECE 320 Homework #3

ITqi na f ha hrr l - r r i d-ni cm:T I c i ^-- ' l - - nndal r la l - ormi no f 1- 'a

UJl t -V LI Ig l lvU! I l l - lJ I DILTOII DI\JLLd.-L d.U ILLLr( lE! / UE LEI- ILI1lg Lt lU

input and output resisLance/ and the vol tage and currentgains for the c i rcui t below

-{ - lo

[-vo' *1Rr

V1= V6y = 50 f

hre = ?a9tK

QQ = loo,q'$

F =tgI

$ . L9-v nV

| = Sool(h€.

2. Design a constant currentbeta:100. hoe= 3.1 mi l l imho.2 s i l icon diodes as a vol tase

source to supply 10 mA to a load. LetVcc:+10 vol ts and Vee=-10 vol ts. Use

reference.

l (€\F

-'o (' c -(:

-^J !i

**-J {\ _

rtr* I

^F r*l "f ;' l. f

-l-" +

a -_ !

I' \< t^ I \' ,,- t:,

{- t't-

'l Ict

j. l3 Ir i5 lr I I t l- 14

7. i r

a J J !"

fr (,t

fl : J

rl li - \e

--i? ,_

-- | / I

|:l -l -,\

_ .C bn

9 -N ;-II

- lq i-

^diT -q

:" o -. -t

lql- l-

,i ra lc t" l- lr.

-L \r/ 1\>

-t o o

(l p3 rt,-

e d fa

-*I l^

s o .J

l_ lt-

lz lt-

California State Polytechnic University, Pomona

Deparhnent of Electrical and Computer Engineering

ECE 320 Quiz#

lo\^ A' /rlgu !, r IName:

Determine rn for the circuit shown

Vrc:0.7 volts

Vr:25.8 mV

0 looL

lr t,7r , € -

1 to,- t _0,- lt ) - - . . - -*-

r r0L r ( r r+1) 1o

= lo '1"/A

1ZJ,! n^ V

' Jc,hlo " 1 l (x, ,1r tva)

+ lo '7

^^ '1 . i t rnna4 = Qi- ta

\-d,* I !LJl-r1-La ! ua !E

nr ^ -L--J -- I - -J

! , IeULIIUd-r arru

Pnl rr l -er lhni c UniversL vr_I vv

-^F6ra+^- Fnni

-aar i nr t

\ - \ - l lLt ! fu LE! l r rY!rrvv! l r rY

i l - r r Dnmnn:Lv! |

f lane r fmart f!vyq!

For the

ECE 320 Homework #4

trni .^r ernnl i f ier c i rcui ts shown beiow, caiculate:LyYV ---

the Vottage 99in,the Current gain,rhe Tnorr t Resistance, andl-ha Orrf nrr t Resistance.ul le

A 4\"""r( , ,

p: too

8.o6 K.Ve L7,Z

rJ G C'

!- \q 1i t il \'-

r{ I ( (

-' 'c:

€f >U

{- 6 f t a 6' v

1f t- l-4

-t ---

J C -: C

rl sl.

Cal i forni-a ScateElectr ical and

Po' i r r tar-hn i r - Tln i r rers ' i 1- rz - Pomgna.vLe4vJ I

Computer Enqineerinq Department

[uE slu FiomeworK f 5

For the c i rcui t shown below, determine:

1 mL ' l r^^^ ^- . i -J. r -1rs vrJJ-Lo.9€ 9eirr

2. The current gain3. The input resistance4. The output resistance( Tha nr*. . , FJWer gar-n

Let Vbe=O.7 vol ts and Va:200.

l3. l t r

frr in N h t

'4 t t J

7 1- jclJ

:-) -*

a <:F >

C alifornia State Po lytechnic University, PomonaDepartment of Eiectrical and Computer Engineering

ECE 320 Midterm Exam

1. Draw the hybrid-li model for the amplifier shown below. Label ALL componentswith appropriate values. Ve: 600, F:49, V1:25.8 mV, and Vs6:0.7 volts.

+f zyl- Vo

2. Determine the voltage gain for the following amplifier circuit. Show EXACTsolution. Vs6:0.7, p = 100, rn:2580, ro= oo.

vcc,lt(

3. Determine the current gain A11=I1lIi for the following circuit. Show EXACTsolution. Vsg: 0.7, p:120, ro: o, and rr- 258. Remember the load!

4,, Find the input and output resistances for the circuit sho'wn below.Vr:25.8 mV, Vsp:0.7, Vn=600, and B:100.

5. Find Ic in the constant currentIz:0.100 mA, I6ss: 15 mA, q=

3l't'sE

source shown below.'2 and P: 120'

Vr:25.8 mV, VsE:0.7,

,**O I

€o tT' c c,l

_q i i -L -r t_ lo le la I F

t+ i<-=

l{ I I'-

It I t< lF li t

t^ lv?

f e 6-

rl (- \ > ) v f

c\ u t 7 s' (

-ie '\

,l) Do tF.

F l> Ie

-t '_t-

-ll^ t+ i- 1

iP IP ieC c

^l - \a

lv ^l-

l + (-)

J- ,/\

-J_ -r I l

a 0 \ :

1f a o C

l/ i It'R ,H

I \ F I i

i l{ l^

* lw t-

'<l" .$

I I )-> r

i\ ='t-

J F u-\-

+ : 7 +

trG aT

i - d C J 5- ')

r J = A \

I i I I I I I I \ i

c' e ; 4

^ ll 1

-€- +

a If q

( I l.

-l F n

r lF la

-. t--l

^ .la f

,) fi'

.l.r {

+ ^i o

( :- r

/i l '-

l -- -:.

-cI I I l I

l; { i,

{ I f/i

-q- ".'

t* t; l)

J I I Il)

ra '\ t/

l i t\F

...b '-

e , i_

,^! :+ Lv

:_ t-L ll

\ .' ^ I )::

T 't-.

? c" ?

rl - 1

C) t,/

; (" c

-. 6- F_

: t=-\

o o : - =

6 d J 9

t- I l^ j!

