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Transcript of ec102 expsheets
R o l l N o O 7 A z e 5 1 8R o l l N o C ? O L e 5 1 9Rol l No C Ts 'ze 5'28
Group No wr7
Department of Electronics & Communication EngineeringEC102 : Basic Electronics Laboratory
EXPT. No. 1 : FAMILIARIZATION WITH THE LABORATORY EQUIPMENT
In the first laboratory you wil l get familiarized with the rnstruments and basic components usually used in thelaboratory Some of the inst ruments are:
1 Mul t ioutput Power Supply, Model APLAB LQ63242 Sweep/Funct ion Generator , Models APLAB 2004 and21043 25 MHz Dual Trace Osci l loscope, Model APLAB 3304M4 D ig i t a l Mu l t ime te r (DMM) Mode ls SCIENTIF IC HM5011-3 and APLAB 1003
All of you are required to get iniroduced to all these instruments in the first laboratory In addition, you should workwith different models rn the coming lab sessions so that you get used to all the instruments in the laboratory
You have to understand the speciflcatrons. operation precautions. and limitations of the instruments by studyingthe manual of the inst ruments The basic in format ion and guidel ines to s tudy the inst rument manuals g iven in th ishandout are only to help you gather complete informatron about the instrument Learning how to read a manualand find required information rs also a part of the lab Do not hesitate to contact your instructor, lab assistant, orteaching assistants for clarif ication and additional information
In addition to understanding the instruments, you wil l learn how to identify various components often used in thelaboratory These include resistance, capacitor, diode, transistor (BJT), potentiometer, transformer, and others lfrequired you wil l also be informed about the use of the breadboard, oscil loscope probes, and other accessories
1.1 POWER SUPPLY
Any electrical or electronic equipment needs power supply for its operation Different electronic components havedifferent requirements of power supply One has to use different voltage sources for powering up differentcomponents in the same c i rcur t , e g
Dlg i ta l lCs requrre +5V supplyOperat ional ampl i f iers requi re both +ve and -ve suppl ies (e g t12V)Other hnear devices l ike transistors need different voltages depending on the application
1.1 .1 Multioutput Power Supply, Model APLAB LQ6324:
Refer to the manual of the inst rument , and read Chapter2 (SPECIFICATIONS) and Chapter3 (OPERATION)carefully Study the front panel and identify the power supply points Understand the procedure of using the powers upply
1.2 FUNCTION/PULSE GENERATOR
A function generator is a versatrle instrument essential in electronic laboratories used for testing applications ltgenerates various waveforms over wrde range of frequency and amplitude Study the function generators givenbelow before you carry out the exercise given at the end of the handout However, the features of the functiongenerators wil l be clearer to you during the exercise
1.2.1 Sweep/Function Generator, Model APLAB 2004:
Read the specifications given in the manual Section l l gives various functions the instrument can perform Studythe front panel and learn how to operate various knobs to obtain desired output waveform
1.2.2 Function/Pulse Generator, Model APLAB 2104:
This model contarns almost all the functions of Model APLAB 2004, plus a pulsc gencrator After studying APLABModel 2004 given in section 1 2 I , you need to study on ly the pulse generator part of the instrument
1 .3 OSCILLOSCOPE
An oscil loscope is an essential equipment of any electronics lab, most widely used for observing electrical signalsand for measurement during testing lt is advisable that you spend sufficient t ime to learn the operation of theoscil loscope in detail Give special attention to the section on triggering, as thorough understanding of thetriggering process is essential for trouble-free performance Study the oscil loscope before you carry out theexercise given at the end of the handout However, the features wil l be clearer to you during the exercise
1.3.1 25MHz Dual Trace Oscilloscope, Model APLAB 3304M:
Understand the specifications given in the manual Refer to the front panel diagram and identify the knobs andthei r funct ions, Going through the Operat ing inst ruct rons (Sect ion l l l ) wi l l he lp understand the funct ions of theknobs and operation of the oscil loscope Note that understanding the triggering process is the key to master theosci l loscope - the most important inst rument in an e lect ronic lab
P T . O .
1
1.4 Dig i ta l Mul t imeter (DMM):
A digital multimeter is a handy instrument for quick measurement of common electrical quantities like dc voltage,dc current, ac voltage, ac current and resistance with high precision and a digital readout Get familiar with theconnection points for the measurement of these quantit ies, lf the multimeter is not autoranging type, choose thesmallest possible range that gives valid reading, in order to obtain maximum precision However if the magnitudeis unknown, it is advisable to start with the greatest range and change to smaller ranges step by step ti l l the rangegiving maximum precision is reached
1.4.'l Digital Multimeter, Model APLAB 1003:
Read the technical speci f icat ions g iven on pages 3 - 7 in the manual The operat ing inst ruct ions are g iven onp a g e s T - 1 1
1.4.2 Digital Multimeter, Model sclENTlFlc HM5011-3:
ldentify the keys and connection points from the front panel diagram given on page 5 The technical specificationsare given on page 4, The operating instructions are found on pages 7 -10
EXERCISE
Perform the following exercise and write the observations on this sheet Demonstrate your result to the
Tfuinstructor and get the observations signed Submit it in the next lab session along with the answers to thequestions given at the end
Set a function generator to output a triangular waveform of 2 3 rHz C:-re;: i^e c-iput of the function generatorto Channel 2 of an oscil loscope Adjust appropriate knobs of the osc roscooe tc get a stable drsplay of thetriangular wave Measure the perrod of the waveform by countrng the nurroer cf dtvtstcns per cycie on the timeaxis(x-ax is)of thedisplayandcalculatethefrequencyof thewavefo. ' r iny ' ' :e tHeocsen'at ronsbelorv
Time scale =
Number of d iv is ions =
Period =
Frequency =
With the oscil loscope connected, adjust the knobs of the function generator to obtain a sguare wave of frequency5 kHz and ampl i tude 5 Vp-p by doing measurement on the osci l loscope screen ( ignore the indicator on thefunction generator) Write the following parameters you have set on the oscil loscope
Selected time scale = t - so-flctd\vRequired number of divisions on x-axis = fl = h d\uittoos
Selected ampl i tude scale = I vot t I d iv
Required number of divisions on y-axis = $ d\./ isrons
Q1 Write the values of the resistances (in Q, ko, or
a) green B\ . re Red GolAen
O) $i{ve- R<J- 6'eJ Red Oranl
c ) O ruge OranSe B rowo 6
d ) B . o ^ . G * J $ r o * ' n G o \ l
Q2 What is the value of a capaci tor on which l$$is wr i t ten? 0 '@IJIF
Answer the following questions on a separate sheet and attach it to this sheet
Q3 \Are tE cobur code used to specify the value of a resistance
Q4 How ae catfnde and anode generally indicated on a diode?
