MODULE 3

FILTERS & TIMERS

Topics Covered
MODULE
3

Active Filters
-

Analysis
of first orde r LPF & HPF
filter

Working
of Band Pass & Band stop
Filters

FILTERS
A
filter
isa
frequency selective circuit
that, pas ses
a s pecified b and of frequencies and blocks or
attenuates signa lsof frequencies ou tside this
band
.
Filter
may be classified
in
a n umber of ways .
Analog
or digital
Pass ive or active
Audio or radio
frequency

FILT ERS
Analog
filters
ar ede signe d topr oces s
analo g
signa ls while
Digital
filters
pr oces s ana log signa ls usin g digital techn ique .
Dep en ding
on the
type of elements
use d inthe ir
con side ra tion, filter smay be classifie d as
pa ssiveor active
.
Ele ments
us e d in
Pass ive
filters
ar e
resistors, cap acitors and
inductors
.
Active
filters
, on theoth er hand , employ
transistors or
OPAMPs
,in add ition tothe re sistor and capacitor s.
Dep en ding up on the e leme ntsthe fre que ncy r ange is
decided.
RCfilters
ar e us e d fo r aud io o r
low frequency operation
.
LC
filters
ar e e mployed at R Fo r
high frequencies
.

ACTIVE FILTERS
The most commonlyusedfilters are
:
Lowpassfilters
High passfilter
Bandpassfilter
Bandreje ctfilter.
All pass
filter

FILTERS
The fre que ncy r es po nse char acter istics of the
Low
Pass &
High Pass
filter.
The
idealrespon seis shownby dashedline. Whilethe solidlines
indicatesthepractical filter respon se

FILTERS

A
low passfilter has a constantgain from0Hz toahigh
cutoff freque ncy
f
H
.

Therefore
, the bandwidth is
f
H
.
After
thatthe gain
dec rea ses asfreque ncy increa ses. The freque ncy range0
to
f
H
Hz is calle dpass band a nd beyond
f
H
is calle dstop
band.
Simila rly
,a h igh p ass f ilter ha s a constantgai n fromver y
high freque ncy toalow cutoff freque ncy
f
L
.
below
f
L
the
gain dec rea sesas freque ncy dec rea ses.

The
freque ncy range
f
L
o o˚› v
below
f
L
is cal le dstop ba nd.

FILTERS
The
frequen cyrespon secharacteristics of
theBand Pass&Band Reject
filter.
The
ideal response is shown by dashed line. W hile the solid lines indicates the
practical filter response

FILTERS
The
frequency response characteristics of the
All pass
filter.
The
ideal response is shown by dashed line. W hile the solid lines indicates the
practical filter response
FirstOrderLowPassFilter
:
Itshows a firstorder low passButter
-
worthfilter that uses
a
RC
networkfor filter ing ,
opamp
is used in non
-
inver ting
configuration, R1
and
Rf
decide s the gainof thefilter.

FrequencyResponseCur ve

FirstOrderLowPassFilter
:

Impedanc eacrosscapac itorCis given as

C=
-
jX
c
ÁZ˚„
-
1

Wh ere
X
c
=

Û
Ê
„o
Therefore
-
jX
c
=

Ú
’

Û
Ê
„o

Ac cording
tovoltage divider rule , the voltageat the non
-
invertingterminalis:

V
1
=
?
’

~
?
’

xV
in
eq.1

FirstOrderLowPassFilter
:

The o utput is given a s

V
o
=A
f
V
1

Whe re
A
f
=
s

E
~
„
~

Therefore
V
o
=
(
s

E
~
„
~

Ú
)V
1

Substitute the value of V1

V
o
=(
s

E
~
„
~
Ú
)(

]v
’
Û
Ê
„ ~o
>
5
)

]v
=

(
’
Û
Ê
„~ o
>
5

]v
=

(
5
>
Ý
:

W
Ñ
Ñ
¹
;

Thu s the low pas sfilter has a ne arly constant gain

A
f
from0 Hz to high cut off
freq ue ncy
f
H
.
At
f
H
the gain is 0.707
Af
and after
f
H
it decreas es at a constant rate
with an increas es in frequ ency.
f
H
is called cutoff
freq ue ncy.

FirstOrderLowPassFilter:

Thus the low pass filterhas a nearly constant gain

A
f
from 0 Hz to high cut off frequency
f
H
.

At
f
H
the gain is 0.707
A
f
and after
f
H
it decreases at
a constant rate with an increases in frequency.

f
H
is called cutoff frequency because the gainof
filter atthis frequency is reduced by
3dB (=20log
0.707)
from 0Hz
.

Cut off frequency

f
H
is also called
-
3dB frequency,
break frequency or corner frequency.

FilterDesigns

FilterDesign
Example1

FrequencyScaling:

Once a filter is designed there may sometimes be a

need to c hange its
cutofff
frequency
f
H
to a new
cutoff frequency.

The procedure to convert an original

cutoff
frequency
f
H
to a new c utoff frequency
f
H
is called
frequency scaling.

