Elec onic Sys ems
No eboook o Lab Ac i i ies
José An onio
So ia Pé ez
Depa amen d’Enginye ia Elec ònica
Escola Poli ècnica Supe io d’Enginye ia de
Vilano a i la Gel ú
José An onio So ia Pé ez
1
Con en s:
Lab Ac i i y 1. Lab Ins umen a ion…....................................................................2
Lab Ac i i y 2. Time and F equency domains……...............................................24
Lab Ac i i y 3. Linea DC Powe Supplies............................................................50
Lab Ac i i y 4. Swi ching Elec onics: The Bipola Junc ion T ansis o (BJT)....70
Lab Ac i i y 5. Analog Elec onics: The Ope a ional Ampli ie ….....................100
José An onio So ia Pé ez
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Lab Ac i i y nº 1: Lab Ins umen a ion
Main Goal: To lea n how o use he di e en ins umen s o he lab o measu ing elec ical
signal pa ame e s, bo h in con inuous (DC) and al e na e cu en (AC), and o ge used o he
basics o b ead-boa d p o o yping. These skills a e conside ed CRUCIAL o he o hcoming
lab ac i i ies o his cou se and de elopmen o echnical skills du ing you cu en deg ee
p og am.
As such, s uden s a e encou aged o obse e and expe imen wi h he di e en bu ons and
con ols ha ins umen s ha e, and o ollow moun ing ins uc ions ca e ully. The machines o
he lab can be g ouped in he ollowing wo main g oups:
• S imulus (o Signal) gene a ion: The Powe supply o gene a ing con inuous (o DC)
cu en and Wa e o m Func ion Gene a o s o gene a ing ime- a ying signals.
• Measu emen Ins umen a ion: The Mul i-me e , which con ains an ohmme e , a
ol me e and an amme e , all o which a e aimed o measu ing s eady-s a e elec ical
a iables; and he Oscilloscope o isualizing and measu ing pa ame e s in ime- a ying
signals.
.
1 DC Powe Supply
This de ice ixes i s ou pu o a cons an ol age and deli e s ene gy o he ci cui in he o m o
DC cu en . Two models a e a ailable in he labs: 1) The IPS2303DD om ISO-TECH (Fig. 1a)
a L-104; and 2) The E3631A om Agilen (Fig.1b) a L-106. Bo h consis o wo iden ical
ou pu s ( ed boxes) wi h adjus able ol age om 0 o 30V/3A and om 0 o 25V/2A,
espec i ely. Ano he auxilia y high-powe ou pu (o ange boxes) p o ides a ixed ol age o 5V
o a maximum 5A DC cu en (The auxilia y ou pu o he E3631A is a iable and o 6V/5A).
When he ou pu s a e connec ed, he display shows bo h ixed ol age and injec ed cu en o he
use ’s ci cui . The maximum ol age and cu en admi ed o he ci cui is p og ammed h ough
he con ol unc ions in he on panel ( olle s and bu ons inside he blue boxes). Howe e , he
p ocedu e a ies depending on he machine model.
(a) (b)
Figu e 1. Powe supplies a he labs: a) IPS 2303DD om ISOTECH (L-104); b) E3631 om Agilen (L-106).
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Task LAB1: Con igu e one o he ou pu s om he DC powe supply o ope a e a 5V wi h
a maximum cu en o 0.25A. P oceed as indica ed depending on he machine model a ailable a
you wo ks a ion (see below).
DC cu en limi e :
• IPS2303DD: Wi h he de ice u ned OFF, 1) Connec a co d be ween he posi i e and
nega i e e minal a he ou pu you’ e going o use; 2) Tu n he powe ON and obse e
he cu en alue in he display; 3) Use he olle labelled as CURRENT o se he limi o
0.25A; 4) Disconnec he ou pu co d.
• E3631A: In his model you can con igu e he cu en limi e wi hou connec ing a co d a
he ou pu e minals. 1) Tu n he powe ON; 2) Selec he CURRENT op ion om he
ADJUST menu in he on panel on he igh (a digi om he display blinks); 3) Use he
‘<’ and’ >’ bu ons o mo e along he digi s and se he alue wi h he olle un il he
alue 0.25A is shown on he display.
DC Vol age con igu a ion:
• IPS2303DD: 1) Tu n he ins umen ON lea ing ou pu e minals unconnec ed; 2) Use
he VOLTAGE olle o se he ou pu o 5V.
• E3631A: 1) Selec VOLTAGE om he ADJUST bu on ( he display shows he cu en
ol age and one digi blinks); 3) Use he bu ons o mo e along he digi s and se 10V.
A his poin , he machine is eady o ope a e wi h he con igu ed op ions. Howe e , o sa e y
easons, i is p e e able o de elop connec ions wi h unpowe ed ou pu s. In he E3631A model,
an OUTPUT ON/OFF bu on allows hese ope a ions o be made while he machine is u ned
ON. In his case, a message appea s indica ing whe he he ou pu is deac i a ed; hen, he use
can connec he co ds sa e y and push he bu on again o eac i a e he ou pu . In he
IPS2303DD model, howe e , hese ope a ions may be made wi h he machine u ned OFF.
REMARK: You mus WRITE DOWN you answe s in he o m
p o ided a he end o his documen (See Annex 1) and deli e i o
he lab eache a he end o he session.
2 The Digi al Mul i-me e
A digi al mul i-me e (Fig. 2) in eg a es an ohmme e , a ol me e and an amme e in one de ice
and, as such, i can measu e elec ic esis ance, ol age and elec ic cu en ; as well as o he
auxilia y pa ame e s o s a iona y beha io .
F om he di e en e minals on he igh o he on panel ( ed box), he VΩ e minal is in ended
o measu ing elec ic ol age and esis ance, whe eas he e minal labelled as ‘Fuse on Rea
Pannel’ is he poin o elec ic cu en measu emen . The ed colo (as well as he ‘HI’ label)
indica es he POSITIVE connec ion (+), and he black e minal in he middle (also labelled as
LO) is he NEGATIVE (-) one, which is “common” o all h ee measu e a iables.
José An onio So ia Pé ez
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Figu e 2. Digi al mul i-me e 34401A a he L-104 and L-106, cou esy om Agilen Technologies
The de ice unc ion is con igu ed h ough he keypad in he on panel (g een box). The blue
unc ion abo e is selec ed by means o he SHIFT bu on. As such, o measu ing esis ance, DC
ol age and elec ic cu en ; he op ions a e Ω, DC V o DC I (SHIFT > DC V) espec i ely.
Gene ally, he mul i-me e is in ended o iewing s a iona y pa ame e s, which a e e eshed
o e he ime, as in o ma ion can only be p o ided h ough he display. Ne e heless when ime-
a ying signals a e sensed h ough he ou pu e minals, in DC mode (DC V as well as DC I) he
display shows he a e age alue, whe eas in AC mode (AC V and AC I) i shows he ue1
oo -mean-squa e alue (o ms). S ic ly speaking, he a e age alue o any signal x( ) is
ob ained as
( )
∫
=
T
d x
T
x,
1
(1)
whe e T co esponds o he measu ing in e al2 used by he de ice, and he ue ms alue is
ob ained as
( )
.
12
∫
=T
ms d x
T
x
(2)
1 Some mul i-me e s only p o ide he ‘ ms’ alue o sinusoids, since his alue is easily ob ained co ec ing he ou pu peak by a ac o o 0.707,
which equi es less esou ces. Hence, manu ac u es e e o he “ ue ms” implemen a ion when hei ins umen con ains he equi ed
ci cui y o de elop (2). I has o be men ioned, howe e , ha he use ulness o his alue elies on he basis o epe i i e signals, which is a
necessa y condi ion in o de o gi e a s eady alue o his measu e h ough he display.
2 T is au oma ically ixed by he de ice. In DC mode, his alue co esponds o a ime in e al o ixed wid h along which he a e age alue is
es ima ed. As such, i can be seen as he e eshmen ime o he display. In AC mode, he mul i-me e uses a sophis ica ed sys em o de ec
he pe iodici y o signals and, hen, i con igu es T acco dingly. See he manu ac u e use ’s guide o mo e in o ma ion on his opic.

José An onio So ia Pé ez
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Task LAB2: Ge acquain ed wi h he mul i-me e unc ions by ca ying ou he ollowing
measu emen s:
Elec ic esis ance:
• 1) Iden i y each one o he i e di e en esis o s included in he ki . 2) Use he
ohmme e o measu e he esis o s. 3) Tu n he mul i-me e ON and selec Ω in he
con ol panel bu on ( he digi al display shows he message MOHM). 4) Finally connec
he co ds and he esis o as shown in Fig. 3.
• De e mine he de ia ion o each esis o om i s nominal alue acco ding o he
ollowing equa ion. Check whe he he alues a e wi hin ole ances.
()
100%
min
min ×
−
=
alNo
alNo
Óhme e
R
RR
ERROR
(3)
REMARK: The TERMINALS bu on mus be u ned OFF in o de o ac i a e he
on panel.
Elec ic DC ol age:
• Measu e he 5V DC ol age con igu ed in ask LAB1 wi h he ol me e . Con igu e he
ins umen by ollowing hese s eps: 1) Tu n bo h de ices OFF; 2) Connec hem as
indica ed in Fig. 4a; 3) Tu n he mul i-me e ON and p ess DC V in o de o con igu e i
as DC ol me e ( he display shows he message “VDC”); 4) Finally, u n he DC powe
supply ON.
• Repea measu emen s by e e sing ou pu connec ions a he ol me e (Fig. 4b)
Elec ic DC cu en :
• Keep his 5V DC ol age and connec a 1 Kohm esis o o measu e he elec ic DC
cu en low wi h he amme e . As p e iously, 1) Tu n bo h de ices OFF. Make he
connec ions o Fig. 5a; 2) Tu n he mul i-me e ON and selec DC I (SHIFT > DC V) o
con igu e i as an amme e ( he display shows he “ADC” message); and 3) Tu n he DC
powe supply ON.
• Repea measu emen s by e e sing ou pu connec ions a he amme e (Fig. 5b)
Figu e 3. Ou pu connec ion and mul i-me e con igu a ion o measu emen o elec ic esis ance.
José An onio So ia Pé ez
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(a) (b)
Figu e 4. Measu ing elec ic DC ol age om he supply wi h he ol me e ; a) Fo wa d; b) Re e se.
(a) (b)
Figu e 5. Measu ing elec ic DC cu en low. A ows indica e low di ec ion a) Fo wa d; b) Re e se.
3 F om he elec ic diag am o he B ead-boa d p o o ype
A his poin , i becomes necessa y o de ine symbols o ep esen ing he ins umen s, elec onic
componen s and hei elec ical connec ions. This will no only be used ju o d awing he
schema ics o elec onic sys ems bu also o unde s anding hei beha io , which is essen ial in
signal analysis and elec onic design.
Fig. 6 shows basic symbology and common s anda d con en ions used in wi e connec i i y. In
gene al, each elemen is a dipole and i s e minals a e connec ed o o he dipoles. The posi i e
pole o ins umen s is ep esen ed by “+” (Fig. 6a and 6b), and he esis o symbol is depic ed in
Fig. 6c. Mo e han h ee connec ions be ween wi es and/o e minals a e indica ed by a “poin ”,
whe eas a “b idge” (o he omission o poin s) means a c ossing o unconnec ed wi es (NC).
Finally, he GROUND e minal (Fig. 6e) is a common e e ence used in elec ical a iables.
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(a) (b) (c)
(d) (e)
Figu e 6. Basic symbols o he elemen s shown in his documen .
In his sense, a schema ic diag am o he cu en measu emen layou o Fig. 5 is depic ed in
Fig. 7. An a ow ep esen s he di ec ion o I1, which lows om he posi i e o he nega i e pole
o he powe supply. By con en ion, he en ance poin a he esis o se s he posi i e sign o i s
ol age d op (V1). Finally, he supply VCC, he amme e (A) and he esis o (R1) o m a closed
pa h (o mesh), whe eas a node is any connec ing poin be ween wo (o mo e) e minals.
This con en ion is simila o ha used by he mul i-me e . By de aul , elec ic cu en s
ENTERING he ed e minal a e ead posi i e3 by he mul i-me e . So in he i s si ua ion o
Fig. 7a, he alue showed in he display ma ches o I1, bo h in alue and sign, whe eas in he
second one he sign is e e sed -I1.
Ano he elemen , no conside ed an ins umen , bu essen ial when expe imen ing wi h
elec onics, is he es boa d (Fig.8). This boa d is known as he b ead-boa d and i is whe e an
elec onic design is p e iously moun ed and es ed be o e hei comme cial implemen a ion on a
p in ed ci cui boa d (PCB).
The b eadboa d ha e i e unconnec ed e minals, wo columns, each e ically connec ed
(le and igh ); and wo ows, each ho izon ally connec ed ( op and bo om). In addi ion, he
cen al pa ha e six g oups o cells ( om A o F), each wi h 47 x 5 holes ho izon ally connec ed
bu e ically unconnec ed. Knowing his layou is impo an o de elop he ci cui connec ions
p e iously designed on a schema ic. Mainly, i is impo an o place he componen s acco ding o
he schema ic and ensu e ha e minals and wi es a e connec ed p ope ly. Using e minals o
common connec ions, such as he GROUND, de eloping as ewe connec ions as possible in he
b eadboa d and using colo s o assigning g oups o connec ions (i.e: black o g ound
connec ion, ed o + o g ey o -); is impo an o a oid possible p oblems and o allow e o s o
be de ec ed quickly and easily.
3 A simila c i e ion applies o he ol me e , which akes as posi i e all d ops caused by elec ic cu en s
ENTERING he ed e minal, and nega i e o he wise.
José An onio So ia Pé ez
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(a) (b)
Figu e 7 Elec ic diag ams and a iable con en ions using he DC cu en measu emen layou in Fig. 5.
(a) (b)
Figu e 8. O e iew o he b eadboa d: a) Ae ial iew; b) In e nal connec ions o holes.
Task LAB3: Build he simple ci cui s o Fig. 9 on he b eadboa d and ob ain expe imen ally
hei elec ic esis ance:
• In he i s schema ic; 1) Follow he b eadboa d dis ibu ion in Fig. 10; 2) De e mine he
heo e ical alue be ween A and B; and inally; 3) compa e wi h expe imen al esul s.
• In he emaining ci cui s (Fig. 9b and 9c), 1) Use he in o ma ion in Fig. 8 o guess he
connec ions you need o make and; 2) P oceed wi h he calcula ions and measu emen s.
REMARK: The elec ic esis ance be ween wo poin s, A and B,
is measu ed by DISCONNETING ALL SOURCES and
connec ing he ohmme e IN PARALEL. NEVER ouch he
e minals wi h you own hands while ca ying ou his
measu emen .
José An onio So ia Pé ez
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Basic con igu a ion:
• 1) Tu n he wa e o m gene a o ON and con igu e he p e ious se ings (5V-peak
sinusoid and 100Hz- equency) i hey a e no se al eady. 2) Connec a BNC-BNC p obe
be ween he 50Ω gene a o ’s ou pu and he channel CH1 (Fig. 18). 3) Tu n he
oscilloscope ON and, ollow hese s eps o obse e he signal, once he g id appea s (Fig.
17a):
A) Ve ical Panel > “1-knob” > Coupling > GND: The inpu signal disappea
om he sc een and a ho izon al line shows he ze o- ol age e e ence o CH1.
Use he yellow olle o place his line a he cen e o he sc een.
B) Ve ical panel > “1-knob” > Coupling > DC: The sc een shows he wa e o m
ace again.
C) Ve ical panel > VOLTS/ (yellow selec o ): Change he ol age esolu ion o
2V/
D) Ho izon al panel > TIME/ (le selec o om he ho izon al menu): Se he
ime esolu ion o 1mseg/
REMARK: A his poin , you should see a sinus o 10 g id posi ions (o
squa es) wide in he ho izon al axis, due o he ac ha T = 1/FREQ = 10mseg.
Likewise, he e ical ange is 5 g id posi ions wide (2.5 band- o-band beyond
he ze o- e e ence ol age) in he e ical axis.
• 2) Access he TRIGGER menu by p essing he “Mode/Coupling” knob a he igh in he
con ol panel (o ange box). Con igu e he ollowing op ions:
Mode (1) = “Edge”. Sou ce = “CH1”. Slope = “Ascending”. Mode (2) = “Au o”.
Coupling = “DC”.
3) Mo e he LEVEL olle (a discon inuous line appea s and he ex shows he
ac i a ion h eshold DC le el on sc een. 3) Mo e his line up o “2V” and obse e how
he signal shi s sligh ly along he ime axis o se he 2V-le el e e ence a he cen e o
he sc een.
Coupling con igu a ion:
• 1) In he wa e o m gene a o , change he o se se ings o he sinusoid o OFF = 2V. 2)
Use he T igge o ix he signal on sc een. 3) Adap he e ical axis o enclose he signal
as LARGE as possible on he sc een, and he ho izon al axis o obse e 4 CYCLES.
• Con igu e he oscilloscope in AC mode (Ve ical Panel > “1-knob” > Coupling > AC).
Commen bo h esul s:

