System design is an iterative process Will vary from system to system System Planning Tools Initial...

System PlanningSystem design is an iterative processWill vary from system to system

Design and Planning IssuesNetwork design and planning Individual link/route designComponent selection

System Design and PlanningSystem Planning ToolsSystem SpecificationPhotonic Layer DesignPrototype System Performance TestsPhysical planning including cable types, duct routes etcCommunications StandardsCable and Installation StandardsOperational RequirementsElectronicDesign

System SpecificationsWide variety of specifications will emerge at an early stage:Relevant specifications will depend on whether you are the either the system specifier, equipment supplier, installation contractor, sub-contractor.Physical: System topology, including cable location and/or cable routesExisting cable protection, (none or building ducts or underground ducts)Cable specifications based on standards, ( fibre, moisture ingression etc..)Number of fibres per cable, upgrade requirementsNetwork issuesNetwork application and proposed topology, network evolution plansTransmission standards, bit rates, coding, multiplexing etc..Fibre MM or SM, core size, fibre NA, fibre attenuation, fibre dispersion, all with tolerancesConnector type, loss and reflection, tolerancesSplices, mechanical or fusion, loss and tolerancesTermination enclosures, access or patch panels etc..SystemCompleted power and bandwidth budgets, source types: power and spectral width etc..Civil works, delivery of fibre, trunking/conduit installation, splicingSystem testing, acceptance tests, documentation etc..

Tools for System PlanningLink Bandwidth analysisPower Penalty evaluationPower Budget calculationThe purpose of so-called Photonic layer design process is to ensure that:The optical power reaching the receiver is adequate.The link bandwidth is adequate.TransmitterTerminalReceiverTerminalOptical Fibre ConnectorOptical Fibre SpliceOptical FibreLegend

Power Budgeting

Power BudgetingThe purpose of power budgeting is to ensure that:The optical power reaching the receiver is adequate under all circumstancesNo component has an excessive lossTransmitterTerminalReceiverTerminalOptical Fibre ConnectorOptical Fibre SpliceOptical FibreLegendA receiver in an Optical Systemrequires a minimum optical inputpower to operate with a specifiederror probabilityGraph shows error probability versus received power for a 622 Mbits/secsystem

Power Budget DefinitionPower budget is the difference between:The minimum (worst case) transmitter output powerThe maximum (worst case) receiver input requiredPower budget value is normally taken as worst case. In practice a higher power budget will most likely exist but it cannot be relied upon Available power budget may be specified in advance, e.g for 62.5/125 fibre in FDDI the power budget is 11 dB between transmitter and receiverTRANSMITTERRECEIVERFibre, connectors and splicesPower Budget (dB)

Fibre, connectors and splices connect the transmitter to the receiverOPTICALRECEIVEROPTICAL TRANSMITTER

Photonic Layer DesignPower BudgetingThe purpose of so-called Photonic layer design process is to ensure that:The optical power reaching the receiver is adequate under all circumstancesThe link bandwidth is adequate.TransmitterTerminalReceiverTerminalOptical Fibre ConnectorOptical Fibre SpliceOptical FibreLegendPhotonic layer design involves:Carrying out a power budget calculation An evaluation of any power penalties Available power budget may be specified in advance, e.g for 62.5/125 fibre in FDDI the power budget is 11 dB between transmitter and receiverA receiver in an Optical System requires a minimum optical input power to operate as specified

Use of Power BudgetsAssume worst case transmitter output power is -10 dBm and the worst case receiver input power needed is -25 dBm Power budget =- 10 dBm - ( - 25 dBm )= 15 dB That is 15 dB of attenuation is possible over the link before failure occursAs a simple example to find the maximum fibre attenuation we eliminate from the 15 dB budget the loss due to connectors and splices

Less: Connector attenuation = 1 dBTotal splice attenuation= 1.2 dBSo: Total fibre attenuation allowed = 15 - 1 - 1.2 = 12.8 dB

Power budget calculations can produce a number of different results depending on how they are carried out. To check if adequate receiver power will be available, under all conditionsBased on a knowledge of the receiver sensitivity to determine the maximum loss of some component. Simple example to find total fibre loss allowed:Source: Master 5_1

Launch PowerLED/Laser SourceFibreTransmitter output power quoted in specifications is by convention the launch power.Launch power is the optical power coupled into the fibre.Launch power is less than the LED/Laser output power.Calculation of launch power for a given LED/Laser and fibre is very complex.Launch power

Power MarginPower margins are included for a number of reasons:To allow for ageing of sources and other components.To cater for extra splices, when cable repair is carried out.To allow for extra fibre, if rerouting is needed in the future.To allow for upgrades in the bit rate or advances in multiplexing.Remember that the typical operating lifetime of a communications transmission system may be as high as 20 to 30 years.No fixed rules exist, but a minimum for the power margin would be 2 dB, while values rarely exceed 8-10 dB. (depends on system)

Sample Power Budget Calculation (Telecoms)Fibre is normally only available in fixed lengths up to 2 km long, so fusion splices are required, to join lengths. In buildings fibre lengths will be much shorterIn most systems only two connectors are used, one at the transmitter and one the receiver terminal. Power budget calculation including power penalty used to calculate power marginTransmitter o/p power (dBm)Number of ConnectorsConnector loss per connector (dB)Total connector loss (dB)Fibre span (km)Fibre loss (dB/Km)Total fibre loss (dB)Splice interval (Km)Number of splicesSplice loss per splice (dB)Total splice loss (dB)Dispersion penalty estimate (dB)Receiver sensitivity (dBm)Power margin (dB)020.51700.2517.50.8870.043.461.5-306.54AnswerSystem: 70 km span, 0.8 km between splices

Sample Power Budget Calculation (FDDI System)Splices within patchpanels and other splice closuresIn most systems connectors are used at the transmitter and receiver terminals and at patchpanels. Power budget calculation used to calculate power marginTransmitter o/p power (dBm)Number of ConnectorsWorst case Connector loss (dB)Total connector loss (dB)Fibre span (km)Maximum Fibre loss (dB/Km)Total fibre loss (dB)Number of 3M Fibrlok mechanical splicesWorst case splice loss per splice (dB)Total splice loss (dB)Receiver sensitivity (dBm)Power margin (dB)-18.5 dBm min, -14.0dBm max60.714.262.01.5 dB at 1300 nm100.191.9-30 dBm min2.34AnswerAvailable power budget:11.5 dB using worst case value (>FDDI standard)Total loss:9.16 dB3.0