Ir t- t- I

- l{ t{

d- - 'C (-

( 7$ C

6- _- c: (

-,:^ i-

t- l--

i- i:^ a ir

iq lC 'L) i-

California State Polytechnic University, pomonaDepartment of Electrical and Computer Engineering

ECE 320 Quiz #5

Determine the total voltage gain for the circuit shown. Give your answer in linear math.

fnt,In2 : 1000

fe1rf62:o

P1, P2: 100

r l ldB

Ana, = ZofuS,o Avu*,ou

I t r t l t ro " J j

)3 = 1<' l - ' , , , A,

r?JY I_ _ , ,uI

,o A,1tt

11/-' lo A

? - t'tv

Av' S. Z0

loLu. A, / l l tu{v;r

Cal i fornia State, E ' l ar- l . r i r -z I =nr{

' i : : : -

Polytechnic Universl ty, Pomona.Cgmputer Engineeling Department

. i ' ; . '

, . . , ' t . . ' , , . , I

direct .coupled.gai.n ;df ld. input

:. ' - . : .

ECE 32O .Homework # 6

ampl i f ier shown below, f indand output. resigtances.

' j. :

+1^^ r^+-1Lrrg t - rJ Lct l -

I.A f : J C

I -9 : c

6- f C

J , : a 7

Califomia State Polltechnic University, PomonaDepartment of Electrical and Computer Engineering

ECE 320 Quiz #6

Name:-Ju\r"

A, Alrrulv i^

Find Avr for the direct coupled amplifier shown below. Give exact solution.

Fr : Fz: 100

Trl :Tn2:1000

f61:I92: co

Vbrl : Yuez:0.7

i l r , ' l - - r - l

e {' 1*. f ,u,o 'ts

,L- i I Ii -f;J

I 7 - 1a q -b 3

1.: , -4.

! -_:.

l/ { t\'

e e = + a

'4 NJ (l

la i lr

L*-; 'l

CaLifornia StateElectr ical and

Po' i rz ier :hni r : TTni r rers i i rz- PomonaLILJ u4eJl r !

f -nmnrrtar F,nr* i nc.^r i nct Dena rEmentvvlLrvuu!! l r rY*:rev!- : ;Y

For the

.{ \v/

t ruE; 1lv f lomeworK # |

circui ts shown below, determine:

!L^ - ,^1f -^^ ^- . : -

tha nt t r ranl ' f r : Y al_n /l -ha ' i nnlr i - raq' i o-

-h^aur lE r l rvuu !EoIJ Ld.J. I \ -E;

!L^ ^, , r* , , . ] - -^^ i - !

.J *j <-

J: I Il-.

--1 p1

*)*l r'.

.. 1 I,/\

il \_>

-J -'l

rs _ 5

)' { a a

. l: I

California State Polytechnic University, PomonaDepartment of Electrical and Computer Engineering

ECE 320 Quiz#7

")r \^^ A. alqufr i \

Find Avr for the amplifier shown below.

g*:10 mSfd: oo

r i : 1 x 10e

l''" 1

, i ,v tL ' T-=- l'''o fr l,:-'"-l '-lY I \'u' 1 tu' 1,

------r ,, I If \ ' .L-tr

AL -- vat-

'v iIt!-r*-

Lts I ly l l t , to<t

t Ioo Iltul

-' '-'t t 1^, loA t , l

' Ibv"

0, qu1

1^ Lt,t , tocrt') rv

\r , I + 16L!1, loor' t ' )^ ' toua , , 01

A' "v1 : o,gl

I I I.-

-: I i(,

'1 9ti

. ;.tl

.c -:_

I f ^T,\

J -1-"

-\I f*-^

\Fi t\

o r-- 'r

a\ (,.

;a 5-i

/,4 C*

f t 79

rc :'- ll -

tt c J

b et^ 2c

t4 1--

C d e /

]" 1 l--

gI J.-

i.- ll*

s d L I

*-*l rt

E J 3T

t\ fl7

- | \_

......

,i ^ /

.F :. (f'

L 1 ?" a.,

o- f<-

i li J;

(- ,-i--

-lt- I

aI I I I

;i ----

-I I I< a

(4 tn P

ih 4 r" J

I e j t

I t^ < .) o ,

'.a .i-->

t 7 { T

G'- ( 1- o

Y i ; {

rn / n + P ,D F,

+ '-- + 1-l

,l x-\

(- t G !

.))l Ll

-r* i l i_ -ltl

i lt-1

't*t* I 1

( *r __l_

;lt tl JI

PIJ t/ tt ,l tl ll I

l/) tJI J

t\ l\ t\ t-t t>

.li \l ,

I/ l,j il I

l- lo'/

{-l --

_J -r=

,"\) \r

j- , -

) -T IJ

f- l iIr

california state Polytechnic university' Pomona'Electricdl ana conputer Engineering Departnent

ECE 320 Homework #8

1. For the circuits shown, deterrnine Vo . l,Ef fJ=In*r t*tO 1*

ryrite. the

2. For the circuit shown,Rz

equation for Vo.

\ tz\c v\{ l \ r

\ rr-"t!.\

\ 'r.-,

si c./

+ -- va

t__' I ,F

r \t \< I : ;

California State Polytechnic University, PomonaDepartment of Electrical and Computer Engineering

ECE 320 Quiz #8

Name:l "h^ A, Alq.r t i r

Find Vo for the circuit below. Ib-:Ib'Show exact solution.

: 100nA, Vio: -lmV. DO NOT ROI-IND OFF.

uo( - i ,*R. (+- ' \ , 1,"\ n l I

t " ) * i ;c ,(tr r

t \. { - r . l ( - y: l ,\Y ' 'u I"r{t

- o,o6l V

IrDO ny

I t | +

1ro , 1gt ( rof"J _

too. t i " f :>(* l , i * r -v

7' \ t "

.> i L:

'l n 6l

= ,, l?

-ltsl-

f"' ; -!

'l- c - a

? 3 C Ct

I e 7 (-,

- -t (

c I e c

-.- 1.

Cal i fornia State Polytechnic Universi ty, Pomona'

Electr icai and Computer Engineer ing Depar-Lment

ECE 320 Homework #9

Dcsion a s ino1 e staoe trans- i - i -^? --^ ' l i f ier tO meet the fOIIOWing

qnor. i f i r -at ions:

\ /o l f aoe Gain:) -100

P.r l - tarrr \ /n ' i farra: *10-Dd. L- L€ly v v: LsYv

Maximum CoI lector Current: 2 mA

Show the f inal dc schematic for your c i rcui t wi th ai l components

Iabe1ed. Show al l calculat ions, both ac and dc for your c i rcui t .

ver i fv vour resul ts wi th PSPICE

rr 61 a

a / t- , -

1 a- I

1l '-'--

v - --<

i( i.:

ii ic t- \ :-

.l^ la t; ir

I t- l-€

:=4 t- l*i

-:ii li

Ii I o'

rT )ql

l. ; c

J 9- :P -b ;6

in 3 G

h l-. s J q

( , 1r

-J { 4 -7

John A. AlgutriaECE320

3t7 t07

C alifornia S tate P olyechnic University, P omonaDepartment of Electrical and Computer Engineering

ECE 320 Quiz #9

Name:1o\" A(julu

An amplifier is to be designed for use outdoors in a satellite receiving system. Which

A os fe\sl " - , ,^o,JC

' ,Lr i tL. ,

1,r( t , r r ,U, l ,q!^" i f

cAscoDe. AlN PLI f i ET?S

Vi, *\

?crrcnaou

" , , - r l h

c'- I Jc ( (\.d l\

CRscooe

("1< " lw

'*" \ \ tv

Crr+co tT

t '^ f , , i " r^[ .^ r

( ' f . , l \u , . <.