José An onio So ia Pé ez
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Figu e 18. Oscilloscope connec ion o isualizing ime- a ying signals om he wa e o m gene a o .
1s . REMARK: The coupling mechanism is gene ally used o HIDE (NOT
TO REMOVE) he a e age (o DC) inpu componen om a signal. As such, he
signal is o ced o ha e a symme ic ep esen a ion on sc een, despi e he 2V-le el
o se . This is done when he AC mode is selec ed. This mechanism is ex emely
use ul o obse e small AC componen s o e lapped in e y high DC componen s,
which some imes a e o in e es in o de o unde s and he beha io o ce ain
elec onic sys ems.
2nd. REMARK: All con igu a ions explained in his ask a e conside ed
ESSENTIAL o co ec ins umen usage so, mos p obably, you’ll need o epea
hem again du ing his cou se. P ocedu es also apply o CH2, which can be
iewed wi h CH1 simul aneously. As he wa e o m gene a o , ins umen
con igu a ion may be al e ed se e ely o e s uden s by he lab. In hese si ua ions,
i may be wise o upload he manu ac u e ini ial con igu a ions:
 In he menu: Sa e/Recall > S o age > Se -up > Manu .
O he de ice u ili ies (op ional):
• Take he ime o e iew o he in e es ing con igu a ion op ions om he oscilloscope
which could be o in e es o you, such as 1) he Measu e bu on o displaying ime and
ol age measu es au oma ically; 2) he Cu so menu o na ow he measu es; 3) o he
Ma h menu o de eloping ma hema ical ope a ions wi h bo h channels.
Task LAB8: Now connec he wa e o m gene a o a he inpu o he se ies ci cui o Fig.
11, and he CH1 inpu channel in pa allel. Rep esen he ol age wa e o m in each esis o (Fig.
19).
• 1) Moun he ci cui o Fig. 11a. i i ’s no moun ed al eady. 2) Use a “T” connec o a he
CH1 inpu o he oscilloscope and connec he gene a o ou pu , Gen( ), by means o a
BNC-BNC p obe (Thus, you’ll o use an addi ional p o e connec ed a he b eadboa d
(Fig. 19b). Keep he p e ious sinusoid con igu a ion (5V-peak; = 100Hz and OFF = 2.
3) Connec he o he cannel, CH2, in pa allel wi h he second esis o o measu e R2( )
and ep esen i s wa e o m shape. Do no o ge coupling bo h channels in DC mode.
José An onio So ia Pé ez
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(a) (b)
Figu e 19. Oscilloscope and wa e o m gene a o connec ion o measu ing he ol age d op a Gen( ), and, R2( ). a)
Connec ion diag am) B eadboa d connec ion.
Di e en ial mode ( loa ing-poin ol aje):
• Now, disconnec CH2 and connec his channel in pa allel wi h he i s esis o (all
posi i e e minals om he gene a o , CH1 and CH2 mus be TOGETHER. The nega i e
pole o CH2 mus be connec ed be ween R1 and R2). 3) Wha is he p oblem?
• 1) Undo he las change and connec back channel CH2 in R2. 2) Now con igu e he
oscilloscope in di e en ial mode (MATH bu on > Ope a ion > 1 – 2). This ac ion will
gene a e a new pu ple ace on sc een co esponding o he poin wise sub ac ion CH1-
CH2, which is in ac R1( ) = Gen( ) - R2( )
REMARK: Bo h nega i e poles o CH1 and CH2 a e
INTERNALLY CONNECTED. As such, connec ing hem
a di e en ci cui poin s causes sho -ci cui and unp edic ed
ci cui beha io may be o se e e consequences.
José An onio So ia Pé ez
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Annex 1 – Resul s o m
REMARK: S uden s mus PRINT OUT THIS FORM and
BRING i he day o he lab session.
Escola Poli ècnica Supe io d’Enginye ia
de Vilano a i la Gel ú
EEL
Elec onic Sys ems (SIEK)
Lab Ac i i y 1
S uden s: Da e:
1 DC Powe Supply
• Task LAB1:
ILIMIT = ________ VFONT = _________
2 Mul i-me e
• Task LAB2:
2.1 Elec ic esis ance measu emen
R1
R2
R3
R4
R5
Rnominal (Ω)
RÓhme e (Ω)
E o (%)
2.2 DC ol age measu emen
VSUPPLY(Mul i-me e ) = ________ -VSUPPLY(Mul i-me e ) = _________
José An onio So ia Pé ez
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2.3 DC cu en measu emen
IR(1kΩ) = ________ -IR(1kΩ) = ________
3 F om he elec ic diag am o b ead-boa d p o o yping
• Task LAB3:
3.1 Se ies/pa allel esis o associa ion
Se ies
Ci cui
Pa allel
Ci cui
Se ies-pa allel
Ci cui
RTeò ica (Ω)
RÓhme e (Ω)
• Task LAB4:
3.2 Elec ic DC measu es in he se ies ci cui
I
V1
V2
Theo e ical
Mul i-me e
4 Wa e o m gene a o
4.1 AC ol age measu emen om he gene a o ( ms alue)
• Task LAB5:
VAC(Mul i-me e ) = ________
4.2 Elec ic AC measu es in he se ies ci cui
• Task LAB6:
V1(AC)
V2(AC)
Theo e ical
Mul i-me e
José An onio So ia Pé ez
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5 The Oscilloscope
• Task LAB7:
Basic oscilloscope con igu a ion
CH1 VOLT/:
2V/
CH2 VOLT/:
-----
TIME/: 1msec/
Coup: DC
Ze o POS: 0V
Coupling se ing wi h OFF = 2V and DC mode
CH1 VOLT/:
CH2 VOLT/:
-----
TIME/:
Acob: DC
Ze o POS:

José An onio So ia Pé ez
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Coupling se ing wi h OFF = 2V and AC mode
CH1 VOLT/:
CH2 VOLT/:
-----
TIME/:
Acob: AC
Ze o POS:
• Task LAB8:
Rep esen a ion o Gen( ) and R2( ) in he se ies ci cui
CH1 VOLT/:
CH2 VOLT/:
TIME/:
Acob: DC
Ze o POS:
José An onio So ia Pé ez
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Rep esen a ion o Gen( ) and R1( ) wi h CH2 and R1 in pa allel
CH1 VOLT/:
CH2 VOLT/:
TIME/:
Acob: DC
Ze o POS:
Explain he p oblem
____________________________________________________________
_____________________________________________________________
Rep esen a ion o Gen( ), R1( ) and R2( ) using he MATH op ion
CH1 VOLT/:
CH2 VOLT/:
TIME/:
Acob: DC
Ze o POS:
Explain he con igu a ions in he MATH menu he e o iew R1( ) co ec ly
__________________________________________________________________
José An onio So ia Pé ez
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Annex 2 – Resis o alue coding
24
24
Lab Ac i i y nº 2. Time and F equency domains
Main Goal: Lea ning how o de e mine he ansien and equency esponse o any Linea Time
in a ian sys em (LTI) in he o m o a passi e ci cui , by means o he ans e unc ion. This
goal is no only es ic ed o a heo e ical le el bu also conside s echnical de elopmen and
ex ends o measu emen s in o de o know such in o ma ion in eal elec onic sys ems.
1. Capaci o s and induc o s
A capaci o consis s o wo elec odes sepa a ed by an insula ing medium called he dielec ic.
The elec ic cha ge q on he elec odes is p opo ional o he ol age c ac oss he capaci o ,
()( )
C
q
c
=
(1)
whe e C is he capaci ance. The uni is gi en in a ads (abb e ia ed F): 1 a ad equals 1
coulomb/ ol , and habi ual alues a e in he o de o mic o a ads (1μF=10-6F) o pico a ads
(1pF=10-12F). On he o he hand, i s elec ic cu en is gi en by he a e o change o he elec ic
cha ge, so i s ol age/cu en ela ionship is,
( ) () ( )
d
d
C
d
Cd
d
d
i c
c=== c
q
. (2)
Table 1 ep esen s he ma hema ical model o his componen bo h in ime and equency
domain. Mo e p ecisely, using he Laplace T ans o m allows ime ansi ions o be exp essed as,
( ) ( )
sxs
d
dx L×→ −1
(3)
whe e s ≡ d(·)/d is he laplacian ope a o con aining he angula equency ω,
ω
j
s=
(4)
also ela ed o he oscilla ion equency = ω/2
π
which is exp essed in Hz. As such, and wi h he
use o basic heo e ical ules (Ohm’s law, Ki cho law, e c) i is easy o handle he beha io o
eac i e componen s, since knowing i s elec ic impedance Xc is, mos o he imes, enough o
ca ying ou calcula ions. This p inciple is also equi alen in he induc o , whose ol age d op
a ies wi h he magne ic ield
ϕ
as,
( ) ( ) ( )
d
di
L
d
Ld
d
d
L
L=== L
i
φ
, (5)
whe e now L is he induc ance, in hen is (H). Fo his eason bo h componen s a e conside ed
duals ( ha is eplacing i by and by i in one equa ion leads o he o he ) since hei
impedances a e Xc and XL, espec i ely.
Task PRELAB0: Sea ch h ough he In e ne , o any manu ac u e ca alog (such as RS
Amida a, Fa nell in One, Digi-key, Google, e c) a 10nF and a 10μF capaci o .
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31
Figu e 6. Sinusoid o he o m: x( ) = Acos(ω )
These wo pa ame e s a e c ucial since hey speci y ci cui beha io a any equency. In ac ,
he e is a me hod by which calcula ions can be ex ended easily o ANY LTI sys em p o ided ha
he ocus is on knowing only he s eady s a e o he ci cui . This me hodology is e en alid
ega dless o he numbe o esis o s, capaci o s and induc o s included in he ne wo k.
3.2 F equency esponse in s eady-s a e LTI sys ems
In gene al, gi en a LTI-sys em exp essed in e ms o i s ans e unc ion H(s) (Fig. 7), i s module
|H(s)| is ob ained as,
( ) ( ) ( )
22
RI
Hj H j H j
ω ωω
= +
(19)
whe e “R” i “I” deno e espec i ely he “ eal” and “imagina y” (complex) e ms o H(s),
whe eas he phase ∠H(jω) is calcula ed as,
( )
( )
( ) ( )
( )
( ) ( )
1
1
an , si 0
an , si 0
IR
R
IR
R
Hj Hj
Hj
Hj Hj Hj
Hj
ωω
ω
ωω
πω
ω
−
−
 ≥