Sample Power Budget Exercise #1An optical fibre system is to operate at 622 Mbits/sec over a distance of 71 km without repeaters. Fibre with a worst case loss of 0.25 dB/km is available. The average distance between splices is approximately 1 km. There are two connectors and the worst case loss per connector is 0.4 dB. The power margin is to be at least 5 dB. The receiver sensitivity is -28 dBm and the transmitter output power is +1 dBm Determine the maximum allowable attenuation per fusion splice

Solution to Exercise #1Transmitter output power +1 dBmWorst case (lowest) optical output powerReceiver sensitivity-28 dBmMinimum input optical power requiredPower Budget29 dB Difference between transmitter and receiver levels.Less power margin5 dbAllowance for repair etc..Less connector loss 0.8 dBTwo connectors at 0.4 dB max. each.Less fibre loss 17.75 dB71 km at 0.25 dB/kmCalculated total maximum splice loss5.45 dBeg. 29 - 5 - 0.8 - 17.75 dB = 5.45 dBTotal number of splices71There are approximately 71 lengths of fibre in the link so there are approximately 71 splicesAnswer: Maximum splice loss0.076 dB

More Advanced Power Budgets using Power Penalties

More Advanced Power Budgets: Power PenaltiesDispersion.Dependent on bit rate and fibre dispersion, Typical dispersion penalty is 1.5 dBReflection from passive components, such as connectors.Crosstalk in couplers.Modal noise in the fibre.Polarization sensitivity.Signal distortion at the transmitter (analog systems only). More sophisticated power budget calculations will include power penalties.A power penalty is defined as the increase in receiver power needed to eliminate the effect of some undesirable system noise or distortionTypically power penalties can result from:

Dispersion Penalty

Dispersion Penalty Defined as:The increase in the receiver input power needed to eliminate the degradation in the BER caused by fibre dispersionTypical value is about 1.5 dB. Several analytic rules exist:Low pass filter approximation ruleAllowable pulse broadening (Bellcore) rule

Dispersion Penalty VisualisedDefined as the increase in the receiver input power needed to eliminate the degradation caused by dispersionDefined at agreed Bit Error Probability, typically 1 x 10-9In the sample shown the receiver power levels required at 1 x 10-9 with & without dispersion are -35.2 dBm & -33.1 dBm respectivelyThe dispersion penalty is thus 2.1 dB-28-30-32-34-36-38-40Received power level in dBm10-1110-1010-910-810-710-610-510-4Dispersion presentNo dispersion Bit Error ProbabilityDispersion penalty

-28-30-32-34-36-38-40Received power level in dBm10-1110-1010-910-810-710-610-510-4Dispersion presentNo dispersion Bit Error ProbabilityDispersion penalty

Dispersion Penalty Data

Low pass filter approximation rule for the Dispersion Penalty

Dispersion PenaltySimple analytic rule of thumb for calculating the dispersion penalty PdBased on two assumptions: that dispersion can be approximated by a low pass filter response.the data is the dotting 10101010 pattern. B is the bit rate in bits/sec and Dt is the total r.m.s impulse spread caused by dispersion over the fibre. To keep Pd < 1.5 dB, the B.Dt product must be less than 0.25 approximately.PBd=--101101222log(())pDt

Low pass filter approximation Dispersion Penalty Analysis (I)Assume that the transmitted pattern is very simple, e.g. the dotting pattern 10101010..... Also assume that most of the optical power in this pattern is contained in the component at f = B/2, where B is the bit rate and NRZ data is assumed. Finally for ease of analysis assume that A is 1.The extra attenuation caused by dispersion can be approximated by finding H(B/2). Effectively this extra attenuation appears as the dispersion penalty The transfer function for a fibre can be approximated by: ()[2]HfAft()=-12122pDA is the value of H(f) at DC, effectively the fibre attenuation. Dt is the RMS impulse broadening that occurs over the fibre.

Low pass filter approximationDispersion Penalty Analysis (II)Subsitute for H(B/2) using the formula for H(f) evaluated at f = b/2 to find PdTo compensate for this extra attenuation the transmitter output power must be increased by a factor:The dispersion penalty in dB is therefore:Pd=101)(HB210 Log []Pd=-1010 Log )(HB21)(HB2PBd=--101101222log(())pDtRearrange thus:

Allowable pulse broadening (Bellcore) rule for the Dispersion Penalty

Dispersion PenaltyApproach used in Bellcore recommendations for SONET over singlemode fibre, so it can be used for SDHSets defined values on dispersion penalty, 1 dB or 2 dB Based on defining ratio (e) of allowable pulse broadening (total dispersion, Dt) to the bit interval T, for a given dispersion penaltyAllows one to define maximum bit rate Bmax possible for a given dispersion penalty: Bmax < e10-6 .DtTotal dispersion, Dt is in picoseconds, ps, and the maximum bit rate Bmax is in Mbits/sec

Values of allowable pulse broadening ratio eValues shown for Lasers only - LEDs not used with singlemode fibre In practice multi-longitudinal mode lasers are an unlikely choice, most SDH transceivers use single-longitudinal mode lasers Laser TypeDispersion Penaltye valueMulti-longitudinal Mode 1 dB2 dB0.1150.182Single-longitudinal Mode1 dB2 dB0.3060.491

Maximum bit rate v Dispersion for different Penalties

Chart2

49.130.6

54.555555555634

61.37538.25

70.142857142943.7142857143

81.833333333351

98.261.2

122.7576.5

163.6666666667102

245.5153

491306

545.5555555556340

613.75382.5

701.4285714286437.1428571429

818.3333333333510

982612

1227.5765

1636.66666666671020

24551530

49103060

5455.55555555563400

6137.53825

7014.28571428574371.4285714286

8183.33333333335100

98206120

122757650

16366.666666666710200

2455015300

4910030600

54555.555555555634000

6137538250

70142.857142857143714.2857142857

81833.333333333351000

9820061200

12275076500

163666.666666667102000

245500153000

491000306000

2 dB Penalty

1 dB Penalty

Total Dispersion (ps)

Max Bit Rate (Mbits/sec)

Bellcore max bit rate ver d (2)

Max Bit rate (Mbits/sec)