Q5 \Mrat ctes the notch on a tl'ans stcr rndicate?
Q6 Drawaqr€ur tC l l4 famto genera tea var iab levo l tagef rom 0 to 5V us ing a po ten t iometerand a f i xed power
supply of S V Fnd out B|€l-symboi of a potentiometer in your text book and use it in the circuit diagram
t= 0 - t ns f d rvn: 41 drvreionsc= O. t *an ' '5 (= txn)
Y = . I = 2 '?26 Un
trAMILIAEIZATION WITH THI
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X
INDIAN INSTITUTE CF TEGHilOLOGY GUWAHATIDepartment of Electronics & Gommunication Engineefing
EC102 : Basic Elecbonks laboratory
EXPT. No. 2 : DTODE CtRcUtTS
OBJECTIVES : Design and analys is of hal f wave rect i f ier and c l ipp ing c i rcut ts .
MATERIALS REQUIRED. Breadbcard. Equipment _ Function Generator, Oscilloscope. Comoonents
Diode . Cne. Type 1N4CC7 rDiode vottage drop V; = 0.7 \1Zener Diode : One: {Zener vottage {/z = 3.g ViResistance . Four: 56 a. i ke" Z.2ldl. 1.7 l\gCapacitor . One 22 uF.
GENERAL GUIDEL INES / PREQUATIONS
1 Connect the capacitor with correct polarity. The capacitor being of electrolytic type. d ispolarized, and wil l be damaged if connected with incorrecl potaiity Similarly, conhrm ttrepolar i ty of the d iodes before connect ing
2 Keep ground terminals of oscil loscope probes and function generator output connectedtogether throughout the exper iment
3 In an oscil loscope, for higher precision, increase vertical sensitivity (i.e lower value ofvolVdiv) , especia l ly whi le measur ing smal l ampl i tude levels (e g r ipp le vol tage)- you mayneed to swi tch to ac coupl ing whi le doing so.
PART A : HALF - WAVE RECTIFIER WITHOUT FILTER
1 Set the function generator to obtain 10 V peak{o-peak sine wave at 500 Hz frequency Do notconnect any circuit to the function generator Keep dc offset equal to 0 Observe the functiongenerator output on the osci l loscope and ver i fy s ine wave generat ion.
- r ?.€gt up-lhggrcuit as shc',vn in Fig 2 1 (a) without the capacitor C, taking Rt = 2.2 kQ.
3. Now, connect the funct ion generator to the c i rcu i t a t points F1 & F2 as shown in F ig. 2 1(a) .4 Display V, and Vo simultaneously on the oscil loscope Skefch V, and Vo one below the other
wi th ident ica l t ime and ampl i tude axes
Fig 2 1 Half-wave rectif ier
PART B : HALF - WAVE RECT|F |ER W|TH CAPAC|TOR FTLTER
1 N o w c o n n e c t a c a p a c i t o r C = 2 2 p F i n t h e c r r c u i t w i t h c o r r e c t p o l a r i t y a s s h o w n i n F i g 2 1 ( a )2 Display V' and Vu s imul taneously on the osci l loscope Sketch V and Vo over lapping, wi th the
sanre t ime and ampl i tude axes
3 Measure peak- to-peak r ipple vol tage on osci l loscope by enlarg ing Vo to the rnaximum extent .You may have to put the input coupl ing in ac mode whi le doing th is measurement See thegu ide l i nes g i ven a t t he end
Repeat s teps 2 and 3 for R. = 1 rQ and 4.7 kQ. Commenf on the output waveforms and i . ipprevo l t ages
4 Connec t a 56Q res i s tance i n se r i es w i t h C o f F ig 21 (a ) as shown i n F tg 21 (b ) The po in t sacross th is 56Q res is tor are nrar .kecj as p and q.
(b )\ d /
Please notethat : The res is tance 56Q is chosen smal l enough not to af fect the overal l per formanceof the c i rcu i t and at the same t ime to ensLrre an appreciable vol tage across i t This vol tagerepresents the current f lowing through the capacitor.
5 Display and sketch Vo and Vso (i.e voltage across 56Q between 'p' and'q') one below the otherwith identical t ime axes. Mark the ground reference line
A.,F;|UnV is /c (=Voo / 56 ), the current through the capacitor, negative for some portion of a cycle?
n/t' Estimat€ /s,,qe (positive peak of /6).
PART C : CLIPPING CIRCUIT - POSITIVE CLIPPER
1. Connect the c i rcu i t as shown in F ig 2 2 wi thR = 2 2 k Q
2 Set the funct ion generator to get 20 V peak{o-peak sine wave at 500 Hz frequency Observethe funct ion generator output on theoscil loscope and verify sine wave generation
V.3 Connect the funct ion generator output to the
ci rcui t as shown in F ig 22
4. Display and skefch V, and Vo one below theother wi th ident ica l t ime and ampl i tude axes.
5. Superimpose the two waveforms V, and V. andobserve.
6. Set the oscil loscope in X-Y mode (V, to Ch2 : X-input and % to Chl : Y-input) and sketch Voversus V, with equal x and y scales Label thegraph and t icks on the axes.
