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PERFORMANCE TESTING OF TRANSFORMERS
1
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ABSTRACT:
A transformer is the static device of which electric power in one
circuit is transformed into electric power of the same frequency in another circuit. It can rise or lower the voltae in a circuit !ut with a correspondin
decrease or increase in current. It wor"s with the principles of mutual
induction. In our pro#ect we are usin step down transformer for providin
that necessary supply for the electronic circuits.
This pro#ect desined usin the $icrocontroller aids in the "Performance
testing of transformers "of %arious &lectrical and display the data's in the
(C. The transfer rate of this microcontroller is )*++ Baud rate. This ena!les
us to view and trac" the online chanes encountered in the
TRA,S-R$&R of all the parameters. ne of the main advantae of this
pro#ect is it allows us to view all the parameter readins simultaneously on
the screen. It also supports Bac"round (rocessin of the (arameters. The
parameters are classified into Analo and /oic (arameters
0
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BLOCK DIAGRAM:
$icrocontroller A2CTransformer
-lu3 sensor
Ratio Sensor
%oltaeSensor
-requencySensor
$A400
(C
(ower Supply
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ANALOG TO DIGITAL CONVERTER
ADC00 is an 5 !it ana!og to igita! con#erter with eiht input analo channels6 i.e.6 itcan ta"e eiht different analo inputs. The input which is to !e converted to diital formcan !e selected !y usin three address lines. The voltae reference can !e set usin the
%ref7 and %ref8 pins. The step si9e is decided !ased on set reference value. Step si9e isthe chane in analo input to cause a unit chane in the output of A2C. The default stepsi9e is 1).m% correspondin to % reference voltae. ADC00 needs an e3ternalcloc" to operate unli"e A2C+5+; which has an internal cloc". The A2C needs somespecific control sinals for its operations li"e start conversion and !rin data to output pins.
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(in 2escription:
Pin No F$nction Name
1
Analo input pins
I,
0 I,;
I,
; I,*
I,=
* Start conversion> input pin> a low to hih pulse is iven SC
= &nd of conversion> output pin> oes low when the conversion is over &C
5 2iital output !it ; 2
) Input pin> a low to hih pulse !rins data to output pins from the internalreisters at end of conversion
utput ena!le
1+ Cloc" input> to provide e3ternal cloc" Cloc" input
11 Supply voltae> % %cc
10 (ositive reference voltae %ref?7@
1 round ?@v@ ,2
1;2iital output !it
21
1 20
1* ,eative reference voltae %ref?8@
1=
2iital output !its
2+
15 2;
1) 20+ 2*
01 2=
00 Address latch ena!le> Input pin> low to hih pulse is required to latch in theaddress
A/&
0
Address lines
AddressC
0; AddressB
0 AddressA
0*
Analo inputs
I,+
0= I,105
Interfacing ADC00 %it& microcontro!!er
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Introduction
ADC0808 is one of the useful chips from National Semiconductor. See in figure
given aside. In lot of embedded systems micro controllers needs to take analog
input. ost of the sensors AND transducers such as temperature! humidity!
pressure! are analog. "or interfacing these sensors to micro controllers #e
re$uire to convert the analog output of these sensors to digital so that the
controller can read it. Some micro controllers have built in Analog to Digital
Converter %ADC& so there is no need of e'ternal ADC. "or controllers that
don(t have internal ADC e'ternal ADC is used.
)ne of the most commonly used ADC is ADC0808. ADC 0808 is a Successive
appro'imation type #ith 8 channels i.e. it can directly access 8 single ended
analog signals. ADC0808 has an 8*bit data output +ust like the ADC80,. -he 8
analog input channels are multiple'ed and selected according to table given
belo# I) pins using three address pins A! /! and C.