Pr= P-= zoo

EXAr}1PLE

U L ' r ,

<rto ! c_

I t o1'<^ '1 K l f d\ !e

CASCODE CoN FlG^UP-An0(J * Ex,q rnptG t?.rl

R6. r 06s

%14,* Rer

lb,r l?6, n t2as

)= ''(-H#) =,1[';:,1<

tP,ast

4.7K=18 =

l?, l K

t8 ( .?7, tss )

I .9r17 3 , t=-

) v"" -,-Y t Q=zat :. &.*Ir. -.'

)l*. i__=-.-=ri., I--1

to' i p:zoo ,, rc,*Te, \

I l * ,J

r." 2 &,,

IBl .8L + t . l l .

tg- z.ag

JFr eZ

6,zoamA

._u^el-{e.Vg" - VBr.-

rer = r..

= 19.o?^eA<

( l - Vr ^ 29.8r" ,Vl l *B{B

,L 1-b-\- l " \F*t J

4.1 - o.1t . tk

g.L =Z.gtgHA

l. lE =-z_

Ar Taoory\ TErr PEG*NrLE

6; 2Z'S-Z'*-V =l ,3SrtH_"z l1.O1aft =,

Q.,= t ' , = l '3srqr- , = b,Lz- F*t zc,t

T T' 'l-

- - =e- =L=bhhIr \

h, =G, BEcA$sE E,--IL,

4.. - Ya-'Qr - Vir

[o,= (F*Dfe'

Au*. %=vdr

- io p r<.- -pR= =_ frz

gg=-qL

l3R. Rc-=r_

(5 fe- fe =I - -

rn*pre = #-= /1.- l .7 3

- L'b "**

t4urr = Aq . An" = C'X26?.23): -ry3>

F-v -rL

Dl RECT- cot)PLED A/nPLl Fl e{e €xn rv{ Pt-E

Q ruErJ THE Fout-o(^lt$Gr ctf+cutT' CorJ trt 6URftnoA)

orJTPof **

. t r rr . tD RBerR"r, Rer , Rc., Rr, , Q, )AND Q" TD ^

eEr Tr lE

Fouuotrr r r$Gr gpEct FTCAT?oNS i

Av> toZ' ) lK

T-o be>tcr\t A T'l,t-r6- Snq6€ DrfeECT-- cotJP(ED AfiPtJtr(EfL Tb

-t+AvE A fufrtt,s OF tnouE T!+np lO., LET. Tt+E Gnil oF sl7.6E L

BE rn]c.H' GtzEArW? TH,+ro Tne 6*tN Otr SfzsE A.

f trz A tr tBsr f tPPr?o{tm*T7oD , LET Au, c lo, 4vT = Io ( io) =lro

Dgst6^rl^)& T}|E clc,CutT &N Nou BretN ,+s F'ocJ-ows!

lF Pvr = h = . loo r THEd R*, , .= loo BEr

' il<Er

Ltrnt- l ( r \ t =9V Anro lc*,^v- ZmA G\UES

R +- R.- :. 9 u . = 4, fK'.rr-'cr , ' *eL Znft

. -J '

too Re, = t o o (+t, 5:s) = 414 55 -rz-

Sot-Vtr:a THE tu)o E}euAno^J=

R.,- lOoF{sr=o \-Rc,+ Re,=4siro /

AruD Rq-=

Nau.r. Loo4t Lt & 4r z; Lre ser wor _ :

Z t \ tK <- FsouraED spg< r Ftc*Dal)

=ir= or, ll ("" + (r+r) R+

r R*, |f FRe, :3o ) Foq 7tr Ta B * GEERTETT Tlrn,r.r 1. Kr:, mEfl^ls Tltr+T

Rs A*s.o PR. rnusr B?nr BE,'. FR=, >i zg, *., p 7 % = +Li,? (l=^i: ForJuD rlrrsI -Er ) r #f,ss " - or+ .ro

E;....

sE, 11+F.*:rLetroeE) LJBeD A T?ZnrJs t=tvtz trrrrH THE frtl;oustu&

Spgcl FLcAn Ord S

V"*F?v (eee*roood yocrnee)

r.-** \ znA

LpoKrNcr r i l r } tE , - r , f= ' ;* : : .= pAn+ BooKs hrE t t , tL,LFr,uo

Tpgr Iv\ET TPANST sroe. s Cgsr wee) rx I rJ.- rrroraK . u-erts ,cH. jE

THe rv\osr PoPu'uRr€- orlE r T}tE Z$re|uA. OBThrrJ&}&Ar.J OUr?Or

FArvrtcv oF coeUES (V.* us E.), dE Frlro TltAr Tlre ynuytmutt

vourA6e Shlr A) G- cnrrj BF' I\to q{FJfrrE/.L T.+AN ? vot_n , E0 sErn

TltE 'b" pu,ur AT 1A= *'9 ,t Ailo fc-e I n A 6tues \4 ' lo-,

EEF Fte r.re-e 2. NO(r), Ft lJDf ,rlc- ftBr 1rJternruc T11F KVL l-rrEQUAnol.) 6'rue g

sE= .Fr6 i- .