∠=

+<




(20)
whe e he uni s o ∠H(jω) a e in adians. Howe e , mos o he imes H(s) has a nume a o and a
denomina o , bo h con aining eal and complex e ms. In his si ua ions, one can use,
( ) ( ) ( )
( ) ( )
22
22
RI
RI
num H j num H j
Hj den H j den H j
ωω
ωωω
  
+
  
=  
+
  
(21)
o e alua e he nume ical alue |H(s)|, whe e “num” and “den” deno e nume a o and
denomina o o H(s), espec i ely. On he o he hand, o e alua ing ∠H(jω) we use,

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32
Figu e 7. Gene al o e iew o he equency esponse in a LTI-sys em.
Figu e 8. Vol age and ime pa ame e s used in he expe imen al es ima ion o |H(s)| and ∠H(s).
( ) ( )
( )
( )
( )
11
an an
II
RR
num H j den H j
Hj num H j den H j
ωω
ωωω
−−
  
 
 
∠= −
  
  
 
 
  
. (22)
The eade can p o e ha using (21) and (22) in (8) leads o (18): he module and phase esponse
o he se ies RC ci cui . Fu he mo e, i we deno e Vi(ω) and θi(ω) as he inpu magni ude and
phase, espec i ely, a equency ω, he ou pu esponse is gi en by,
( ) ( ) ( )
oi
V Hj V
ω ωω
= ×
and
( ) ( )
oi
Hj
θω ω θ
=∠+
. (23)
Fig. 8 shows he mos ep esen a i e poin s o bo h inpu and ou pu signals o he LTI sys em. In
o he wo ds, he module |H(jω)| is jus hei ou pu -inpu peak ela ion,
( )
o
i
V
Hj V
ω
=
. (24)
whe eas he phase delay ∠H(jω) is e alua ed by measu ing he e e ence poin s 0, 1 and 2.
Then, assuming ha θi = 0, and he e o e ∠H(jω) = θo, he phase is ob ained om he signals as,
33
33
( )
21 12
112
2 , i
2 , i
T
Hj
T
π
ω
π
−
≥


∠=

−<


(25)
Task PRELAB2: Using he capaci o alue C = 10nF, ep esen he wa e o m signals o
he RC se ies ci cui (Fig. 5b) ha would be obse ed on sc een i , ins ead o he squa e signal
inpu , we use a sinusoid wi h ampli ude Vi = 5V, ze o o se , and equency = 1 kHz (ω = 2π )
• Use (18) o ob ain module and phase esponse, and hen de e mine he e e ence poin s o
Fig. 8 by means o (24) and (25) o ca y ou his ask. Use θi = 0 and ix on sc een a
andom poin o 0 on he ho izon al axis. Speci y oscilloscope con igu a ion in o de o
obse e on sc een an en i e cycle o bo h signals in de ail.
Task LAB2: Ob ain he equency esponse o he se ies RC ci cui in he lab.
• 1) Use a C = 10nF and connec he p obe o he 50Ω o he wa e o m unc ion gene a o
(ins ead o he TTL ou pu ) and con igu e an inpu sinusoid o ampli ude Vi = 5V, ze o
o se , and equency =1 kHz. 2) D aw he signals in he g ip p o ided and anno a e he
pa ame e s: Vi, Vo, 0, 1 i 2. 3) Use (24) and (25) o e alua e module and phase; and
compa e wi h (18).
• Repea he p e ious s eps o = 200Hz.
4. 2nd. O de sys ems.
4.1 LTI sys em esponse o a s ep unc ion
The s anda d no a ion o he 2nd. o de LTI sys em is w i en as
()( )
( )
2
22
2
on
i nn
s
Hs K
s s s
ω
ξω ω
= = ++
; o bé
( ) ( )
( ) ( )
2
1
12
o
inn
Vj
Hj K
Vj j
ω
ωωω ω ξω ω
= = −+
. (26)
The ou pu o such a sys em o a s ep unc ion i(s)=Vi/s is,
()
12
212
1
121
p p
oi
ee
KV pp
V
−−


=×+ −


−



(27)
whe e,
2
1,2
1
nn
p
ξω ω ξ
=±−
(28)
a e he oo s o he 2nd. o de polynomial in he denomina o o H(s), known as he sys em poles.
34
34
Gene ally speaking, he beha io o H(s) is bes cha ac e ized by wo pa ame e s: he damping
ac o
ξ
and he na u al equency ωn, espec i ely. Depending on he damping ac o , he e a e
h ee cases:
• Unde damped beha io : 0 <
ξ
< 1
When 0 <
ξ
< 1, p1 and p2 a e complex conjuga e. In his case, (27) can be ew i en as,
( )
2
1
2
1
1 sin an
1
n
oi d
e
KV
ξω
ξ
ωξ
ξ
−−



−



=×− +



−




. (29)
and we ob ain and unde damped beha io , which means ha he ou pu is cha ac e ized by an
ini ial oscilla ing ansien be o e i eaches i s o ced esponse (Fig. 9a). The pa ame e ωd =
ωn(1-
ξ
2)1/2 is called he na u al-damped equency and is he equency du ing he ini ial
ansien . The ele an poin s o his signal can be e alua ed using he exp essions in Table 1.
• C i ical damping:
ξ
= 1
He e, he poles a e eal and equal (p1 = p2 = ωn), and he ou pu has he as es possible
esponse wi hou o e sho ,
( ) ( )
11
n
oi n
KV e
ω
ω
−

=×− +

(30)
• O e -damped:
ξ
> 1
When
ξ
>1, he poles a e eal bu di e en . The ou pu (27), which esponds o an exponen ial
law, inc eases slowly un il i se les o i s s eady s a e. Howe e , in his case we may dis inguish
wo si ua ions: one in which bo h poles a e close each o he and ano he whe e p2 ge s o e p1 (
ξ
>> 1→ p1 >> p2). In he las case, H(s) can be app oxima ed o a 1s . o de sys em o he o m,
( ) ( )
( )
1
2
2
ˆlim o
pi
s p
Hs K
s s p
→∞ =+
�
(31)
whe e,
2
2
11
ˆ1
nn
p
τξω ω ξ
= = −−
(32)
would co espond o he new ime cons an esul ing om his es ima ion.
In gene al, he o de o H(s) depends on he deg ee in he denomina o . Since he laplacian
ope a o s = d(·)/d also ep esen s he de i a i e in he di e en ial equa ion, he o de is also
es ablished by he numbe o capaci o s and induc o s, p o ided ha elemen s o he same ype
do no o m se ies o pa allel associa ions.
35
35
(a)
(b)
Figu e 9. Unde damped beha io in a 2nd. O de LTI sys em (K=1). a) Ou pu wa e o m; b) De ining σ.
Pa ame e
Exp ession
Obse a ions
1. Delay ime ( d) ------
I can only by e alua ed by
using (27)
and imposing
o( ) = 0.5Vi
2. Rise ime ( )
1
1 an
d
dd
ωπβ
ω σω
−
−

= =

−

See Fig. 9b
3. O e sho ime ( p)
p =
π
/ωd
3. O e shoo (SIP)
( )
( )
( )
2
1
op o
o
SIP e
ξπ
ξ
−−
−∞
= =
∞
o
(
p
),
o
(∞) ou pu alue a
= p and s eady s a e,
espec i ely
4. Se ling ime (
s
)
(* app oxima ed alue)
s = 3/(ξωn)
E o 5% o Vi
s = 4/(ξωn)
E o 3% o Vi
Table 1. Impo an pa ame e s o he unde damped esponse o a s ep unc ion.
36
36
4.2 Response o he se ies RLC ci cui o a s ep inpu
One e y popula and didac ical example o a 2nd o de LTI sys em is he se ies RLC ci cui (Fig.
10) which consis s o a esis o , a capaci o and an induc o . Using a ol age di ide , he
capaci o ol age (in s domain) is exp essed as,
( ) ( )
( ) ( ) ( )
c
ci
Lc
Xs
s s
RXs Xs
=++
(33)
whe e, Xc(s) = 1/(Cs) and XL(s) = Ls a e he impedances o he capaci o and he induc o ,
espec i ely. A e ea anging (33), he s anda d exp ession becomes,
( ) ( )
( )
( )
2
11
11
c
i
s Cs LC
Hs R
s R Ls ss
Cs L LC
= = =
++ ++
(34)
and, he e o e, he gain ac o , he na u al equency and he damping ac o a e,
K = 1;
1
n
LC
ω
=
and
2
RC
L
ξ
=
. (35)
Task PRELAB3: On he B ead-boa d empla e, ep esen he necessa y componen and
ins umen connec ions om Fig.11 you’ll need o de elop in o de o measu e he esponse o
an inpu s ep o he se ies RLC ci cui .
Task LAB3: Ob ain he ue esponse o he se ies RLC ci cui and compa e measu emen s
wi h he heo e ical alues.
• 1) E alua e he heo e ical alue o
ξ
and
ωn
by means o (35) and hen e alua e he
o e sho (SIP) and he peak ime ( p) using he in o ma ion in Table 1. 2) Moun he RLC
ci cui . 3) Connec he TTL ou pu o he wa e o m gene a o and se a equency =
100Hz. Use he “T” connec o . 4) Con igu e he oscilloscope in o de o obse e he
ini ial ansien o CH2, in one o he ascending s eps o CH1, in much de ail. D aw he
wa e o ms on he g id. 5) Anno a e he peak and ise ime, p and ; he damping ac o ξ
and he o e sho SIP, and compa e wi h he heo e ical ones.
• 1) Fo R=100k, e alua e he new alues o ξ and ωn by means o (35) and es ima e he
heo e ical ime cons an τ using (32). 2) Change he esis o in he ci cui and d aw he
new signals. 3) Measu e he se ling ime ( s
→
5τ in hal a cycle) and es ablish he
expe imen al τ o he ci cui . Compa e he alues.

37
37
Figu e 10. Schema ics o he se ies RLC ci cui and i s equi alence in s domain.
Figu e 11. Ci cui and ins umen connec ions o Task LAB3.
REMARK: The oscilloscope has a esis o RCH2 = 1MΩ and a capaci o CCH2 =
13pF in CH2 which connec in pa allel wi h he ci cui ou pu (Fig. 12) when p obes
a e plugged in. This connec ion has consequences in he ue alue o he pa ame e s
in (35). In ac , one can p o e ha he new ans e unc ion conside ing hese in e nal
componen s becomes
( ) ( )
( )
2
2
2
1
EQ
c
iCH EQ
EQ
CH EQ
KLC
s
Hs s K L RR C K
ss
LC
LR C
= = 
+
++



(36)
whe e
2
1
CH
R
KR

= +


;
n
EQ
K
LC
ω
=
;
2
2
2
CH EQ
CH EQ
L RR C
KR LC
ξ
+
=
pe
2EQ CH
C CC= +
. (37)
Fo he same eason, when R = 100k he se ling alue c(∞) dec eases o Vi/K =
4.5V. This analysis could be e en mo e complex i he in e nal componen s o CH1
a e also conside ed.
4.3 The elec ic esonance phenomenon ( he se ies RLC ci cui case)
When RLC ci cui s a e powe ed by sinusoids o he o m i( ) = Visin(ω ) (Fig. 6) he e is an
in e es ing phenomenon called elec ic esonance which occu s a a ce ain equency.
In he se ies RLC ci cui , o example, le us de ine ZT as he global impedance o he passi e
ne wo k. When XL(jω) = -Xc(jω) = +j/Cω, he esis o ol age is maximum. Tha is, when he
38
38
(a) (b)
Figu e 12. E ec o connec ing CH2 a he ou pu o he RLC ci cui . a) De ail o CH1 and CH2 showing he inpu
esis ance RCH2 and he capaci o CCH2 which is added o he ci cui when he p obe is connec ed. b) Resul ing
schema ics conside ing hese wo componen s.
Figu e 13.Mul i-me e connec ion o measu ing he elec ic esonance.
( ) ( ) ( )
T Lc
Z j RX j Xj
ω ωω
=++
, (38)
1
j
jL CLC
ωω
ω
=  → =
, (39)
ne wo k p oduces i s minimum impedance ZT(jω ) = R, so ha he maximum esis o cu en
becomes R(jω ) = Vi/R. To his equency ω = ω we e e o as he esonan equency.
Task LAB4: Using he mul i-me e , de e mine he expe imen al esonan equency ω o
he RLC ci cui (Fig. 13).
• 1) Con igu e he wa e o m gene a o o he same sinus signal in ask LAB2 (5V-peak,
ze o o se ) bu use a equency = 100Hz ins ead. 2) Connec he ol me e wi h he
esis o R in pa allel. Use he AC measu emen op ion (ACV). 3) In he wa e o m
gene a o , inc ease he equency un il he esis o ol age R eaches i s maximum
alue. 4) Anno a e he equency he peak VR and he ms alue VR ms.
39
39
Annex 1 – Resul s o m PRELAB
REMARK: You MUST do hese ac i i ies BEFORE THE LAB
SESSION CORRESPONDING TO PRT2
Escola Poli ècnica Supe io d’Enginye ia
de Vilano a i la Gel ú
EEL
Elec onic Sys ems (SIEK)
Ac i i y 2: Time and F equency domain
PRELAB
S uden s: Da e:
PRELAB 0: D aw he con ou package o a 10nF and a 10μF capaci o
How is he pola i y indica ed?
10nF:
_____________________________________________________________________________
_____________________________________________________________________________
10μF:
_____________________________________________________________________________
_____________________________________________________________________________
40
40
PRELAB1. Se ies RC ci cui – Response o a s ep unc ion.
Wa e o m unc ion gene a o con igu a ion, moun ing diag am, and
wa e o m aces o be obse ed on he sc een
Check he op ions you belie e you need o he speci ied con igu a ion
- OUTPUT: TTL 50Ω.
- FUNTION: De aul SQUARE SINUS TRIANGULAR
- OFFSET: De aul Value: _____________
- AMPLITUDE: De ec e Vaue: _____________
- FREQUENCY: ________________
Rep esen a ion o i( ) and c( )
CH1 VOLT/:
1V/
Ze o POS: -2V
CH2 VOLT/:
1V/
Ze o POS: -2V
TIME/: 500mseg/
Coupling: DC
47
47
Annex 3 –Basic Laplace T ans o ma ions
( )
F(s)
Uni impulse
1
S ep unc ion u( )
1s
2
1s
()
1
1!
n
n
−
−
n = 1, 2, 3, ...
1n
s
n-1 n = 1, 2, 3, ...
1
!
n
ns
+
e-a
1
sa+
e-a
( )
2
1
sa+
( )
1
1
1!
n a
e
n
−−
−
n = 1, 2, 3, ...
( )
1
n
sa+
ne-a n = 1, 2, 3, ...
( )
1
!
n
n
sa
+
+
sin(ω )
22
s
ω
ω
+
cos(ω )
22
s
s
ω
+
sinh(ω )
22
s
ω
ω
−
cosh(ω )
22
s
s
ω
−
( )
11a
e
a
−
−
( )
1
ss a+
( )
1
a b
ee
ba
−−
−
−
( )( )
1
sasb++
( )
1
b a
be ae
ba
−−
−
−
( )( )
s
sasb++
( )
11
1
a b
be ae
ab a b
−−