Fig 2.2 Posi t ive c l ipper
.1 I
\- __
,ffi - Draw the circuit diagrams for : (a) -ve clipper'6 ,/
V (b ) +ve and -ve c l iPPer
Pre observation readinq :
(a) Draw the expected waveforms at - (i) Step no 4 of PART A
--!,*,
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( i i ) Step no 2 of PART B and
( i i i ) Step no 4 of PART C
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Department of Electronics & Comrnunacafiion EngmeeringEC102 : Easic Eiectrcnics Laborarory
EXPT No. 3 : DIODE CIRCUITS - i l
,Smoum ltr,e
OBJECTIVES : Des ign and ana lys is o f fu l l -wave :=c : : ie r z ' i !2 ' tE" -33- a uLr
M A T E R I A L S R E Q U I R E D
. B r e a d b o a r dn EqutPmentn Conrponents
Trans formerDrOeGZener D iodeResrs tanceCaPacr to r
Osc i l loscope
O n e . 2 3 0 V t o 1 2 - 0 - 1 2 VTwo: Type 1N4007 (Forward vo l tage draa v . = ! i , . ,One {Zener vo l tage V: = 6 2Y)F ive ' l 0 O, 220 Q,470 O, 560 Q, 1 x f )O n e . 1 0 0 p F
GEI . IERAL GUIDELINES
1 Switch on the marns supply to the iransformer- only after you have made al l c:tel-:cn- 'eihcrs ,rorder to avotd electr ic shock)
2 Aiso, whrle making any changes In ihs 6i16ri1, switch off the mains supply to the rans;ci ' i r- : ier
3 Connect the capacitor with correct polanty The capacitor being of elecirolyt ic type. t ,s ci ,3rz3ca n d w i l l b e d a m a g e d i f c o n n e c t e d w i t h i n c o r r e c t p o l a r i t y S i m i l a r l y , c o n f i r m t h e p o l a r T t y c i : : e : : : e sbefore connecting
4 U s e " l l r l e " a s t h e s o u r c e o f t r i g g e r i n g i n t h e o s c i l l o s c o p e P u t t h e o s c i l l o s c o p e r n C H G P n c c e
PART A : FULL - WAVE RECTIFIER (F\ruR) WITH CAPACITOR FILTER
i ) Full-wave rectifier (FWR)
Set up the circuit as shown in Fig 3 1 without the capacitor C and resistance Rcr The transformer TXhas rating ol 230V Io 12-0-12 V, 1A Take Rr = 1 kQ Connect transfci-mer primaD^t6 the mains anilswitch on the mains Disptay the secondary voltages Vqo and Vac (Vrc to Ch-1, Vs6 to Ch-2) on theoscil loscope. Make sure that both the "probe grounds" are connected to the circuit ground- Sketch thewaveforms overlapping, with the same time and amplitude axes They should be l8C" out of phase
Drsplay and sketch the full-wave reciif ied output Vo across R1 Measure the peak voltager in both halves
230 V( r rns)A C
nar i ts
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Fig 3 ' i Ful l-wave recri i ier wrth capacitor f i l ter
Q. 1 i f r fe peax ar rp l r t r - ides are no t equa l what cou ld be lhe reason?
I N o r v J J r l r r € c t C = ' O O p F a n d R . : : ' i l a s s n c w n r n F r g 3 l R e a C t h e g u r d e l i n e 3 N o r e t n a t R . : r spreser r t ' y s ro r red Shetcn V, and measure V. lpeek- tc -peak rpp te vor tage) Set rhe cscr l loscooe channe ltD ; t : eL)L tL , ! t ,L j .31d , rc rease ver t rc . r i sensr t i v i t y 'Oecre?Se V/d iv \ r ^ / l t i i e measur rng y ,
4 Remove the shotl acr-Lrss Rc- ano sk3tch 16 b' i observ,nc V". Esi imate /r,ro" (posit ive peak of / ;)
Rr
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i i i Cofnparison with half-wave recti f ier (HWR)
; Pei love ci iooe D2 The circr.r i t rs now a H\l /R wtth C-f i i ter
2 Sketch /1 arrd estimate i", , ,uu
3 Norn; put lhe shof across Rcr Sketch V'". and treasure i ts ampli tude
r! Conrpare y/ val,-res tn FWR and H\A/R
Q 2 ' , / Jha t a re the f rpp le i requenc ies in FWR and HWR?
Q. 3 i l w l r rch c i rcur t / r , , ,0 " rs more seveTe?
o"l,,lli,iii,,,, ffi*',
PART B : FULL - WAVE RECTIFIER (FWR) WITH ZENER REGULATOR
Rerirove Ri from Frg 3 1 Connect a zener diode Dz with series resistance R = 56C O as shcwn inFig 3 2, (RL.r remains shorted) The voltage across D7 wil l now be the desired (regulated) output voltageVop whrch w i l l supp ly cur ren t / . to an ex terna l lo id Rr
Wi th R. = { l reasL lTe Vr , ru , , & V a t 1 :o in i '1 (unregu la te i ou tpu i ) , and Vra ,aa , & Vn a t pcr , t - l ' i : -eguta ted
or,rtput) (You wrl l f inq y,n lo De',/ery srnal l . l rence rncrease osci l loscoce sensit ivtty suitably;
230 V(fms)AC
matns
' : ' - Fiq 3 2 Ful l-wave i-ect i frer lvtth zener reoulator.
Ca leu la te . Voau= Vo, ru , . - V , l 2 , an1 y 'aq :u = ' ' /1 . - .2 , - ' " ' = 2 = , r ta ,
Hencedetermine lq , 12 , and/ r (a l l averageva iues ; ano ' f iepovue-d tssmaions P: '= i . ' : - - . v := . .F . , :and P6= Vn ld. ' ,r 'n = voltage across R = V33,- Vaa2it
Repeat siefj 2 and 3 for Rr = .1 k!) 47C (l. ani 220,) ?r,,.e.5e rneasu:red ar ;arcJl,a@d rE,rr.ritss : 3shown below
'r t=it,tE-::i'- S -:etinei aS
*, fr8q = -- - , . , --- r - . ' . / ' ,p t , ' tL,); . i - . ) l (V', ,nr,)r. to-1,t"D jX 100
@-{: FC }], ; : l : :e-,,e ! : :r .sgural icn ior Scme l,_? V'hy cices i i ocCur?
{ ! . ,6 : , r r r$ l l ina f . s ; rE - - i . : - r i - la i : .L , r : ;n t ihe zener regu ia lo r (Jnoer ies t ) can supp iy? Grven tha tE nm,= i l l l i l i i i 4 , a ra j - : -B - : , : - - - t : i ,a : l i ss ica t lcn tn lhe zener i s l l W
9 - f ; l i m m - u r y i 1 d i i ; , - q : r : ' . " = - - - : : t p ' a y c e a n e v L - n : r i g h e r l l ? W h a t j s i h r s , ' n a x r r n u m v a l u e ?: leqil i[h$r L ,=
'
f t r u m F u @ . 3 s c j e l . ] S J i l - = ; ; - : - : i a : l c e S . l c u w t i | u s e t n [ h e m o d i f i e d c l i c L r i t i o r i h e r n a X I m ! m 1 ., '9 , 1 . ; f r la l6 ;p ;14 ; f f1 ,$Gqe,a : u3 : : .= - : : :gs " t i
' t zu \ l 1VV,2W 5Wetc i
V (rrfis
B
INDIAN TNSTITUTE OF TECHNOLOGY GUWAHATIDEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING
EC102 : BASIC ELECTRONICS LABORATORY
Expt. No. 4 : Study of Common-emitter Amplif ier
OBJECTIVES:
l. To carry out an approximate DC and AC-analysis of the given CE amplifier.2. To determine the voltage gain, the "maximum undistofted peak-to-peak output voltage
swing" (MUOVS) and the maximum input voltage for undistorted output.3. To study the effect of emitter bypass capacitor on voltage gain.