V.c - .I*,R", Vee - Vg =os"/

Rgr =t^ f r I r FV

-- \ r -

-DZ--Ut<L-U>

_- Vc<- - VsF, - Esr (.p"') R=,

hr* efls

DR f,Br ( Fo r) Rsr

Tl+er.l

vb -. +q 1{ Er

Ro= 1- o,? - ( ro- fXroo t r ) (++,ss)

Ruon+eq ftpepon€H fs _

.= Bza K-sa-

lF Qq= l ruf t AND -trpt leeT*BL) VE- = f,o Rr = I rtr+ (+v,ss.) = ttl,ss: nrvAND' Vg=%e+ye =O.J *A,o++5;5.x O,7t !?ot \ [cc-VB= 1^o,?r l= g,?6V., ! , g.zeov

Dnoppeo r4rceoes fie .r THl,s p,,fy.ni*t G{vEs g,.6rr-7[t4*

rv, usr- BE

Tl+F Ft,?Sf srrFFGF lSsBconJD atv6g

frND vu" = L{'sf rlF WE DEcrDr T?l r rsEHras;f stZtg (rrg A&*txt

Vt=9 ' '

lF Ec.g * E*., r @ Ycg =

.Axlo %= v.€-4.^. ,= q:

.Noril 6npLETE:

) .Ler ts. tno+l€ or" To TH+.

( t re)(++_r-)= 'H,r ls.s, vocr=?,!8 = 4,s-g V

Vgz-- ./,sg -'o,-J = 3,gs ,t.

S*rttE TtZA^Jsrsr?€ AS lil TT,IE

?-rs6Fr

.r_c.g =

h.n4*F>7 m A

LAND,F

= 3, tS,E

lnf t , R.+[Zes c! . f td

Xee=lou4 ) P=loa

= Ir , , .a)R=" =

r>nEz ts

\b-+ rEzu Qzp

9oBS v

JLjAt, l r a+\-, -vw J

Lf t >

lt 'qPEOA,rtc€

TltEr.) R-_= {Soo - BgSo = 6.53 -e_z

CHECK T?) SEE, t}JHAr VRLUeS Forr .6nro A,uDUJE ATCT1JTLLY SEE Il-) T}TES C{RCU1Y

l4e-*r* l

. H,tug\D -tr l\AODEL

T..*-c.mtrE

6,trc-oqe =f = +oo

l+,.5/r .+ v44= Vcgrrr+r

aA't - -"Lt a

Av- =- RLt. =- %- - =- Gslo' 'L ' q=-q; ;= #e==-o,r7

Avr= Ar, ' Ay' , = 16,, to

r l ''71,2 f ier l l ( F) Re, = Bz6K l l Qoo)+{,ss' I l l

= 4, i l8{ F-

Ft6i ura^e ?_ Fe mtLv o F C(]AVE€

- p.r l[ eer,- r l ,

_- r+r+ss ll Cr""Xsaso )R=, =l ?F,trts

:P'AVE F\ET- aLr

- 'F 6e^,rraFaTILL OF TLTE RE4 O I eED 6pEt: |,R cr+I?0ruSLrJe

af 4,ss

O."^^a,^ f-*o-"tf-ee re fu

a""?&r/-t* a;4 j^re f* -/**t*^*-.-

e'utztat-t. *,a.E*.i

d^+..,^t J-J* 3&^, @ A ca,,Fv 1z 4k-^J,eI-* tAt

il; -?;+r-u;E ztzz-6' i/-

u)a- Ed--t+rtufr .6-..r{)-14- Flt; *f**rt; Ht *' a--<-e* fi.*m

rt^w ga-<^-'sfui*a -a--**J -fr-rn

4a, fr.* a-,^2 Rs

/*t d*- /fs;4L;-^-TL/* H- (ftlte-?- ?-; j'1.4,,.^4-t- A* *#.

: r^i*X- *-'3 -Btf.-- etuf - '

'tru - --

A.--Rc-/1l1 -' Re'

g{ \r'e- +-E1,rrr-- 14", Av U-a;i -il- Efi**E -* -*"nfiLe-.f ,tW"**

lO -- -Ia (34"- ?1*;rr< e,-i..i.,, L4 tyr. FJ+-+ M-|--,t

a-,"4 ;- d4*?+rJ 4* -f,4as ,-fr6;* )

lO: *_ Ro=tOREr\E

/J.-- L,',/('*- u"-"*^,-Co-- c--'^J a,a- aH+ .fa +rc** A" cJ;aA,eAr-L A

+a*n - fr-'-^* "t t o , -fl*- e darfr;w ,X * t>.ypr--A oarL^raa

H* e-+r;t1:-* ";ti

-,"4t cA"-.n-.p H'g+ d.t A<aai--Z , -L,,.X ^;U U+-u.^€a..l

fA-\ 4.c #^- M, Rc= lOqE -+ Rc^ tORs =o

Rc+ R.e =t{ .*rO

b)c- +;-,^J tfl--.t RE = {o?.*- e.4 A R.. n Rg = t(og | -r-- + L{og _sz_-

7r*a* 4>e- ca-.+) aLt fl-- -q pc*--* . -8"^-t ,, zkful.-,u:<- -4-Ei-ILe

Q R-*-- * ;rt wi,tJ b- rtc-c-il+* a^*+ .Ib,&e-Aeifr".s- ^u+ti-a&{,. frc-a-,*a-;Atbu

V.r*..o-,.( q uoLTs, I** { TrYrA

db ; G4zf'^, fu ?7,4r-t &<.w, 4-f-a--c-/-{-u;e*urr.4 n* 4 V ,,.t*,,e- l+ard cufia^i*

j^td'l' h,e 7 ax a---J hfe. > S #-<+r+. a- z+",a--r^.<-/a-*ft-e+*a* d,^-t&

"{",*l<-it* Aar.6,trfi.o-r a, P.trzzzzf+ -P'a^ hte-A?* I*r*;*--) G4. t\fua /CIa

{%*^i } . A Auzz-zzft* J4 e L4e}"1f {^"+ry fe-t;.@ -fu*s,aia*aw -d-."*! A**

$.*n* = ba ,s a^4, f.o-o-o.A4 = {CC r","-A . U d*; y,-ettU cL -e4cs-at-E ^4- t-r e -f ,

'i-WJ*.-4-r"4 4e-!e-4-t} a--?vd i4-4ee. ;E juaLuAA- *-uz-z--*.

i*-*u -*1-

5s 'hou

rt"1t-l I.5g-=--E----

X.4r,1 +AhA

b ss-'.fio't.