Dispersion Ps1 dB Penalty2 dB Penalty

10,0003149

90003455

80003861

70004470

60005182

50006198

400077123

3000102164

2000153246

1000306491

900340546

800383614

700437701

600510818

500612982

4007651228

30010201637

20015302455

10030604910

9034005456

8038256138

7043717014

6051008183

5061209820

40765012275

301020016367

201530024550

103060049100

93400054556

83825061375

74371470143

65100081833

56120098200

476500122750

3102000163667

2153000245500

1306000491000


2 dB Penalty

1 dB Penalty



Comparison of max bit rates

Max Bit rate (Mbits/sec) using Bellcore approachUsing

Dispersion Ps1 dB Penalty2 dB Penalty2 dB Penalty

10,000314927

9000345530

8000386134

7000447038

6000518245

5000619854

40007712367

300010216489

2000153246134

1000306491268

900340546298

800383614335

700437701383

600510818447

500612982536

4007651228670

30010201637893

200153024551340

100306049102680

90340054562978

80382561383350

70437170143829

60510081834467

50612098205360

407650122756700

3010200163678933

20153002455013400

10306004910026800

9340005455629778

8382506137533500

7437147014338286

6510008183344667

5612009820053600

47650012275067000

310200016366789333

2153000245500134000

1306000491000268000


Allowable pulse broadening (Bellcore)

Low pass filter approx



Comparison of "Bellcore" and "low pass filter" rulesLow pass filter approximation rule is more pessimistic than the allowable pulse broadening (Bellcore) ruleFor SDH/Sonet Bellcore rule is normally adopted

Chart1

49.126.8

54.555555555629.7777777778

61.37533.5

70.142857142938.2857142857

81.833333333344.6666666667

98.253.6

122.7567

163.666666666789.3333333333

245.5134

491268

545.5555555556297.7777777778

613.75335

701.4285714286382.8571428571

818.3333333333446.6666666667

982536

1227.5670

1636.6666666667893.3333333333

24551340

49102680

5455.55555555562977.7777777778

6137.53350

7014.28571428573828.5714285714

8183.33333333334466.6666666667

98205360

122756700

16366.66666666678933.3333333333

2455013400

4910026800

54555.555555555629777.7777777778

6137533500

70142.857142857138285.7142857143

81833.333333333344666.6666666667

9820053600

12275067000

163666.66666666789333.3333333333

245500134000

491000268000






Max Bit rate (Mbits/sec)

Dispersion Ps1 dB Penalty2 dB Penalty

10,0003149

90003455

80003861

70004470

60005182

50006198

400077123

3000102164

2000153246

1000306491

900340546

800383614

700437701

600510818

500612982

4007651228

30010201637

20015302455

10030604910

9034005456

8038256138

7043717014

6051008183

5061209820

40765012275

301020016367

201530024550

103060049100

93400054556

83825061375

74371470143

65100081833

56120098200

476500122750

3102000163667

2153000245500

1306000491000


00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

2 dB Penalty

1 dB Penalty




Max Bit rate (Mbits/sec) using Bellcore approachUsing

Dispersion Ps1 dB Penalty2 dB Penalty2 dB Penalty

10,000314927

9000345530

8000386134

7000447038

6000518245

5000619854

40007712367

300010216489

2000153246134

1000306491268

900340546298

800383614335

700437701383

600510818447

500612982536

4007651228670

30010201637893

200153024551340

100306049102680

90340054562978

80382561383350

70437170143829

60510081834467

50612098205360

407650122756700

3010200163678933

20153002455013400

10306004910026800

9340005455629778

8382506137533500

7437147014338286

6510008183344667

5612009820053600

47650012275067000

310200016366789333

2153000245500134000

1306000491000268000






Calculating the Dispersion Penalty(Low pass filter approx rule)

Finding the Total Chromatic DispersionTotal Chromatic Dispersion, Dt = Dc x S x L

where:Dc is the dispersion coefficent for the fibre (ps/nm.km)S is transmitter source spectral width (nm)L is the total fibre span (km)Assuming singlemode fibre so there is no modal dispersionDoes not include polarization mode dispersionTypically the dispersion coefficent will be knownEg. ITU-T Rec.G.652 for singlemode fibres circa 1550 nm states: Attenuation < 0.25 dB/km Dispersion coefficent is 18 ps/(nm.km)

Total Dispersion ExampleTotal Dispersion, Dt = Dc x S x L

= 17 ps/nm.km x 0.1 nm x 50 km

= 85 ps total dispersion

50 km of singlemode fibre meeting ITU G.6521550 nm DFB laser with a spectral width of 0.1 nm

Dispersion Penalty Calculation50 km of singlemode fibre meeting ITU G.6521550 nm DFB laser with a spectral width of 0.1 nmSystem operating at 2.5 Gbits/secTotal Dispersion, Dt = 90 ps as before

Dispersion Penalty:

The Penalty is thus = 1.2 dB

PBd=--101101222log(())pDt85ps Must adjust power penalty

Graphical Evaluation of the Dispersion PenaltyApproximate dispersion penaltyDraw line vertically from dispersion to meet curveDraw line horizontally to meet dispersion penalty axisRead off dispersion Example shown for STM-16124 ps gives a penalty of 2.7 dBExact calculated value is 2.64 dB

Chart5

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps

Dispersion Penalty in dB (STM-16)

Fomula and Data

Dispersion Penalty calculation and graphing for design exercises

Formula used:

STM-1STM-4STM-16STM-64STM-256

SDH Bit Rates1.55E+086.22E+082.45E+099.95E+094.00E+10

Max dispersion0.00000000290.00000000070.000000000200

Dispersion increment (max dispersion /40)0.00000000010000

DispersionDisp in psDispersionDisp in psDispersionDisp in psDispersionDisp in psDispersionDisp in psPenalty dB

000000000000

10.000000000172.5967414618018.082687739604.596607404701.131131375800.28131237320.0027151891

20.0000000001145.1934829237036.165375479209.193214809302.262262751600.56262474630.0108709564

30.0000000002217.79022438550.000000000154.2480632187013.78982221403.393394127400.84393711950.0244980301

40.0000000003290.38696584730.000000000172.3307509583018.386429618604.524525503301.12524949270.043648054

50.0000000004362.98370730920.000000000190.4134386979022.983037023305.655656879101.40656186580.0683942453

60.0000000004435.5804487710.0000000001108.4961264375027.579644427906.786788254901.6878742390.0988323393

70.0000000005508.17719023280.0000000001126.578814177032.176251832607.917919630701.96918661220.1350818484