MATERIALS REQUIRED. Breadboard. Equipnrent and parts
Tlans istor,R es istorVar iab le res is to rCapacitor
R;:1 K
Fig. | : Common-emitter ampli f ier
Importanr: You are expected to complete Part I at hnme and come to the Lab with a neatreport shuwing all calculations. You will be allowed to continue with the rest of the experimentonly after the instructor has checked the report.
Part-I. Pre-erperiment preparation
Approrircate DC and AC-analvsis:
Mult i-output Power Supply, Function Generator, Oscil loscope. DigitaiMult imeterOne- NPN type 2N2222A.F i ve - 470O, 1KO,2 .2KO.22 KO. 100KO.One - lKCl Pot. (Potentiometer).T l r ree - 10 pF . l 0 1 tF ,22 pF
Carry out an approxirnate DC-analysis byo f , the fb l low ing assumpt ions :
(a) /u, , L,, u) /r, so that 1,,,
(b) Vn,, = 0.65 V
using the values given in Fig. I and by rnaking use
- l- t ! t 2
[-.lnder the'se assumptions, you should be able to estimate the. DC qr-rant i t ies (quriescent values) Vt1,V-, , ,1 ' , , ,1, ,{x Iu)
Vc- l2V
l0prF
-->t-
Z J N
r R o lvl*. 470 o
- l -
. Voltage gain A, = -r - ' ( = -+;v ---1- 1
rh ,, i 0 r" V.,.it I ,,.
(4 .1)Vl I/l
t,T
rvhere V, =T:the thermal voltage; k: Boltzffrann's constant= 1.38 x 10-23 J/l(.
q: 1 ; x 10-le Couiornb, T is temperature in oKelvin.
Take tr', = 25mV (at a room temp of 20o C)
In (J.1). w'e have used the approxirnation 4 - (p +1\r" = pr"
\ote: The approximation does not require the knowledge of p
. MUO\'S:2 + Min{Vgs -Vc. Vc -Ve i
Q: lconnecting an electrobrtic capacitor) How' do 1'ou decide that the + terminal of Crshould be connected to the Rr-Ru node and the - terminal to the source v; ? Likewise,for C: and Ce..
2.1 Experimental determination of the quiescent voltages and currents:
a) Before assembling the circLrit, rneasure the actual values of the resistors by rneans of aDigital Multi lvleter (DNIM). fRemember you are using resistors with l07o tolerance].The actual values are to be useC in determining the currents.
b) Now assemble the circr-rit, apply Vsc and note the following:- rneasure Vss using DVIM; it should be around 0.6 - 0.7 V indicating that BE-jLrnction
is tbrward biased.- Measure V6 ahd check if VE < Vc < Vcc.A value of Vg midway between Vs and V66
is preferable (Q: Why is such a value preferable?).
, Af your measurements agree, you are along the right path.\/
c) Now neasure Vs, VE , V6 and \,'r-g : then using the measured resistance values, determine
Is, is, 16 and hence F (F:lc/Ie).
d) Compare the experimentally determined values of the currents and voitages with thoseyou obtained throLrgh approximate anaiysis.
e) Compare the experimentally cieteimined value of p with tl-re approximate value stated in
the manural or given by the La'o Instructor.t ) Compute Ay (equat ion . l .1 ) us ing the exper imenta l l y de termined va lues o f Rr .and [g .
Use V1:25mV.
2.2 Voltage gain without load resistence R1 :
. Disconnect Cr.
. Adjust FG to get approximatel .v i0-20 mV peak-to-peak sinusoid at 1 kHz (display in Ch-I) . Appty' this vol ta-ee at arnpl i f ier input (v;) .
. Displa-v col lector vol tage irr Ch-i l of CRO(use DC-cor"rpl ing). Note the 180' phase
dif ference between the input and the output. Adjust v in ampl i tude to get a cortvenientvalue for peak-to-peal< collector voltage vc,pp ( say 2 V). Use appropriate verticalsensi: iv i ry (Vidiv). Note the correspondif lg vi ,pp (rnV). Experirnental ly obtained volta-eegain is therefore:
_ ' y ' 1 . . ! , t , - _ 2 V = j e o
A, = -v t- j 'P 20 co(
.)
. Compare this value with the computed values obtained in step 2.1(f).Also compare thisvalue with the value estimated in your pre-reading assignment-
3. Maximum undistorted output voltage swing (MUOVS)
. lncrease v; slowly till you observe a slight flattening of vg waveform at irs peaks (eitherpositive peaks or negative peaks). The peak-to-peak value of the output signal fiust at theonset of distortion/clipping) is the MUOVS. Measure the correspondi.g r; pp, the peak-to-peak input voltage.
This information is useful in an amplifien it rclls the user that fte iryIt should not exceedthis value for faithful amplification of the signal, else digrtbns sts in-
r Now increase v; beyond this point and observe the orryn uraveform- The sinusoid getsincreasingly flattened and becomes more like a squarc wave-(overdriving an amplifier leads to heavy distortion)
[ !! Square-wave from a sine-wave ]
4. Voltage-gain with load resistance R1:
The output of an amplifier normally drives a load resistance R1 which may represent anactual load Iike an ear-phone or a loudspeaker, or the input impedance of another state ofamplif ier.. Connect Rs (see circuit) to the collectorthrough the coupling capacitor Cz(Cz blocksthe
DC voltage at the collector and allows only the AC i.e. the signal component to passthrcugh).
. Measure Av with R1 connected. (you would observe a reduced Au since &,."r = & lln, I.
5. Effect of Ce on A" :
. Get back to the conditions in Part Z-Zi.e. v; at I kHz, its amplitude adjusted to get vc,pp r2V .
r Now, remoye Ce (with ckt. powered) and note the drastic reduction in vg,pp. You have tochange to approgriate V/div in your CRO. Determine the gain of the CE amplifier withunbypaSsed Rs.
. Compare your observation with the theoretical value
,4,. =- oR, = - &," (R,, +r") RE
. Display and sketch v; and vE waveforms. Note the arnplitudes andbetween them.