sr.lan o'g = 5,0 -5.9

d2 -owm'

r1+- -r-.'rf

+-tgut

> r?'L(TV?n

h\w oe = (, b) y w bqz'z

gwle?,z =twJ (

vwbqz't

>{h€'5f =(ss'hoz) -SL= ^'Y']il

!* !T*,*+ ryT p trq ?1ry

lAwzh.tt =(^5) UnLqZ,t =t-b]J

= )tvu.n .tt-tv3 =d = 39v-tf,vC4b

t L+r LqZ,e + A* T : -uof, J

JV ' SL= ajYsc'o = lV

---'f; j]J|=--goF'T :' F5-F-._-36 - -tn-: -=rr

hb'h = (t ,bo'hX.-ar x bb'o) - 5- = -2)J-rg"- ?Di =* >n

awobb,e =-ffi= + - -T = =a

_goh,Q = L,A- -Sot'l = 3€n -€6 = 3n

7to€l' b + 151',: LE RrY + 'tY ?.-Sot'i =(f)G: --nff=u{l

: *.-rg 7#n W W ffzl

-,.'--l-J ":*1 rc L-.-rd*-f 4 ryffi\qd,u, -g

b '{Ta d*^{ c'r-o?{' 'a6t}

5l-?l'9t-,* :d>[ :. (a uoz/ 'h) 5?r '() - 7 b.oal' h

(-ta *

----' --{tt'o

==4 €? t'o - tt6

tgr,)rtzt' o) = ?9tl

aJ h.b-z =

l - ( i *

Q poror

L I rr E:Aq V<€

t rl Vcs

dc- Loo..A Ltne.

1 V.eU = !{.- -<'rt-,+-AA O-;rr4 r'cLa ?Ls1L,.. ry

Qq = l ' "A. - { -J. .

*a)h. t - , ?. ^ atr-hfe =;F- =(oO

!- rvr A (d"d + tttu cAt-rv\&4* ,1 d*. a.^+.r* W ),

hfe =- {oo ,R.= L+ooo ("-W *oqr) , R e = go1

H*- fu a,f e.e*t .--7a,8- *"JL o-5 z*--.r,".*rt^-t" ditr

/t4,r-r*. ry d-.1'a'T/*.1-

.ri H& fr-aa;,*-hL

a-4^4 13 =_ lao + _(r + F) R€ = {tot }yoZ = gl.%1 R

-d* #4r-r;1e ,; ,/ t.Solx , Fr.. tuu<r .+< !.tEajz dn; ,o

Qg = I m'9 , V.no =?.5,

f R. o-.U Rt +r^**

O---Y\-A--

4/-;,'*4

(o rz-rzecno *l 6FFsEIID4L

Vo= (v* -va) Avoa

( Vro ) Auoc t | ' ' , , " .Es=aq#r,;re=ro ttffi'')

l l f+ \ rJYJ,"{tg\ = 4 ,v-

t : I I n, .L+ / 'ttftr

50, 4 nlz , Ee ? to nh , AND Ia! lz .EfA tA!4^,

t- (n fiPrc*L v*urle )J

V= l , (zs.s, , , rv) !^ (HJ = o. '7oot1z=6 uoLTS

@ *d n"Z, IB=lorrA, ANo Co= tZ.SoolboZPf+

Ln+e Aotrrna$ dF L etE.,c;rmo/',

V: a(25,3n+v] Lr-(ry \- \ l?,eoofEff i )

= o 'Joot4l ' I I oocr:

:, AV * ;1oo lLl?-;3U- . l " r lqt- t t

LgBl B -taV

30) Vio = aV Avo,-

6Alt-l Avou- Ay

= | ,88 r3-,uv (roo r)

= le 'e '13 rr+V

-/HnLF F[uiEB Foll.lf

-/- 3CB

-- - Au.u--+ At''.

Erccess GRITU

tsArsgr^1trn-t

+Lr , r ,+ l -Tv

- i t{Q,".

vo--){t

\tsHULL - |

.+v - oreEt NcJr_L

uo = vo (- k) + f;Rr + v* (H.-,) :t o" (F +r\ '%.W Y,^ H #,H

Uco , = tt*

u uuED I

LLS I f.Je THE NU uu POIEAJTIO nn gf€*':

R * = Rri\ Bu R'. -- | uPUr RF:sr sto R.Rp = reeDe4a< REsisfoE

t r f4c = (orrt tcEryisftntrN R€Snierc

- Vo = - cr Rr 1 A=urnf NG v,f Y"! , lF i f =o t*e,-J +=i l r*

Vo = - Cp RF -- - ii Ro -=€r Uo =-v; ( nr) = -U* ( H)

Uo -BeuLi. Rd

-Vo=1,( f i r tR;) |n='orntNGV,*V'At. lDi f ,=o, i [=6

56, Vo = ip (er+ Rd ) *r l+ =i i ; Ha ** (no+ni \ =uh / f ie+Rr \

R.-. - t \ - ; - /

H-=ftS)=ft+l)C-o II'\PeN.SAT.1 OL\

l r * i [n*= Lf

c- d Rc-=FF=Rc Re \ ...iF=t l ) k,* l

Re' I;fiu=r 6R Re=R

(n/^JNF€T?aNs w,{.tc/.+ ADDre+-DBdr/(,;

NorJ FqR oruffi_J_aenmxErZS - __

- le- THF FEgsT?+rrJG Si{ouLp lr$cR-EArsE, Tr+Eil mutn-pl{-tsj-Ql4

I!--TIte REEtsn+rUcE sr.*ouLp DkaeAsE,*Trred_brvr_ue-e_y_G.PAl

ct(Jt-AtJ T.

1\ fe- l \2 lT

Cuftn-.E*ta fuOg,

, . . . - ,F eE--

4 l pCu{i 't{

? g,J ;ufi;?# *Fr;"1:t-JdG,ct

I\+sf 'Jf #I4'ouTi=ur

t l?uf +la4tF. i - tJt i

o*6:tJf4\R.atJ lT

-1, llJ\tGut

clF4u tT

,'ff0"

l " Vo,-Get- =*ta1ueli ) facrae F FEI=oE*'

lf.rt'rf

Pp'€*t t-Et

CUR-f,=Pr' 1Atf lPLlf l&

rlou{?r€F €*ete$ll

lr.rtuT <t1;+ euml:r. \ ,

Rr^ l r f

I t \ar \ rF

Clf<.rrtT

{-"*,PSEAT ?

* t"Lto.a = As?rpd U '$f,

eu€*SJ1 frgogr}ta

Se(qt€ =*Q!L'eq)

fr"nsu.s'-

'ffr"\

r r i" 1o'

1*.rAlI-#1* sr"rf?rt

f f- i , -

.ar (Re)Cnr. .

