Source to Fiber Power Launching

7/23/2019 Source to Fiber Power Launching

1/80

UNIT 4

Source to fber Power

Launching


2/80

Coupling Efficiency

s

F

P

P==

soursethefromemittedpower

fibertheintocoupledpower [5-1]

Source Optical Fiber

sP

FP


3/80

Output Patterns Optical output of a luminescent source is usually

measured by its radiance B at a given diodecurrent.

Radiance: It is the optical power radiated into a

unit solid angle per unit emitting surface area and

is generally specified in terms of watts per square

centimeter per steradian

!he angle that" seenfrom the center of a

sphere" includes a

gi#en area on the

surface of that sphere


4/80

Output Patterns !he angle that" seen from the center of a sphere"

includes a gi#en area on the surface of thatsphere

!he #alue of the solid angle is numerically equal

to the si$e of that area di#ided by the square of

the radius of the sphere

Radiance = Power / per unit solid angle %perunit emitting surface area


5/80

&adiance '(rightness) of the source

B=Optical power radiated from a unit area of the source into aunit solid angle [watts*'square centimeter per stradian)]


6/80

Surface emitting LEDs output pattern:

cos)"' +BB =

This is lambertian pattern,which means that thesource is equally brightwhen viewed rom any

direction.


7/80

Power oupled from source to t!e fi"er

rdrdddB

dAdABP

s

r

s

A

sssF

m

f f

=

=

=

ma%+

+

,

+

,

++

sin)"'

)"'

sourcetheofangleemissionsolidandareaand ssA

fiberofangleacceptancesolidandareaand ffA Total coupledpower is

summing upthecontributionrom eachindividualemitting pint

source oincremental


8/80

.ower coupled from /E0 to the iber

rdrdB

rdrdB

rdrddBP

s

r

s

r

s

r

s

s

s

,,

++

+

,

+

ma%+

,

+

+

,

+ +

+

+

23

sin

sincos,ma%+

=

=

=

= ,

1+

,,,

+

,,

step/E0" ,)23' nBrBrP ss


9/80

.ower coupling from /E0 to step-inde% fiber

!otal optical power from /E0 If we consider that the .s is emitted fromthe source of area 3s

sincos,

sin)"'

,*

+

+

,,

+

,

,

+

,*

+

==

=

BrdBrP

ddBAP

sss

ss

=arP

r

a

arP

P

ss

s

ss

if)23'

if)23'

,

,

,

step/E0"


10/80

.ower coupling from /E0 to graded-inde% fiber


11/80

Fiber separation

l hi


12/80

Power launching During transmission, optical power

launched into a fber is independent othe wa!elength o the source butdepends onl" on its brightness#

The number o modes that canpropagate in graded$inde% fber o coreradius a and or parabolic profle is

Number o modes operating in &''nmwill be two times than no# o modes at()'' nm#

The radiated ower er mode


13/80

perture

-anuactures supplied light source with a short fberpigtail which is then attached to the source to a

s"stem# This pigtail should be connected to a s"stem fber with

identical N and core diameter#

t this .unction around '#( to ( d/ optical power is

lost# n e%cess power loss will occurs in the s"stem fber in

addition to the coupling loss, which is due to the

modes scattering out o fber#

Optical power is measured when the launched modesha!e come to e+uilibrium and fber is o larger length#

The launched modes attain e+uilibrium at appro%# 0'm rom the fber starting point#P50 : optical power measured at 0' m#

1distance

at which modes become e+uilibrium2


14/80

Optical Detector


15/80

Re#uirement for t!e optical detector

!he detector must satisfy following requirements

for better performance 4igh sensiti#ity at the operating wa#elengths

4igh fidelity

/arge electrical response to the recei#ed optical signal

3 minimum noise introduced by the detector

tability of performance characteristics

mall si$e

4igh reliability

/ow cost


16/80

Optical detection principles

!he basic detection process in an intrinsic absorber is illustrated

in igure 61 which shows a p7n photodiode

!his de#ice is re#erse biased and the electric field de#elopedacross the p7n 8unction sweeps mobile carriers 'holes and

electrons) to their respecti#e ma8ority sides 'p- and n-type

material)

3 depletion region or layer is therefore created on either side ofthe 8unction

!his barrier has the effect of stopping the ma8ority carriers

crossing the 8unction in the opposite direction to the field

4owe#er" the field accelerates minority carriers from both sidesto the opposite side of the 8unction" forming the re#erse lea9age

current of the diode

$!us intrinsic conditions are created in t!e depletion region


17/80


18/80


% p!oton incident in or near t!e depletion region of t!is

device w!ic! !as an energ& greater t!an or e#ual to t!e

"and'gap energ& Egof t!e fa"ricating material 'ie hf : Eg)will e%cite an electron from the #alence band into the

conduction band

!his process lea#es an empty hole in the #alence band and is

9nown as the photo-generation of an electron7hole 'carrier)pair" as shown in igure 61'a)

Carrier pairs so generated near the 8unction are separated and

swept 'drift) under the influence of t!e electric field to

produce a displacement "& current in t!e e(ternal circuit ine(cess of an& reverse lea)age current 'igure 61'b))

.hoto-generation and the separation of a carrier pair in the

depletion region of this re#erse-biased p7n 8unction is

illustrated in igure 61 'c)


19/80


$!e depletion region must "e sufficientl&

t!ic) to allow a large fraction of t!e incident

lig!t to "e a"sor"ed in order to ac!ieve

ma(imum carrier pair generation

4owe#er" since long carrier drift times in the

depletion region restrict t!e speed of

operation of the photodiode it is necessar& to

limit its widt!.

$!us t!ere is a trade'off "etween t!e num"erof p!otons a"sor"ed *sensitivit&+ and t!e

speed of response.


20/80


%"sorption

!he absorption of photons in a photodiode toproduce carrier pairs and thus a photocurrent is

dependent on the absorption coefficient ;+of the

light in the semiconductor used to fabricate the

de#ice

3t a specific wa#elength and assuming only

band-gap transitions the photocurrent Ip

produced by incident light of optical power .ois

gi#en by


21/80


,uantum efficienc&

!he quantum efficiency < is defined as t!efraction of incident p!otons w!ic! are a"sor"ed

"& t!e p!oto'detector and generate electrons

w!ic! are collected at t!e detector terminals

where rp is the incident photon rate 'photons per

second) and re is the corresponding electron rate

'electrons per second)


22/80


Responsivit&

!he e%pression for quantum efficiency does not in#ol#e

photon energy and therefore the responsivit& R isoften of more use w!en c!aracteri-ing t!e

performance of a p!oto'detector

It is defined as

where Ipis the output photocurrent in amperes and .ois

the incident optical power in watts 'ie output optical

power from the fiber)

!he responsivit& is a useful parameter as it gives t!e

transfer c!aracteristic of t!e detector 'ie

photocurrent per unit incident optical power)


23/80


24/80

P!&sical Principles of P!otodiodes

!he most common semiconductor photo-detector

is thepinphotodiode#

!he de#ice structure consists of p and n regions

separated by a #ery lightly n-doped intrinsic 'i)

region


25/80

ontd

In normal operation a sufficiently large re#erse

bias #oltage is applied" so that the iregion is fullydepleted of carriers

=hen an incident photon has an energy : Eg of

semiconductor material" the photon gi#e up itsenergy and e%cite an electron from #alance band

to the conduction band

!his process generates the free electron-holepairs" 9nown as photo-carriers

3s shown in figure on ne%t slide


26/80


27/80

ontd

!he detectors are designed so that these carriers

are generated in the depletion region where mostof the light absorbed

!he high electric field present in the depletion

region causes photo-generated carriers toeparate and be collected across the re#erse7

biased 8unction

!his gi#e rise to a current low in an e%ternalcircuit" 9nown as p!otocurrent.

P! t t


28/80

P!otocurrent

Optical power absorbed in a distance x" in the depletion region can

be written in terms of incident optical power "

3bsorption coefficient strongly depends on wa#elength

!he upper wa#elength cutoff for any semiconductor can be

determined by its energy gap as follows

!a9ing entrance face reflecti#ity into consideration" the absorbed

power in the width of depletion region" w" becomes

)1')')'

+

xsePxP

=)'s

)'xP+P

'e>)

,?1)m'g

cE

=

)1)'1'

)1')'

)'

+

)'

+

f

w

p

w

RePh

q

I

ePwP

s

s

=

=

or longer wavelengt!0 t!e

p!oton energ& is not

sufficient to e(cite an

electron from t!e valance

"and to conduction "and.


29/80

Optical 3bsorption Coefficient


30/80

Responsivit& !he primary photocurrent resulting from absorption is

@uantum Efficiency

Responsivit&:

)1)'1' )'

+ f

w

p RePh

qI s =

hP

qIP

*

*

photonsincidentofApairsatedphotogenerhole-electronofA

+

=

=

[3*=]

+

h

q

P

IP==


31/80

&esponsi#ity #s wa#elength

% l ! P! t di d *%PD+


32/80

%valanc!e P!otodiode *%PD+3.0s internally multiply the

primary photocurrent before it enters

to e%ternal circuitry

In order to carrier multiplication

ta9e place" the photo-generated

carriers must tra#erse along a high

field region

In this region" photo-generatedelectrons and holes gain enough

energy to ioni$e bound electrons in

>( upon colliding with them

!his multiplication is 9nown asimpact ioni-ation

!he newly created carriers in the

presence of high electric field result

in more ioni$ation called avalanc!e

effect

3each$Through PD structure 13PD2showing the electric felds in depletionregion and multiplication region#

Optical radiation

Below the diode breadownvoltage a fnite carriers arecreated, whereas abovebreadown the number o carriers are infnite.ommonl" used structure or

achie!ing the multiplication is3PD

!his configuration is 9nown as


33/80

!his configuration is 9nown as

pBpnB reach-throughstructure

!he layer is basically an

intrinsic material

!he term reach-through arisesfrom photodiode operation

=hen a low &( #oltage is

applied" most of the potential

drop is across pnB8unction

!he depletion layer is widen

with increasing the bias until a

certain #oltage is reached at

which the pea9 electric field at

the pnB8unction is about the 5-

1+ D below that needed to

cause the a#alanchebrea9down

3t this point" the depletion

layer 8ust reac! t!roug! to the

nearly intrinsic region

In general" the &3.0 is operated in the fully

depleted mode

/ight enters the de#ice through the pB and isabsorbed in the material" which acts as a

collection region for photo-generated carriers

pon being absorbed the photon gi#e up its

energy" and created the electron-hole pairs

!hese carriers drift through the region in thepnB8unction" where a high electric filed e%ists

It is in this high$feldregion that carriermultiplication ta5esplace#


34/80

&esponsi#ity of 3.0

!he multiplication factor 'current gain)Mfor all carriers generated in thephotodiode is defined as

=here is the a#erage #alue of the total multiplied output current F

is the primary photocurrent

!he responsi#ity of 3.0 can be calculated by considering the current gain

as where &+is the unity gain responsi#ity

p

M

I

IM =

MI PI

MMh

q+3.0 ==

P!oto detector Response $ime


35/80

P!oto'detector Response $ime

$!e response time of a p!oto'detector wit! its output circuit depends mainl&

on t!e following t!ree factors:1 !he transit time of the photo-carriers in the depletion region

1. Diffusion time of photo-carriers outside depletion region

2. R time constant of the circuit

!he photodiode parameters responsible for abo#e factors are the absorption

coefficient ;s" the depletion region width w" thephoto diode 8unction and pac9age

capacitances" the amplifier capacitance" the detector load resistance" the amplifier

input resistance" and thephotodiode series resistance


36/80

P!otodetector Response $ime


37/80


1 !he transit time of the photocarriers in the depletion region !he response

speed of a photodiode limits by the time it ta9es photo-generated carriers to

tra#el across the depletion region

!he transit time depends on the carrier drift #elocity and the

depletion layer width w" and is gi#en by

, 0iffusion time of photo-carriers outside depletion region !he diffusionprocesses are slow compared wit! t!e driftof carriers in the high-field

region

!herefore" to ha#e a !ig! speed p!otodiode0 t!e p!oto'carriers must "e

generated in t!e depletion region or so close to it t!at diffusion times

are less or e#ual to t!e drift time!his response time is descri"ed "& t!e rise time and fall time of the

detector output when the detector is illuminated by a step input of optical

radiation 3s shown in the figures on ne%t two slides

or full& depleted region t!e rise time and fall time are t!e same.

dt dv

d

dv

wt =

.h t di d t ti l l


38/80

.hotodiode response to optical pulse

Full" depleted region

.h t di d t ti l l


39/80

.hotodiode response to optical pulse

Typical response time o the photodiode that is not ullydepleted



40/80


G &C time constant of the circuit !he circuit after the photo-detector

acts li9eRlow pass filter with a pass-band gi#en by

!!R

B

,

1=

da!"s! RRR +== andHH


41/80

>arious optical responses of photo-detectors


42/80

>arious optical responses of photo-detectors

!rade-off between quantum efficiency F response time

To achie!e a high quantume!ciency, the depletion

layer width must be largerthan

1the in!erse o the absorptioncoe6cient2,

so that most o the lightwill be absorbed#

t the same time with largewidth, the capacitance issmall and RC timeconstant getting smaller,leading to asterresponse, but wide width

results in larger transittime in the depletionregion# Thereore there is atrade"o# between widthand $%# It is shown that thebest is7

s*1

ss

w *,*1


43/80


44/80

tructures for Ina3s 3.0s

eparate-absorption-and multiplication '3J) 3.0

Ina3s 3.0 superlattice structure '!he multiplication region is composed

of se#eral layers of In3la3s quantum wells separated by In3l3s barrier

layers

-etal contact

InP multiplication la"er

IN8as bsorption la"er

InP bu9er la"er

InP substrate

light

!emperature effect on a#alanche gain


45/80

!emperature effect on a#alanche gain

!he gain mechanism of an

a#alanche photodiode is #ery

temperature-sensiti#e because

of the temperature dependence

of the electron and hole

ioni$ation rates

!his temperature dependence is

critical at high bias #oltage

where small changes in

temperature cause largechanges in the gain

3s shown in the figure for si

a#alanche photodiode

Comparison of photodetectors


46/80

Comparison of photodetectorsPindiode


47/80


48/80


49/80

Example


50/80

Bandgap and photodetection

(a) Determine the maximum value of the energy gapwhich a semiconductor, used as a

photoconductor, can have if it is to be sensitive to yellow light (600 nm).

(b) A photodetector whose area is 510-2cm2is irradiated with yellow light whose

intensity is 20 mW cm2. Assuming that each photon generates one electron-hole

pair, calculate the number of pairs generated per second.

Solution

(a) Given, = 600 nm, we needEph

= h=Egso that,

Eg=hc/ = (6.62610-34J s)(3108m s-1)/(60010-9m) = 2.07 eV

(b) Area= 510-2cm2andIlight

= 2010-3W/cm2.The received power is

P=Area Ilight

= (510-2cm2)(2010-3W/cm2) = 10-3WN

ph= number of photons arriving per second =P/E

ph

= (10-3W)/(2.0591.6021810-19J/eV)= 2.97871015photons s-1 = 2.97871015EHP s-1.

Example


51/80

(c) For GaAs,Eg= 1.42 eV and the corresponding wavelength is

=hc/Eg= (6.62610-34J s)(3108m s-1)/(1.42 eV1.610-19J/eV) = 873 nm (invisible IR)

The wavelength of emitted radiation due to EHP recombination is 873 nm.

(d) For Si,Eg= 1.1 eV and the corresponding cut-off wavelength is,

g=hc/Eg= (6.62610-34J s)(3108m s-1)/(1.1 eV1.610-19J/eV)

= 1120 nm

Since the 873 nm wavelength is shorter than the cut-off wavelength of 1120 nm,

the Si photodetector can detect the 873 nm radiation (Put differently, the photon

energy corresponding to 873 nm, 1.42 eV, is larger than theEg, 1.1 eV, of Si which

mean that the Si photodetector can indeed detect the 873 nm radiation)

Bandgap and Photodetection

(c) From the known energy gap of the semiconductor GaAs (Eg= 1.42 eV), calculate the

primary wavelength of photons emitted from this crystal as a result of electron-hole

recombination. Is this wavelength in the visible?

(d) Will a silicon photodetectorbe sensitive to the radiation from a GaAs laser? Why?

Solution

Example


52/80

&bsorption coe!cient

'a( ) dis the thicness o a photodetector material, Iois the

intensity o the incoming radiation, the number o photons

absorbedper unit volume o sample is

hd

dInph

+e(p*34

(a) IfI0is the intensity of incoming radiation (energy flowing per unit area per

second),I0exp( d )is the transmitted intensity through the specimen with

thickness dand thusI0exp( d )is the absorbed intensity

Solution

Example


53/80

0

0.2

0.4

0.6

0.8

1

800 1000 1200 1400 1600 1800

Wavelength (nm)

Responsivity (A/W)

The responsivity of an InGaAspin photodiode

InGaAspinPhotodiodes

Consider a commercial InGaAspinphotodiode whose responsivity is shown in fig.

Its dark current is 5 nA.

(a) What optical power at a wavelength of 1.55 m would give a photocurrentthat is twice the dark current? What is the QE of the photodetector at 1.55

m?

(b) What would be the photocurrent if the incident power in a was at 1.3 m?What is the QE at 1.3 m operation?

Solution


54/80

Solution

(a) At = 1.5510-6m, from the responsivity vs. wavelength curve wehave R0.87 A/W. From the definition of responsivity,

we have

From the definitions of quantum efficiency and responsivity,

Note the following dimensional identities: A = C s-1and W = J s-1so that A W-1= C J-1.

Thus, responsivity in terms of photocurrent per unit incident optical poweris also charge

collected per unit incident energy.

4+*+*

PI

WPowerOpticalIncidentAntPhotocurreR

ph

nWWA

A

R

I

R

IP dark

ph5.33

+/67.4

+*345118

4

hc

e

h

eR

9+74*74.4+3455.3+*34:.3*

+/67.4+*/342sec+*34:1.:*38

62;

mcoul

WAsmJ

e

hcR


55/80

Optical receiver operation


56/80

undamental receiver operation


57/80


3n optical &% consists of photo-detector" an amplifier"

and signal processing circuitry


58/80

Digital Signal $ransmission



59/80


!he transmitted signal is two-le#el binary data

stream consisting of either a + or 1 in a timeslot of duration !b

!his slot is 9nown as bit period

!o transmit these bits we assume A#$ andCoding technique is%R&

Error Sources


60/80

Error Sources

Errors in the detection mechanism can arise from #arious

noises and disturbances associated with the signal

detection system

!he term noise can be defined as Kany unwanted

components of electrical signal that tend to disturb the

transmission and processing of the signal in a physicalsystem" and o#er which we ha#e no controlL

!here are #arious sources of noise li9e internal" e%ternalM

4ere" our focus is only noise due to internal source li9e

shot noise and thermal noise

=hich is due the spontaneous fluctuations of current and

#oltage in electric circuit

Error Sources


61/80

o Sou ces

Error Sources


62/80

!he random arri#al rate of signal photons

produces a shot noise at the photo-detector !his noise depends on the signal le#el" when

using the a#alanche photodiode in &%" an

additional shot noise arises due to multiplicationprocess

!his noise is increases with increasing the

a#alanche gain J

3dditional photo-detector noise come form the

dar9 and lea9age current" which are independent

with photodiode illumination

Error Sources


63/80

!hermal noises arising from the detector load

resistor and from the amplifier !he analysis of the noises and resulting error

probabilities associated with the primary

photocurrent generation and the a#alanchemultiplication are complicated" since neither of

these process is aussian

!he primary photocurrent generated by the

photodiode is a time-#arying process resulting

from the random arri#al of photons at the

detector

Error Sources


64/80

If the detector is illuminated by an optical signal

p't)" then a#erage number of electron-hole pairs 2generated in a time N is

!he actual number of electron-hole pairs n that are

generated fluctuates from the a#erage #alue

according to the .oisson distribution

It is not possible to predict e%actly how manyelectron-hole pairs are generated by a 9nown optical

power incident on the detector is the origin of the

type of shot noise called quantum noise

==

+

)'h

EdttP

h%

O)'

n

e%nP

%n

r

=

Error Sources


65/80

3 further noise source is I#I" which results from

the pulse spreading in the fiber

Receiver onfiguration


66/80

g

3 schematic diagram of &% is shown below !he

G basic stage of &% are a photo detector" anamplifier" and an equali$er



67/80

g

.hoto-detector may be a#alanche with a gain J or pin for

which JP1

!he photodiode has a quantum efficiency < and a capacitance

cd

!he detector bias resistor &b which generates the thermal

noise current ib't) !he amplifier has an i*p impedance which is a parallel

combination of &aand Ca

>oltage appearing across this impedance causes current to

flow in the amplifier output !he amplifier is basically #oltage-controlled current source

!he equali$er that follows the amplifier is a linear frequency-

shaping filter to rectify the II effect



68/80

g

!he binary digital pulse train incident on the

photo-detector

!he mean output current from the photodiode at

time t resulting from the pulse train Eqmentioned abo#e

=here" p't) is o*p optical powerQ bn is theamplitude" hp is the recei#ed pulse shape" and &+

is the responsiti#ity

=

=n

'pn n!th'tP )')'

=

==n

'pn !th'MtMPh

qti )')')' +

Digital Receiver Performance


69/80

g

In a digital &% the amplified and filtered signal

o*p of the equali$er is compared with thethreshold le#el once per time slot to determine

whether or not a pulse is present at the photo-

detector in the time slot

Ideally" the o*p signal #out't)would always e%ceed

the threshold #oltage when 1 is present and would

be less than the threshold when no pulse was sent

(ut in actual system" de#iation from the a#erage

#alue of #out't) caused by #arious noises"

interference from ad8acent pulses" etc

Pro"a"ilit& of Error


70/80

&

One common way to calculate the error rate or 'it

error rate 'BER)" di#ide the number 2e of errorsoccurring o#er a certain time inter#al t by the

number 2tof pulses transmitted during this inter#al

=here (P1*!b

!ypical error rates for optical fiber

telecommunications system range from 1+-Rto 1+-1,

Jeaning the one error for e#ery billion pulses sent

!o compute the (E& at &%" we ha#e to 9now the

prob 0istribution of signal at the equali$er o*p

Bt

%

%

%BER e

t

e ==


71/80

.1'#) is the prob !hat the equali$er o*p #oltage is less than # when a logical 1 pulse is sent

.+'#) is the prob !hat the equali$er o*p #oltage is e%ceed # when a logical + pulse is sent

Pro"a"ilit& of Error


72/80

&

If the threshold #oltage is #ththen the error prob .e

is defined as =here a F b are determined by the a priori

distribution of the data =here f+'y) is aussian

distribution

)')' +1 ththe v'PvaPP +=

==

==

thth

thth

vv

th

vv

th

d((fd))PvP

d))fd))PvP

)')1*')'

)')+*')'

1+

++


73/80

dvv'

vP

dv

'v

vP

esf

th

th

v

on

on

on

th

v off

off

off

th

ms

=

=

=

,

,

1

,

,

+

,*)'

,

)'e%p

,

1)'

,

)'

e%p,

1

)'

,

1)'

,,

-ean is band :; is!ariance


74/80

=

=

=

=

==

x

)

on

thon

off

offth

*

*

x

e

d)exerf

v''v

*

*

e*erf

dxe*PBER

+

,*

,*

,

,

,

,)'

,

1)

,'1

,

1

1)'

$!e ,uantum Limit


75/80

=hen all system parameters are ideal and the

performance is limited only by the photo-detection

statistics

In other words" suppose we ha#e an ideal photodiode

ha#ing


76/80

3lthough" digital transmission through optical lin9

ha#ing wide usage" there are many applications foranalog lin9s as well

!hese range from indi#idual ? S4$ #oice channel

to microwa#e lin9s operating in 4$ region

or analog &%" the performance is measured in

terms of asigna+-to-noise ratio

!he simplest analog lin9 use 3J for signaltransmission

hown in the ne%t slide


77/80

%nalog R(


78/80

!ransmitted optical power p't) and modulation

inde% are in the form

.t is the a#erage transmitted optical power" s't) is

analog modulation signal" TI is the #ariation currentabout the bias point" and I(is the bias current

In order to minimi$e the distortion" it is desire to

confine the modulation process in the linear region 3t the &% end" the photocurrent generated by

analog optical signal is

[ ]

B

t

I

Im

tmsPtp

=

+= )'1)'

[ ]

[ ])'1

)'1)' +

tmsMI

tmsMPti

p

rs

+=

+=

%nalog R(


79/80

=here IpP&+.ris the primary photocurrent

!he mean square signal current at the photo detectoro*p is

!he mean square noise current is

I0 is the primary dar9 current" I/ surface lea9age

current" 'J) e%cess photodiode noise factor" ( noise

(=" &eq equi#alent resistance of photo-detector load

and amplifier" and tnoise figure of baseband amplifier

( ) ( ),,+,

,

1

,

1prs MmIMmPi ==

t

eq

B",p% F

R

!B-BqIBMFMIIqi

?,)')',

,, +++=

%nalog R(


80/80

=ith the assumption" the negligible lea9age

current" the *2

( )

( )

( ) )'1Q?,

1

?,

1

?)')',

,

1

?)')',

,

1

,,

+

,,

,

,

,

+

,

+

,

,

pinforM

FR

!B-Pm

FR

!B-mI

FR

!B-BMFMIIq

MmI

FR

!B-BMFMIPq

MmPii

%#

t

eq

B

r

t

eq

B

p

t

eq

B,p

p

t

eq

B,r

r

%

s

=

=

++

=

++

=

=

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