+−

−

( )( )
1
ss a s b++

48
48
( )
F(s)
()
2
11a a
e a e
a
−−
−−
( )
2
1
ss a+
( )
2
11a
a e
a
−
−+
( )
2
1
ssa+
( )
sin
a
e
ω
−
( )
22
sa
ω
ω
++
( )
cos
a
e
ω
−
( )
22
sa
sa
ω
+
++
()
2
2sin 1
1
n
nn
e
ξω
ωωξ
ξ
−−
−
2
22
2
n
nn
ss
ω
ξω ω
++
()
2
2sin 1
1
n
nn
e
ξω
ωω ξφ
ξ
−
− −−
−
2
1
1
an
ξ
φξ
−

−

=

22
2
nn
s
ss
ξω ω
++
()
2
2
1 sin 1
1
n
nn
e
ξω
ωω ξφ
ξ
−
− −+
−
( )
2
22
2
n
nn
ss s
ω
ξω ω
++
1-cos(ω )
( )
2
22
ss
ω
ω
+
ω -sin(ω )
()
3
22 2
ss
ω
ω
+
sin(ω )- ω -cos(ω )
( )
3
2
22
2
s
ω
ω
+
( )
1sin
2
ω
ω
( )
2
22
s
s
ω
+
cos(ω )
( )
22
2
22
s
s
ω
ω
−
+
( ) ( )
12
22
21
1cos cos
ωω
ωω

−

−
(ω1 ≠ ω2)
( )( )
2222
12
s
ss
ωω
++
( ) ( )
1sin cos
2
ωω ω
ω

+

( )
2
2
22
s
s
ω
+
49
49
P ope ies o he Laplace T ans o ma ion
1
ℒ[A·F( )] = A·F(s)
2
ℒ[ 1( )± 2( )] = F1(s)± F2(s)
3
( ) ( ) ( )
1
1
0
nnk
n nk
nk
d sF s s
d
−
−
±
=

=−±

 ∑
L
on
( ) ( )
1
1
1
k
k
k
d
d
−
−
−
=
4
()( ) ( ) ( )( )
10
1
1
n
nk
n nk
k
Fs
d d
ss
±−+ = ±
=
 
= +
 
∑
∫∫ ∫∫
L
5
( ) ( )
0
Fs
d s

=


∫
L
6
( ) ( )
0
0
lim
s
d F s
∞
→

=


∫
L
; si
( )
0
d
∞
∫
exis eix
7
() ( )
a
e Fs a
−

= +

L
8
( ) ( ) ( )
1as
a a eFs
−

− −=

L
pe a ≥ 0
9
( ) ( ) ( )
1n
n
n
n
d
Fs
ds

= −

L
n = 1, 2, 3, ...
10
( ) ( )
1
s
Fs
∞

=


∫
L
; si
( )
0
1
lim
s
→
exis eix
11
( )
aF as
a


=




L
12
( ) ( ) ( ) ( )
1 2 12
0
d F s F s
ττ

−=


∫
L
13
( ) ( ) ( ) ( )
1
2
cj
cj
g F p G s p dp
j
π
+∞
−∞

= −
∫
L
José An onio So ia Pé ez
50
Lab Ac i i y 3. Linea DC Powe Supplies
Main goal: Knowing he basic s ages ha make up a low-powe DC supply (line
ans o ma ion, ol age ec i ica ion, il e ing and s abiliza ion) and lea n he unc ion
ha basic semiconduc o s (diodes, b idge ec i ie s, Zene and in eg a ed ci cui s)
de elop wi hin his elec onic sys em.
1 In oduc ion
A DC powe sou ce p o ides a con inuous DC ol age o a ci cui . To make his
possible, i is necessa y o ans o m he high-powe line ol age, which is in he o m
o a sinusoid o
220 · 2 311V=
V peak and 50Hz, by means o se e al ope a ions
implemen ed in s ages (Fig. 1):
• The ans o me gene a es ano he ol age ( S) o he same ype as in he powe
line ( AC) a he second winding, bu o a much lowe ampli ude. This alue
depends on he numbe o u ns o bo h windings (N1 - p ima y and N2 –
seconda y, whe e N1 >> N2) and is calcula ed as:
2
1
S AC
N
N
=
(1)
• The ec i ie is implemen ed by means o diodes and con e s he ou pu om
he ans o me in o a unipola ol age o conside able ipple.
• The ipple a he ec i ie ou pu is educed e en mo e wi h a il e ing s age,
which is esponsible o emo ing he componen s o highe equency. The
ipple ob ained wi h his ope a ion, howe e , depends on o he ac o s
belonging o he ou pu load (such as impedance and load cu en ), and canno
be emo ed comple ely.
• This is p ecisely he unc ion o he las s age, he ol age egula o , which
makes he DC ou pu independen om he inpu line.
2 Rec i ie ci cui s ( ec i ie diodes)
We’ll s a wi h he ec i ie diode, he mos common nonlinea semiconduc o in
elec onics (Fig. 2a) which ac s as a semi-con olled swi ch (Fig. 2c and 2d):
• When a nega i e ol age is applied o bo h e minals (acco ding o he e e ence
in Fig. 1b, < 0), his de ice beha es as an open ci cui (Fig. 2c). In his
si ua ion, i s elec ic cu en , om anode o ca hode,is ze o and i is said ha he
diode is e e se biased, o i wo ks in OFF mode.
• On he o he hand, i he elec ic cu en is posi i e (i > 0) he de ice ac as
sho ci cui (Fig. 2d) and i is said ha he diode is o wa d biased. I wo ks in
ON mode.
The ue beha io , howe e , a ies sligh ly. In ON mode, i u ns ou ha he ol age
om anode o ca hode ( ) is no qui e ze o, bu has a small alue close o 0.7V ( he ue
alue depends on diode he ma e ial used by he manu ac u e ). One way o
ep esen ing his h eshold consis s in adding an addi ional sou ce (VD = 0.7V) in se ies
wi h he ideal model (Fig. 3).
José An onio So ia Pé ez
51
Figu e 1. Block diag am co esponding o he di e en s ages o he DC powe supply. These a e
he necessa y s eps o he AC-DC ene gy con e sion o he powe line AC.
(a) (b)
(c) (d)
Figu e 2. The ideal diode model: a) Symbol; b) i- cha ac e is ics; c) OFF ope a ion; d) ON ope a ion.
(a) (b)
Figu e 3. a) T ue and linealized i- cha ac e is ics; b) Equi alen linealized model.
One basic applica ion which makes use o he diode cha ac e is ics is he ec i ie (Fig.
4). This ci cui consis s o a diode D and a esis o R connec ed in se ies. When a
sinusoid ol age I = VPsin(2π ) is in oduced as inpu , he diode will be in ON mode
whene e I( ) ≥ VD, and in OFF mode o he wise. Since in his mode iD becomes ze o,
he ou pu ol age in he esis o R is also ze o.
José An onio So ia Pé ez
52
(a) (b)
Figu e 4. a) Single-phase hal -wa e ec i ie ci cui . B) Vol age wa e o ms I( ) – blue; and O( ) - ed.
Figu e 5. O – I ans e cha ac e is ics o he hal -wa e ec i ie in Fig. 3a.
Thus, he ci cui “ ec i ies” he nega i e cycle om he unique (o single-phased) inpu .
Du ing he posi i e cycle, he ou pu will be he same as he inpu bu emo ing he
h eshold VD co esponding o he ol age d op on he diode (Fig. 5). Hence, he name
o he ci cui : he single-phase hal -wa e ec i ie .
In p ac ice, he a e age ou pu ol age VO(a ) is de e mined o e an en i e cycle as,
( )
( ) ( ) ( )
00
11
sin
22
TPD
ID P D
O a
VV
V d V d V
T
π
ωω
ππ

= − −−

∫∫
��
, (2)
whe e VP co esponds o he inpu ampli ude and depends on he ans o me windings
I = S. As o he diode, he a e age and maximum alue o elec ic cu en , ID(a ) and
IDmax , espec i ely is ob ained as
( )
( )
O a
D a
V
IR
=
and
Omax
max PD
D
VVV
IRR
−
= =
, (3)
whe eas he maximum epe i i e ol age d op in OFF mode , VRRM1 is,
VRRM = max{- D( )} = VP. (4)
This in o ma ion ega ding he hal -wa e ec i ie is impo an in p ac ice, as i speci ies
which is he co ec diode o use on one hand, and hen i pe mi s a i s glance o he
main DC powe sou ce pa ame e s, such as he DC ou pu o he powe ans e ed by
he sou ce.
1 VRRM s ands o Maximum Repe i i e Re e se Vol age and is he maximum ol age he diode can ake,
om ca hode o anode, when i is e e se biased. Tha is ID = 0A.

José An onio So ia Pé ez
53
(a) (b)
Figu e 6. (a) Two-phae ha -wa e ec i ie . (b) Single-phase ull-wa e ec i ie (o b idge ec i ie ).
Elec ical
a iables
Single-phase
Rec i ie
(hal -wa e)
Two-phase
Rec i ie
(hal -wa e)
Single-phase
Rec i ie
( ull-wa e)
VO(a )
2
PD
VV
π
−
2PD
VV
π
−
22
PD
VV
π
−
V
RMM
V
P
2V
P
V
P
- V
D
IDmax
PD
VV
R
−
PD
VV
R
−
2
PD
VV
R
−
ID(a )
( )
O a
V
R
Table 1. Summa y o speci ica ions co esponding o he di e en ec i ie ci cui s.
The ec i ie ci cui s in Fig. 6, imp o e he ea u es o he hal -wa e ec i ie . On one
hand, he wo-phase hal -wa e ec i ie inc eases he capaci y o ou pu powe
ans e ed o he load because using wo phases doubles he a e age DC alue on he
esis o O. On he con a y, howe e , he diodes mus s and wice he inpu ol age
when ope a ing in OFF mode (VRRM ≈2VP). The bene i s o he single-phase ull-wa e
ec i ie (o b idge ec i ie ), on he o he hand, a e simila o he wo-phase ec i ie bu
wi h a e e se ol age VRRM ≈VP (see Table 1).
Task PRELAB1: In he B ead-Boa d empla e p o ided a he end o he
documen , d aw he connec ions co esponding o he wo ec i ie s shown in Fig. 7, o
be implemen ed in he lab on he 3 d. session. Include he connec ions om he
ans o me , componen s and oscilloscope.
Task LAB1: In each ci cui in Fig. 7, ob ain he wa e o m a he second winding
in he ans o me I( ), he ou pu O( ) and he ol age in one diode D( ).
• 1) Moun he ci cui in Fig. 7a. 2) Tu ning bo h ans o me and oscilloscope
OFF, connec he p obes and wi es. When you inish, u n bo h de ices ON. 3)
Con igu e CH1 and CH2 as indica ed in o de o obse e bo h signals in de ail.
4) Selec he MATH op ion and ac i a e he SUBSTRACTION ope a ion
(pu ple ace: CH1 – CH2). 5) Ob ain he alues o VRRM and VO(a ) by means o
he MEASURE op ion o bo h channels.
José An onio So ia Pé ez
54
(a)
(b)
Figu e 7. Diag am connec ions he wo ec i ie s necessa y o ob ain I( ), D( ) i O( ) in he lab. a)
Single-phase hal -wa e ec i ie . b) Two-phase hal -wa e ec i ie .
• Simila ly, p oceed wi h he second ci cui (Fig. 7b) o ob ain he wa e o m
signals co esponding o he wo-phase hal -wa e ec i ie .
REMARK: I is e y impo an NOT MANIPULATING OR NOT
MODIFYING PROBE CONNECTIONS while he ans o me is on, in o de
o p e en he in e nal p o ec ion uses o 0.5A om b eaking. Fo he same
eason, emembe NOT TO CONNECT he nega i e e minal o he p obes a
di e en poin s in he ci cui .
As he bene i s o he single-phase ull-wa e ec i ie a e qui e accep able, i s use is
ex ended as pa o many comme cial DC low-powe supplies2. Because o he ou
diodes, his ci cui inc eases in complexi y and olume. Fo una ely, oday he e a e
many in eg a ed ci cui s including he ou diodes in a single package, such as he
b idge ec i ie s (Fig. 8), which eases connec i i y and implemen a ion.
3 Fil e ing s age
The subsequen s ep o he ec i ica ion o he nega i e cycle in he inpu line consis s in
educing he ipple. The easies way consis s in connec ing a capaci o in pa allel wi h
he load (Fig. 9a) in o de o cause a smoo h ansi ion be ween cycles (Fig. 9b), hus
“ il e ing ou ” he high- equency componen s o he inpu line. The ull sequence o
Fig. 9b de elops as ollows:
2 In gene al, he low-powe DC supplies a e hose p o iding a maximum ou pu cu en IO = ID(a ) < 2A.
José An onio So ia Pé ez
55
(a) (b) (c)
Figu e 8. Th ee b idge ec i ie s commonly used in DC powe supplies: a) he W10G-E4 om Vishay; b)
he KBPC5010 om Fai child Semiconduc o ; c) he DF06 om In e na ional Rec i ie
(a)
(b)
José An onio So ia Pé ez
56
Figu e. 9. Single-phase hal -wa e ec i ie wi h il e . a) Schema ics. b) Wa e o ms co esponding o
ol ages in O, I; and elec ic cu en s iD, iL. We assume RC >> T.
• The diode allows he elec ic cu en o low o small pe iod o ime (say ∆ = 2
– 1). The ON mode begins a = 1, a his momen he inpu eaches he ou pu
alue, which was decaying as a esul o he capaci o discha ge du ing he
p e ious in e al.
• When I has jus eached he maximum alue (we use he app oxima ion VP – VD
≈ VP o simpli y ou commen s), and assuming ha he ou pu ansi ion is much
slowe in ela ion o ha o he inpu because R and C a e designed so ha
τ = RC >> T, he diode s ops conduc ing a 2 and u ns OFF.
• When he diode is OFF (in almos all he ull cycle T), he capaci o C ans e
i s cha ge o he esis o R. The e olu ion o O( ) is gi en by (5) whe e 2 = 0 is
assumed in o de o simpli y ou commen s:
( ) ( ) ( ) ( )
2
RC RC
OO O O P
e Ve
−−
= ∞+ − ∞ =