- Re, ' Rq // (g'" IlllgqnEs=

E.ltqJr",)fre, I hft r'

+ex[(aor +Ls + '&'il'"ll,g \l ' ro ' , r " ' J '

4-. -hs

\hfis /

7.lf oarr. lT- sttf'ut} 8E A.tatEb l?rf,r .sra6e .2 n* Nor fiav. ArN lut,,,uFrrcE orJ .?rE .,,uJ alWoENs16. ec, wl

. : Ir rftE coolc1116 cttp$ctmt ,s ltLso t"tE C5. Fasre6E Z B.or ttb FrlEpue,uc_f EFFe.f uft .DsE

. By THE RAtx,r5,s aF Tz,E . lrr s?+r,a.. {. s*,. '-'+ 2o Fos C.'.

. _nq€rn,op"rro)+ , -&'n: R,

ti.= t.uflti,e *. I:or.R

h"', . a.zFllt.o6ts: ?os-n-

4or.-s}=[-El .A"*{raro-earu,o). - *F fr;. -l;(*.,11Au = -lg3 ' \ l-i

'z l ,osp(t t t r )z l ' - lo7 J

Av; = ltLI -67

c1,= cp I Cc.*r C^t

e%= (t t le/)e, = ( t++.s:a).=o,o- ' '=

. c i : f lpf + sopf + t lospf s. 6E.o pf

' t"r 4i*u "llr*. fl ft, . g.EgK lln"' Rg= o .'. .Frut = O

l;ii,$iili i l

ii$iifi;liiIi.iiiI

t tz.,l R .

arrFE-= E;ry5:r'IP wE t€5lrrrtE'nr*rX4r'7s ;.hnadg lGr)D wlle .W,

g dtuurdat, .d' fr'tl cr;.M i-rf,-r;.ta fa iA i)r,o, *a+A"t'+tilft;- od ilS ZISE.

tl drEarft;^' fu V #t

.ya. t* afr<nLq f i tzra (6.sqnE) ' - a

-U-O;-"Iafu 74., -tn;A*a.a,.e EdhA- ?-;* a-J*^ILa-4esl4, ,Lr*J" of 4r* Uft u=a.i<n

ffi (-c1F4t)

7.{ twr.

4*a.arr (nqt R )c"

err (&,tFrr)1,"rSE

.. rt..H:.e-.Drr llll| fDnilc|ttD:,3

,., AEqrmldCF THRr Eoril TEnNIlTSIDps. FRE rDEDn(*L.(amF-hBstflrr?[reN flrotrE E[}| ]GBrlr FIIE .tparrnccc)

- TftBr!hic.,= hiea = l.iBK

l?.r. ru/l,r*' Iunt-sEx-= t.318K g't,sur

l{ i.= ;1rorrs ____AESa}ILU_6_JF3 A g_

,fr.f - arr.6Lzl.r t.Ur!.)Zr.F

, ,ft'Gd e]ffl

.f$umr$e fi*r fiElr tRE:rb|- tDErunctc(a(sc & Fef|q. &fq|flpTroro FF4fdSF fttE'i', ffi6 gttts.

. awwtJ'fl"'')Ets; 't"lvft . o;E.? = Er.Btttt

Eco Brg- €,qg., i ' i l

f r " &.*Q. ?, ' lF lSnAQ= 3!#- rc.g?

.. .rE

4.3 uar.f5,

t i t 'nr*

E: 13,9O st

;' i I 'Fl i , I

:.i i; Ii:Ilit' i i ' I

'.i|:I: i i l l

*l,lti

;ililriiir' t l ' f ii i l ' I::ii![i:itf- : l : :

i , i i li:ilI.'iiIi : ; f Ir i l : {,.iliI'r i i i li,iiIi.ii:$r , i l l I; l l :$, i i : ti i i i I

;:ilif" i i r ii ; l l, i l t t:,; l i I

r l ,s

r' l l,Ii:ilIrilrf, i l i l;jilil: i l i I' i l i l:,i i:It . l l i l

l:: ;, i

a;n= Eur" + Qr, + Con3-

: . . . . . i : . '

.:tuEEEmilE , uJrE ttAvE TltE .Fq"otdfltJ6rBnr;.= Fceilnchllr{ia.l . ,F-fdT; L },,,"= '

* f l= =

: ; F 448' tRHt f rs ' lp 's6ue. +. [ f- ,tb rrrevrrr& . :.' . .t+"; . = lS..sL H'g .' F.-..' t"t{n

r r | .+- = 9,856. orf i E "er - r r in-=f f i - . : . . ^Nrnl,

;'ri.Ia'frft::

t'ol err R-. f-

. Av - ' - { ,Ea'L

4t = q61'ET

tu"' ffi= l':,:l tw':e,ffi:tr-

J,?( slfl- ra-D-EeuJ- THE, ..Bo.EE--.RAor .a.p DrE--.€&)nfi MPuft€& gmrorSg

: . -UJrr reRE-.Ar.uFAsr -A. &- eFtE -Lcr- ffi& - i i

| *FR hl t - oo I rH€Islore=qoafw,

s*,,HPF

. l-Fl=I

e", # R"-

\-\P1:I Iirir liti.li ; l

LPf:V-

nptT'4-

g,, -\4{irL==

/*,lt"T

Hf l:'Ft

A Hr:'trCe

*.-*\\- , , I

? R.:\ - "

{u#n'-i* r*

t-IFtr

tL Af,tr

\ \*__

. "l- --+ t'

, : '*--*O l

. f\PF

,/)lLc

c,<- voReL

'-"HtI

Lqrrr) trfLeQU Enlcf REsPoos€

c.b-zt (e=+ n;) c=

zs (n" " RL) Cs

S." =zf i RJce

F\ lGt+ F'aeQ\) en-)cY ra"eSPO r$5€

R; = Ru,\ \Ru.-\lG* rp*,)P-)

( -Lr . .r', L zfr Rr,

(r' n (p")Re)

+ Ca"* ( t-n',!

2n R;c"

c*ot ( r -

) '*J-Ay

Rr'= R"ll\-ri- + (ff*,\\fZ*,1[Gt

el = R=\[R, l l r"\\ e I Ri =

Ci =ar i *Cu*rCrrci = C- i

Rl= R"l IR,- l [ (%

Co= C.^lu* C.e

.Ll l to:

5€L€cnPG I, =lnnA

rH€*.) t*=?=*= 4,*A

Vcc- Vgeqts

25.*ntV1,uh

13p,'t - -- rrf

= LL - z,zzgafu*

= 6.45' , K

-zlo ( s*)' 6,r+SL

l ,2S F(o- _ t tf f i?=-te?,s

An=. \

-zao.!f,Es9)- = -too6,r+5K

Qzon'Ar=-F#." = - too

=- i1 ,72

Au[LEnAJc- Voularee Ga r,,.:

b) ex,ncr DESt6r0 CASE Q.l.ftmPLE - Flro p

SEITI ru e Av =- too

so - FS= -too

FR" = loo rrT eNo F =

p : ,oz r'r.