80.0000000006580.77393169470.0000000001144.6615019166036.772859237209.049051006502.25049898530.1772876696

90.0000000007653.37067315650.0000000002162.7441896562041.3694666419010.180182382302.53181135850.2256220879

100.0000000007725.96741461830.0000000002180.8268773958045.9660740465011.311313758102.81312373160.280287236

110.0000000008798.56415608020.0000000002198.90956513540.000000000150.5626814512012.442445133903.09443610480.3415180866

120.0000000009871.1608975420.0000000002216.99225287490.000000000155.1592888558013.573576509803.3757484780.4095860768

130.0000000009943.75763900380.0000000002235.07494061450.000000000159.7558962605014.704707885603.65706085110.484803489

140.0000000011016.35438046570.0000000003253.15762835410.000000000164.3525036651015.835839261403.93837322430.5675287486

150.00000000111088.95112192750.0000000003271.24031609370.000000000168.9491110698016.966970637204.21968559750.6581728449

160.00000000121161.54786338930.0000000003289.32300383320.000000000173.5457184744018.09810201304.50099797060.7572071394

170.00000000121234.14460485120.0000000003307.40569157280.000000000178.1423258791019.229233388804.78231034380.8651729097

180.00000000131306.7413463130.0000000003325.48837931240.000000000182.7389332837020.360364764605.0636227170.9826930827

190.00000000141379.33808777480.0000000003343.5710670520.000000000187.3355406884021.491496140405.34493509011.1104867628

200.00000000151451.93482923670.0000000004361.65375479150.000000000191.932148093022.622627516305.62624746331.2493873661

210.00000000151524.53157069850.0000000004379.73644253110.000000000196.5287554977023.753758892105.90755983651.4003654669

220.00000000161597.12831216030.0000000004397.81913027070.0000000001101.1253629023024.884890267906.18887220961.5645578805

230.00000000171669.72505362220.0000000004415.90181801030.0000000001105.721970307026.016021643706.47018458281.7433051182

240.00000000171742.3217950840.0000000004433.98450574990.0000000001110.3185777116027.147153019506.7514969561.9382002602

250.00000000181814.91853654580.0000000005452.06719348940.0000000001114.9151851163028.278284395307.03280932912.1511536696

260.00000000191887.51527800770.0000000005470.1498812290.0000000001119.5117925209029.409415771107.31412170232.3844801144

270.0000000021960.11201946950.0000000005488.23256896860.0000000001124.1083999256030.540547146907.59543407542.6410182765

280.0000000022032.70876093130.0000000005506.31525670820.0000000001128.7050073302031.671678522807.87674644862.924298239

290.00000000212105.30550239320.0000000005524.39794444770.0000000001133.3016147349032.802809898608.15805882183.2387820676

300.00000000222177.9022438550.0000000005542.48063218730.0000000001137.8982221395033.933941274408.43937119493.5902194264

310.00000000232250.49898531680.0000000006560.56331992690.0000000001142.4948295442035.065072650208.72068356813.986191245

320.00000000232323.09572677870.0000000006578.64600766650.0000000001147.0914369488036.19620402609.00199594134.4369749923

330.00000000242395.69246824050.0000000006596.7286954060.0000000002151.6880443535037.327335401809.28330831444.9569908252

340.00000000252468.28920970230.0000000006614.81138314560.0000000002156.2846517581038.458466777609.56462068765.5673701254

350.00000000252540.88595116420.0000000006632.89407088520.0000000002160.8812591628039.589598153409.84593306086.3008871493

360.00000000262613.4826926260.0000000007650.97675862480.0000000002165.4778665674040.7207295293010.12724543397.2124639905

370.00000000272686.07943408780.0000000007669.05944636440.0000000002170.0744739721041.8518609051010.40855780718.4050800276

380.00000000282758.67617554970.0000000007687.14213410390.0000000002174.6710813767042.9829922809010.689870180310.109953843

390.00000000282831.27291701150.0000000007705.22482184350.0000000002179.2676887814044.1141236567010.971182553413.0649289137

400.00000000292903.86965847330.0000000007723.30750958310.0000000002183.864296186045.2452550325011.25249492660

STM1 graph

STM1 graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM4 Graph

STM4 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM16 Graph

STM16 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM64 Graph

STM64 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


MBD0005C0EC.unknown

Dispersion Penalty for STM-1

Chart4

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


Fomula and Data


Formula used:



Max dispersion0.00000000290.00000000070.000000000200



000000000000

10.000000000172.5967414618018.082687739604.596607404701.131131375800.28131237320.0027151891

20.0000000001145.1934829237036.165375479209.193214809302.262262751600.56262474630.0108709564

30.0000000002217.79022438550.000000000154.2480632187013.78982221403.393394127400.84393711950.0244980301

40.0000000003290.38696584730.000000000172.3307509583018.386429618604.524525503301.12524949270.043648054

50.0000000004362.98370730920.000000000190.4134386979022.983037023305.655656879101.40656186580.0683942453

60.0000000004435.5804487710.0000000001108.4961264375027.579644427906.786788254901.6878742390.0988323393

70.0000000005508.17719023280.0000000001126.578814177032.176251832607.917919630701.96918661220.1350818484

80.0000000006580.77393169470.0000000001144.6615019166036.772859237209.049051006502.25049898530.1772876696

90.0000000007653.37067315650.0000000002162.7441896562041.3694666419010.180182382302.53181135850.2256220879

100.0000000007725.96741461830.0000000002180.8268773958045.9660740465011.311313758102.81312373160.280287236

110.0000000008798.56415608020.0000000002198.90956513540.000000000150.5626814512012.442445133903.09443610480.3415180866

120.0000000009871.1608975420.0000000002216.99225287490.000000000155.1592888558013.573576509803.3757484780.4095860768

130.0000000009943.75763900380.0000000002235.07494061450.000000000159.7558962605014.704707885603.65706085110.484803489

140.0000000011016.35438046570.0000000003253.15762835410.000000000164.3525036651015.835839261403.93837322430.5675287486

150.00000000111088.95112192750.0000000003271.24031609370.000000000168.9491110698016.966970637204.21968559750.6581728449

160.00000000121161.54786338930.0000000003289.32300383320.000000000173.5457184744018.09810201304.50099797060.7572071394

170.00000000121234.14460485120.0000000003307.40569157280.000000000178.1423258791019.229233388804.78231034380.8651729097