(4.2)
the phase-relationship
. Display and sketch v6 and v6. Note the amplitudes and the phase relationship. Please notethat you are in DC coupling mode of the CRO, Please ensure that when you pressed theground options in CHl and CHZ, both the horizontal traces (of CHl and CH2) arec_oinciding. Also ensure that the V/div of CHI is equal to V/div of CH2.
r Increase v; gradually and observe how vs and vq change. Continue to increase v; till youobserve the -fve peak of vE (almost) touching the negative peak of vc. When this occurs,we say that the BJT has gone into saturation (vgg = 0).
Q: What do you observe if v; is increased beyond this point ?
i
Ft
It
I,t
-3-
l*r:::::::=
STUDY OF COMMON-ETqITTIR AN PLIN EP\
OB][CT)VE :--21
,) G o"rJ. an opptoximo.le DC & kt oralolsfs 6) qNenJ
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irn , t' t!'La T'l *^. undr:hur tecl
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t.38 X r5'3.1\ftt <)
4
V r Zs ,nN .tA'zo"L)-a'
Aff^ri r"cJ eJ !,, = (,pr)r. ̂ _L"
P't UDVJ v.-vef
- R.1. A"vr
k=I]x1.6
?RE - ExP EEI u ENT PRTzA RATI DN :
PART 7
+$o b
n EP.
22-t4*
hyu,*fu -b-c ̂ T
K= D'z k-
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T
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l /L2(-r^ , ?r^loo
c. tg l tst, -29 t to -D
i -
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9^ = 2' t6v
["' f* *'J#?*T'I
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) { c , = l o ' v
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t ^ - t iarrTn k_vt
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?nr nr t,le y€-t
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jun clron Ja
V
tsE
r l '83 V
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= 5,38V
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rte
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= tJe
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A Squo*re n)attefrrn apf"ri4 ,
2.4
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TITUTE OF
of Electronics & C', EC 1 O2: Basic EleEtroniEb Li$erdory.-
EXPT. No. 5 : OPERATIONAL AMPLIFIER - |
OBJECTIVE : Realizatron of arroi,fer circuits wrih Op-Amp (Operational Amplifter)
MATERIALS REGIUIRED. Breadboard. Equipment. Gomponenb
OPAmPResistance
: iftfitiouFut DC Power $.rpply, Functron €enerator, Oscilloseope,
: Ore: LM741: Firre: 1 kA (1 no), 10 kf) (1 no),12 kO (2 nos), 100 lql no).
PRECAUTIOIIS AND GUtrIEUNES
1, The op-amp gpnerally rrcrks on spllt power supply (eg r12V). Both positive and negative porversupplies npust be present ntrenener op-amp is powered The range of power supply is fiom t5 V tot15V.*do not brget to conned the common terminal of the power supply to the ground on thebreadboard
2.t6nnecting only orre srde of pou,er supply cr intercfranging pcitive and negative power spoliesdamages the oFarp.
3, For connecting powersupply, you have b follow the procedure as given below,
, - J I a. Disconnect the porer supply to cFamps.,.\y 1-r-f b. Swi@r-anthe porersr.pp!
#' fi i c. Set rre outsut volt€ge as required (e g- t12 V)S
- *'; d S$dtdr offthe poler supply. ::e. Connect the poner stpply b op-arps-f. Switch on the pouer s.p:!
.{ For any lC, never exceed the input voltage @old tfie porer sr4piy hnils
5. Use the herizontal stnps of the breadbod &r pos s.Fply- T+ te pouer gpply hr eadl |G fro.n/these su#Iines.
,t: i.l:. ] ,
6. Keep ffid terminals of the oscilloecope prdrs and functi:n generator ouput and porrer supply,€omrRotr connected together thrbughout the e$eriment
Pre-experiment Readinq:
QbEia.heoreiical values of Vo I Vi for s@ 5 d F.rt A tlo thb for Part B also.
PART A: INVERTING AMPLIFIER
1 Assenrb ie the c i rcu i t shown tn Frg : . " , : -
- - : ' l ' ' i a :cR: = 1 kQ Make sure the po lver s lc l . : : - , - : s :a ' - -c : - : :to the circuit ground
R, / l00kol i)
--',/',, =-__. ?fld'
/ ^ t l 0 k Q
200 mVp-p, 1 kHz sine wave at V from the functionator and see the outout.
bbserve Vo and.M-1i"and determine voltage gain A = Vo I V; t \c t - - t lAiso obtain A for Vi = 199..nVp-p and 300 mVp-p
,4r' Change Rr & Rz to 1C0 kQ & 10 kO and determine A for V' ='i 100 mVp-p, 200 mVp-r and 300 mVp-p
5 Now apply a fraction of the voltage V, (keeoing V, at 200 mVp-p) to the pcint X' through the poientral dllde!'qrcuit as shownin Fig 9 2 and note the values of Volor
trin O "l
,q1
Inverting :'nplifier
R , /( r l ) /n_- -
l0 kaI kr)
To point X
Compute Vo / V for ( i) and ( i i )
F ig 9 2 Voltage Divider
PART B : NON- iNVERTiNG A lv lPL lF lER' 1 I Acco* l i lo tha r r r - r , i ShO." r i r - 'n F iC ? - ' : , ' . ^ = . = a iC
'an6
- . _ ' . ^ \ 4 - -r ' - ^ \ i l t 4 t c : - . : - - _ = : - - _ . :
? \ Ann l v 2OO m\ /n - r - <1 , , ; s -= , ' , ? , a z - .
) , A ^ ^ ^ - ^ : - l l = . = - - ' a . : - - Z : = i 2 ^ - = t , V ,
- , 5 u - L . = - , - - - = . - - , -
t v ' o ' , u E r \ ' r - ^ - : - - - C . = C A I U I. . . : ^ . . ^ ^ ^, , , - . , \ i 1 ' n \ / ^ - - - - - : - _ - \ - -V - . U V r l v J - v 4 - ! r , - - = - e , -
5) Now app ly a i rec i ion o i tne , /o i ia3e ' r Lkeec . r , ' a t 200mvn-n) to the nnrn : X : i ra "c r - l -e :c te i i a : . :e : c i rcu i t" ' Y Y /
as shown in F iq 9 2 and ic te i le Ja ,ues o f t - ' : 'F ig 9 3 i ' Jon- inved inc a- . ' - '
R i i 0 0 k l l\ i )
- ' t / - . = - ; i c
4 / 1 7 l 0 k O
It R,
D
r0 kal ld)
Compute \ " io i v , io t ( i ) anc i i i )
Q1 For a source w i th h igh in te rna l impedance wh ich conf igura t ion ( rnver t ing or ncn- in , r : r " - :suitable forlesigning a good ampli f ier?