. (5)
He e, (∞) = 0 is he hypo he ical ol age he capaci o would each in an e en
o pe manen discha ge, = ∞, and ( 2) ≈ VP co espond o he ini ial alue o
his in e al. Assuming ha RC >> T, a good app oxima ion is:
1
RC
eRC
−
−�
(6)
• Since
( )
( )
11
RC
O P P P
V V Ve V RC
−
=−−��
, equa ing (6) and (5) allows he
ipple o be es ima ed as:
PL
P
VI
T
VV
RC RC C
= =�
(7)
Knowing his pa ame e , he a e age alue o he ou pu ol age VO(a ) is de e mined as
()
2
P
O a
V
VV−�
. (8)
Finally, we ob ain he a e age and maximum alue o he elec ic cu en lowing
h ough he diode, ID(a ) and ID(màx) espec i ely. Once again, hese pa ame e s a e
c ucial o selec ing one diode om he di e en supplie s. Taking in o accoun ha he
diode s ops conduc ing when I( ) ≈ VP, he conduc ion in e al ∆ can be es ima ed by
means o VP – V = VP cos(ω∆ ), whe e ω = 2π . = 2π/T co esponds o he angula
equency o he inpu line. Assuming ha ω∆ is oo small, he e m cos(ω∆ ) can be
app oxima ed as
(
)( )
2
1
cos 1 2
ωω
∆=− ∆
. So, he conduc ion angle α becomes
2
P
VV
αω
= ∆=
. (9)
José An onio So ia Pé ez
63
b) Connec ions co esponding o he wo-phase hal -wa e ec i ie (Fig. 7b)
PRELAB 2. Vol age il e
Connec ions co esponding o he single-phase hal -wa e ec i ie using il e (Fig. 10)

José An onio So ia Pé ez
64
PRELAB 3. Es abili zado de ensió Zene
Connexions de la on d’alimen ació DC comple a amb egulado Zene (Fig. 14)
PRELAB 4. Regulado de ensió in eg a
Connexions de la on d’alimen ació DC comple a amb egulado in eg a L7805 (Fig.
16)
José An onio So ia Pé ez
65
Annex 2 –Lab ac i i ies
REMARK: You MUST PRINT OUT his o m and
TAKE IT WITH YOU he day o he lab session
Escola Poli ècnica Supe io d’Enginye ia
de Vilano a i la Gel ú
EEL
Elec onic Sys ems (SIEK)
Ac i i y 3: In oduc ion o DC supplies
FULL DE RESULTATS
Es udian s: Da a:
LAB 1: Vol age ec i ie s
Wa e o ms I( ); O( ) and D( ) = I( ) - O( ) obse ed in he single-phase
hal -wa e ec i ie (Fig. 7a).
CH1 VOLT/: 5V/
Ze o POS1: 0V
CH2 VOLT/: 5V/
Ze o POS2: 0V
MATH VOLT/: 5V/
TIME/: 5mseg/
Acob: DC
VRRM: ____________ VO(a ): _____________
José An onio So ia Pé ez
66
Wa e o ms I( ); O( ) and D( ) = I( ) - O( ) obse ed in he wo-phase
hal -wa e ec i ie (Fig. 7b).
CH1 VOLT/: 5V/
Ze o POS1: 0V
CH2 VOLT/: 5V/
Ze o POS2: 0V
MATH VOLT/: 10V/
TIME/: 5mseg/
Acob: DC
VRRM: ____________ VO(a ): _____________
LAB 2: Vol age il e
Wa e o m co esponding o O( ) using C = 100nF.
CH1 VOLT/: 5V/
Ze o POS1: -5V
TIME/: 2mseg/
Acob: DC
VOmax: ________ VOmin: ________ V : ________ VO(a ):_______
José An onio So ia Pé ez
67
Wa e o m co esponding o O( ) using C = 10µF.
CH1 VOLT/: 5V/
Ze o POS1: -5V
TIME/: 2mseg/
Acob: DC
VOmax: ________ VOmin: ________ V : ________ VO(a ):_______
Wa e o m co esponding o O( ) using C = 100µF.
CH1 VOLT/: 5V/
Ze o POS1: -5V
TIME/: 2mseg/
Acob: DC and AC
VOmax: ________ VOmin: ________ V : ________ VO(a ):_______
Explain he esul s:
____________________________________________________________
____________________________________________________________
____________________________________________________________
José An onio So ia Pé ez
68
____________________________________________________________
____________________________________________________________
LAB 3: Vol age egula o
Wa e o ms co esponding o c( ) and O( )
CH1 VOLT/: 5V/
Ze o POS1: -5V
CH2 VOLT/: 5V/
Ze o POS1: -5V
TIME/: 2mseg/
Acob: DC
Va iable
R
L
= 560Ω
R
L
= 1kΩ
R
L
= 10kΩ
V
VO
IL
Table 3. Elec ic a iables co esponding o he Zene egula o
Is V independen om VO? Explain why
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
LAB 4: Vol age egula o using in eg a ed ci cui
Va iable
R
L
= 390Ω
R
L
= 1kΩ
R
L
= 10kΩ
V

José An onio So ia Pé ez
69
VO
IL
Taula 4. Elec ic a iables co esponding o he IC egula o L7805
Explain he di e ence o esul s ega ding o he Zene con igu a ion o
sec ion LAB3. Wha a e he imp o emen s and d awbacks o his
con igu a ion?
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
José An onio So ia Pé ez
70
Lab Ac i i y 4. Swi ching Elec onics: he Bipola
Junc ion T ansis o (BJT)
Main goal: To unde s and he pe o mance o he bipola ansis o s (aka BJT)1 and
knowing i s main applica ion in he ield o swi ching elec onics (analog, digi al and
mixed).
1 In oduc ion
In his lab ac i i y you’ll ge in oduced o he mos common h ee- e minal elec onic
de ice: he bipola junc ion ansis o (BJT). I s ope a ion p inciple is qui e simila o a
wo- e minal cu en sou ce which is con olled om ano he e minal. Tha is, he
elec ic cu en a he base e minal (B) se s (o con ols) he amoun o cu en lowing
om he collec o e minal (C) o he emi e (E).
Bo h elec ic symbols and cu en / ol age con en ions a e shown in Fig. 1. In gene al,
we ind wo ypes o BJT: he npn (Fig. 1a) and he pnp (Fig. 1b). Thei main di e ence
lie on he sign con en ion used in all a iables, which is opposi e in ela ion o he
o he .
As o he elec ic cu en s in each o he e minals, i holds ha :
E BC
iii= +
. (1)
On he o he hand, BE co esponds o he ol age d op be ween base and emi e
e minals, whe eas CE is he collec o -emi e ol age.
Unlike he diode, he BJT is able o ope a e up o h ee egions depending on he
di e en condi ions ha may be gi en in he elec ical a iables when he h ee
e minals a e connec ed o o he componen s (see Table 1):
• When he base cu en iB is ze o, he e is no cu en low a he collec o e minal
iC=0. In his case, we say ha he BJT ope a es in he CUTOFF mode. This
happens whene e he BE ol age is unde he h eshold le el VBEγ ( ypically
VBEγ = 0.7V), speci ied by he manu ac u e ’s da ashee .
• When he elec ic powe a he base is signi ican ly enough so as o make he
base cu en iB g ea e han ze o, he BJT lea es he cu o egion and en e s in
ACTIVE mode. The BJT will emain in his egion as long as iB is signi ican ly
enough o keep he CE ol age abo e he h eshold le el VCE(sa ) (also speci ied
in he da ashee ). In his si ua ion, BE=VBEγ and iC is p opo ional o iB. The gain
in cu en ha is ob ained be ween his o a iables is deno ed as hFE and is also
p o ided by he manu ac u e in he da ashee .
1 F om now on we will use hese e ms o e e o his ype o elec onic semiconduc o
José An onio So ia Pé ez
71
(a) (b)
Figu e 1. The BJT. Symbols and elec ic cu en / ol age sign con en ions. a) npn, b) pnp.
Ope a ing zone
Elec ical condi ions
Elec ical beha io
Cu o (OFF) BE < VBEγ , CE > VCE(sa ) iB = 0, iC = 0
Ac i e iB > 0, CE > VCE(sa ) BE = VBEγ, iC = hFEiB
Sa u a ion (ON) iB > 0, iB > iC/hFE BE = VBEγ, CE = VCE(sa )
Table 1 Ope a ing modes in he npn BJT: elec ic condi ions and de ice beha io a e speci ied. The same
conside a ions apply o he pnp ype when changing he a iable index, i.e. CE → EC.
• When iB is e y la ge, he ela ion iC = hFEiB is no ul illed anymo e and he BJT
en e s he SATURATION mode. The ol age CE akes i s minimum alue
( CE(sa )), and BE is he same as in he ac i e egion, VBEγ.
Fig. 2 summa izes he BJT i- cha ac e is ics. In ac , he base-emi e junc ion ac s as a
diode: in bo h ac i e and sa u a ion egions his BE junc ion is in ON mode ( BE = VBEγ i
iB > 0), whe eas in he cu o egion his junc ion is in OFF mode ( BE < VBEγ i iB = 0).
In o de o unde s and hese h ee ope a ing egions, conside he BJT ci cui o Fig. 3,
whe e Vin is some a iable inpu ol age. Applying bo h KVLs a he inpu and ou pu
meshes (le and igh , espec i ely) we ob ain:
0
in B B BE
V Ri − −=
(2)
2
0
C C CE
Ri − −=
(3)
• CUTOFF ope a ion: The bounda y o Vin be ween he cu o and ac i e mode is
ob ained by using he condi ion BE < VBEγ and se ing iB = 0 in (2) (see Table 1). So
he condi ion o Vin in he cu o egion is,
in BE
VV
γ
≤
. (4)
Since iC = 0, he condi ion CE > VCEsa mus hold, so,
( )
2CE CE sa
VV= >
(5)
José An onio So ia Pé ez
72
(a) (b)
Figu e 2. The BJT i- ans e cha ac e is ics. a) Inpu : iB – BE. b) Ou pu : iC – CE.
Figu e 3. Schema ics o he basic BJT con igu a ion: npn ype.
• ACTIVE ope a ion: I is clea ha he inpu condi ion mus be opposi e o (4) i
he BJT is o ope a e in his egion. Indeed, exp essing iB om (2) and using he
equali y BE = VBEγ we ob ain,
0
in BE
B in BE
B
V
i VV
R
γ
−
= ≥→ ≥
. (6)
Howe e , his is no he only condi ion o he ac i e egion because, on he
o he hand, when iB is la ge enough he BJT may en e he sa u a ion egion. The
o he bounda y is de e mined using he condi ion CE > VCE(sa ). In addi ion, since
we ha e iC = hFEiB in ac i e mode, using (6) in (3) leads o he condi ion,
2 ()CE sa
in B BE
C FE
V
VR V
Rh
γ
−
≤+
, (7)
The e o e, he ac i e egion is ob ained wi hin he inpu ange,
José An onio So ia Pé ez
79
Figu e. 8. Enabling Sys em o a 7-segmen BCD display o be implemen ed in Task LAB2.
(a) (b)
Figu e. 9. O he mechanical and passi e elemen s o he ci cui in Fig. 9. a) DIP8-swi ch3 used in he
ac i a ion o all leds om he 7-segmen s BCD display; b) In eg a ed ci cui 9A102G. I con ains eigh
1kΩ esis o s wi h one e minal Connec ed o a common pin.
Task PRELAB2. Iden i y he new componen s in he ci cui o Fig. 8. Then, use
he Boa d empla e o d aw he connec ions you need o de elop in o de o make he
enabling ci cui o Fig. 8 wo k.
• Use he web o looking o in o ma ion on he 9A102G and LSD5355
in eg a ed ci cui s. In he case o he 9A102G speci y he meaning and he way
3 DIP – Dual In-line Package