180.00000000131306.7413463130.0000000003325.48837931240.000000000182.7389332837020.360364764605.0636227170.9826930827

190.00000000141379.33808777480.0000000003343.5710670520.000000000187.3355406884021.491496140405.34493509011.1104867628

200.00000000151451.93482923670.0000000004361.65375479150.000000000191.932148093022.622627516305.62624746331.2493873661

210.00000000151524.53157069850.0000000004379.73644253110.000000000196.5287554977023.753758892105.90755983651.4003654669

220.00000000161597.12831216030.0000000004397.81913027070.0000000001101.1253629023024.884890267906.18887220961.5645578805

230.00000000171669.72505362220.0000000004415.90181801030.0000000001105.721970307026.016021643706.47018458281.7433051182

240.00000000171742.3217950840.0000000004433.98450574990.0000000001110.3185777116027.147153019506.7514969561.9382002602

250.00000000181814.91853654580.0000000005452.06719348940.0000000001114.9151851163028.278284395307.03280932912.1511536696

260.00000000191887.51527800770.0000000005470.1498812290.0000000001119.5117925209029.409415771107.31412170232.3844801144

270.0000000021960.11201946950.0000000005488.23256896860.0000000001124.1083999256030.540547146907.59543407542.6410182765

280.0000000022032.70876093130.0000000005506.31525670820.0000000001128.7050073302031.671678522807.87674644862.924298239

290.00000000212105.30550239320.0000000005524.39794444770.0000000001133.3016147349032.802809898608.15805882183.2387820676

300.00000000222177.9022438550.0000000005542.48063218730.0000000001137.8982221395033.933941274408.43937119493.5902194264

310.00000000232250.49898531680.0000000006560.56331992690.0000000001142.4948295442035.065072650208.72068356813.986191245

320.00000000232323.09572677870.0000000006578.64600766650.0000000001147.0914369488036.19620402609.00199594134.4369749923

330.00000000242395.69246824050.0000000006596.7286954060.0000000002151.6880443535037.327335401809.28330831444.9569908252

340.00000000252468.28920970230.0000000006614.81138314560.0000000002156.2846517581038.458466777609.56462068765.5673701254

350.00000000252540.88595116420.0000000006632.89407088520.0000000002160.8812591628039.589598153409.84593306086.3008871493

360.00000000262613.4826926260.0000000007650.97675862480.0000000002165.4778665674040.7207295293010.12724543397.2124639905

370.00000000272686.07943408780.0000000007669.05944636440.0000000002170.0744739721041.8518609051010.40855780718.4050800276

380.00000000282758.67617554970.0000000007687.14213410390.0000000002174.6710813767042.9829922809010.689870180310.109953843

390.00000000282831.27291701150.0000000007705.22482184350.0000000002179.2676887814044.1141236567010.971182553413.0649289137

400.00000000292903.86965847330.0000000007723.30750958310.0000000002183.864296186045.2452550325011.25249492660

STM1 graph

STM1 graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM4 Graph

STM4 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM16 Graph

STM16 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM64 Graph

STM64 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


MBD0005C0EC.unknown

Dispersion Penalty for STM- 4

Chart3

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


Fomula and Data


Formula used:



Max dispersion0.00000000290.00000000070.000000000200



000000000000

10.000000000172.5967414618018.082687739604.596607404701.131131375800.28131237320.0027151891

20.0000000001145.1934829237036.165375479209.193214809302.262262751600.56262474630.0108709564

30.0000000002217.79022438550.000000000154.2480632187013.78982221403.393394127400.84393711950.0244980301

40.0000000003290.38696584730.000000000172.3307509583018.386429618604.524525503301.12524949270.043648054

50.0000000004362.98370730920.000000000190.4134386979022.983037023305.655656879101.40656186580.0683942453

60.0000000004435.5804487710.0000000001108.4961264375027.579644427906.786788254901.6878742390.0988323393

70.0000000005508.17719023280.0000000001126.578814177032.176251832607.917919630701.96918661220.1350818484

80.0000000006580.77393169470.0000000001144.6615019166036.772859237209.049051006502.25049898530.1772876696

90.0000000007653.37067315650.0000000002162.7441896562041.3694666419010.180182382302.53181135850.2256220879

100.0000000007725.96741461830.0000000002180.8268773958045.9660740465011.311313758102.81312373160.280287236

110.0000000008798.56415608020.0000000002198.90956513540.000000000150.5626814512012.442445133903.09443610480.3415180866

120.0000000009871.1608975420.0000000002216.99225287490.000000000155.1592888558013.573576509803.3757484780.4095860768

130.0000000009943.75763900380.0000000002235.07494061450.000000000159.7558962605014.704707885603.65706085110.484803489

140.0000000011016.35438046570.0000000003253.15762835410.000000000164.3525036651015.835839261403.93837322430.5675287486

150.00000000111088.95112192750.0000000003271.24031609370.000000000168.9491110698016.966970637204.21968559750.6581728449

160.00000000121161.54786338930.0000000003289.32300383320.000000000173.5457184744018.09810201304.50099797060.7572071394

170.00000000121234.14460485120.0000000003307.40569157280.000000000178.1423258791019.229233388804.78231034380.8651729097

180.00000000131306.7413463130.0000000003325.48837931240.000000000182.7389332837020.360364764605.0636227170.9826930827

190.00000000141379.33808777480.0000000003343.5710670520.000000000187.3355406884021.491496140405.34493509011.1104867628

200.00000000151451.93482923670.0000000004361.65375479150.000000000191.932148093022.622627516305.62624746331.2493873661

210.00000000151524.53157069850.0000000004379.73644253110.000000000196.5287554977023.753758892105.90755983651.4003654669

220.00000000161597.12831216030.0000000004397.81913027070.0000000001101.1253629023024.884890267906.18887220961.5645578805

230.00000000171669.72505362220.0000000004415.90181801030.0000000001105.721970307026.016021643706.47018458281.7433051182

240.00000000171742.3217950840.0000000004433.98450574990.0000000001110.3185777116027.147153019506.7514969561.9382002602

250.00000000181814.91853654580.0000000005452.06719348940.0000000001114.9151851163028.278284395307.03280932912.1511536696

260.00000000191887.51527800770.0000000005470.1498812290.0000000001119.5117925209029.409415771107.31412170232.3844801144

270.0000000021960.11201946950.0000000005488.23256896860.0000000001124.1083999256030.540547146907.59543407542.6410182765