Q2 Design an Ampli f ier sysiem to obtain a gain rJf -50'for a source with high internal resisiar.- ' : ,
use combinations of invert ing and non-invert ing: corrf igurations
EXPT 5 : OPL RATI()NI ALAltlPLI FIER - I/
Fu, a s0urce with hUh in ln6sl impedence
su i\able for "Ieriqn,n( a $ood arnplifr utrl
A nrr,' , t{ o n - lnverhng A*plif, edr-
- Desitnan ornp lifi er- Sgstam Fo ohtain d g J,h
Ih*nt.rnel E€IEg; You *.g u.se
tn(ertn 3
[ntw *
and fion-tnv{ r\d contigurat ioos-
Rs
,1nihi6,h co n8guratioo wif h
[n"".t rg ;t Pon-\n.rrtrqf
oP f,mplifiq, Grcuib wiFh 0p- hry [Opornhonet A"6C-)
Qrn.h'on 2
fot o soune
oP
R
Rz is very srna\\
R is the s 'arne va lue-Taking Ra:and R3
R.7qrE
as t\re \oterna\
, so that R+R3
irnpedence oF Vi
-50
f xptain etro ns
rL hlh* source. h., h,gh inte.nel imp.J** I
I(o) lnvnrHng Arnp\ i f ie t
t1,1e hove \' -0 -* 0 - Vq
ffi-r.a
Vo -R, A -= , ' . t 1 V -
V; Rf,a
buL Zt>Ri , i=1,2
th, Non-lnverh ng A*pl, 'f i 'u
tZ
= cvrrent lshou,n)
not m6tter ,
A"-- l*
(non-i.,")
N6h.i*0
Vi(vith .r)
_ Rr.Rn*z
Av-)o
9z+ I
( [o 's very small)
V=V'-Wher- i- - ' l =Q
.'- lt doct
Gain
rL' Gdn
whtl ivo the
Rr/ff,
6$n 1,rrrt J
VU = t2V
d'(?
6l
t\^w
; EXPT.5 . PRE- EXFERIMENT RE\DING
PART t l2v
lNVERrrnra AHpLlFt€.R
vot-M ltll
- leV
\NVERTTNCI
/-
ftMruHEE.
V=V,ltdu. tuvolt,lq *d;viloTu.l rr rn I
V6t tagI vr d er fnekes Vo\tag e a t X : Vr /Z
( i rRo lo k ru Y,
t , , l \ ? t
Rz I tt-n: loklr .:) Vo = -$
V''
PI\RT I] :Nthl- rrrlrrpp,rruq ANtLtrlEq
V0LTA6E DarER
Lfvl?+t
- tzv
NoN-l^,VtRl!ArGi
q:I&R}'
_\2Rz
Vo1>-r \ r
y"
ot\r
V , /z - Voh
K,
. : V ' - Vo_2Rr R,
yIt-.+.1
! -5
| [R,+RrJ -
2Rz
rir Ioo k-n-
r'\ 2 lu t_c
( l l ) l0 k_n-
I k-n-
5s
!V,
l l= - :
1
I-AB OBSERVATIONS# \ tfii= \okrt
0J. [npr,+ hIf,\e
flutg,r Wave
Re= lldt
: VL (p-p) =: 'Vo
(e-p ) =
NVTRIHIr ANIP
Lgo.sll Ll l4{g
2Vt ' ' t
A - -[o, \
lOOrnV
lqo nn v
Ar -q'1
3oomVL.\6rl
9-e +
ots. tl z
Nos, -tt rvgRl lhlG N{t\P'
2OO roV
2 -ls v
A= ffig\o-"5
100rnv
1.08 v
fi = l0.g
3 ooffr V
T .ZV
A = l0'6n
(zt F=-ll r
C' \nput wave
Outg,t Wave
5trE s
Vi cp -pl
Vo te -p)
V, [p-rt
Votp 1')
A=
(el hf* Wwe,0.r$* W rvc :
[NVI&T[NC' Anqr. 6\or.t'INVERT
Rr= (ooksr Rt=
[np"t Wwe ' Vi [p- \o) =
Ooif" t Wrve t . , Vocp-p =
1o kr
( l t I O0 rnv ( \ kr+o1.02v :
\b-u,
\00 coVI t6 v
A= \\ A
2O0 r"V2.jv
fir
Ilnguf W?v e
0,rlpf W.-v.
A= I" =., V;I '
lng"f Wavt,
0+put VtJ.,r,,.
"4iry"=
.. ,- Vi
, \l r' [p-pr =
, \o [P- l ' )=
\/, Ir" -p) =
!" t e-p) --
2Oo"nV
2V
A= lO
(a $oo rnv * Pn
3\
Aro
A= llE
i (),O mVj lsv
= 1 I .t6+
r. Rr= \00
A$.,- a pplv;ng Voltno. Diu,4..
Rz = lO
Ilntt W av. '.
AUul-g,ut W avr :
A,- \o
v,'
R,, =
ln p+
0utpur
Vi q,-pr
Vo,p-p,
l0
W uv"
W*.
R" =
Vitp-f,) =
Vo(Plr) =
A=
-rS$ ,
N V'R1\ NC AM ?.
2OO"V
6 gcl 'r', V
, 3'1-S
bBs ' zlz
NdNl -tNVrRr lxr o, P.r.te.