José An onio So ia Pé ez
80
o speci ying he common pin. Which ype o BCD display is necessa y o in
Fig. 8: common ca hode o common anode?
Task LAB2. Moun he ci cui o Fig. 8 and check i s beha io
• 1) Moun he ci cui on he B ead-Boa d. Place he componen s so as o
minimize wi e connec ions. 2) Wi h he selec o swi ch a posi ion S = A,
connec he powe supply VCC = 5V. 3) Wi h all swi ches in he DIP8-swi ch
u ned on, change he selec o posi ion (S = B). Ma k he leds co esponding o
he numbe ep esen ed in he display.
• Change he posi ion o swi ches in o de o ep esen o he decimal numbe s and
cha ac e s. De elop h ee examples, and indica e you selec ion in he esul s
o m speci ying he con igu a ion o swi ches in he able.
• How would you use he wa e o m gene a o in o de o show he numbe 8
(including decimal poin ) wi h a blinking pa e n o 1-second in e al? Speci y
he con igu a ion o he wa e o m gene a o .
4. La ch SET/RESET (Op ional sec ion)
In he digi al unc ions in oduced in sec ion 3, he logic ou pu is upda ed by he inpu s
a he same ins an ime . Tha is, he inpu s, and solely he inpu s, speci y he ou pu o
he sys em. This pe o mance is known as a “memo y-less” sys em.
Digi al ci cui s become in e es ing when hey ha e memo y. Tha is, hey ecall hei
las p e ious s a es. This allows, among di e en hings, digi al coun e s, a i hme ical
accumula o s and all o ms o ci cui s ha wo k in a sequen ial ashion (one unc ion
execu ed a e he o he ) o be implemen ed. Hence, i is said ha his so o digi al
sys ems use “sequen ial logic”.
The mos basic memo y uni in digi al ci cui s is known as he la ch (o wo-sho
mul i ib a o ). One ype is he SET/RESET mul i ib a o (Fig. 9). I s ou pu can be
SET {Q = 1} o RESET {Q = 0}. In gene al, he ou pu is modi ied using he 2nd and 3 d
combina ion in Table 4 bu , i S = 0 and R = 0, i emains unchanged, emembe ing he
alue upda ed in he p e ious s a e (see Fig. 10).
Fig. 11 shows he elec ic diag am o a SET/REST mul i ib a o implemen ed wi h
disc e e componen s, including wo bipola ansis o s. As he NOT ga e, bo h BJT can
ope a e ei he a cu o (IC = 0) o sa u a ion (VCE ≈ 0) mode. This is he ci cui
pe o mance:
• When he powe supply VCC is connec ed, bo h BJTs (T1 and T2) s a hei
conduc ion cycle, since bo h base e minals a e d i en by posi i e ol ages: T1
h ough esis o s R2 – R6 – R7; and T2 h ough R1 – R5 – R8. Howe e , no bo h
ansis o s a e iden ical (because o he ole ances wi hin hei manu ac u ing
p ocess caused by di e en le el o impu i ies in he silicon ma e ial), so one
ansis o will conduc be o e he o he .
José An onio So ia Pé ez
81
(a) (b)
Figu e 9.SET/RESET mul i ib a o . a) Symbol; b) Implemen a ion using 2-inpu NOR ga es.
Cases
S
R
Q
!Q
1
0
0
Q
*
!Q
*
2
0
1
0
1
3
1
0
1
0
4
1
1
X
X
Table 4. T u h able o he SET/RESET mul i ib a o . Q* and !Q* deno e p e ious ou pu (be o e a ne
upda e o he SET/RESET e minals is eached. !Q means in e sion o Q. The combina ion S=R=1 is no
alid in he SET/RESET mul i ab a o and is deno ed wi h X.
Figu a 10. Beha io example o he SET/RESET mul i ib a o by means o a ime diag am. No e ha he
ou pu can be ei he Q = 0, o Q = 1 wi h S = R = OFF, depending on he p e ious s a e.
José An onio So ia Pé ez
82
Figu e 11.Schema ics o he SET/RESET mul i ib a o implemen ed by means BJTs.
A s a up, assume ha T1 is he i s BJT conduc ing when S = R = OFF. Then,
T2 = OFF and iC2 = 0. In his case, V!Q > VD2 = Vγ and he led D2 will be u ned
ON. The cu en low a he base o T1, iB1 is hen exp essed as:
!11
167
26 7
Q BE BE
BRR
VV V
iii RR R
γγ
−
=−= −
+
(20)
whe e V!Q can be ob ained om he KCL applied a he collec o e minal o T2,
! ! 1!
26 2
2 62
CC Q Q BE Q
R R RL
L
V V VV VV
iii R RR
γγ
−− −
=+→ = + →
62 122 26
!
62 22 26
CC L BE L
Q
LL
V RR V RR VRR
VRR RR RR
γγ
++
→= ++
(21)
Thus, iB1 will be la ge enough o cause he sa u a ion o T1 (T1 = ON) and,
he e o e, i s collec o -emi e ol age will dec ease d as ically ( Q = VCE1 (sa ) ≈
0.2V). Since his po en ial is no enough o d i e he base o T2, BE2 =
VCE1(sa )R8/( R8 + R5) < VBE2γ, his ansis o will wo k on cu o mode. These will
be he ini ial condi ions o he ci cui , he RESET s a e (Q = 0 and !Q = 1).
• Now, assume ha he swi ch S is ac i a ed (S = ON) o a small ime pe iod.
Then, iB2 is momen a y ixed by R3 (g een pa h o Fig. 12a). The alue o his
a iable du ing his in e al is exp essed as:
José An onio So ia Pé ez
83
(a)
(b)
Figu e 12. Idea del uncionamen de la bàscula RS. a) Condició de SET. b) Condició de RESET. El camí
ma ca en e d indica el camí que causa la la sa u ació del BJT, men e que el e mell indica el camí de
ci culació de co en pe ac i a els Leds.
22
2
35858
// //
CC BE BE
B
VV V
iRRRRR
γγ
−
= −
+
(22)
and is la ge enough o cause he sa u a ion o (T2 = ON). Since CE2 = VCE2(sa ) ≈
0.2V, his po en ial will no only be enough o main ain led D2 on bu will also
cu o T1 (T1 = OFF). Tha is, bo h ansis o s change hei beha io (SET: Q =1
i !Q = 0) and now he led ha glows is D1.
José An onio So ia Pé ez
84
The eade can no e ha his new si ua ion is gua an eed e en a e he ading o
S( ) as iB2 will be gi en wi h an exp ession simila o (20) bu wi h esis o s R1,
R5 and R8,
22
2 58
15 8
Q BE BE
B RR
VV V
iii RR R
γγ
−
=−= −
+
(23)
when S=R=OFF, so he ol age VQ is also analogous o (21). In o he wo ds, he
new ou pu s a e,
5 1 2 1 1 15
! 2( )
511115
0
CC L BE L
Q Q CE sa
LL
V RR V RR VRR
V V
RR RR RR
γγ
++
= =
++ ; �
(24)
• Fo e u ning o he RESET s a e, he use mus ac i a e he swi ch R (R = ON).
Bo h BJTs will exchange again hei ope a ion (T2 = OFF and T1 = ON) and Q
= 0; !Q = 1 (Fig. 12b). The p ocedu e by which T1 is se o ON is analogous o
ha jus explained abo e o T2 and he ou pu s will be gi en again by (21).
Task PRELAB 3. D aw he componen connec ions o he SET/RESET
mul i ib a o om Fig. 11 in he Boa d empla e p o ided.
Task LAB 3. Check he co ec ope a ion o he SET/RESET mul i ib a o .
• 1) Moun he ci cui . Use he ollowing componen s:
T1 = T2 = BC547C, R1 = R2 = 1k, R3 = R4 = 1k2, R5 = R6 = 10k, R7 =R8 =100k,
RLED1 = RLED2 = 1k8, D1 = D2 o h eshold ol age: Vγ=1.2V.
• 2) Connec he powe VCC = 5V and check which led is u ned on. 3) Push he
RESET bu on (R) i D1=ON, o push SET (S) i D2 = ON). Bo h leds should
change ope a ion mode. 4) Check ha pushing again he same bu on (R o S
depending on he ini ial case) does no al e he ope a ion o leds. 5) Push he
o he bu on o e u n o he ini ial case.
REMARK: Use wi es o implemen ing he push bu ons by
connec ing one end o VCC and emula e he e ec o se ing S( ) and R( )
o “1” by connec ing momen a ily he o he end o he wi e o R3 and R4,
espec i ely.
• Explain a possible u ili y o he SET/RESET ci cui in digi al elec onics.

José An onio So ia Pé ez
85
Annex 1.- BJT applica ions ope a ing in he ac i e egion
This sec ion conside s wo ypical applica ions o BJTs ope a ing in he ac i e egion.
No ac i i ies a e p oposed, since he main goal he e is jus o show he ad an ages and
he u ili y o his ope a ing egion. The signal ampli ie and he cu en sou ce cons i u e
wo o he main gene al pu pose applica ions o he BJT ope a ing in his mode.
A1.1 Signal ampli ie using BJT
One basic applica ion whe e he BJT is “always” assumed o ope a e in ac i e mode is
called he ol age ampli ie (o he signal ampli ie ). This elec onic sys em is used e y
o en o imp o e he powe o audio and senso signals. S ic ly speaking, i s
unc ionali y consis s in “inc easing” he inpu ol age magni ude in o de o p o ide
mo e powe o he ou pu .
The ollowing exp ession ep esen s he ma hema ical unc ion co esponding o his
ope a ion
( ) ( )
ou in
k =
(1)
whe e k > 1 is he gain ac o o he elec onic sys em, ou is he ou pu and in he inpu
o be ampli ied. Figu e A1 shows he block diag am co esponding o his ope a ion.
The slope o he inpu /ou pu ans e cha ac e is ics ou – in (Fig. A2) gi es an idea o
he gain ha is ob ained a he ou pu .
One way o implemen ing he ampli ie by means o a BJT consis s in changing he
sou ce in in Fig. 3 by he same signal sou ce in( ) and modi ying RB o so as o ope a e
in he ac i e egion. Un o una ely, he npn BJT can only ope a e in ac i e mode when
in > VBEγ, so he ci cui admi s only posi i e alues o in. This p oblem can be sol ed
adding a DC ol age in se ies wi h in so ha an o se ol age le el and all alues om
he inpu in can be posi i e, bu his would inc ease he implemen a ion cos o he
ampli ie because ano he DC powe supply (o ba e y) is equi ed.
The BJT ampli ie in Fig. 3 de elops i s unc ionali y and ci cum en s he o se
p oblem using one single DC ol age sou ce. This basic ampli ie is know as he
Common Emi e (CE) ampli ie . In o de o design i s componen s, he analy ical
p ocess consis s o he ollowing h ee s eps:
A. O se es ima ion (VOUT) (o ansis o biasing):
The ou pu o se is es ima ed by jus conside ing he DC ol age supply (VCC) and
disconnec ing he emaining independen sou ces ( he AC inpu , in( ) = 0, in his
case). I capaci o s exis s hey a e conside ed as open ci cui s because when s = 0, hei
impedance becomes in ini e (ZC(s) → ∞). In ac , he goal o C1 is o pe mi he biasing
o he BJT h ough esis o R2 and connec he AC inpu sou ce o he base junc ion so
ha he inpu signal can be ampli ied.
José An onio So ia Pé ez
86
Figu e A1. Block diag am o he BJT ol age ampli ie . The inpu magni ude in is inc eased by a ac o k
a he ou pu ou .
Figu a A2. Inpu /ou pu ans e cha ac e is ics: ou – in o he ol age ampli ie
Figu e A3 Common Emi e ol age ampli ie using BJT.
When only he DC sou ce is conside ed he ci cui can be simpli ied o ha o Fig. 4a
(jus use he The enin equi alen obse ed a he base e minal). Assume ha he BJT is
ope a ing in he ac i e egion. The cu en IB is ob ain by means o he KVL exp ession,
()
12
/ / 0.
B B BE E E
V R R I V RI
γ
− −− =
(2)
José An onio So ia Pé ez
87
(a) (b)
Figu e A4. Analy ical diag ams o he BJT ol age ampli ie . a) DC analysis. b) AC analysis
whe e VB = R2VCC/(R1 + R2). Since IE = IB + IC = IB(hFE + 1), equa ing IB leads o:
()
( )
( )
212
12
// 1
CC BE
B
E FE
V RRR V
IR R Rh
γ
+−
=++
(3)
whe e he e m RE(hFE +1) he inpu esis ance (Rin(BJT)) he BJT has in his ci cui . I
we design he esis o s so as o ob ain Rin(BJT) >> R1//R2 (10 imes: Rin(BJT) ≈ 10 R1//R2),
hen IC can be app oxima ed and es ima ed as
B BE
C FE B
E
VV
I hI R
γ
−
=�
. (4)
In o he wo ds, he base DC ol age VB and he esis o RE con ols he amoun o
elec ic DC cu en low in he he collec o e minal IC . Wi h his app oxima ion, he
base cu en can be unde es ima ed (IB ≈ 0) and he ou pu o se VOUT is exp essed as
B BE
OUTCCCCCCC
E
VV
V VRIVRR
γ
−
=−=−
(5)
B. Vol age gain es ima ion (k):
The gain ac o is ob ained by conside ing jus he AC sou ces (AC) om he ci cui
and se ing he DC supply o ze o (VCC = 0). In his case, elec oly ic capaci o s a e
conside ed sho -ci cui s a ela i ely highe equencies (s = jω = j2π whe e > 1kHz)
an hei impedances can be unde es ima ed, |ZC(s)| → 0. The capaci o C1 will hen
connec he AC sou ce o he base junc ion o he BJT and he inpu AC esis ance o
he ampli ie , Rin becomes
( )
12 ()12
// // // // 1
in in BJT E FE
R RRR RRRh= = +
(6)
José An onio So ia Pé ez
88
Since, b( ) = in( ) and he base-emi e junc ion can be conside ed a biased diode
du ing he ull inpu ange, he swing o he base-emi e ol age will be negligible be( )
= 0, so in p ac ical e ms i can be assumed ha he inpu ol age alls on RE( ).
Fo his eason, he collec o cu en ic( ) is ob ained as
()( ) ( )
RE in
c
EE
i RR
= =
(7)
and he ou pu AC ol age exp ession, o( ) = - RC( ) = -RCic( ) is ob ained as:
( ) ( )
in
ou C
E
RR
= −
(8)
Thus, he ol age gain (k) o he ci cui is
()
()
ou C
in E
R
k R
= = −
(9)
Finally, we can use (5) and (9) o ob ain he ull DC and AC ou pu , OUT( ), by means
o he supe posi ion p inciple
( ) ( ) ( )
( )
C
OUT OUT ou CC B BE in
E
R
V V VV
R
γ
= + =− −+
(10)
C. Es ima ion o he ou pu swing (∆ ou ):
We de ine as he ou pu swing o he limi a ion in dynamic ange ∆ ou exis ing a he
ou pu o he ol age ampli ie when he BJT lea es he ac i e egion, and which is
no mally exp essed in e ms o he maximum peak alue ha can be ob ained a he
ou pu wi hou causing signal dis o ion.
Theo e ically, he inpu in( ) he e is no limi o bo h he inpu and ou pu ampli ude. In
p ac ice, howe e , his assump ion is no ue because he BJT could lea e he ac i e
egion. When his happens, he esul a he ou pu is a pulsa ing signal o conside able
dis o ion in ela ion o ha o he inpu .
Figu e A5 illus a es he oo o his p oblem. A in( ) = 0, he ze o e e ence a he
ou pu is ixed by he BJT ope a ing poin Q = {IC, VCE}. When he inpu a ies, his
poin mo es along a s aigh line which depends on he design o esis o s RC and RE. To
his line we e e o as he load line.
The exp ession ep esen ing his line can be de e mined i bo h DC and AC analysis a e
o e lapped when ob aining he collec o -emi e ol age. On one hand, he con ibu ion
o inpu a ia ions o his a iable (Fig. A4b) is ob ained by he KVL,
José An onio So ia Pé ez
95
PRELAB 1. The logic in e e (The NOT ga e) using BJT.
Rep esen he wa e o ms you expec o see o B( ) and CE( )
CH1 VOLT/:
Ze o POS:
CH2 VOLT/:
Ze o POS:
TIME/:
Acob:
PRELAB 2: Elec onic swi ch wi h 7-segmen BCD Display.
D aw he in e nal connec ions o he in eg a ed ci cui 9A102G and LSD5355