280.0000000022032.70876093130.0000000005506.31525670820.0000000001128.7050073302031.671678522807.87674644862.924298239

290.00000000212105.30550239320.0000000005524.39794444770.0000000001133.3016147349032.802809898608.15805882183.2387820676

300.00000000222177.9022438550.0000000005542.48063218730.0000000001137.8982221395033.933941274408.43937119493.5902194264

310.00000000232250.49898531680.0000000006560.56331992690.0000000001142.4948295442035.065072650208.72068356813.986191245

320.00000000232323.09572677870.0000000006578.64600766650.0000000001147.0914369488036.19620402609.00199594134.4369749923

330.00000000242395.69246824050.0000000006596.7286954060.0000000002151.6880443535037.327335401809.28330831444.9569908252

340.00000000252468.28920970230.0000000006614.81138314560.0000000002156.2846517581038.458466777609.56462068765.5673701254

350.00000000252540.88595116420.0000000006632.89407088520.0000000002160.8812591628039.589598153409.84593306086.3008871493

360.00000000262613.4826926260.0000000007650.97675862480.0000000002165.4778665674040.7207295293010.12724543397.2124639905

370.00000000272686.07943408780.0000000007669.05944636440.0000000002170.0744739721041.8518609051010.40855780718.4050800276

380.00000000282758.67617554970.0000000007687.14213410390.0000000002174.6710813767042.9829922809010.689870180310.109953843

390.00000000282831.27291701150.0000000007705.22482184350.0000000002179.2676887814044.1141236567010.971182553413.0649289137

400.00000000292903.86965847330.0000000007723.30750958310.0000000002183.864296186045.2452550325011.25249492660

STM1 graph

STM1 graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM4 Graph

STM4 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM16 Graph

STM16 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM64 Graph

STM64 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


MBD0005C0EC.unknown


Chart2

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


Fomula and Data


Formula used:



Max dispersion0.00000000290.00000000070.000000000200



000000000000

10.000000000172.5967414618018.082687739604.596607404701.131131375800.28131237320.0027151891

20.0000000001145.1934829237036.165375479209.193214809302.262262751600.56262474630.0108709564

30.0000000002217.79022438550.000000000154.2480632187013.78982221403.393394127400.84393711950.0244980301

40.0000000003290.38696584730.000000000172.3307509583018.386429618604.524525503301.12524949270.043648054

50.0000000004362.98370730920.000000000190.4134386979022.983037023305.655656879101.40656186580.0683942453

60.0000000004435.5804487710.0000000001108.4961264375027.579644427906.786788254901.6878742390.0988323393

70.0000000005508.17719023280.0000000001126.578814177032.176251832607.917919630701.96918661220.1350818484

80.0000000006580.77393169470.0000000001144.6615019166036.772859237209.049051006502.25049898530.1772876696

90.0000000007653.37067315650.0000000002162.7441896562041.3694666419010.180182382302.53181135850.2256220879

100.0000000007725.96741461830.0000000002180.8268773958045.9660740465011.311313758102.81312373160.280287236

110.0000000008798.56415608020.0000000002198.90956513540.000000000150.5626814512012.442445133903.09443610480.3415180866

120.0000000009871.1608975420.0000000002216.99225287490.000000000155.1592888558013.573576509803.3757484780.4095860768

130.0000000009943.75763900380.0000000002235.07494061450.000000000159.7558962605014.704707885603.65706085110.484803489

140.0000000011016.35438046570.0000000003253.15762835410.000000000164.3525036651015.835839261403.93837322430.5675287486

150.00000000111088.95112192750.0000000003271.24031609370.000000000168.9491110698016.966970637204.21968559750.6581728449

160.00000000121161.54786338930.0000000003289.32300383320.000000000173.5457184744018.09810201304.50099797060.7572071394

170.00000000121234.14460485120.0000000003307.40569157280.000000000178.1423258791019.229233388804.78231034380.8651729097

180.00000000131306.7413463130.0000000003325.48837931240.000000000182.7389332837020.360364764605.0636227170.9826930827

190.00000000141379.33808777480.0000000003343.5710670520.000000000187.3355406884021.491496140405.34493509011.1104867628

200.00000000151451.93482923670.0000000004361.65375479150.000000000191.932148093022.622627516305.62624746331.2493873661

210.00000000151524.53157069850.0000000004379.73644253110.000000000196.5287554977023.753758892105.90755983651.4003654669

220.00000000161597.12831216030.0000000004397.81913027070.0000000001101.1253629023024.884890267906.18887220961.5645578805

230.00000000171669.72505362220.0000000004415.90181801030.0000000001105.721970307026.016021643706.47018458281.7433051182

240.00000000171742.3217950840.0000000004433.98450574990.0000000001110.3185777116027.147153019506.7514969561.9382002602

250.00000000181814.91853654580.0000000005452.06719348940.0000000001114.9151851163028.278284395307.03280932912.1511536696

260.00000000191887.51527800770.0000000005470.1498812290.0000000001119.5117925209029.409415771107.31412170232.3844801144

270.0000000021960.11201946950.0000000005488.23256896860.0000000001124.1083999256030.540547146907.59543407542.6410182765

280.0000000022032.70876093130.0000000005506.31525670820.0000000001128.7050073302031.671678522807.87674644862.924298239

290.00000000212105.30550239320.0000000005524.39794444770.0000000001133.3016147349032.802809898608.15805882183.2387820676

300.00000000222177.9022438550.0000000005542.48063218730.0000000001137.8982221395033.933941274408.43937119493.5902194264

310.00000000232250.49898531680.0000000006560.56331992690.0000000001142.4948295442035.065072650208.72068356813.986191245

320.00000000232323.09572677870.0000000006578.64600766650.0000000001147.0914369488036.19620402609.00199594134.4369749923

330.00000000242395.69246824050.0000000006596.7286954060.0000000002151.6880443535037.327335401809.28330831444.9569908252

340.00000000252468.28920970230.0000000006614.81138314560.0000000002156.2846517581038.458466777609.56462068765.5673701254

350.00000000252540.88595116420.0000000006632.89407088520.0000000002160.8812591628039.589598153409.84593306086.3008871493

360.00000000262613.4826926260.0000000007650.97675862480.0000000002165.4778665674040.7207295293010.12724543397.2124639905

370.00000000272686.07943408780.0000000007669.05944636440.0000000002170.0744739721041.8518609051010.40855780718.4050800276