C'.= )h- = !-F'fr'^'/rr r€ f,g

lF EB ! S 9er€crEtr To BE

'Eg -- to.;.t A THe,$ C6 = ?..S9ts

AND F= 'oz(z 'sae), ,= Sl ,6

lEg = S.uA r1ra.r

ns: W=.s,rb<

p= .oz(5. lbta) = 163,2.' At'tQ

set-ecD uu P = (oz,z lftJot,se rHryr Exrq rrnar..,ls,etuRl

Gt ves

ft. = 5K (nrt: HAS r$o1. cHArJ6@ Fr;aly. fue rresr\\ q-lxArnPLe ,/

Re* W= #= t '8614--

loOq1 - f6o C6--

Rc, €K

fzaN+ z.s?R

F= too

Av.Jp* = -1g:z (#- = ^ Z-6,R.: -/oo' ' fb --E:r6F- - s. ,6K - +

*5-esre r*l eY.AtvtPLE l* J.

=peias Av ) - too

AsP -to

SoLrl Tl o O

BnrreaY vor5P6g =BAi-{'EAY CUAAeNT- =

OpEA4Q p6 lErvtP =

c HEAp ['\*t \

t,t>qQutc-r.

\ovZrafr !hr+r.SooK .{i..>r-: r'-. -[ "

lol5c-

Yg = -FR:Yd n'T . '

A=-F#F."= RellCn

Ro = R.llQ

a) brcesTl cAFE efAMpf-S -rreoasT'c+ei9 F :{0t)

* t(."*'*) r lnaa

' l ' I

" ' : '

o- _ Vc<.-VtEE Io - o.?<g=-=-:

f€ loth

A.r= *FR* = -I""_(sp). = _lg3,g'

-r fn Z,53la €

{ r ="i#-- ".sEK

Jqtofi

= i:el(

SEt*ecn r\9G. I., = | f**,.-

trrof,,€f- Ct-eE p -- 'rca

... Ets= +; E_PI"o

-- lo2^A

59 IB = V.cc-* VBE =)" Rei

cH€APFf, &Stef,.T r'QrJ, q4,eq e I R,c.JtT

'. .: TO m9er sPEcs

idvpcrr ctt l€ut7- - €.uRRerui- l i i l loelz

T =1o-

I.= !t

-vo +* l ,_L Rc

/@\\ Rc-Rc l

= b. /R..-R"-)Rr- \ R.- /

o* (q-il)

*: = u, (i-h-)

r. = v" (8.-+1. )kT'-=a- /Fu+F , \*c-- '_\-

AuD .a ' -T Gg:-

- Hu* t(c.

Gnru - "uTeur brv'DeD BY t Ntr

-T Rt ' 2

fo =E' = Lc- fl = *8F Rr-tt2c

tr i = ro (R*1c".)Ret

riEPfu, = F.fu..fuLOF-

f ' . Ib / Rri +Ru \\-fao- I

c\ R(u ff {3(,jTFuT. Lo€tr,41 t^.]AEbS

'NTPQT

Ri=far (F. , )ReEe= Ig*Sr

!"= P tt'r Ie= (prr)I6 (P (F* ' )#+,) IrL =,Rc

[,r+ ( p-rr) Rg

TT+E6ot

LooKl rrJG Fea(^

I Npof 6rvESyo

Ro= R.ll#,

trJr TL+Vr[ =oGrues

{ro--|_--r

I [" 'f ?on fF 'pl l' : \O++

tu!'+ l

6 g+t) Re

frr' .* Reto'

.,UrP.Jr BACK

"T *ReP*'

r/p+')

TOUJA(A.D 3

Dea,u +n o f\l otr €trtrrctg{-tcY Fla-

I . SEie.\E=-tr=D <o,\ i FL6'. l |e.AfioNl

- r / {<-L," b€. <-Sera\E= -FEs{ l 'u l . - t ' {o

CLt+g /+ frivlPt-t F-l F,e-S

a.€ cer

= VprPz

1 *rFC-l iFrE ALJEtr.?*+drE por4 €r? (a.) ro T'l+E o LSTp{-lT €lR-Cu tT- NE

P= tr V ) sP€€tFtc*tLf: Pd,o= I..V.a

b) fiAq EprecTrva Fourq"- (rms) DEL\uereeD ra Frt€ LoAD is

P=T:V h,-r Vu**=FrI**==F

c) ereia-re*rcY t=- "j*H: E* - Y+ = r_ t vr r* Jn= E p4" - E4vcc- zLffiS

?I faYlrt -q* , Vr*n= LP

Tr^* -I'm,.crz

r t . l

V^ = vnaAts-Vrrr l r3t -

EqclAnrol*) cnru) At-so BE ExPG-es5lED As F'LL ows

rn 21.q lnf.(/irIrG

d \ Ff?o n^. Tli t9 LA3T-

tF VftuP = O

Vn'u+r = .t'ec

EQUAT]DEJ WE sEE THAT

' [:. Zs?s e Ttits tS THE mA]sfl unEFFrc I erJcY FA A3Erate= FED <riacurT-

rdo to!t\ |I \i.-

California State polytechnic University, pomonaDepartnent of Electrical and ComputerEngineering

ECE 320 Midterm Exam

il 1- Draw the hybrid-n small-signal ac model for the circuit shoranr below. Label allcomponents.

Y. p= zrof1' : loo

-v g: g'ooK-

,t 2'+'|c

\l 3. Find Ai for the amplifier shown below.

Find Av for the arnplifier shown below. show e4lrct sol*tion. Do not ro'nd off!f-----f.-+tt

Vs3= a.J pz t?€r l1' =?9.8tnt l

Vp:8ao

I l=oO p=z-eo

[p: too

'\J 4- Find the i'put and output resistarrces for the circuit shown below.

Vo ?= Snn

t.r.tr!5.'