In the ADC0808! ref %1& and ref %*& set the reference voltage. If ref %*&23nd and
ref %1&24! the step si5e is 4647 2 9.4:m. -herefore! to get a 0m step si5e
*
http://www.engineersgarage.com/electronic-components/adc0808-datasheethttp://www.engineersgarage.com/articles/embedded-systemshttp://www.engineersgarage.com/electronic-components/adc0804-datasheethttp://www.engineersgarage.com/articles/embedded-systemshttp://www.engineersgarage.com/electronic-components/adc0804-datasheethttp://www.engineersgarage.com/electronic-components/adc0808-datasheet
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Pin Config$ration of ADC 00
I/O Pins (Analog channel selection)
Descri'tion
5
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ADC devices * Analog*to*digital converters are among the most #idely used
devices for data ac$uisition. Digital computers use binary %discrete& values! but in
the physical #orld everything is analog. -emperature! pressure! humidity and
velocity are a fe# e'amples of physical $uantities that #e deal #ith everyday. A
physical $uantity can be converted into electrical signals using a device called as
transducer. -ransducers are also referred to as sensors. =e need an analog to
digital converter to translate he analog signals to digital numbers so that the
microcontroller can read and process them. An ADC has n*bit resolution #here n
can be 8! 0! 6! 7 or even 6, bits. -he highest*resolution ADC si5e! #here step
si5e is the smallest change that can be discerned by an ADC.
CS * Chip select is an active lo# input used to activate the ADC0808 chip. -o
access the ADC080,! this pin must be lo#.
. RD (read) * -his is an input signal and is active lo#. -he ADC converts the
analog input to its binary e$uivalent and holds it in an internal register. @D is
used to get the converted data out of the ADC0808 chip. =hen CS20! if a high*
to*lo# pulse is applied to the @D pin! the 8*bit digital output sho#s up at the D0 >
D? data pins. -he @D pin is also referred to as output enable %)
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ADDRSS !I" A# $# C * -he device contains 8*channels. A particular
channel is selected by using the address decoder line. -he -A/;< sho#s the
input states for address lines to select any channel.
Address !atch na%le (A!) * -he address is latched on the ;o# > Bigh
transition of A;
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=here Dout 2 digital data output! in 2 analog input voltage! and step si5e is the
smallest input change.
ALGORIT(M
. Start.
6. Select the channel.
:. A ;o# > Bigh transition on A;< to latch in the address.
,. A ;o# > Bigh transition on Start to reset the ADC(s SA@.
4. A Bigh > ;o# transition on A; ;o# transition on start to start the conversion.
?. =ait for
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• A;
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If you #ant to interface sensors like ;:4 #hich has output 0mvC then I #ould
suggest that you set the ref1 to 6.47v so that the step si5e #ill be
Step si5e2 %6.47 * 0&6472 0 m.
So no# #hatever reading that you get from the ADC #ill be e$ual to the actual
temperature.
Ste's to 'rogra, ADC *-*-
-he follo#ing are steps to get data from an ADC0808. Select an analog channel
by providing bits to A! /! and C addresses according to the -able > Analog
channel selection.
. Activate the A;< %Address ;atch
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unctional %loc diagra, o IC ADC *-*-
1;
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Interacing - channel -%it ADC to
-*01
)*) MICROCONTROLLER
1
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A microcontroller ?also $C or C@ is a functional computer system8
on8a8chip. It contains a processor core6 memory6 and proramma!le
inputDoutput peripherals. $icrocontrollers include an interated C(6
memory ?a small amount of RA$6 proram memory6 or !oth@ and
peripherals capa!le of input and output. $icrocontrollers are used in
automatically controlled products and devices.
+ASICS,
A desiner will use a $icrocontroller to
• ather input from various sensors
• (rocess this input into a set of actions
• se the output mechanisms on the $icrocontroller to do
somethin useful.
MEMOR- T-PES,
RAM,
Random access memory.
Ram is a volatile ?chane@ memory.
It eneral purpose memory that can store data or prorams.
&3: hard dis"6 SB device.
ROM,
Read only memory.
Rom is a non volatile memory.
This is typically that is prorammed at the factory to have certain
values it cannot !e chaned.
1*
http://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Integrated_circuithttp://en.wikipedia.org/wiki/Input/outputhttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Integrated_circuithttp://en.wikipedia.org/wiki/Input/output
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&3: cd...
)*)*. ARC(ITECT/RE OF ATC1.
1=
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01. Arc&itect$re,
5+1 Architecture contains the followin:
• C(
• A/
15
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• ID ports
• RA$
• R$
• 0 TimersDCounters
• eneral (urpose reisters• Special -unction reisters
• Crystal scillators
• Serial ports
• Interrupts
• (S<
• (roram Counter
• Stac" pointer
Pin Descri'tion,
1)
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5+1 contains ;+ pins 0 (ins are used for ID purpose
0 (ins for crystal oscillator to produce cloc"
0+
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0 (ins for Supply and round1 (ins for reset the controller
• (ort +:
(ort + occupies a total of 5 pins. It can !e used for input or
output. To use the pins of port + as !oth input and output ports.&ach pin must !e connected e3ternally to 1+E ohm pull8upresisters. This is due to the fact that (+ is an open drain.