José An onio So ia Pé ez
96
Speci y he meaning o he e e ence 9A102G:
Speci y common e minal a he 9A102G IC:__________________________________
Con igu a ion used in he 7-segmen BCD display:______________________________
PRELAB 3 (Opcional). SET/RESET mul i ib a o
José An onio So ia Pé ez
97
Annex 3 –Lab ac i i ies
REMARK: You MUST PRINT OUT his o m and TAKE
IT WITH YOU he day o he lab session
Escola Poli ècnica Supe io d’Enginye ia
de Vilano a i la Gel ú
EEL
Elec onic Sys ems (SIEK)
Ac i i y 4: Swi ching Elec onics: The Bipola T ansis o (BJT)
RESULTS FORM
S uden s: Da e:
LAB 1. The in e e logic (NOT Ga e) using BJT.
Rep esen he wa e o ms o B( ) and CE( ) om he oscilloscope
CH1 VOLT/:
Ze o POS:
CH2 VOLT/:
Ze o POS:
TIME/:
Acob:
José An onio So ia Pé ez
98
Speci y he alues o B and CE bo h a cu o and sa u a ion egions
VB (cu o ) : ___________ VB(sa u a ion) : ___________
VCE (cu o ) : ___________ VCE(sa u a ion) : ___________
LAB 2. Elec onic swi ch wi h 7-segmen BCD display
• Display isualiza ion wi h S = B and S1=...=S8 = ON4
• Visualiza ion wi h S = B and h ee andom examples
1) 2) 3)
Exemple
S
1
S
2
S
3
S
4
S
5
S
6
S
7
S
8
1
2
3
Table A3.1 Speci y swi ch posi ions in each example. Use ON and OFF o speci y whe he he swi ches
a e OPEN o CLOSED, espec i ely.
4 Ma k he segmen s you belie e will glow a e se ing he speci ied con igu a ion.
José An onio So ia Pé ez
99
• Speci y he wa e o m gene a o con igu a ion o obse ing he numbe “8”
(decimal poin included) wi h a blinking pa e n o ONE SECOND.
- SORTIDA: TTL 50Ω.
- FUNCIÓ: De ec e SQUARE SINUS TRIANGULAR
- OFFSET: De ec e Valo : _____________
- AMPLITUD: De ec e Valo : _____________
- FREQÜÈNCIA: ________________
LAB 3 (Op ional). SET/RESET mul i ib a o
Explain he beha io obse ed in he SET/RESET mul i ib a o and speci y some use
o his ci cui in digi al elec onics:
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
José An onio So ia Pé ez
100
Lab Ac i i y 5. Analog elec onics: The Ope a ional
Ampli ie (OPAMP)
Main Goal: Knowing he ope a ion p inciple o he ope a ional ampli ie and o
unde s and i s u ili y in analog elec onic applica ions, such as audio ampli ie s and signal
syn he iza ion sys ems.
1 In oduc ion
The ope a ional ampli ie (OPAMP) is a ol age ampli ie wi h “ex emely” high gain.
Fo example, he popula 741 has a ypical gain k = 200,000, whe eas he gain o mo e
expensi e in eg a ed ci cui s wi h ad anced ea u es, such as he e e ence OP-77 is k =
12,000,000. Due o such high alues, he gain is o en exp essed in V/mV (o V/μV) and
decibels. In he la e case, he scale ans o ma ion used is
( )
10
20log
dB
kk=
. (1)
Thus, he OP-77 has a ol age gain o 12V/μV, which is also equi alen o 141.6 dBs.
Figu e 1 shows he symbol o he OPAMP and he DC powe -supply connec ion o make i
wo k ( hough mos o he imes he powe -supply is no ep esen ed in he diag am in o de
o minimize schema ic clu e ing). The inpu s, iden i ied by he “-” and “+” symbols a e
designa ed in e ing and non-in e ing, espec i ely. Thei ol ages wi h espec o g ound
a e deno ed N and P, and he ou pu ol age as O. The a owhead o m poin ing o he
igh speci ies he signal ansmission di ec ion om he inpu o he ou pu . Figu e 1b
shows he equi alen ci cui o a p ope ly powe ed OPAMP. Though he in eg a ed ci cui
i sel does no ha e g ound pin, he g ound symbol ep esen s he common poin o he
symme ic powe supply o Fig. 1a. The model includes a ol age sou ce con olled by D,
o gain ac o k, he di e en ial inpu esis ance d and he ou pu esis ance o,
espec i ely.
Figu e 2 shows he inpu -ou pu ans e cha ac e is ics ( O- D) o his componen . Taking
in o accoun ha D = P – N co esponds o he di e en ial inpu ol age, his elec onic
de ice is ma hema ically modelled as
, o
, o
, o
OH
OH D
OL OH
OD D
OL
OL D
V
V
k
VV
k
kk
V
V
k
>



= ≤≤


<


. (2)

José An onio So ia Pé ez
101
(a) (b)
Figu e 1. The OPAMP: a) Symbol and powe connec ion; b) In e nal ma hema ical model. This in eg a ed
ci cui ope a es as a ol age ampli ie . The alues in ed indica e componen pin o he e e ence LM741,
which is mos used in 8-pin in eg a ed ci cui s.
Figu e 2. The OPAMP ans e cha ac e is ics O – D. The ho izon al axis has been ex ended (μV scale) in
o de o show he linea egion in mo e de ail.
The supply ol ages se he uppe and lowe limi s, and he ou pu swing o he ampli ie
VOL < O < VOH: VOH = (7) - VD op-ou i VOL = (4) + VD op-ou ; wi h (7) being he posi i e
supply and (4) he nega i e one. The ol age d op in o ma ion can be ob ained om he
manu ac u e ’s da ashee , and o he 741 his alue is abou VD op-ou = 2V.
Since he 741 is powe ed wi h (7) = - (4) = VCC = 15V and he ou pu ange is Δ O = ±13V,
he inpu ol age is bound o be e y small (Δ D = Δ O /k = ±65μV). Fo Fo ins ance, o
sus ain O = 6V and unloaded 741 equi es D = 6/200,000 = 30μV.
By connec ing ex e nal componen s a ound an OPAMP, we ob ain wha we shall
hence o h e e o as an OPAMP ci cui . Unde s anding he di e ence be ween an
OPAMP ci cui and he OPAMP i sel con aining all he ci cui y o de eloping i s
unc ion is c ucial. One example is he nonin e ing ampli ie .
José An onio So ia Pé ez
102
Task PRELAB0. Iden i y he new componen s you a e going o use in his lab
ac i i y: he powe ansis o s and he OPAMP.
• Sea ch he impo an in o ma ion ega ding he LM741 (o UA741) in eg a ed
ci cui , he powe BJTs: he BD243 and BD244; Find he manu ac u e ’s da ashee
o each de ice and ep esen hei con ou package in he box p o ided. Indica e pin
name and dis ibu ion.
• Read he elec ical cha ac e is ics om he OPAMP and speci y open-loop ol age
gain (k) d op-ou and maximum powe supply.
2. The nonin e ing ampli ie
The ci cui o Fig. 3a consis s o an OPAMP and wo ex e nal esis o s: R1 and R2. To
unde s and i s unc ion, inding he ela ion be ween OUT and IN is necessa y. To his end,
he ci cui is ed awn as in Fig. 1b, whe e he OPAMP has been eplaced by i s equi alen
model (Fig. 1a), he in e nal esis o s ha e been emo ed ( D →∞ and o→0) and he
esis i e ne wo k has been ea anged s a egically o emphasize i s ole in he ci cui (Fig.
3b).
OUT can be ound by means o (2) bu exp essions o P and N mus be ob ained
p e iously. By inspec ion, i holds ha
P IN
=
. (3)
On he o he hand, using he ol age di ide a he ou pu yields
1
12
N OUT
R
RR
=+
. (3)
In ac , he ol age N ep esen s he ac ion (o “sample”) o OUT ha is being ed back o
he in e ing inpu in o de o be compa ed wi h he sys em inpu . So he sys em e o ,
cha ac e ized by ε is
1
12
D P N IN OUT
R
RR
ε
==−= −+
. (4)
Using he ela ion (2), OUT = k D allows he ou pu o be exp essed as,
1
12
O IN OUT
R
k
RR