380.00000000282758.67617554970.0000000007687.14213410390.0000000002174.6710813767042.9829922809010.689870180310.109953843

390.00000000282831.27291701150.0000000007705.22482184350.0000000002179.2676887814044.1141236567010.971182553413.0649289137

400.00000000292903.86965847330.0000000007723.30750958310.0000000002183.864296186045.2452550325011.25249492660

STM1 graph

STM1 graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM4 Graph

STM4 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM16 Graph

STM16 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM64 Graph

STM64 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


MBD0005C0EC.unknown


Chart1

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


Fomula and Data


Formula used:



Max dispersion0.00000000290.00000000070.000000000200



000000000000

10.000000000172.5967414618018.082687739604.596607404701.131131375800.28131237320.0027151891

20.0000000001145.1934829237036.165375479209.193214809302.262262751600.56262474630.0108709564

30.0000000002217.79022438550.000000000154.2480632187013.78982221403.393394127400.84393711950.0244980301

40.0000000003290.38696584730.000000000172.3307509583018.386429618604.524525503301.12524949270.043648054

50.0000000004362.98370730920.000000000190.4134386979022.983037023305.655656879101.40656186580.0683942453

60.0000000004435.5804487710.0000000001108.4961264375027.579644427906.786788254901.6878742390.0988323393

70.0000000005508.17719023280.0000000001126.578814177032.176251832607.917919630701.96918661220.1350818484

80.0000000006580.77393169470.0000000001144.6615019166036.772859237209.049051006502.25049898530.1772876696

90.0000000007653.37067315650.0000000002162.7441896562041.3694666419010.180182382302.53181135850.2256220879

100.0000000007725.96741461830.0000000002180.8268773958045.9660740465011.311313758102.81312373160.280287236

110.0000000008798.56415608020.0000000002198.90956513540.000000000150.5626814512012.442445133903.09443610480.3415180866

120.0000000009871.1608975420.0000000002216.99225287490.000000000155.1592888558013.573576509803.3757484780.4095860768

130.0000000009943.75763900380.0000000002235.07494061450.000000000159.7558962605014.704707885603.65706085110.484803489

140.0000000011016.35438046570.0000000003253.15762835410.000000000164.3525036651015.835839261403.93837322430.5675287486

150.00000000111088.95112192750.0000000003271.24031609370.000000000168.9491110698016.966970637204.21968559750.6581728449

160.00000000121161.54786338930.0000000003289.32300383320.000000000173.5457184744018.09810201304.50099797060.7572071394

170.00000000121234.14460485120.0000000003307.40569157280.000000000178.1423258791019.229233388804.78231034380.8651729097

180.00000000131306.7413463130.0000000003325.48837931240.000000000182.7389332837020.360364764605.0636227170.9826930827

190.00000000141379.33808777480.0000000003343.5710670520.000000000187.3355406884021.491496140405.34493509011.1104867628

200.00000000151451.93482923670.0000000004361.65375479150.000000000191.932148093022.622627516305.62624746331.2493873661

210.00000000151524.53157069850.0000000004379.73644253110.000000000196.5287554977023.753758892105.90755983651.4003654669

220.00000000161597.12831216030.0000000004397.81913027070.0000000001101.1253629023024.884890267906.18887220961.5645578805

230.00000000171669.72505362220.0000000004415.90181801030.0000000001105.721970307026.016021643706.47018458281.7433051182

240.00000000171742.3217950840.0000000004433.98450574990.0000000001110.3185777116027.147153019506.7514969561.9382002602

250.00000000181814.91853654580.0000000005452.06719348940.0000000001114.9151851163028.278284395307.03280932912.1511536696

260.00000000191887.51527800770.0000000005470.1498812290.0000000001119.5117925209029.409415771107.31412170232.3844801144

270.0000000021960.11201946950.0000000005488.23256896860.0000000001124.1083999256030.540547146907.59543407542.6410182765

280.0000000022032.70876093130.0000000005506.31525670820.0000000001128.7050073302031.671678522807.87674644862.924298239

290.00000000212105.30550239320.0000000005524.39794444770.0000000001133.3016147349032.802809898608.15805882183.2387820676

300.00000000222177.9022438550.0000000005542.48063218730.0000000001137.8982221395033.933941274408.43937119493.5902194264

310.00000000232250.49898531680.0000000006560.56331992690.0000000001142.4948295442035.065072650208.72068356813.986191245

320.00000000232323.09572677870.0000000006578.64600766650.0000000001147.0914369488036.19620402609.00199594134.4369749923

330.00000000242395.69246824050.0000000006596.7286954060.0000000002151.6880443535037.327335401809.28330831444.9569908252

340.00000000252468.28920970230.0000000006614.81138314560.0000000002156.2846517581038.458466777609.56462068765.5673701254

350.00000000252540.88595116420.0000000006632.89407088520.0000000002160.8812591628039.589598153409.84593306086.3008871493

360.00000000262613.4826926260.0000000007650.97675862480.0000000002165.4778665674040.7207295293010.12724543397.2124639905

370.00000000272686.07943408780.0000000007669.05944636440.0000000002170.0744739721041.8518609051010.40855780718.4050800276

380.00000000282758.67617554970.0000000007687.14213410390.0000000002174.6710813767042.9829922809010.689870180310.109953843

390.00000000282831.27291701150.0000000007705.22482184350.0000000002179.2676887814044.1141236567010.971182553413.0649289137

400.00000000292903.86965847330.0000000007723.30750958310.0000000002183.864296186045.2452550325011.25249492660

STM1 graph

STM1 graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM4 Graph

STM4 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM16 Graph

STM16 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


STM64 Graph

STM64 Graph

0.0027151891

0.0108709564

0.0244980301

0.043648054

0.0683942453

0.0988323393

0.1350818484

0.1772876696

0.2256220879

0.280287236

0.3415180866

0.4095860768

0.484803489

0.5675287486

0.6581728449

0.7572071394

0.8651729097

0.9826930827

1.1104867628

1.2493873661

1.4003654669

1.5645578805

1.7433051182

1.9382002602

2.1511536696

2.3844801144

2.6410182765

2.924298239

3.2387820676

3.5902194264

3.986191245

4.4369749923

4.9569908252

5.5673701254

6.3008871493

7.2124639905

8.4050800276

10.109953843

13.0649289137

Dispersion in ps


MBD0005C0EC.unknown

Link Bandwidth Analysis

Link Bandwidth Analysis A link bandwidth analysis can answer the following questions:The frequency response required for optical devices eg. source/detector/fibre.The bandwidth of a particular electronic subsystemThe magnitude of bandwidth limiting, so that a power penalty can be calculated Normal approach is carry out a worst case analysis using the risetimes of the various components. Bandwidth can then be determined approximately from the expression:3 dB bandwidth = 0.35Total risetime tr3 dB bandwidth (MHz) = 350Total risetime tr in nsor

Evaluating Link RisetimeIf a system consists of n subsystems, each with an individual risetime then the total risetime tr is given by:In an actual analysis the risetimes to be included are typically:Source risetime.Detector risetime.Receiver electrical risetime = 0.35/(rec BW).Fibre modal dispersion, if present.Fibre material dispersion.From this formula tr can be found OR if tr is specified, then the subsystem risetime can be found by rearranging the formula.