To c hange a high cutoff frequency , multiply R or C

by the ratio of the original cutoff frequency to the
new cutoff frequency

FrequencyScaling:

Tochange the cutoff freq ue ncy from1 KH z to 1.6 KHz forthe

previousexample

Multiplythe resistor15.9K
Q
by the ratio
1NECEJ=H
%QPKBB
BNAMQAJ?U
JAS
?QPKBB
BNAMQAJ?U

L
s-* V
s
ä
x-*V

L
r
ä
xtw
Therefore new resistorR= (15.9K
Q
)( 0.625)=9.94K
Q
Since9.94k
Q
isnot standard10K
Q
potentiometercanbe
used & a djusted
New cutoff freque ncy
f
H
=
5
6
Ê
:
4
ä
45Á¿
;
:
=
ä
=8Þ
Q
;
=1. 6KHz

FirstOrderHighPassButterworthfilter
:

TheHigh Passfilterhas
a constant gain from ver yhigh
frequencyto a low cutofffrequency
fL
,
below
fL
thegain
decreasesas frequencydecreases.

Thefrequencyrange
fL
oovvˆ
below
fL
iscalled stopband
.

The
High Passfilteris formedbyinterchangingR andC in
a low passfilter.

Thelower cutoff frequencyis

f
L
.
Thisis thefrequencyat
whichthemagnitudeof thegain is 0. 707timesits pass
bandvalue.
All
frequencieshigherthan
f
L
are passband
frequencieswith th ehighestfrequencydeterminedby
theclosedloop band widthof theOPAM P.

FirstOrderHighPassButterworthfilter:

FirstOrder
HighPass
Filter
:

Impedanc eacrosscapac itorCis given as

C=
-
jX
c
ÁZ˚„
-
1

Wh ere
X
c
=
Ú

Û
Ê
„o

Therefore
-
jX
c
=

Ú
’

Û
Ê
„o

Ac cording
tovoltage divide r r ule , th e voltage at th e non
-
invertingterminalis:

V
1
=

~
?
’

xV
in
eq.1

V
1
=

~
>
Ú

’
Û
Ê
„o
xV
in
=
Ý6
Ê
ÙË ¼
Ý6
Ê
ÙË ¼
>
5
T8
EJ

Band
Pass
Filter
:

The band pass filter passes aband offreque ncie s betwee n a

lower cutoff freque ncy,
f
L
, and anupper cutoff freque ncy,
f
H
.

Where
f
H
>
f
L

If
the twofilters(high and low)band pass are connectedin
serie s it
becomes
band
pass filter
whose gain freque ncy
response is
shown

Frequenc ies
below
f
L
and above
f
H
arein the stop
band or are
said tobe attenuated.

Band
Pass
Filter
:

There are basically twotype sof

bandpass
filters
viz

Wide
bandpass
and

N
arrow
bandpass
filters.

A
bandpass
filter is defined as awide
bandpass
if itsfigure of
mer itor qualityfactor Qisless than
10.

If
the
bandpass
filters
have a
Q> 10
theyare
calle dthe nar row
bandpass
filters.

Thus
Qis a measureof sele ctivity,mea ningthe higherthe
value of
Q the mo resele ctive
is the filter,or the
narroweris
the bandwidth (BW).
The relationship betwee nQ , 3
-
db
bandwidth, and the
ce ntre
freque ncy fcis given by an
equation
Q=
Ù
Ö
»Ð

L
Ù
Ö
Ù
Á
?
ÙÅ

And
B
?

B
*
B
.

Band
Pass
Filter
:

Freque ncy Response of Band PassFilter

The upper and lower cut

-
off freque ncy points for a band pass
filtercan be found using the
below formula.

F
c
=
5
6
Ê
˼

WideBand
Pass
Filter
:

Awide band pass filter canbe formed bysimplycascadinghigh

pass and low pass
section.

To obtain a
±
20
db
/decade band pass filter,a firstorder high
pass filter and a first
order low
pass sec tionsare
cascade d,.

In other words, the order of the BandPass Filter Circuit

Diagramdepe nds uponthe order of theHigh pass and Low
passsections.

NarrowBand
Pass
Filter
:

Anarrow
bandpass
filter
hasa multiple fee dbac k.

This
filter employsonly one op
-
amp, as shown in the figure.
1.
Ithas twofee dbackpaths,and this isthereason thatitis
calle da multiple
-
fee dbac kfilter
.
2.
The
op
-
amp is used in the inver tingmode.

If
the
bandpass
filters
have a
Q> 10
theyare
calle dthe nar row
bandpass
filters.

BandRejectFilter
:

BandStopFilter
stops or attenuatesa
rangeof freque ncie s
betwee n twocut
-
off freque ncie s
f
L
and
f
H
while
pass
allthe
freque ncie s below
f
L
and above
f
H
.

Thus
range of freque ncie s betwee n
f
L
and
f
H
constitutesa stop
band in whichattenuationtothe freque ncie s is infinite ide ally.
The freque ncie s below
f
L
and above
f
H
constitutetwoseparate
pass bandsin whichattenuationtothefreque ncie s iszero
idea lly
.

mayalsobe c lassifiedas (i) wide

-
band and (ii) narrowband
rej ec tfilters.

WideBandRejectFilter
:

Awide band
-
stop filter
uses
a low
-
pass filter,a high
-
pass filter
and a summingamplifie r
as
shown infigure.

For
aproper band rej ec tresponse, the
lowcut
-
off frequency
f
L
of high
-
pass filter m ust be largerthan the high cut
-
off
frequency
f
H
ofthe low
-
pass filter.

In
addition, the
passband
gain
of both the high
-
pass and low
-
passsectionsmustbe
equal
.

NarrowBandRejectFilter
:

This is alsocalled anotch filter

. Itis commonlyused for
attenuationof a single freque ncy such as 60Hz power line
frequenc y hum.

The
mostwidely used notchfilter is the twin
-
T
network.

This isa passive filter composed oftwoT

-
shaped networks.
One T
-
network ismade up of tworesistorsand a capac itor,
whilethe other ismade oftwocapacitorsand aresistor.

NarrowBandRejectFilter
:

One drawbac k
of
above notchfilter (pas
sive twin
-
Tnetwork)is
thatit has relatively low figure of
Qua lityfactor
Q
.

However, Qof the networkcanbe inc rea sed significantlyif itis

used with thevoltage
follower.
He re the outputof the volt
age
follower is supplied bac ktothejunc tionofR/2 and 2C.

The
voltage gainis equal to1atlow and high freque ncie s.

NarrowBandRejectFilter
:

The
voltage gainis equal to1atlow and high freque ncie s.

In
betwee n, there isa freque ncy fcat whichvoltage gaindrops
tozero.Thus such a filter notche sout,or blocksfreque ncie s
nea r fc.

The
freque ncy
at
which maximum
attenuation
occursiscalle d
the
notch
-
out
freque ncy given by
fn
= Fc=
1/4
‰
RC
Notchfiltersare mostcommonly
used in com munications
and
biom edicalinstrume nts for e liminating the undesired
frequencies.

AllPassFilter
:

An all
-
pass filter
is thatwhichpasses allfreque ncy components
ofthe input signalwithout
atten uation

It
but provides predic table phase shifts for different
freque ncie s of the inputsignals.

The
all
-
pass filtersare alsocalle d delayequa lizersor phase
correc tors.

An
all
-
pass filter withthe output lag gingbehind theinput is
as
shown

THANK YOU

All
PassFil ter
:
The outputvoltage
V
out
ofthe filter circuitcan be obtainedby
usingthe super position
theorem
StepI

Considerinput at Inver tingter minalonly

o
=
-
Ë
Ù
Ë
5
:
8EJ

Now
R
f
=R
1
Hence

o
=
-
8EJ

All
PassFil ter
:

Step2

Considerinputat
Non Inverting
terminalonly
o
= [1+
Ë
Ù
Ë
5
?
:
8
a

Now
R
f
=
R
1

o
=
[1+
Ë
Ë
?
T

8
in
ÁZ˚„ O
-
1

Wh ere
X
c
=
5
6
Ù¼

Therefore

o
=
?
6Ý ÑÖ
Ë
?
Ý Ñ¼
xVin

All
PassFilter
:

Step 3:

Bysu pe rposition The orem

V
o
=

o
+

V
o
=
-
Vin+
?

Û
’

~
?
’

xV
in

V
o
=[
-
1+
?
6
Ý

Ë
?
Ý

]V
in

Bu t reactance of capa citor is given as

X
c
=

Û
Ê
„o

Hen ce V
o
=[
-
1+
?
6Ý
-
.

Ñ´
Ë
?
Ý
-
.

Ñ´
]V
in
V
o
=[

F
s
+
?
6Ý
?
Ý
>
6

Ù¼Ë
?
8 EJ
V
o
=[
i>
6

Ù˼
?
6Ý

F
i
=
6

Ù˼
]
8 EJ
V
o
=
[

F
i>
6

Ù˼

F
i=
6

Ù˼
]
Vin

All
PassFilter
:
D ivideNumerato r&D eno minato rby
t
j
=
[
í
>
.

Ñô
7
Õ
í
=
.

Ñô
7
Õ
]
Vin
Therefore
V
o
=
[
í
>
Ý6

Ù˼
í
=
Ý6

Ù˼
]
Vin as j=
-
1/ j

Hence the voltage gain is given by

]v

L
[
í
>
Ý6

Ù˼
í=
Ý6

Ù˼
]

The ma gnitud eof v

]v

L
¾
í
=
6

Ù˼
6
¾
í=
6

Ù˼
6
=1
From
eq uations given ab ove it is obvious
that
The
amp litude of
V
ou t
/
V
in
is un ity,
that
is
|
v
ou t
| = |v
in
|throug hout the us efu l freq ue ncy
range

All
PassFilter
:
The pha se shift between Vo an dVin is given by
Ø=
-
2tan
-
1
2
‰
fRC

Hence the phase

shift b etween the inputand
out pu t voltages is a
functionof frequency
.

As p hase shift obtained is negative, the output lags from input

By interchanging t he p ositions of R andC in t he

circuit, the
outpu tcan
be made
positive or leading
the input
.
These filters aremost commonly used in communications.For instance,
whensignals are t ransmittedover transmission lines (such astelephone
wires) from one point to
another
point, theyundergo changein phase.
To compensate for such pha sechanges, all
-
pass filters are employed.

TIMER

IC555timer is a one of the mostwidely used ICin ele ctronics

for
itsrobust and stable propertie s.

It
works as square
-
wave form gene ratorwithduty cycle var ying
from50% to100%,Oscillatorand can alsoprovide time
de lay
in
circuits
.
Pin
Diagram of 555 IC

TIMER
I nte rnal
Ci rcuit Di agram of 555 I C

InternalCircuitDiagramof555IC
Basics Conce pts:

Comparator:The Comparatorare the basic ele ctronic

component whichcomparesthe twoinput voltages i.e.
betwee n theinver ting (
-
)and the non
-
inver ting (+) input and if
the non
-
inver ting input is morethan the inver tinginput then
the output of the comparatoris high. Alsothe input resistanc e
ofan ideal comparatoris infinite.
Voltage
Divider: As we knowthat theinput resistanc eofthe
comparatorsis infinitehenc e the input voltageis divided
equa llybetwee n the three resistors.The value be ing V
in
/3
acrosseac hresistor.

Flip/Flop
:Flip/Flop isamem or yele mentof Digital
-
ele ctronics.

ı˚„ÁÁ
o}Á]PZX

InternalCircuitDiagramof555IC

Func ti on
of
dif fe re nt
Pins
:
-

1
.
Gro u nd
:
Th is
p in
is
u s ed
to
p ro vid e
a
z ero
vo lt a g e
ra il
to
th e
Inte gra ted
c ircu it
to
d ivi de
th e
s u p p ly
p o te n ti a l
b e twe e n
th e
th re e
r e s is to r s
s h o wn
in
th e
d ia g ra m
.

2
.
Tri g g er
:
As
we
c an
see
th at
th e
vo lt a g e
at
the
n on
-
in ve rt in g
e nd
of
th e
c o mp a rator
is
V
in
/
3
,
so
if
th e
tri gg e r
in pu t
is
u s ed
to
s et
th e
o u tp u t
of
th e
F/F
to

s tate
by
a p p l yin g
a
vo lt a g e
e qu a l
to
or
less
than
V
in
/
3
or
any
n e g ati ve
p u ls e ,
as
th e
vo lt a g e
at
th e
n on
-
in ve rt in g
end
of
th e
c o mp a ra to r
is
V
in
/
3
.

3
.
Ou tput
:
It
is
th e
o utp ut
p in
of
the
IC,
c o n ne cte d
to
th e

(Q
-
ba r)
of
th e
F/F
wit h
an
in ve rt e r
in
b e twe e n
as
show
in
th e
fi g u re
.

4
.
Res et
:
Th is
p in
is
u s ed
to
re se t
th e
o utp ut
of
the
F/F
r e g ard le ss
of
th e
in iti a l
c o n d itio n
of
th e
F/F
a nd
a lso
it
is
an
a cti ve
lo w
P in
so
it
c o n nec ted
to

state
to
a vo id
any
n o is e
in te rfe re n ce ,
un les s
a
re s et
op e ratio n
is
requ ir e d
.
So
mos t
of
th e
ti me
it
is
co n n ec ted
to
th e
Su p p ly
vo lt a g e
as
s h o wn
in
th e
fi g u re
.

5
.
Contr o l
Vo lta g e
:
As
we
can
se e
that
th e
p in
5
is
c o nn e cte d
to
the
in ve rt in g
inpu t
ha vin g
a
vo lt a g e
le ve l
of
(
2
/
3
)
V
in
.
It
is
us ed
to
o ve rr id e
th e
in ve rt in g
vo lt a g e
to
c ha n g e
th e
wid th
of
th e
o u tp u t
s ig n a l
ir r e s p e c ti ve
of
th e
RC
ti min g
n e two rk
.

6
.
Thre sh o ld
:
Th e
p in
is
c on n e cte d
to
th e
non
-
in ve rt in g
in p ut
of
th e
fi rs t
co mp a rator
.
Th e
o u tp ut
of
th e
comp a ra to r
wil l
be
h ig h
wh e n
th e
thre s h o ld
vo lt a g e
will
be
more
than
(
2
/
3
)
V
in
th u s
re s e tt in g
th e
o u tp u t
(Q)
of
th e
F/F
fr o m

to

7
.
Dis c h arg e
:
Th is
p in
is
us e d
to
d isc h arg e
th e
timing
c ap a c ito rs
(c a p ac it ors
in vo l ve d
in
th e
e xte rn a l
c ir c u it
to
mak e
th e
IC
b e h a ve
as
a
s q u are
wa ve
g e n e rator)
to
gro u nd
wh e n
th e
o u tp u t
of
Pin
3
is
s wit c h e d
to

8
.
Su pp ly
:
Th is
p in
is
u s ed
to
p rovid e
th e
IC
wit h
the
s u pp ly
vo lt a g e
fo r
th e
fu nc ti on in g
and
c a rr yin g
of
th e
d iffe re n t
o p e ra ti o n s
to
be
fu lf il le d
wit h
th e
555
ti me r
.