= −

+

. (5)
Collec ing e ms and sol ing he a io OUT / IN leads o,
José An onio So ia Pé ez
103
(a) (b)
Figu e 3. The nonin e ing ol age ampli ie . a) Schema ics; b) Block diag am o he nonin e ing
con igu a ion aimed a co ec ing he e o signal D = IN – N so he he inpu can ack he sample P =
OUTR1/(R1+R2).
1
12
'11
OUT
IN
Ak
kR
A
kRR
β
= = =
+++
(6)
Whe e we shall designa e k = A and β = R1 / (R1 + R2). This esul e eals ha he ci cui o
Fig. 3 consis ing o an OPAMP and a esis o pai is i sel ano he ol age ampli ie wi h
di e en gain. This is no su p ising, as he wo ampli ie s, while sha ing he same ou pu
OUT, ha e di e en inpu s, namely D in he case o he OPAMP and IN o he ci cui . To
unde s and his di e ence, k is e e ed o as he open-loop gain, and k’ as he closed-loop
gain.
• The ideal OPAMP
Conside ing he simplici y o he analysis co esponding o he he noni e ing
con igu a ion, and i s ideal closed-loop esul s, we wonde whe he he e is no a simple
echnique o de i e simila esul s in o he mo e complex OPAMP ci cui s, bypassing mos
o he edious algeb a.
Such a echnique exis s and is based on he ac ha when he OPAMP is ope a ed wi h
nega i e eedback, in he limi k →∞ i s inpu ol age app oaches ze o ( D = OUT / ∞ = 0).
As such, since D = P – N in he limi i holds ha ,
lim
NP
k
→∞
=
. (7)
This p ope y, e e ed o as he inpu cons ain makes he inpu e minals seem as i hey
we e sho ed oge he , hough hey a e no . Addi ionally, an ideal OPAMP d aws no
cu en a i s inpu e minals “+” “- since i s di e en ial inpu esis ance is also e y la ge.
In o he wo ds o ol age pu poses he inpu po seems o be sho ed, bu o cu en
pu poses i seems o be open. Hence he popula designa ion “ i ual sho ”.
José An onio So ia Pé ez
104
De ini ion 1: When ope a ed wi h nega i e eedback, he ideal ope a ional
ampli ie will ou pu wha e e ol age and elec ic cu en { OUT ,iOUT} i
akes o d i e D = 0 (o equi alen ly o o ce N o ack P) bu wi hou
d awing any cu en a ei he inpu e minal (iN = iP = 0).
F om Fig. 1b i can be seen ha is he ol age N which acks P and no he o he way
ound. O he wise, he OPAMP would be unable o con ol he sys em and (7) will ne e
hold. Thus, he OPAMP con ols N ia he ex e nal eedback ne wo k and he ou pu is
always wi hin he linea egión o Fig. 2, so ideally he ol age gain o he ci cui is
'2
1
1
lim 1
1
OUT ideal A
IN
R
A
k
AR
ββ
→∞
= = = +
+�
(8)
To unde s and be e he unc ionali y o he OPAMP, conside he elec ic diag am o Fig.
4, whe e, by inspec ion, we ha e P = N = IN( ). Since he ope a ional d i es OUT o
wha e e N = P i akes o cause iN = iP = 0, i holds ha iR1 = iR2,
() ( ) ( )
2
0
1
IN IN OUT
RR
−−
=
. (9)
Equa ing (9) in o de op ind he a io OUT( )/ IN( ) leads o he gain ac o ,
2
1
1
OUT
IN
R
R
= +
(10)
which is equi alen o ha o (8). In gene al, when ope a ed wi h nega i e eedback he
OPAMP ob ains he ou pu ac ion ough he pa h connec ed om he ou pu o N ( om
OUT o N, and om N o g ound). On he o he , wi h posi i e eedback (pa h owa ds P
ins ead o N), o no eedback a all, he OPAMP ac as a ol age compa a o : posi i e
sa u a ion (VOH when P > N) o nega i e sa u a ion (VOL when P < N; ).
3. Cu en d i e
Ob iously, he e a e a wide ange o applica ions wi h h OPAMP using nega i e eedback.
The idea ha he ou pu alue can be se ega dless o he load connec ed o i makes he
OPAMP a good candida e o de eloping complex elec onic sys ems wi h mul i-s age
connec ion (one s age connec ed a e he o he ). In Annex 1, he eade can ind a
summa y o applica ions using a single o se e al OPAMPS.
In p ac ice, howe e , he de ini ion o he ideal OPAMP is only alid wi hin he limi a ions
speci ied by he manu ac u e and, consequen ly, hey may be aken in o accoun in design
pu poses. Fo ins ance, one may be emp ed o connec a 8Ω-speake a he ou pu , and use
he nonin e ing con igu a ion as an audio ampli ie . Howe e , i VOUT = 10V he OPAMP
mus be able o d aw 1.25A, a oo much in ela ion o he maximum 10mA o he 741.
José An onio So ia Pé ez
111
(a) (b) (c)
Figu e 10. The h ee mul i ib a o ypes and hei ope a ion p inciple: a) F ee- unning; b)One-sho c) Two-
sho .
• F ee- unning mul i ib a o wi h OPAMP
In he ee- unning mul i ib a o wi h OPAMP o Fig. 11a, he capaci o C and he esis o
R in he nega i e eedback, and he esis o s R1 and R2 (posi i e eedback) o m an
in e ing T igge Schmi .
When (7) = - (4) = VCC = 15V and assuming symme ic ou pu sa u a ion, VSAT = +13V and
–VSAT = -13V since he posi i e eedback is p edominan in his ci cui 7, he h esholds a
P will also be symme ic wi h ±VT = ± VSATR1/( R1+ R2) and he signal o he in e ing
inpu , while he in e ing inpu N he ol age is de e mined by he RC ne wo k.
A powe u n-on ( = 0), OUT will swing ei he o +VSAT o –VSAT. Assume iy swings o
+VSAT, so ha P = +VT. This will cause he esis o R o cha ge C owa ds +VSAT, leading o
an exponen ial ise in N wi h ime cons an τ = RC.
As son as N ca ches up wi h P = +VT < N a = 1, he ou pu snaps o –VSAT. This will no
only snap P = -VT bu i will e e se he sing o he capaci ance cu en . As such, o > 1
he capaci o ol age will decay exponen ially owa ds –VSAT un il i caches up wi h P = -
VT > N a = 2. A his poin , he ou pu will snap again o +VSAT hus epea ing he cycle.
I is e iden ha once powe ed, he ci cui has he abili y o s a and sus ain oscilla ions:
wi h O snapping back and o h be ween +VSAT and -VSAT; and N slewing exponen ially
om +VT o -VT and ice e sa; so he wa e o m signal becomes squa e and pe iodic (Fig.
11b). Thus, i is in e es ing knowing he oscilla ion equency 0 which can be ound om
he pe iod T as T = 1/ 0.
7 One may hink ha his ci cui uses nega i e eedback, because o he RC ne wo k, and ha he concep o
ideal OPAMP can be he e o e applied. Howe e , when ano he b anch is p esen in he posi i e pa h, and in
he absence o ex e nal inpu sou ces (as i is he case o his cexampl), he posi i e eedback p e ails o e
he nega i e eedback and will o ce he OPAMP o ope a e in sa u a ion mode, wo king as a ol age
compa a o .

José An onio So ia Pé ez
112
(a) (b)
Figu e 11. F ee- unning mul i ib a o using OPAMP. a) Elec ic diag am. b) Time signals a he ou pu OUT
and he in e ing inpu N ( ed ace).
Thanks o he symme y o he sa u a ion le els, he ou pu O has a du y-cycle, D =TH/T o
50% (=0.5), so inding he in e al ange ∆ = 2 – 1 = T/2 is necessa y. Using he s anda d
exp ession co esponding o he capaci o cha ge/discha ge8 in his ange,
( ) ( ) ( ) ( ) ( )
22 1
C N C CC
e
∆
−

= = ∞+ − ∞

(18)
whe e C(∞) = -VSAT; i holds ha o ∆ = T/2, N( 1) = +VT, N( 2) = -VT; and τ = RC we
ob ain,
ln
2
SAT T
SAT T
VV
TRC VV

+
=
−

. (19)
Subs i u ing VT = VSATR1/( R1+ R2) and equa ing 0 = 1/T i leads o,
0
1
2
11
2 ln 1 2
TR
RC R
= = 
+


, (20)
I can be obse ed ha 0 depends only on he ex e nal componen s. In pa icula , i is
una ec ed by VSAT, which is an ill-de ined pa ame e which a ies om one OPAMP o
ano he : any a ia ion in VSAT will cause VT o a y in p opo ion, hus ensu ing he same
ansi ion ime and, hence, he same oscilla ion equency. On he o he hand, he
maximum ope a ing equency is de e mined by he OPAMP slew- a e o exp ession (15).
8 See he documen o PRT2, whe e he s ep esponse o he RC ne wo k was conside ed, in o de o
unde s and exp ession (11) in he in e al ∆ = 2 – 1
José An onio So ia Pé ez
113
Task PRELAB2 (Op ional). In he B ead-boa d empla e ep esen he
componen dis ibu ion and wi e connec ions co esponding o he OPAMP-based ee-
unning mul i ib a o o Fig. 12 o be implemen ed in he lab.
Task LAB2 (Op ional). Moun he ci cui and check he pe o mance o he
OPAMP-based ee- unning mul i ib a o (Fig. 12).
• 1) Moun he ci cui . Connec he DC powe -supply and oscilloscope p obes as
indica ed in Fig. 12. Tu n he powe on and ep esen he capaci o ol age C in
CH1; and he ou pu OUT in CH2. 2) Ob ain he h eshold alues: ±VSAT, ±VT; and
measu e he oscilla ion equency 0. 3) Compa e he expe imen al esul s wi h he
heo e ical alues ob ained by means o (16).
Task PRELAB3 (Op ional). How would you connec he wo ci cui s o his
ac i i y (Fig’s. 9 and 12, espec i ely) in o de o syn hesize and o hea a low sound o
500Hz h ough he speake ? Rep esen he ci cui in he box p o ided and speci y
componen alues.
Task Lab3 (Op ional). Moun he ci cui om PRELAB3 and check i s elec ic
ope a ion.
• 1) Moun he ci cui . 2) Using he oscilloscope and/o he mul ime e ep esen he
wa e o ms and ob ain he da a you belie e i is impo an in o de o unde s and
ci cui beha io .
• Commen esul s ega ding he sound syn hesize .
Figu e 12. Moun ing diag am co esponding o he ee- unning mul i ib a o in he lab.
José An onio So ia Pé ez
114
Annex 1 – OPAMP basic con igu a ions (wi h nega i e eedback)
The OPAMP ci cui s o his sec ion a e conside ed basic. Ve y o en, hese ci cui s a e
used as s ages o e y complex analog elec onic sys ems. In he e, all con igu a ions use
nega i e eedback ope a ion. Only he connec ion diag am (wi hou DC supply) and he
ans e unc ion o each ci cui is speci ied in Table 1. The analy ical p ocess necessa y o
ob ain hese unc ions a e le o he eade as an exe cise.
Ci cui name
Connec ion diag am
Func ion
Vol age
Followe
1
O
I
=
OI
=
Nonin e ing
ampli ie
2
1
1
O
I
R
R
= +
In e ing
Ampli ie
2
1
O
IN
R
R
= −
In e ing adde
Ampli ie
1
Ni
OF
ii
R
R
=
= − ∑
José An onio So ia Pé ez
115
Di e en ial
Ampli ie
24
2
134
21
1
1
O
RR
RRR
R
R

=+−

+

−
* I R1 = R2 = R3 = R4
21O
= −
I/V Con e e
(T ne wo k)
OI
kRi= −
whe e
22
1
1RR
kRR
=++
Howland’s
cu en sou ce
41 23
123
1
O
I
RR RR
iRRR
R

−
= +


+
* i R4/R3 = R2/R1
1
I
O
iR
=
De i a o
( ) ( )
I
O
d
RC d
= −
( )
()
O
I
s RCs
s= −
In eg a o
( ) ( )
( )
0
0
1
OI
c
d
RC
=−+
+
∫
( )
( )
( )
0
1
Oc
I
s
s RCs s
=−+
* Habi ually 0 = 0
José An onio So ia Pé ez
116
Ins umen a ion
Ampli ie
(2 OPAMPS)
( )
21Od
A = −
22
11
12
d
RR
ARR

=++


Ins umen a ion
Ampli ie
(3 OPAMPS)
( )
21
Od
A
= −
32
1
12
d
G
RR
ARR

= +


Nega i e
Impedance
Con e e
(NIC)
1
2
EQ
R
RR
R
= −
* I R1 = R2
EQ
RR= −
Taula 1. Di e ses con igu acions bàsiques amb un o a is ope acionals, i la se a unció de ans e ència

José An onio So ia Pé ez
117
Annex 2 – Resul s o m PRELAB
REMARK: You MUST hese ac i i ies BEFORE THE LAB
SESSION CORRESPONDING TO PRT5
Escola Poli ècnica Supe io d’Enginye ia
de Vilano a i la Gel ú
EEL
Elec onic Sys ems (SIEK)
Ac i i y 5: Analog Elec onics: The ope a ional ampli ie (OPAMP)
PRELAB
S uden s: Da e:
PRELAB 0: D aw he con ou package packages co esponding o he LM741; he
BD243 and BD244.
Pa àme e
LM741
Obse acions: Comen manu ac u e obse a ions
k
∆
O
V
CC
SR
Taula A2.1 Ano i la in o mació ela i a al BC547C que ha oba al ull de ca ac e ís iques
José An onio So ia Pé ez
118
PRELAB1. Audio ampli ie wi h OPAMP
Rep esen e he con ou package o he po en iome e and speci y pin unc ion
Speci y connec ion and con igu a ion o he DC-powe supply so as o ob ain a symme ic
powe DC- ol age o ±15V
Rep esen he componen connec ions o he audio ampli ie
José An onio So ia Pé ez
119
PRELAB2(Op ional): OPAMP ee- unning mul i ib a o
Rep esen he componen connec ions o he OPAMP-based ee- unning
mul i ib a o
PRELAB3 (Op ional): Sound syn hesize
Rep esen he elec ic diag am co esponding o he sound syn hesize
José An onio So ia Pé ez
120
Annex 3 – Lab ac i i ies
REMARK: You MUST PRINT OUT and TAKE IT WITH
YOU he day o he lab session
Escola Poli ècnica Supe io d’Enginye ia
de Vilano a i la Gel ú
EEL
Elec onic Sys ems (SIEK)
Ac i i y 5: Analog Elec onics: The ope a ional ampli ie (OPAMP)
RESULTS FORM
S uden s: Da e:
LAB1. Audio ampli ie .
Rep esen he wa e o ms IN( ) and OUT( ) (1V-peak IN)
CH1 VOLT/:
Ze o POS:
CH2 VOLT/:
Ze o POS:
TIME/:
Acob: