Optical Soft Copy May- June 2013

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PART B

11.a)i) Derive the mode equations for circular fiber using Maxwell’s equation

Modes

The exact solution of Maxwell’s equations for a cylindrical homogeneous core

dielectric waveguide* involves much algebra and yields a complex result Although the

presentation of this mathematics is beyond the scope of this text, it is useful to consider

the resulting modal fields. n common with the planar guide T! "where Ez # $% and TM"where Hz # $% modes are obtained within the dielectric cylinder. The cylindrical

waveguide, however, is bounded in two dimensions rather than one. Thus two integers, l

and m, are necessary in order to specify the modes, in contrast to the single integer " m%required for the planar guide. &or the cylindrical waveguide we therefore refer to T! lm

and TMlm modes. These modes correspond to meridional rays traveling within the fiber.

'owever, hybrid modes where Ez and Hz are non(ero also occur within the cylindricalwaveguide. These modes, which result from s)ew ray propagation within the fiber, are

designated '!lm and !'lm depending upon whether the components of H or E ma)e thelarger contribution to the transverse "to the fiber axis% field. Thus an exact description of

the modal fields in a step index fiber proves somewhat complicated.

&ortunately, the analysis may be simplified when considering optical fibers for communication purposes. These fibers satisfy the wea)ly guiding approximation where

the relative index difference + . This corresponds to small gra(ing angles in n fact is usually less than $.$- "-% for optical communications fibers. &or wea)ly guiding

structures with dominant forward propagation, mode theory gives dominant transverse

field components. 'ence approximate solutions for the full set of '!, !', T! and TM

modes may be given by two linearly polari(ed components .These linearly polari(ed "/0%modes are not exact modes of the fiber except for the fundamental "lowest order% mode.'owever, as in wea)ly guiding fibers is very small, then '!1!' mode pairs occur which have almost identical propagation constants. 2uch modes are said to be degenerate.

The superpositions of these degenerating modes characteri(ed by a common propagationconstant correspond to particular /0 modes regardless of their '!, !', T! or TM field

configurations. This linear combination of degenerate modes obtained from the exact

solution produces a useful simplification in the analysis of wea)ly guiding fibers.


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The relationship between the traditional '!, !', T! and TM mode designations

and the /0lm mode designations is shown.. The mode subscripts l and m are related to theelectric field intensity profile for a particular /0 mode .There are in general 3l field

maxima around the circumference of the fiber core and m field maxima along a radius

vector. &urthermore, it may be observed from Table 3. that the notation for labeling the

'! and !' modes has changed from that specified for the exact solution in the

cylindrical waveguide mentioned previously. The subscript l in the /0 notation nowcorresponds to '! and !' modes with labels l 4 and l 5 respectively. The electric field

intensity profiles for the lowest three /0 modes, together with the electric fielddistribution of their constituent exact modes, are shown in &igure 3.6.


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t may be observed from the field configurations of the exact modes that the field

strength in the transverse direction " Ex or Ey% is identical for the modes which belong to

the same /0 mode. 'ence the origin of the term 7linearly polari(ed’. 8sing !q. for thecylindrical homogeneous core waveguide under the wea) guidance conditions outlined

above, the scalar wave equation can be written in the form where is the field " E or H%,

n is the refractive index of the fiber core, k is the propagation constant for light in avacuum, and r and are cylindrical coordinates. The propagation constants of the guidedmodes lie in the range9where n3 is the refractive index of the fiber cladding. 2olutions of the wave equation for the cylindrical fiber are separable, having the form9

where in this case represents the dominant transverse electric field component. The periodic dependence on following cos l or sin l gives a mode of radial order l . 'encethe fiber supports a finite number of guided modes of the form

11.a)ii)

11.b)i) Explain the ra theor of fiber with a special mention about !"#$ %cceptance

angle and &%.' #efer the (uestion 1.b.i) in the %nna universit (* &+,-DE

/01


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11.b)ii) Describe the single mode fiber and their mode 2field diameter.3hat are the

propagation modes in them4

Single Mode Fibers

The core size of single mode fibers is small. The core size (diameter) is typically

around 8 to 10 micrometers (μm). A fiber core of this size allows only the

fundamental or lowest order mode to propagate around a 1300 nanometer (nm)

wavelength. Single mode fibers propagate only one mode, because the core size

approaches the operational wavelength (λ). The value of the normalizedfrequency parameter (V) relates core size with mode propagation.

In single mode fibers, V is less than or equal to 2.405. When V ≤ 2.405, single

mode fibers propagate the fundamental mode down the fiber core, while high-order

modes are lost in the cladding. For low V values (≤1.0), most of the power ispropagated in the cladding material. Power transmitted by the cladding is easily lost atfiber bends. The value of V should remain near the 2.405 level.

Single mode fibers have a lower signal loss and a higher information capacity

(bandwidth) than multimode fibers. Single mode fibers are capable of transferring higher

amounts of data due to low fiber dispersion. Basically, dispersion is the spreading of lightas light propagates along a fiber. Dispersion mechanisms in single mode fibers are

discussed in more detail later in this chapter. Signal loss depends on the operationalwavelength (λ). In single mode fibers, the wavelength can increase or decrease

the losses caused by fiber bending. Single mode fibers operating at wavelengths larger

than the cutoff wavelength lose more power at fiber bends. They lose power because lightradiates into the cladding, which is lost at fiber bends. In general, single mode fibers are

considered to be low-loss fibers, which increase system bandwidth and length.

M+DE 25"E6D D"%ME!E#

The typical core diameter of communication single mode fibers is from :;$umfor operating wavelength .-um to .6um. &iber with a core diameter less than about ten

times the wavelength of the propagating light cannot be modeled using geometric optics

as we did in the explanation of stepaussian power distribution "lasers used in communications are Gaussian power

distribution% in a single mode optical fiber, the mode field diameter "M5D% is defined asthe point at which the electric and magnetic field strengths are reduced to ?e of their


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maximum values, i.e., the diameter at which power is reduced to ?e3 "$.-6% of the pea)

power "because the power is proportional to the square of the field strength%.

&or single mode fibers, the pea) power is at the center of the core. Mode fielddiameter is slightly larger than the core diameter, as shown in the following illustration.

Mode Theory :

The mode theory, along with the ray theory, is used to describe the propagation

of light along an optical fiber. The mode theory is used to describe the properties of lightthat ray theory is unable to explain. The mode theory uses electromagnetic wave

behavior to describe the propagation of light along a fiber. A set of guided

electromagnetic waves is called the modes of the fiber.

1/.a)i) Describe the expression for material dispersion and wave guide dispersion

and explain them.

o Material dispersion occurs because the spreading of a light pulse is

dependent on the wavelengths' interaction with the refractive index of the

fiber core. Different wavelengths travel at different speeds in the fiber

material. Different wavelengths of a light pulse that enter a fiber at one

time exit the fiber at different times. Material dispersion is a function of

the source spectral width. The spectral width specifies the range of

wavelengths that can propagate in the fiber. Material dispersion is less at

longer wavelengths.

o Waveguide dispersion occurs because the mode propagation constant

(β) is a function of the size of the fiber's core relative to the

wavelength of operation. Waveguide dispersion also occurs because light

propagates differently in the core than in the cladding.

o In multimode fibers, waveguide dispersion and material dispersion are

basically separate properties. Multimode waveguide dispersion is generally

small compared to material dispersion. Waveguide dispersion is usually

neglected.

o However, in single mode fibers, material and waveguide dispersion are

interrelated.


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• The total dispersion present in single mode fibers may be minimized by tradingmaterial and waveguide properties depending on the wavelength of operation.


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Material Dispersion:

Material dispersion occurs because the index of refraction varies as a function ofthe optical wavelength. Or alternately, we can say that β varies with n(λ).

Material dispersion is an intramodal effect and of particular importance for single-mode and LED systems.

Let the variation in the index of refraction be n(λ). The propagation constant isnow

The group delay due to material dispersion is then

The total dispersion of a length L is then

In terms of rms, the pulse spread σmat is


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Waveguide Dispersion:

. @aveguide dispersion occurs because a single


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o The first term in the equation is a constant. It is the time delay for a light

pulse traveling in a waveguide where n2 = a constant.

o The second term above is the group delay arising from waveguidedispersion.

o The author then shows the V factor in terms of Bessel functions.

Main message on waveguide dispersion:

o The group delay is different for every guided mode.

o For small radius waveguides, waveguide dispersion can be significant.

o For large radius waveguides (multimode), waveguide dispersion is verysmall and can be neglected.

1/.a)ii) Describe various tpes of fiber connectors and couplers

5iber connectors

Cemountable fiber connectors are more difficult to achieve than optical fiber

splices. This is because they must maintain similar tolerance requirements to splices inorder to couple

light between fibers efficiently, but they must accomplish it in a removable fashion. Also,the connector design must allow for repeated connection and disconnection without

problems of fiber alignment, which may lead to degradation in the performance of the

transmission line at the Doint. 'ence to operate satisfactorily the demountable connector must provide reproducible accurate alignment of the optical fibers. n order to maintain an

optimum performance the connection must also protect the fiber ends from damage which

may occur due to handling "connection and disconnection%, must be insensitive toenvironmental factors "e.g. moisture and dust% and must cope with tensile load on the

cable. Additionally, the connector should ideally be a low


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expanded beam connectors. Futt


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"a% cleaving the fiber before insertion into the ferruleE

"b% inserting and bonding before cleaving the fiber close to the ferrule end faceE

"c% using either "a% or "b% and polishing the fiber end face until it is flush with the end of the ferrule. 0olishing the fiber end face after insertion and bonding provides the best

results but it tends to be time consuming and inconvenient, especially in the field.

Dule! and "ultile#$%er connectors

A number of duplex fiber connector designs were developed in order to provide

two


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the American Iational 2tandards nstitute "AI2% specification for use within optical

fiber /AIs This connector plug will mate directly with connectori(ed optical /AI

components "i.e. transmitters and receivers%. A duplex fiber connector for use with the&iber Cistributed Cata nterface also subsequently became commercially available. t

comprised two 2T ferrules housed in a protective molded shroud and exhibits a typical

insertion loss of $.G dF. 'ence, such duplex connectors were preferred for their simplicity. Multiple


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A possible drawbac) with fusion splicing is that the heat necessary to fuse the

fibers may wea)en the fiber in the vicinity of the splice. t has been found that even withcareful handling, the tensile strength of the fused fiber may be as low as -$ of that of

the uncoated fiber before fusion JKef. LL. The fiber fracture generally occurs in the heat

affected (one adDacent to the fused Doint. The reduced tensile strength is attributed to thecombined effects of surface damage caused by handling, surface defect growth during

heating and induced residential stresses due to changes in chemical composition. t is

therefore necessary that the completed splice is pac)aged so as to reduce tensile loading

upon the fiber in the vicinity of the splice.

Mechanical splicing

A number of mechanical techniques for splicing individual optical fibers have

been developed. A common method involves the use of an accurately produced rigid

alignment tube


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into which the prepared fiber ends are permanently bonded. This snug tube splice is

illustrated in &igure 6.:"a% JKef. L: and may utili(e a glass or ceramic capillary with an

inner diameter Dust large enough to accept the optical fibers. Transparent adhesive "e.g.epoxy resin% is inDected through a transverse bore in the capillary to give mechanical

sealing and index matching of the splice. Average insertion losses as low as $. dF have

been obtained with multimode graded index and single


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18.a)i) Draw the structure of 96ED and E6ED $ explain the principles of operation

Edge emitter 6EDs

Fasic high


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The enhanced waveguiding of the edge emitter enables it in theory to couple O.6

times more power into low


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9uperluminescent 6EDs

Another device geometry which is providing significant benefits over both 2/!Csand !/!Cs for communication applications is the superluminescent diode or 2/C. This

device type offers advantages of9 "a% a high output powerE "b% a directional output beamE

and "c% a narrow spectral linewidth 1 all of which prove useful for coupling significantoptical power levels into optical fiber "in particular to single


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18.a)ii) Draw the in7ection 6aser diode structure explain it. ' #efer the question

18.a)i) in anna universit (* /01

18.b)i)Draw the *"& and %*D photo detectors and explain their operations.

PIN PHOTODIODES

A PIN photodiode is a semiconductor positive-negative (p-n) structure with an

intrinsic region sandwiched between the other two regions (see figure 7-2). It is normally

operated by applying a reverse-bias voltage. The magnitude of the reverse-bias voltage

depends on the photodiode application, but typically is less than a few volts. When no

light is incident on the photodiode, a current is still produced. This current is called the

dark current.The dark current is the leakage current that flows when a reverse bias is

applied and no light is incident on the photodiode. Dark current is dependent ontemperature. While dark current may initially be low, it will increase as the device

temperature increases.

Response Time

There are several factors that influence the response time of a photodiode and itsoutput circuitry .


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The most important of these are the thickness of the detector active area and thedetector RC time constant. The detector thickness is related to the amount of time

required for the electrons generated to flow out of the detector active area. This time is

referred to as the electron transit time. The thicker the detector active area, the longer the

transit time will be.

Figure 7-3. - A schematic representation of a photodiode.

Figure 7-2. - The basic structure of a PIN photodiode

The capacitance (C) of the photodiode and the resistance (R) of the load formthe RC time constant. The capacitance of the photodetector must be kept small to preventthe RC time constant from limiting the response time. The photodiode capacitanceconsists mainly of the junction capacitance and any capacitance relating to packaging.

The RC time constant is given by tRC = RC. Trade-offs between fast transit times andlow capacitance are necessary for high-speed response.

However, any change in photodiode parameters to optimize the transit


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time and capacitance can also affect responsivity, dark current, and coupling efficiency. A

fast transit time requires a thin detector active area, while low capacitance and high

responsivity require a thick active region.

The diameter of the detector active area can also be minimized. This reduces the

detector dark current and minimizes junction capacitance. However, a minimum limit onthis active area exists to provide for efficient fiber-to-detector coupling.

Linearity

Reverse-biased photodetectors are highly linear devices. Detector linearity means

that the output electrical current (photocurrent) of the photodiode is linearly proportionalto the input optical power. Reverse-biased photodetectors remain linear over an extended

range (6 decades or more) of photocurrent before saturation occurs. Output saturation

occurs at input optical power levels typically greater than 1 milliwatt (mW). Because fiber

optic communications systems operate at low optical power levels, detector saturation is

generally not a problem.

AVALANCHE PHOTODIODES

An avalanche photodiode (APD) is a photodiode that internally amplifies the

photocurrent by an avalanche process.

Figure 7-4 shows an example APD structure. In APDs, a large reverse-bias

voltage, typically over 100 volts, is applied across the active region. This voltage causes

the electrons initially generated by the incident photons to accelerate as they move

through the APD active region.

As these electrons collide with other electrons in the semiconductor material, they

cause a fraction of them to become part of the photocurrent. This process is known as

avalanche multiplication. Avalanche multiplication continues to occur until the electrons

move out of the active area of the APD.

The gain of the APD can be changed by changing the reverse-bias voltage. A

larger reverse-bias voltage results in a larger gain. However, a larger reverse-bias voltage

also results in increased noise levels. Excess noise resulting from the avalanche

multiplication process places a limit on the useful gain of the APD. The avalanche

process introduces excess noise because every photogenerated carrier does not undergothe same multiplication.

The noise properties of an APD are affected by the materials that the APD is made

of. Typical semiconductor materials used in the construction of low-noise APDs include

silicon (Si), indium gallium arsenide (InGaAs), and germanium (Ge).


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.

U Figure 7-4. - The basic structure of an APD

Trade-offs are made in APD design to optimize responsivity and gain, dark

current, response time, and linearity. This chapter does not attempt to discuss trade-offs in

APD design in more detail. Many aspects of the discussion provided on responsivity, dark current, and response time provided in the PIN photodiodes section also relate to APDs.

The response time of an APD and its output circuitry depends on the same factors as PIN

photodiodes. The only additional factor affecting the response time of an APD is the

additional time required to complete the process of avalanche multiplication. To learn

more about APD design trade-offs and performance parameters.


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18.b)i)Derive the expression for 9 of both *"& and %*D photo detectors .

PHOTODETECTOR NOISE & S/N:

• Detection of weak optical signal requires that the photodetector and itsfollowing amplification circuitry be optimized for a desired signal-to-noise ratio.

• It is the noise current which determines the minimum optical power level thatcan be detected. This minimum detectable optical power defines the sensitivity of photodetector. That is the optical power that generates a photocurrent with theamplitude equal to that of the total noise current (S/N=1)

Figure shows an example APD structure. In APDs, a large reverse-bias voltage,

typically over 100 volts, is applied across the active region.

This voltage causes the electrons initially generated by the incident photons to

accelerate as they move through the APD active region.

As these electrons collide with other electrons in the semiconductor material, they

cause a fraction of them to become part of the photocurrent.

This process is known as avalanche multiplication. Avalanche multiplication

continues to occur until the electrons move out of the active area of the APD.

The gain of the APD can be changed by changing the reverse-bias voltage. A

larger reverse-bias voltage results in a larger gain. However, a larger reverse-bias voltage

also results in increased noise levels.

Excess noise resulting from the avalanche multiplication process places a limit onthe useful gain of the APD. The avalanche process introduces excess noise because every

photogenerated carrier does not undergo the same multiplication.


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S =

signal power from photocurrent

N photodetector noise power + amplifier noise power

Signal Calculation:

Consider the modulated optical power signal P(t) falls on the photodetector withthe form of

P(t ) = P [1+ ms(t )]0

Where s(t) is message electrical signal and m is modulation index. Therefore theprimary photocurrent is (for pin photodiode M=1):

i =ηq

MP(t ) = I P

[DC value] + i p

(t )[AC current]ph

h ν

The root mean square signal current is then

is 2 = i p 2 M 2 = σs 2

i 2 = σ2 = m

2 I P

2

for sinusoidal signal p p 2

Noise Sources in Photodetecors :

l The principal noises associated with photodetectors are :1- Quantum (Shot) noise: arises from statistical nature of the production

and collection of photo-generated electrons upon optical illumination. It

has been shown that the statistics follow a Poisson process.

2- Dark current noise: is the current that continues to flow through the bias


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circuit in the absence of the light. This is the combination of bulk dark

current, which is due to thermally generated e and h in the pn junction,

and the surface dark current, due to surface defects, bias voltage an

surface area.• In order to calculate the total noise presented in photodetector, we should sum up

the root mean square of each noise current by assuming that those areuncorrelated.

• Total photodetector noise current=quantum noise current +bulk dark current noise+ surface current noise

Noise calculation :

Quantum noise current (lower limit on the sensitivity):

i 2 = σ 2 = 2qI P BM 2 F ( M )

Q Q

B: Bandwidth, F(M) is the noise figure and generally is

F ( M ) ≈ M x 0 ≤ x ≤ 1.0

Bulk dark current noise:

2 2

= 2qI D BM

2

F ( M )i DB = σ DB

Surface dark current noise

2

= σ

2

= 2qI L Bi DS

DS

The total rms photodetector noise current is:

i N 2 = σ N 2 = iQ 2 + i DB 2 + i DS 2

= 2q( I P + I D ) BM 2 F ( M ) + 2qI L B

The thermal noise of amplifier connected to the photodetector is:

iT 2

= σ T 2 = 4 k BTB R L


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S/N CALCULATION:

Having obtained the signal and total noise, the signal-to-noise-ratio can be written as:

S =

iP 2 M 2

+ I ) BM 2 F ( M ) + 2qI

B + 4k TB / R N 2q( I

P D L

L B

Since the noise figure F(M) increases with M, there always exists an optimum value of M thatmaximizes the S/N. For sinusoidally modulated signal with m=1 and F ( M ) ≈ M x

:

x+2

=2qI L + 4k BT / R L M

opt + I D ) xq( I P

1.a) 3hat are the various tpes of pre amplifiers available for optical networ:s and

explain.

The choice of circuit configuration for the preamplifier is largely dependent upon the

system application. Fipolar or field effect transistors "&!Ts% can be operated in three usefulconnections. These are the common emitter or source, the common base or gate, and the emitter

or source follower for the bipolar and field effect transistors respectively. !ach connection hascharacteristics which will contribute to a particular preamplifier configuration.

t is therefore useful to discuss the three basic preamplifier structures "lowimpedance,

high


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choosing a transistor with characteristics which give a high current gain at a low emitter

current in order to maintain the bandwidth of the stage. Also, an inductance may be inserted at

the collector to provide partial equali(ation for any integration performed by the stage. Thealternative connection giving very low input impedance is the common base circuit.

8nfortunately, this configuration has an input impedance which gives insufficient power gain

when connected to the high impedance of the optical detector. The preferred preamplifier

configurations for low


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Two configurations which provide a low


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1.b) 3ith diagram explain the following

a. Measurement of #efractive index profile

b. Measurement of ut off wavelength

' #efer the question 1.b) in %nna universit (* &+,-DE /01

1;.a)i) Explain the 9%-9% *rotocol and modified 9%-9% *rotocol of broadcast and select

networ:s

The nternet 0rotocol "0% is a networ) layer "i.e. layer - protocol in the V2 model% that

contains both addressing and control information to enable pac)ets "or datagrams% to be routed

within a networ). The nternet can be characteri(ed as a logical architecture "independent of any particular networ)% which can permit multiple different networ)s to be interconnected enabling

each networ) node to communicate without the need to )now which networ) it is using or how

to route information between them. As indicated in &igure 6.6, the 0 provides the means of communication between the lin) and transport layers. A virtual connection is established

between nodes requiring communication when 0 is combined with a specific higher level

protocol such as the Transmission Rontrol 0rotocol "TR0% or the 8ser Catagram 0rotocol "8C0%

&or this role TR0?0 is preferred, since 8C0?0 does not guarantee reliable delivery of data incomparison with TR0?0, which generally encapsulates data from the lin) layer protocols such as

!thernet The 0 provides protocols for both the functions of signaling and routing required to

carry the entire signal operation necessary to transmit and receive from optical nodes. Thesignaling protocols include Multiprotocol /abel 2witching "M0/2% and >enerali(ed

Multiprotocol /abel 2witching ">M0/2% while the routing protocols include the Vpen 2hortest<

0ath &irst "V20&%, the ntermediate


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overlap of 0 pac)ets which map significantly outside the ATM cell si(e. Therefore service

providers are considering running 0 content directly over 2VI!T "i.e. 0 over

2VI!T%. n order to carry 0 pac)ets, however, mapping of the 0 pac)ets directly to the2C'?2VI!T frames is required and the resultant technique is referred to as pac)et over

2VI!T "0o2%. This mapping of 0 frames can be accomplished in three stages. n the first

stage the data is segmented into 0 pac)ets which are then encapsulated via the 0ointto


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6aers

hierarchy of signals, all multiple of basic rate "6$.G::%

basic rate about 6$ Mbps to carry C2- payload

bit


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path 1 end


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• 2TM


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changes are equivalent to self

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Optical Soft Copy May- June 2013