PINO UTDIAGRAM OF 555 TIMER IC

Three
5
kilo
ohm
internal
resistors
act
as
potential
divider,
providing
bi as
voltage
of
2
/
3
Vcc
to
upper
com parator
and
1
/
3
Vcc
to
lower
comparator
whe re
Vcc
is
the
supply
voltage
.
The se
two
voltage
levels
h elp
in
findi ng
timing
inter val
.

We
can
vary
time
inter val
by
apply ing
voltage
to
control
voltage
input
ter minal
.

In
standby
/
stable
state,
the
output

of
the
SR
control
flip
flop
is
high
.
This
makes
the
outpu t
low
because
of
power
amplifie r
which
is
basically
an
inver ter
.

A
negative
going
pulse
is
applie d
to
pin
2
..

At
the
negative
going
edge
of
the
trig ger,
as
the
trig ger
goes
below
1
/
3
vcc
,
the
output
of
lower
comparator
goes
high
and
sets
the
SR
flip
flop
.
At
that
time
the
output
of
UC
is
zero
.

When
trig ger
becomes
positive
and
goes
above
1
/
3
Vcc
output
of
LC
will
be
zero
as
well
as
UC
is
zero
.

Wh en
trig ger
goe s
above
2
/
3
Vcc
the
output
of
UC
is
high
and
it
will
reset
the
flip
flop
.
[A
1

The
re set
input
prov ide s
a
mechanism
to
reset
the
flipflop
,
which
over rid es
the
effect
of
any
change
in
output
of
LC
.
This
over r iding
reset
is
effective
when
t he
reset
input
is
less
tha n
0
.
4
V
.

Wh en
reset
is
not
used
it
is
return ed
to
Vcc
.

Trans i stor
Q
2
acts
as
a
buffer
to
is olate
the
reset
input
of
the
FF
and
transistor
Q
1
.
Q
2
is
driven
by
an
internal
reference
vo ltage
Vref
obtained
from
supply
voltage
Vcc
.

ASTABLE MULTIVIBRATOR

The
timing
resistor
is
now
split
into
two
sections
R
A
and
R
B
.

Pin
7
of
discharging
transistor
is
connected
to
the
junction
of
R
A
and
R
B
.

When
the
power
supply
is
connected
the
ex ter nal
timing
capac itor
C
cha rges
towards
Vcc
with
a
time
constant
(R
A
+
R
B
)C
.

During
this
time,
output
is
high
as
reset
R
=
0
,
set
S
=
1
and
this
combination
makes
[A
0
whi ch
holds
transistor
Q
1
in
off
state
.
Betwee n
1
/
3
V
cc
and
2
/
3
V
cc
the
LC
as
well
as
UC
is
off
and
the
output
continues
in
the
previous
state
.

After
time
T,
when
the
capacitor
vo ltage
is
just
greater
t han
2
/
3
V
cc
the
upper
comparator
trig gers
the
control
FF
so
that
[A
1
.

This
ma kes
Q
1
on
and
capacitor
C
starts
di scharging
towards
ground
through
R
B
and
transistor
Q
1
with
a
time
constant
R
B
C
.

Current
also
flows
into
transi sto r
Q
1
through
R
A
.
Resisto rs
R
A
and
R
B
must
be
large
enough
to
limit
this
current
and
prevent
dama ge
to
discharge
transistor
Q
1
.

The
min imu m
value
of
R
A
is
approxim ately
equal
to
V
cc
/
0
.
2
where
0
.
2
A
is
the
maximum
current
through
the
on
transi sto r
Q
1
.

During
the
discharge
of
the
timing
capac itor
C,
as
it
rea che s
just
less
than
V
cc
/
3
,
the
lower
comparator
is
trig gered
and
at
this
stage
S=
1
and
R=
0
,
which
turns
[A
0
.

If
[A
0
it
removes
the
discharge
path
for
capacitor
since
Q
1
is
in
open
circuit
.

The
capac itor
per iodically
cha rges
and
discharges
between
1
/
3
V
cc
and
2
/
3
V
cc

The
length
of
the
time
that
the
output
remains
high
is
the
time
for
the
capac itor
to
cha rge
from
1
/
3
V
cc
to
2
/
3
V
cc

Voltageacrosscapac itor=
V
c
=
Vcc
(1
-
e
-
t /RC
)

Let t
1
be the timetakenby the circuittocha rge from0to2/3
Vcc

Att=t
1
V
c
=( 2/3)
Vcc

2/3
Vcc
=
Vcc
(1
-
e
-
t 1/RC
)

2/3= (1
-
e
-
t 1/RC
)

e
-
t
1
/RC
= 1/3

Taking logarithm
t
t
1
/RC =
ln
(1/3)

-
t
1
=RC
ln
(1/3), t
1
= RC
ln
3= 1.09 RC(seconds)