200 mV
Crrpht
+lv
VotT
Inv.,ling A*pl;{,,, ,
+lOu +--mV
vit
- \ooftrV
Y
8r t0ks--T;=16
Y
(p-pl= t v
fi*. -oIrntl
0
N,rn- l lvnrt 'nq Ampli fre. :
- H 0thv
Vt 1.0?ES Y,:ir-qli- trtY-
X{rrt et rnr)r
K
trme(ms )+
Vrf
f nve'hlq Arnpl i f ie.
f t
\ loltaXe Gain A= bV;
Fu' & =l_0r,rr ,R. {h
Fo' fu r lookn ,
:
A = - 1-95+
A =- l(t- 06l
l \ - ' l a r/ - l : l - 15
,\l \ =-0 1l
AFt..
t:l 0 r
fo'
P,,.r
R " lo l<Ir
app\y in1| Vot l age Div id o. 2
lo0 krL&R,
[,nr.i2
lo t 'n
lo k^l
I t(rL
B : Non - Inv.rhnj Arnpl;Fie,
FI-.rr Hr l0 ko
|?" =
lk* I
1 - n
l-,rr l{r [Otlho
| l " -
tokn '
A n r -AH lar opp\y ing \o l t a
Fo r l{ ' l0O ksr(l"
- r,t . t
'
Fo, \ = lOt , 'D r tl\a I K-n-
A : t0.1 r+
r | -422
A= 5-5
A= F-s
UbJECTIVE I-V\/VU/\.\,.\^ /t\.t
VOLf A6= T0 fRE QutN Cy coNvE BrER
Eu'g''^5 s- **ff I' l*r*^j
@-twaJer
' +7zv
&
V;
Rt
C lRculT DIaEKAM
C,= O.otrrF
:
rh l ?€ 6Rnroq
2 ? - r 2 ! 2 2,!ii,!r,2.2r3 g,
L r,1
- l 2 v
{7+l
s'6 k a_
f
1'
WoRv<rN G :- lnih *
e"ya&or C
a conaktnl- vc^l,- tr Lvr/grJ an4 p . Thu
f" c.l^,.'g"d *l
oq,d volh..1e V.
(vottt. *j ph. s)
Th e corlporcrlo r o.rh" ul V.
.)hen Vc
is d-t
ir ',nolnf-r ' -LZV
"%{" a}o}e'
TV." *"e)y \ncve..z;,rj vo'llc,ge VoJ ---0 J
.a@rY)eA , teas ' fno . -BV , | fu r
V" increoreJ +uc t - t l k l l-J
,aJ Vc t".o -.^ - 12 V &
I
OESIRVAIIONS
R, I Lt, t>-
L-Lt )L
3.3 k)L
5 'e KA-
V. =- -fsv to - Sv
- 4'sv
Re,rBtq.ncc-
I k-t-
2.zkn_
3-3 Kx
5 -6 k .L
0"., *u"rV
TP-xi.*t 5 v
, L%sla1ca
?e 5 .o V
tb
Lecfr;vsel jr 1.'1 lkl-lc f
/'
e Tener d"o"le
Z.Lk A- . .r€-trsl-o r @L
b
ll ,'. Yt
3 V
-+ 4^Ag
Liwls
- 4v
- ,€ ' *2 2^2KL
:l;i& *r:S. *. $w*:
PRICATJII ON5 IN LXPT
4 F Tcr.h e Su-re +haj f
o.e,e,- tY?\ Vt "n
d r-D can nec-lad
4D clvctrib yr^d,
ftoh *vc & -ve p utDer j *p p [ ;er ra rru I,
r)be-ne.ver- O?- Aryl? -L4 poraera-el ,
1 1) o "'l f ,Xuf lx ({rnnssg
f*a *"?Pq {_o th" 3
rou'' cJ
he
fl
be yruenl
C',mm w1 l-er.nl ncrl
bre-ad board,
poo er -r qr plra o4+ 'J)o
r^,.1- in \erch on c1€ * vc & _\eJ
"t.F rr>ou-lcl elounge ttta op-ornp,
r be o r&ra cl ;_
Ll'1> f LU @ Ft-m chbn G e-nr-tr,.lt-
Sco; f<- l l * %t f rocext r" rc. r t be Fe.ueue orc- ls{a; 3,2,1O UU
F* tC .J"'p r,ever e xrea d Vi bey on c) | oci>er-
St"Tp! !r'rih.
f l *hu osci l lascopeKu?
3 'o.t', c)
p -be, belun cI
& f g"oe,' t"??!
fu"Pu.rf.rotJ &rna
f,grrni '.''OJa
& d*
chbo J
encea'For ouiT*+
eoryrrnon con nacl-ed fo3eFt'rr
exper;rnenl-'
?RE- Ex PEc-t MErur R€*atNq\Pou? - tT
+ r2v 1i"t.
9,.- Dh-z' A'b o'r,,u ,Uzvu';L , 1
T^; ,, V^to'
k "rt-
Al* (LA'
Vn = ' l2V t>h
Ar^A LA"u4AQ^^t wt
c
thl L*P e-* t'a"'t^-'tz- (
lgI
t tLv7\e
.127 +Y' B.741
Ir
- /2 \
qRAr oRINr e
la ,Z r.-r,-i
Zouzt '6 ,2 v
- IDV
t^> L KAD<'| |
QRooP- t7
' , B
Vb= -S,bt4g{V.
wAL;/bL a/^e.aa2-t'0
fut V,-- -5,D+zsv
=(4 Dp.*), r(e. ,t 'qs)(o,ot)
f = l ,LL A.wr(zc-
lrvhe*- V o
V : -tLv
No *:* i-bu'-s /7":o-1fu e-Vn :
', = q
a
r/\LE lzTo): 5'€
IE- = l+' S? g 'wnA
q":d _ o l . E
L ,t* au^*"f T
6RaiP-W
frI
i
v h
f \ / )
r ( v "e )
- 5 ,04 |
tI
vta)
v) , r . r ) . ^ o
) / 6-{*:- *---- -**-"-?--}I
: I L t ' . \I f i v ' ' " i . )
, j
JII;i- ' - 1
Expe.imen{ No.6 : Otsretiona\ Amp\ifier App\'cotions - I : Group lT
> OBJECTIVEIo desfgn
"PRE-EX(Annn*na)
"08R"
d p re<,'or'on rech'fr'er frr e srno\l Ac signo\.
P OBS
SERVATIONS
\nl , lhout Capaofu'
with coptdlo' ,ciir hl,lhouL Copacito'
,. Qair'r '. Vi ,o-r, = lo0 rnv (b.low) = 50 *V € belo* th. y=o Q.rrs
=ll,n= l0kn
( l l )I
Without R2 (u
(Att - anneocb,d)
., Vt
J;- W,lh Capaqtor
!
50mv 50 *v
h 5o*v
2-6 v
5.2 V \
tr) rnv
0{5 v
.i, V'lln ce po dfor
\lo telovu
\t 5 rnV
htO mv
2 js v
+Vl
W i+ho* Ca pe.rtc,r
Gai6 = Vo /u ;Gan = u%,
*=o.q
ffiu= q[
19. t50
- r
ffi -- to4
lkn
J0 ko
100 ko
ftmovta)0'0s v
t Li* (e)--&
. ,vy
R. = \\< r'
h hrth f o+a**tur
V
/ E
I
_ hE"$_{,r
Rt = \okc - Wi lh capa ' i l t r- (eDacr\-of femov<d
' a .