• (ort 1:
(ort 1 occupies a total of 5 pins. It can !e used as input or output .In contrast to port +6 this port does not need any pull upresisters since it already has pull up resisters internally. To ma"e
port 1 an input port6 it must !e prorammed as such !y writin1 to all its !its.
• (ort 0:
(ort 0 occupies a total of 5 pins. It can !e used as input or output. It already has pull8up resisters internally. To ma"e port 0an input6 it must !e prorammed as such !y writin 1 to all its
!its.
• (ort :
(ort occupies a total of 5 pins. It can !e used as input or output. (ort has the additional function of providin somee3tremely important sinals such as interrupts.
Arc&itect$re,
T%o t2'es of arc&itect$re are fo!!o%e*
I. %an8,euman Architecture: The width of address and data !us issame.
II. Faward Architecture: The !us width of address and data maynot !e same. (ipelininin is possi!le here.
$icrocontrollers have !uilt8in peripherals6 they are61@ $emory
a. (roram memory ?&. (R$6 -lash memory@ !. 2ata $emory ?&. RA$6 &&R$@
0. ID (orts. A2C
01
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;. Timers. SART*. Interrupt controllers
(
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01. T$toria!, Instr$ction Set4 Timing4 an Lo%5Le#e! Info
In order to understand88and !etter ma"e use of88the 5+16 it is necessary tounderstand some underlyin information concernin timin.
The 5+1 operates !ased on an e3ternal crystal. This is an electrical devicewhich6 when enery is applied6 emits pulses at a fi3ed frequency. ne canfind crystals of virtually any frequency dependin on the applicationrequirements.
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also has two really slow instructions that require a full ; cycles to e3ecute88if you were to e3ecute nothin !ut those instructions youd find performanceto !e a!out 0+6) instructions per second.
It is aain important to emphasi9e that not all instructions e3ecute in thesame amount of time. The fastest instructions require one machine cycle ?10crystal pulses@6 many others require two machine cycles ?0; crystal pulses@6and the two very slow math operations require four machine cycles ?;5crystal pulses@.
,T&: $any 5+1 derivative chips chane instruction timin. -or e3ample6many optimi9ed versions of the 5+1 e3ecute instructions in ; oscillator cycles instead of 10> such a chip would !e effectively times faster than the5+1 when used with the same 11.+) $h9 crystal.
Since all the instructions require different amounts of time to e3ecute a veryo!vious question comes to mind: Fow can one "eep trac" of time in a time8critical application if we have no reference to time in the outside worldH
/uc"ily6 the 5+1 includes timers which allow us to time events with hih precision88which is the topic of the ne3t chapter.
01. Timers
The 5+1 comes equipped with two timers6 !oth of which may !e controlled6set6 read6 and confiured individually. The 5+1 timers have three eneralfunctions: 1@ Eeepin time andDor calculatin the amount of time !etweenevents6 0@ Countin the events themselves6 or @ eneratin !aud rates for the serial port.
The three timer uses are distinct so we will tal" a!out each of them
separately. The first two uses will !e discussed in this chapter while the useof timers for !aud rate eneration will !e discussed in the chapter relatin toserial ports.
(o% oes a timer co$nt6
0;
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Fow does a timer countH The answer to this question is very simple: A timer always counts up. It doesnt matter whether the timer is !ein used as atimer6 a counter6 or a !aud rate enerator: A timer is always incremented !ythe microcontroller.
Programming Ti', Some derivative chips actually allow the proramto confiure whether the timers count up or down. Fowever6 since thisoption only e3ists on some derivatives it is !eyond the scope of thistutorial which is aimed at the standard 5+1. It is only mentioned herein the event that you a!solutely need a timer to count !ac"wards6 youwill "now that you may !e a!le to find an 5+18compati!lemicrocontroller that does it.
/SING TIMERS TO MEAS/RE TIME
!viously6 one of the primary uses of timers is to measure time.
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/ets say we want to "now how many times the timer will !e incremented in.+ seconds. thenyou e3ecute your event6 reset the timers6 and wait for the timer to count upanother 0+ times. In this manner you will effectively e3ecute your eventonce per second6 accurate to within thousandths of a second.
Thus6 we now have a system with which to measure time. All we need toreview is how to control the timers and initiali9e them to provide us with theinformation we need.
Timer SFRs
As mentioned !efore6 the 5+1 has two timers which each functionessentially the same way. ne timer is TI$&R+ and the other is TI$&R1.The two timers share two S-Rs ?T$2 and TC,@ which control thetimers6 and each timer also has two S-Rs dedicated solely to itself ?TF+DT/+ and TF1DT/1@.
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T/1 Timer 1 /ow Byte 5Bh
TC, Timer Control 55h
T$2 Timer $ode 5)h
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The individual !its of T$2 have the followin functions:
T$2 ?5)h@ S-R
+it Name E8'!anation of F$nction Timer
= AT&1
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Timer mode J+J is a 18!it timer. This is a relic that was "ept around in the5+1 to maintain compata!ility with its predecesor6 the 5+;5. enerally the18!it timer mode is not used in new development.
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0 -2h --h
-2h -2h
; -2h -&h
-2h --h* -2h -2h
= -2h -&h
As you can see6 the value of TF+ never chaned. In fact6 when you usemode 0 you almost always set TF3 to a "nown value and T/3 is the S-R that is constantly incremented.
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can use the real Timer 1 as a !aud rate enerator and use TF+DT/+ as twoseparate timers.
T&e TCON SFR
-inally6 theres one more S-R that controls the two timers and providesvalua!le information a!out them. The TC, S-R has the followinstructure:
TC, ?55h@ S-R
+it Name+it
AressE8'!anation of F$nction Timer
= T-1 5-hTimer . O#erf!o%. This !it is set !y themicrocontroller when Timer 1 overflows.
1
* TR1 5&hTimer . R$n.
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Initia!i>ing a Timer
,ow that weve discussed the timer8related S-Rs we are ready to write codethat will initiali9e the timer and start it runnin.
As youll recall6 we first must decide what mode we want the timer to !e in.In this case we want a 1*8!it timer that runs continuously> that is to say6 it isnot dependent on any e3ternal pins.
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actually happened was that the timer value was 1;D0 ?hih !yte 1;6 low !yte 0@ !ut you read 1D0.
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chec" if the T-3 !it is set. If T-+ is set it means that timer + has overflowed>if T-1 is set it means that timer 1 has overflowed.
/ow !yte of 1)6;= ?1)6;* 7 1 K 1)6;=@
MOV TMOD4?0.>(ut Timer + in 1*8!it modeSET+ TR0>$a"e Timer + start countinN+ TF04B>If T-+ is not set6 #ump !ac" to this same instruction
In the a!ove code the first two lines initiali9e the Timer + startin value to1)6;=. The ne3t two instructions confiure timer + and turn it on. -inally6the last instruction N+ TF04B6 reads JOump6 if T-+ is not set6 !ac" to thissame instruction.J The JPJ operand means6 in most assem!lers6 the addressof the current instruction. Thus as lon as the timer has not overflowed andthe T-+ !it has not !een set the proram will "eep e3ecutin this sameinstruction. After 1D0+th of a second timer + will overflow6 set the T-+ !it6
and proram e3ecution will then !rea" out of the loop.
Timing t&e !engt& of e#ents
The 5+1 provides another cool toy that can !e used to time the lenth of events.
-or e3ample6 let's say we're tryin to save electricity in the office and we'reinterested in how lon a liht is turned on each day.
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state of the e3ternal pins. Fowever6 now it would !e nice if an e3ternal pincould control whether the timer was runnin or not. It can. All we need to dois connect the lihtswitch to pin I,T+ ?(.0@ on the 5+1 and set the !itAT&+.
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free9es the oscillator disa!lin all other chip functions until the ne3t
hardware reset.
OSCILLATOR C(ARACTERISTICS,
4TA/1 and 4TA/0 are the input and output6 respectively6 of an
invertin amplifier which can !e confiured for use as an on8chip oscillator>
&ither a quart9 crystal or ceramic resonator may !e used. To drive the device
from an e3ternal cloc" source6 4TA/0 should !e left unconnected while
4TA/1 is driven. There are no requirements on the duty cycle of the
e3ternal cloc" sinal6 since the input to the internal cloc"in circuitry is
throuh a divide8!y8two flip8flop6 !ut minimum and ma3imum voltae hih
and low time specifications must !e o!served.
IDLE MODE,
In idle mode6 the C( puts itself to sleep while all the on chip peripherals remain active. The mode is invo"ed !y software. The content of
the on8chip RA$ and all the special functions reisters remain unchaned
durin this mode. The idle mode can !e terminated !y any ena!led interrupt
or !y a hardware reset. It should !e noted that when idle is terminated !y a
hard ware reset6 the device normally resumes proram e3ecution6 from
where it left off6 up to two machine cycles !efore
the internal reset alorithm ta"es control. n8chip hardware inhi!its access
to internal RA$ in this event6 !ut access to the port pins is not inhi!ited. To
eliminate the possi!ility of an une3pected write to a port pin when Idle is
terminated !y
*
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Reset6 the instruction followin the one that invo"es Idle should not !e one
that writes to a port pin or to e3ternal memory.
)*)*= PIN DIAGRAM OF ATC1.
=
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AT 5)C1
)*)*) PIN DESCRIPTION
VCC,
5
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Supply voltae.
GND,
round.
Port 0,
(ort + is an 58!it open8drain !i8directional ID port. As an output port6
each pin can sin" eiht TT/ inputs.
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to (ort 0 pins they are pulled hih !y the internal pull8ups and can !e used as
inputs.
(ort 0 pins that are e3ternally !ein pulled low will source current ?II/@
!ecause of the internal pull8ups.
RST,
Reset input a hih on this pin for two machine cycles while the
oscillator is runnin resets the device.
ALE3PROG,
Address /atch &na!le output pulse for latchin the low !yte of the
address durin accesses to e3ternal memory. This pin is also the proram
pulse input ?(R@ durin -lash prorammin. In normal operation A/& is
emitted at a constant rate of 1D* the oscillator frequency6 and may !e used for
e3ternal timin or cloc"in purposes. ,ote6 however6 that one A/& pulse is
s"ipped durin each access to e3ternal 2ata $emory.
PSEN,
(roram Store &na!le is the read stro!e to e3ternal proram memory.
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&3ternal Access &na!le. &A must !e strapped to ,2 in order to
ena!le the device to fetch code from e3ternal proram memory locations
startin at ++++F up to ----F. ,ote6 however6 that if loc" !it 1 is
prorammed6 &A will !e
internally latched on reset. &A should !e strapped to %CC for internal
proram
e3ecutions. This pin also receives the 10volt prorammin ena!le voltae
?%((@ durin -lash prorammin6 for parts that require 108volt %((.
TAL.,Input to the invertin oscillator amplifier and input to the internal
cloc" operatin circuit.
TAL=,
utput from the invertin oscillator amplifier.
Port Pin A!ternate F$nctions
(.+
(.1
(.0
(.
(.;
(.
(.*
(.=
R42 ?serial input port@
T42 ?serial output port@
I,T+ ?e3ternal interrupt +@
I,T1 ?e3ternal interrupt 1@
T+ ?timer + e3ternal input@
T1 ?timer 1 e3ternal input@
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&at is MA=)=
$a300 is desined !y $a3im Interated (roducts. This IC is widely used in RS00Communication systems in which the conversion of voltae level is required to ma"eTT/ devices to !e compati!le with (C serial port and vice versa. This chip contains
chare pumps which pumps the voltae to the 2esired /evel. It can !e powered !y asinle 7 volt power supply and its output can reach 7Q=. volts.$A400 comes in 1*(in 2ip and many other pac"aes and it contains 2ual 2rivers. It can !e used as ahardware layer convertor for 0 systems to communicate simultaneously.$a300 is one of the versatile IC to use in most of the sinal voltae level conversion pro!lems.
Constr$ction of MA=)=,
$ostly $A400 used in 1*8pin 2I( pac"ae it consist of ma#or !loc"s .It can only !e powered !y volts to ma"e it power supply compati!le with most of the em!eddedsystems. -irst !loc" is the voltae dou!ler in this ic switched capacitor techniques is usedto ma"e the voltae dou!le .nce the voltae is dou!led second !loc" will converts thatvoltae to 71+ and 81+. The third !loc" consists of 0 transmitters and 0 receivers which
;0
http://electricaltechnology.org/wp-content/uploads/2014/10/What-is-MAX232.png
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actually convert the voltae levels.