Let t
2
bethe time takenby t hecircuit to chargefrom 0 to 2/ 3
Vcc

Att=t
2
V
c
=(1/ 3)
Vcc

1/ 3
Vcc
=
Vcc
(1
-
e
-
t
2
/RC
)

1/ 3= (1
-
e
-
t
2
/RC
)

e
-
t
2
/RC
= 2 /3

Tak inglogarithm
t
t
2
/RC =
ln
(2/ 3)

-
t
2
= RC
ln
(2/3 ), t
2
= RC
ln
(3/2 )=0.405 RC (seconds)

So t he t imeto chargefrom 1/ 3
Vcc
to 2/ 3
Vcc
is

t
HIGH
=t
1
-
t
2
= 1.09 RC
-
0.405 RC = 0. 69 RC

Here
outpu t
is
high
when
capacitor
charges
to
2
/
3
Vcc

t
HIGH
=
0
.
69
(R
A
+
R
B
)C
.

The
output
is
l ow
when
the
capacitor
discharges
from
2
/
3
Vcc
to
1
/
3
Vcc
.

t
LOW
=
0
.
69
R
B
C

Both
(R
A
and
R
B
)
are
prese nt
in
the
charging
path
but
only
R
B
is
present
in
the
discharge
path
.

Total
time
T=
t
HIGH
+
t
LOW

T=
0
.
69
(R
A
+
R
B
)C+
0
.
69
R
B
C
=
0
.
69
(R
A
+
2
R
B
)C

F=
1
/T
=
1
.
45
/
(R
A
+
2
R
B
)C

WAVEFORMSOF ASTABLE
MULTIVIBRATOR

MON OSTABLEMULTIV IBRATOR

WAVEFORMSOF MONOSTABLE
MULTIV IBRATOR

MONOSTABLE OP ERATION

In standbystateFF h olds transistor Q1 on, thu sclampingthe

external timing capacitorC to ground .

The outp utremains at ground potential,

i.e
; LOW.

As t rig ger passes through

Vcc
/3 , the FF is set
i.e
˚’
the transistor Q1 off andshort circuit across the timingcapacitorC
is released.

o}ÁP}˚ Z]P
i.e
,
Vcc
.

Voltageacross capacitorrises exponentially through Rtowards

Vcc
with a t imeconstant RC.

After t ime period T t hecapacitorvoltage is just greater tha n2/ 3

Vcc
andthe upper comparator resets the FF
ie
., R=1andS=0

u l˚’ [AíUv’]’ıP}˚’ ıZ˚„˚P]

capacitorC rapidly to ground potential

Voltageacross capacitor=
Vc
=
Vcc
(1
-
e
-
t/RC
)

Att=T
Vc
=(2/ 3)
Vcc

2/ 3
Vcc
=
Vcc
(1
-
e
-
T/RC
)

2/ 3= (1
-
e
-
T/RC
)

e
-
T/RC
= 1/ 3

Tak inglogarithm
t
T/RC =
ln
(1/ 3)
-
T = RC
ln
(1/ 3), T= RC
ln
3= 1.1RC (seconds)

PHASE LOCKED LOOP

Impo rtan t
bu il di ng
bl oc k
of
li ne ar
syste ms
.

A
ph ase
-
lo cked
loop
(PLL)
is
an
ele ctron ic
circu it
with
a
vo lt age
-
or
cu rren t
-
dri ve n
osc il la tor
th at
is
consta nt ly
ad ju sted
to
mat ch
in
ph ase
(and
thus
l o ck
on)
th e
freq ue nc y
of
an
in pu t
sig na l
.

A
phase
-
lo cked
lo op
(PLL)
is
a
co nt rol
syste m
th at
ge ne rate s
an
ou tp ut
sig na l
whose
ph ase
is
relat ed
to
th e
ph ase
of
an
in pu t
sig na l
.
Phase
-
lo ck ed
loops
h ave
wide
appl icati on s
in
radio,
tel eco mmu ni cat io ns,
compu ters
an d
ot he r
ele ctron ic
ap pl ic at io ns
.

Th ey
can
be
use d
to
de mo du la te
a
sign al,
reco ve r
a
sign al
fro m
a
no isy
co mmun ic at io n
ch anne l,
gene rate
a
sta ble
freq ue nc y
at
mul ti pl es
of
an
in put
freq uency
(frequ en cy
synt he sis),
or
distrib ut e
p rec is el y
ti med
clo ck
pu lse s
in
di gi ta l
lo gi c
ci rcu it s
suc h
as
mic rop roc esso rs
.

BASIC BLOCK OF PLL

Basic b locks of PLL includes

Phase detector/ comparator

A low pass filter

Anerror am plifier

A voltage controlled oscillator

VCO
is
a
free
r unning
mult ivibrato r
and
operate s
at
a
set
frequency
fo
called
free
running
frequency
.

Determined
by
external
timing
capacitor
and
an
external
resistor
.

Can
be
shifted
to
either
side
by
applying
dc
control
voltage
Vc
to
terminal
of
IC
.

The
frequ enc y
deviation
is
directly
prop orti onal
to
dc
control
vo ltage
and
the
name
voltage
controlled
oscillator
.