( 6ho&ed )
L -->
'vVt luov+€?(n!
- t \ O n v*\5omv
VY
, )
R" = too t<c
- v{tVh cuFutiio'q- Clp. "rAmoved' ( Jh o/l-el)
l -+-2-1r!-1.6v
- CAp . r-emoVed LShoft-ea )
\ r oY \
I
-t{-?V*5'2v
R 1 r w o v e J
8y connerhng thn components Ct furm an tc os shou:n 'rn.lhe ciro,bdiagran$ , wc ob{aio d\1on-\nvertrng scoplifiqg ar stago I ond, a
h$9-u,a{e pre<rsion rectrfier (ur g"g"tE) garn {or o smolr sc s(1ns\.
- Tbu op-Amp genere\ly wotKs on a iptll- go^ier sspp\y (ot +12y) .Hanoe. both -tve and -{e
F,$€r srpplies frtush be present whenever \5g
Op-Rrnp is purrered 5donot <r:crnect cle sd€, ocro{echange +ve/-va.- \Nhi\e e*lrttFrrng oo the pallcr t^+p\
suiKh oo tns oso\loscc?e frrs\, hen \hB po.Jar .Wy f"iha.circptL ,Md ffnalty r-tha $nchron qeneralof .
Fo\\our ths rc)tLrse ordef tnord.. tL surt\fi off -lhe por,u supily
For €n \C, f\erler sxceed the r$pot vo\lage beyood *he pouts sUpp}\rrniFt (o{ irz v)-I!re
ovt\\os.cpe probQ, to $roood, ffrndron genco]a ootpu] gru,.:n&term',nal end itre po$er 6oppy gvtooc} {ercn,no\ fn"xt be, cr:nrpsed.
to a carnmon gruuncl and renniln crsnne.led througbo$ tYre exgL-
' QUESTION9
loO r*V
P- I'
- ln 1neVr-O
lh. nuw circuit with changedpo\arif ies oP thn Jioae rb:II
lzvof
l 1
T'
\ , = I00 m{ (p+)
ln the +ve ha\f Scle ,. - lv;-v = v' =+ v, -_ v'r
,rIq,-/\Now , 9_-J = V'- v*
f = ] " = +
..' V). = ll v,' ., Vo( r* 'Hl
I-ve he lF qgcl o
= O --V" :llo
* 5r{)*'J
r+ t')Vr' =
- t-4v
Vo = - l to V ;(t+ ff)
Thrr, when tha diodes ore connecled wt\h chrilgea polarities, V* and Vo wi\lheve 4ha VvrvaRrrns ds ehourn.
'lhe r^ra,vefrrcn of \=- r6rlhrx,'yy\qpendent cF-t}.)e
poloritr'es oP 5s iiodes, ba.lr Vo ir ima6e.J ahout the. F- y:o ex.i: (*irre)
snd there*m.is oleo e Phese differenco of(7I) v{tEn corngared t"*n'e €€s€',(r,tn*t rrF# chenging diodepolantres) ioitia qrcuib .
rN h rq€
t t . t 4 t { f
'/wlro J
. r I
2 I ;
TX?ERI|/INT NO: 5
OPLRATIONAL AMPLI FIER 5 -T-
Obiective r-\- -{-^----
fr,li Q ni n4 o 9re-cis nr rr
0o{o. o srnoU' ftC s ig nctl '0c
C IRCUIT D r n 6Rnr'r
loo rn\ p-pLmn4t
qr-n
recfi{ ien
C--rouF
IO KA
Frceis ionHnlfl Naua rccf i f icr wifh gaio
Lm 74tt tzv
tN ' .+ t+€
Non . Inve.r trrp
A*pti f ier
D-a*o ncuX-Utw 'vv^ c*'l' X ".^-o'l y,
Ar_ Y
/ v7>x tDf-f
/ /D
D/ - a"t+a f>
\_u"lo
\r\A
V
r I- )1-
. t .
? l l
V* r-
b/n
fo (t,^,r ') 'Vy
VK
l roo - /*j,t i '9 Y
orr'r/+'
-/e 4
-fo : l a-z'
Ituo (<D- D,&6>s j) u,,aU
-+ - lDOb n , , . r \ , /
T^ ar :f^"d,)( *f
I Fo ltrt ill fr,L (a.,.--z
1(
coPt - I o3
W{/uLonk 1 ,
V) : lo u'tu
7A* , , {7e--<4u h4*-on /A *rt
(^;
V* - vr-
lo
P-lD :
:)
3 -'-',
:Ll
o,0rrei)Vrt
u,
v, ("*) @f
t@ tra / / - / / -L
e - l loV,.t
4e_U-(
=O
l
V. foro-Rl u7- "4L
v\
, l tO u-, t / t -p
v5L: rn V
r 1
vrt
\. t - d , T !
V " l l i n l 1 -1*.," +
\ r ' r ' h
r . ' . r ;+hn rJ
' , l ; , : ' " n , , , , t -
i_rl
: , 4
* 5 c r r
\ 1v x
CT\JECT IV Ery
-TrL /e^x-L .<;y-a-tx
W .oi""'t,-<'e'rob-L .a-tfl-t4a-(A,/0
CIP.CU IT D tA h B-AM
Vr'hLD '
7r
L o n 'cooNT
.-F-;-^Gple I1I
ii
Illl
I
OflsrR vATt oxl
lo o oDo o IIr o Io 0 0 t0 to I
lo o tlo 0 Do oo tI r o II oo (
Io t0
5v
JV
-3v
- 5v
IIil
lir
T<oo - to
''ry:-cqd
F
r
o
€(.LJ
t-Z)oq)
t-
p
\o
oo
fi
Ft
o
Io
LJ
o
poo
-f,
C
oH
o
fr
oi{
o
sc
o
Fi
ofi
o
a')
O
oIJ
(L(-
o
^ d ^d
2*
-{
PKtrC-AtJ'TtO NS
/C-D-^r"o 61.va- /{^d-* 4
,2x C-n-zol .Cl'r-- .z'*-P+-tI
4-^-^-A #.*: '''-t-'--'-'- 4'I t . 4'a
>e; P/ i/' t {*n'zL' 46 f-
\/ %.+::1--*'- C'-t t
f o*t ' V
a ./: ,j f/;, 't<g,/w.c