E8terna! com'onents,
$a300 requires minimum ; e3ternal capacitor. Their %alue can rane from 1uf to 1+uf and1* volts or more ratin. There are many different versions of this versatile ic availa!leeach of them Require different capacitor value for proper wor"in.
;
http://electricaltechnology.org/wp-content/uploads/2014/10/Required-Capacitors-Value-for-MAX232-IC.pnghttp://electricaltechnology.org/wp-content/uploads/2014/10/max232-Copy.png
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A''!ication an $ses of MA=)=,
(remierly $A400 is used in Serial communication. (ro!lem arises when we have tocommunicate !etween TT/ loic and C$S loic !ased systems. RS00 isinternationally defined standard named as &IADTIA8008& and in this standard loic + is
the voltae !etween 7 to 71 and loic 1 is defined as the voltae !etween 8 to 81.InTT/ loic + is defined is !y + volt and 1 is defined !y volt so in this scenario this is avery handy IC to !e incorporated.
)* POER S/PPLIES
The present chapter introduces the operation of power supply circuits
!uilt usin filters6 rectifiers and voltae reulators. Startin with an AC
voltae6 a steady 2C voltae6 is o!tained !y rectifyin the ac voltae then
filterin to a dc level and -inally Reulation is usually o!tained from an IC
voltae reulator unit6 which ta"es a dc voltae and provides a some what
lower dc voltae6 which remains the same even if the input dc voltae varies
or the output load connected to the dc voltae chanes.
+LOC DIAGRAM,
The ac voltae6 typically 0+v is connected to transformer6 whichsteps the ac voltae down to the level for desired dc output. A diode rectifier
provides a full wave rectified %oltae that is initially filtered !y a simple
capacitive filter to produce a dc voltae.
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Transformer Rectifier -ilter Reulator
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This resultin dc voltae usually has some ripple or ac voltae
variation. A reulator Circuit can use this dc input to provide a reulated that
not only has much ripple voltae
But also remain the same dc values even if the input dc voltae
chanes. This voltae Reulation is usually o!tained usin one of a num!er
of popular voltae reulation IC nits.
TRANSFORMER,
A transformer is the static device of which electric power in one
circuit is transformed into electric power of the same frequency in another
circuit. It can rise or lower the voltae in a circuit !ut with a correspondin
decrease or increase in current. It wor"s with the principles of mutual
induction. In our pro#ect we are usin step down transformer for providin
that necessary supply for the electronic circuits.
RECTIFIER,
The full wave rectifier conducts durin !oth positive and neative half
cycles of input a.c. input> two diodes are used in this circuit. The a.c. voltae
is applied throuh a suita!le power transformer with proper turns ratio. -or
the proper operation of the circuit6 a center8tap on the secondary windin of
the transformer is essential.
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2urin the positive half cycle of ac input voltae6 the diode 21 will !e
forward !iased and hence will conduct> while diode 20 will !e reverse
!iased and will act as open circuit and will not conduct.
In the ne3t half cycle of ac voltae6 polarity reverses and the diode 20
conducts6 !ein forward !iased6 while 21 does not6 !ein reverse !iased.
Fence the load current flows in !oth half cycles of ac voltae and in the
same direction. The diode we are usin here for the purpose of rectification
is I,;++1.
FILTER,
The filter circuit used here is the capacitor filter circuit where a
capacitor is connected at the rectifier output6 and a 2C is o!tained across
it. The filtered waveform is essentially a 2C voltae with nelii!le
ripples6 which is ultimately fed to the load.
REG/LATOR,
The output voltae from capacitor is more filtered and finally
reulated. The voltae reulator is a device6 which maintains the output
voltae constant irrespective of the chane in supply variations6 load
variations and temperature chanes. Fence IC=5+ is used which is a 7v
reulator.
CIRC/IT DIAGRAM OF POER S/PPLIES,
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other windins ets deteriorated due to fault. It was also concluded that theTransformation and turnsratio of isolation transformer are and respectively.
REFERENCES
1 A. R. 2evidas6 $. %. Ramesh6