If
an
input
signal
Vs
of
f requency
fs
is
applied
to
PLL
the
phase
detector
compares
phase
and
frequency
of
incoming
signal
to
that
of
outpu t
of
Vo
of
VCO
.
If
two
signals
differs
in
frequency
or
in
ph ase,
an
error
voltage
Ve
is
generated
.

The
pha se
detector
is
a
multipli er
and
produces
sum
(
fs
+
fo
)
and
difference
(
fs
-
fo
)
components
at
the
outpu t
.

The
high
frequency
component
(
fs
+
fo
)
is
removed
by
low
pass
filte r
and
difference
fre quency
component
is
amplified
and
applied
as
control
vo ltage
Vc
to
VCO
.

The
s ignal
Vc
shifts
the
VCO
frequency
in
a
direction
to
reduce
the
frequency
difference
between
fs
and
fo
.

Once
this
act ion
starts
we
say
that
signal
is
in
capture
range

The
VCO
continues
to
cha nge
frequency
till
it s
outpu t
frequency
is
sa me
as
input
signal
frequency
.
The
circuit
is
said
to
be
locked
.

Once
locked
the
output
frequency
fo
is
identical
to
fs
except
a
finite
phase
difference
¥
.

Th e
pha se
di fferen ce
¥
ge nerates
a
co rrec ti ve
cont rol
volt ag e
Vc
to
shift
the
VCO
freq ue nc y
from
fo
to
fs
an d
main tai n
th e
lo ck
.

Once
lo ck ed
PLL
trac ks
th e
freq ue nc y
ch an g es
of
in pu t
si g n al
.

PLL
g o es
thro ugh
3
sta ge s
1
.
free
run ning
2
.
ca pt ure
3
.
lo cke d
or
trac ki ng

As
capture
starts
a
small
s i ne
wave
appears
.
This
is
due
to
differenc e
frequency
between
the
VCO
and
input
signal
.

The
dc
component
of
t he
beat
drives
the
VCO
towards
the
lock
.

Each
cycle
causes
the
VCO
frequency
to
move
closer
to
inp ut
frequency
change
.

The
difference
in
frequency
becomes
small er
and
a
large
dc
component
is
passed
by
filter,
shifting
the
VCO
frequency
.

The
proce s s
continues
unti l l
the
VCO
l ocks
on
to
the
signal
and
the
frequency
is
dc
.
The
low
pass
filter
controls
the
capture
range
.

Definitions

Lock
in
Range
.
Once
PLL
is
l ocked
it
can
track
frequency
changes
in
the
incoming
signals
.
The
ra nge
of
frequ e ncie s
over
which
the
PLL
can
maintain
lock
with
the
incoming
signal
is
called
lock
in
range
.
Lock
in
range
exp re s sed
as
%
of
fo
the
VCO
frequ enc y
.

Capture
range
t
Th e
range
of
frequenci es
ove r
which
the
PLL
can
acquire
lock
with
an
input
signal
is
called
capture
range
.
Expressed
as
%
of
fo
..

Pull
in
time
:
the
total
time
taken
by
the
PLL
to
establish
l ock
is
called
pull
in
time
.
This
depends
on
initial
phase
and
frequency
differenc e
between
two
signals
.
Phase Detector / Comparator

SchmittTriggerorRegenerativeComparator
Circuit

A
Schmitt
trig ger
ci rcuit
is
also
called
a
regenerative
comp arator
circu it
.
The
circuit
is
de sign e d
with
a
positi ve
fe edback
and
hence
will
have
a
regenerative
action
which
will
make
the
output
switch
leve ls
.
Als o,
the
use
of
posit ive
vo ltage
feedback
instead
of
a
negative
feedback,
aids
the
feedback
voltage
to
the
input
voltage,
instead
of
opposing
it
.

The
use
of
a
regenerative
circuit
is
to
remove
the
difficulti e s
in
a
zero
-
crossing
detector
circuit
due
to
l ow
frequency
signals
and
input
noise
voltages
.

It
is
basically
an
inverting
comparator
circ uit
with
a
posi tive
feedback
.
The
purpos e
of
the
Schmitt
trig ger
is
to
conve rt
any
regular
or
irregular
shaped
input
wavefo rm
into
a
square
wave
output
voltage
or
pulse
.
Thus,
it
can
also
be
called
a
squaring
circuit
.

As
sh own
in
the
circuit
diagram ,
a
voltage
divider
with
resi stors
Rdiv
1
and
Rdiv
2
is
s et
in
the
posi tive
fe edback
of
the
741
IC
op
-
amp
.
The
same
values
of
Rdiv
1
and
Rdiv
2
are
used
to
get
the
resi stance
value
Rpar
=
Rdiv
1
||Rdiv
2
which
is
connecte d
in
ser ie s
with
the
input
vo ltage
.
Rpar
is
u sed
to
m inimize
the
offset
prob lem s
.
The
voltage
across
R
1
is
fedback
to
the
non
-
inverting
input
.
The
input
voltage
Vi
trig gers
or
changes
the
state
of
output
Vout
ever y
time
it
exceed s
it s
vo ltage
leve ls
above
a
certain
threshold
value
called
Upper
Thre shold
Voltage
(
Vupt
)
and
Lower
Threshold
Voltage
(
Vlpt
)
.