$rr3o.ol

" F. Determine the current in the road for the circuit shown below.J(

-f.loRa' ,TLC2

f ,= lrAEo= lo7.?b*A

Et zg.Br,nV1

Vg": O.?

r. = -L"-:-Li' rL

For the configuration sho$n belou'. finishtlie design to meel ihe fbllou,ing

V€e; roVg": o,?V1 : 25 'BaV

Ta^^, ^ 2*4

! .e = l .A

TF,q -

AY=-l f

For the configuralion shoq,n belorv. finish the design Io meet dre foliowingspecificarions:

6Rc7. Re8. Rb

Vpg^+19

v^ f tnn: o 'o\

- A t -

HV: - l5

Vp= -3Ip95: lOnA

rDq = \ ' t 'A9. Rdi0. Rs

[,urrri.!*"''. ,s,'ll>

Vr. - V,r( t f - o.'-) -_ l.{- ",

%F(l t t )k zap rh4i.'") 316pfz. 3 tt

= lzf * 7,(^

7.V'",i

- tzr(a ) - - 8.7f/(

'b(/rr t )& ) 46q.rzt(ne[5J 1. y8 qE(

V -- o,6v

tlnn - I uts

tr,. A

r{priJt,

nVT f l^S =r/4(,, T'vD

_-_---.-_--f

l --T--I

a )o'z - )oz

*4*n=1J-"-1

od r9n

\ .'. i f l

i iLr '1 [

I i.ts/ I\ \ { ' / r\ . f

.*-*"t

;'t- lr+ *:,.1,r

L .__ _1.* ,

I,.{; . irt-,

l_ _ ' , /i | " !r i

:1 ' ; . . l i

'n \ t .' lr'\

l id l

{1)i , i l

._ i / ; .

i i . .\*-{'

II A t , i . ,, . \ '

\.;, . !.j, ;-, i ;

-r . 'L7

\2 ii - r, I

. r l -

-, ,i t.

\ { ,1

t.- __

I :. t:

I ---.

a; /.il

i .'i':,1 t ,,':

';,/.,' '""','

'-..j' '*-ti''_ , t.r\

t"' 'i ,', 'J lt'",i::;l

/r')'.!f

nl{l''

/-!.!';'7trtf,'

.l 'r; ,'

]: r,l

i' J 'j-

r'l l1.Y t'

,,f '/

ilz' .t:/

i 1r i ' i ,,'t ,f ':,y'r'

l ' 'i'l

il ,-,, / ,,, irl

i:t {,, 1. 1-' , I ',,,- -_ , .r, ,i"

ntJ ./' 'tt,4

'lr i't

.- a/'

i7 -.. ".'

'- t '1:l

, ,J I

lJ "r" ,-

LJ I-l{ F{l.,1

r i i--ii\:

"l '"1 r -l-J

tJ / -+f

,. .:.i i,l:','/

1r;.,. . ,it

'- i',.1 ''ll

r,Jff .\J

I-T. I

,ll- i

jl- i',i !r,.ii

-:_ , I i

I tt t / t3 lo4

Ir ,_,1+

!p - ' $pgl

f :: I l){7rVi t 2t" t ,^Y

lgu ' - o.? V

{- r= F tJg,o

i - o.- l

2 5.8 n"V

-r6 - ln ' l{, / A

f ool< + (rr ' r ) ( Po)

I "Z(, K

\1, . loo'r , ? -----F = 2q? l<

J c rl ./ '0'l bv la

"\J(c.

\ gt -' o"?

f , , i 2 ' lYrr ' 1Sl0Yor- F

{L-T----:- *e r 1--i ^^;**t *r?r,. 'i,'r" t' ,0 1* 1.*4 ,.r L- -I" 1-*-)

lr*V., - ,u,p Rr. Ail. 1lt't iYL - | - . - 1"" . - t l . l_-- / l ; '1Lo5tUl h rn- f q t, iss'1 )Au.

?rOOK-

, , / , t /" r, l t

{ o'* u"

I i r . iSE

V*' o-7

e-3{ ,"L-I

I Qs, i l l rB, t r ' r r*Lb

7' r", ll ( sz

o, (*toj = zo(o +t,,)

r lt1 tA ll1l y_

- t / ,

F-t !4 l l l {1 ' 4 ' :s 'e

= - '1"(y

Jf-"-I,1,

+ i .vf, \ -

/ll r : , : "

--44-----J

fr lt-

rV toot

l "qQ'lI

(,X' aTr/

L - \ l, t-'\t

|+--' ..-lV *-oeTVIOl,4

l'' '''' "

,a'\, ,.'T)\.t./ ,, -. ,/

no7 .')

V'i . TA L'o -- t3ft

A-l-\['Lh

- lA- -J\

s l:^ ) A" ) t

*"1lo+J *'t,("[,

( Vl,l. ;yt )oo( "1 el / = 'T- V - t\l'Lt

=',, /

1 -1- cot t td- t frr

vt c'srt " :n;;i; -{ '"t

111 ;1r

ytr!.?-i': ;-i -L

N 7.0 -_oN

V{6 i . .,.,,

+l €t "f ir('l

-9r*o tV..----- .> 1r-

0+'" l i,vts

lc =6L

, , f ,slx,1,

f , ,&f"n iuu] ( . . i rc,. i l ' r

f l ; . , la,7e- o' ]1. f

f ''' lry

T, * ' Ie: l^A

!/s = Io k= ( ua)(t r)= { v

Vg. VE aVea ' (+a-J, ' ( -V V

V*r., . J Vr..

r r \1,g, L.^] ViQ,<-+-:

Vr ' f fl . ,or ' . A

Fo-\1 -- \ l - -+v$' . . ( (

(g, , (g,

to,{r-

=53Ktg, = !L\1J: l \r*/ i_ Vs )

t r r\J l

, \/ \. l 1

t*{F"}_ . t - -

, ls,llQ,,. + lr ,r ', P'i1/t"ell/^)'tle -*-

, " i lF"

r r^ dlr / l s : Lt /'|JI --'..."%

# pl l qJ tc * i_ ' r . l r l r + (2,11){ f r t l :or 1r) \ ), t )

,, / , ', io*'ti,

r'i : : &-tT,:

- ' l JL. l!

-tu *-)!q

J.at ---{

i ' j 'unL]AL

)Vto j- (

c_r ^r

of ! tF1

Foi2tt l

V.d A;,t l o{{t^}

- , | l€(

t. t ralt 1f tfi^Clit !1rr y,-.17.i

AwfrL- oft

r J- \ l i - \

Vi- V0=u1'--1t . , ' )1 F -- J i l

\ r t lu lo ' '

\ i ' 1 lVr - v0

r l.JPT

-T-JF 1",: h"t

klat n

E7uot7 o"

] \ , - "

| \-_ \

320 winter 07 cockrum

y e r e

f t e r

requisit e

t s ma y b e d e d u

n cla s s o t e s

e g e r completion o

p oin t s d e d u c

n y e d

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