Let
us
assum e
that
the
invert ing
input
voltage
has
a
slight
posit ive
value
.
Thi s
w i ll
cause
a
negat ive
value
in
the
output
.
This
n egative
vo ltage
is
fedback
to
the
non
-
inverting
termina l
(+)
of
the
op
-
amp
through
the
voltage
divider
.
Thus,
the
value
of
the
negative
vo ltage
that
is
fedback
to
the
positi ve
term inal
become s
highe r
.
The
value
of
the
negative
vo ltage
becomes
again
higher
until
the
circu it
is
drive n
into
negative
saturation
(
-
Vsat
)
.

Now,
let
us
assume
that
the
inverting
input
voltage
has
a
slight
negative
value
.
This
will
cause
a
positi ve
value
in
the
output
.
This
positive
voltage
is
fedback
to
the
non
-
inverting
terminal
(+)
of
the
op
-
amp
through
the
voltage
divider
.
Thus,
the
value
of
the
positi ve
vo ltage
that
is
fedback
to
the
positi ve
te rminal
becomes
high er
.
The
value
of
the
positive
voltage
becomes
again
higher
until
the
circuit
is
driven
into
posit ive
saturation
(+
Vsat
)
.
This
is
why
the
circuit
is
also
named
a
regenerative
comparator
circuit
.

When
Vout
=
+
Vsat
,
t he
voltage
across
Rdiv
1
is
called
Upper
Thresh old
Vo l tage
(
Vupt
)
.
The
input
voltage,
Vin
must
be
slightly
more
po siti ve
than
Vupt
inorder
to
cause
the
output
Vo
to
sw itch
from
+
Vsat
to
-
Vsat
.
When
the
input
voltage
is
l e ss
tha n
Vupt
,
the
outpu t
voltage
Vout
is
at
+
Vsat
.

Upper
Threshold
Voltage,
Vupt
=
+
Vsat
(R div
1
/[Rdiv
1
+Rdiv
2
])

When
Vout
=
-
Vsat
,
the
voltage
across
Rdiv
1
is
called
Lowe r
Thresh old
Voltage
(
Vlpt
)
.
The
input
voltage,
Vin
must
be
sli ghtly
more
negaitive
than
Vlpt
inorder
to
cause
the
out put
Vo
to
switch
from
-
Vsat
to
+
Vsat
.
When
the
input
voltage
is
less
tha n
Vlpt
,
t he
output
voltage
Vout
is
at
-
Vsat
.

Lower
Threshold
Voltage,
Vlpt
=
-
Vsat
(R div
1
/[Rdiv
1
+Rdiv
2
])

If
the
value
of
Vupt
and
Vlpt
are
higher
than
the
input
noise
voltage,
the
positi ve
fe edback
will
el i minate
the
false
outpu t
transiti ons
.
With
the
help
of
posit ive
feedback
and
its
regene rative
behaviour
,
the
output
voltage
will
switch
fast
between
the
positive
and
negative
saturation
voltages
.

HysteresisCharacteristics

Since
a
comparator
circu it
with
a
positi ve
feedback
is
used,
a
dead
band
condition
hystere s is
can
occur
in
the
output
.
When
the
input
of
the
comparator
has
a
value
higher
than
Vupt
,
its
output
switches
from
+
Vsat
to
-
Vsat
and
reve rt s
back
to
its
or iginal
state,
+
Vsat
,
when
the
input
value
goe s
be l ow
Vlpt
.
This
is
shown
in
the
figure
be l ow
.
The
hysteresi s
voltage
can
be
calculated
as
the
diffe rence
betwe en
the
upper
and
lower
threshold
voltages
.

Vhysteresis
=
Vupt
t
Vlpt

Subsitut ing
the values of
Vupt
and
Vlpt
from the above equations
:
Vhysteresis
=+
Vsat
(Rdiv1/Rd iv1+Rdiv2)
t
{
-
Vsat
(Rdiv1/Rd iv1+Rdiv2)}

Vhysteresis
= (Rdiv1/ Rdiv1+Rdiv2) {+
Vsat
t
(
-
Vsat
)}

ApplicationsofSchmitt
Trigger

Schmitt
trig ger
is
mo stly
us ed
to
convert
a
ver y
slow ly
var ying
input
vo ltage
into
an
output
having
abruptly
var ying
wavefo rm
occurring
precise ly
at
certain
predetermined
valu e
of
input
vo ltage
.
Schmitt
trig ger
may
be
used
for
all
applications
fo r
whi ch
a
general
comparator
is
used
.
Any
type
of
input
voltage
can
be
converted
into
its
corre spon ding
square
s i gnal
wave
.
The
onl y
conditi on
is
that
the
input
signal
must
have
large
enough
excurs ion
to
carr y
the
input
vo ltage
beyond
the
limits
of
the
hystere sis
range
.
The
amplitude
of
the
square
wave
is
indepe ndent
of
the
peak
-
to
-
peak
value
of
the
input
waveform
.