Sample Problems involving a Dispersion Penalty

Power Budget Exercise #4 Part 1An optical fibre system operates at 1550 nm at a bit rate of 622 Mbits/sec over a distance of 71 km Fibre with a worst case loss of 0.25 dB/km is available. The average distance between splices is approximately 1 km. There are two connectors and the worst case loss per connector is 0.4 dB.The worst case fusion splice loss is 0.07 dBThe receiver sensitivity is -28 dBm and the transmitter output power is +1 dBm The source spectral width is 0.12 nm and the fibre dispersion meets ITU recommendations at 1550 nm (17 ps/nm.km)Use the Low Pass Filter Approximation rule - formula or graphDetermine worst case power margin, taking account of a power penalty

Power Budget Exercise #4 Part 2The system described in Exercise #2 is to be upgraded to 2.5 Gbits/secThe span, fibre, connectors, splices are unchanged. The new transmitter output power and spectral width is the same The receiver sensitivity remains at -28 dBAgain use the Low Pass Filter Approximation rule - formula or graphDetermine the new worst case power margin, taking account of a power penalty

Options to Handle Poor MarginClearly negative margin is a problemCould assume higher performance transmitter (higher o/p power) at higher bit rate but would be offset by lower receiver sensitivity, so probably no net gainOther options:Given this is an upgrade scenario (fibre is installed), best approach it to measure actual attenuation and maybe dispersion, rather than use predicted values, probably will give acceptable margin. Might also consider the use of a dispersion compensation module

More Advanced Power Budgets using a Statistical Approach

More Advanced Power Budgets: Statistical Analysis ApproachIgnoring the statistical nature of component performance by using worst case values in every case can create extremely overconservative designs.Using average values only will give a more optimistic power budget but it may not be right every timeIn finding the total loss caused by fusion splices, if the worst case loss for a fusion splice is simply multiplied by the number of splices involved, the result would be a figure for the total splice loss that would virtually never occur in practice.

3M Fibrlok average splice loss = 0.1 dBExample:3M Fibrlok splice loss

More advanced Power Budgets: Statistical Analysis ApproachIgnoring the statistical nature of component performance by using worst case values, in every case, can create extremely overconservative designs.If this approach continues into the installation, time will be wasted trying to solve "conditions" that do not really exist.In finding the total loss caused by fusion splices, if the worst case loss for a fusion splice is simply multiplied by the number of splices involved, the result would be a figure for the total splice loss that would virtually never occur in practice. Example:

Probability Density Function OverviewArea under probability density function (PDF) for a random variable X indicates probability that the random variable will take on a value within a specified range.For example above the probability that a random variable X lies between X1 and X2 is given by the area of the shaded portion under the PDF curve Variety of PDFs exist, Gaussian (or Normal) PDF is one of the most commonAverageor meanvalueProbability Densityor Number of OccurrencesPDFRandom Variable ValueX1X2

Gaussian DistributionAverageor mean, mProbability Densityor Number of OccurrencesStandard deviation, sParameter valuemm+sm+2sm+3s 50% 84.13% 97.73% 99.87%Gaussian Distribution Curve

Statistical Confidence - Gaussian PDF84.13% of the values contained within range zero and one standard deviation above average. 97.73% within range zero to two standard deviations above average. 99.87% within range zero to three standard deviations above average. Averageor mean, mProbability Densityor Number of OccurrencesStandard deviation, sParameter valuemm+sm+2sm+3s 50% 84.13% 97.73% 99.87%Gaussian Distribution Curve

Using Statistical Component LossesComponent loss tends to follow a Normal (Gaussian) statistical distribution.In a statistical approach the average value and the so-called standard deviation for component losses are found from the manufacturers data.The statistical loss value used in the power budget calculation is then found by adding together the average value and one or more standard deviationsStatistically it is possible to predict how reliable the statistical loss value is:In power budget calculations, generally, the two standard deviation value is normally used. Difficulties can arise in getting statistical information on components. In this case use worst case for that component. Called a semi-statistical approachAverage + 1 Standard DeviationStatistical confidence level = 84.13 %Average + 2 Standard DeviationsStatistical confidence level = 97.73 %Average + 3 Standard DeviationsStatistical confidence level = 99.87%

Statistical Power Budget Example (I)Power budget calculation to calculate power margin with worst case values

Statistical Power Budget Example (II): Component DataConnector LossMechanical Splice Attenuation:

Average: 0.1 dB Standard Deviation: 0.03 dB Cable Attenuation:

Average at 1330 nm: 1.15 dB Standard Deviation: 0.17 dB

Statistical Power Budget Example (III)Repeat power budget calculation using average plus one standard deviation

Comparison of ResultsWorst caseAverage + 1 std devAverage + 2 std devTotal Connector AttenuationTotal Splice AttenuationTotal Fibre AttenuationAvailable Power Margin4.26 dB1.9 dB3.0 dB2.34 dB3.24 dB1.6 dB2.98 dB3.68 dB2.64 dB1.3 dB2.64dB4.92 dB

Power Budget Exercise 5 :using a Statistical Approach

Statistical Power Budget Exercise 5 (Long-Haul)A 622 Mb/s optical transmission system is to operate at a wavelength of 1550 nm over an unrepeatered distance of 51 km. The transmitter available has a minimum fibre coupled output power of +4 dBm, while the receiver has a worst case sensitivity of -28 dBm.

Two types of fibre are available with different specifications as shown in Table 1 below. Two connectors are used in the system. The average distance between fusion splices is 700 m. The connector and fusion splice losses are shown in Table 2.

Statistical Power Budget Exercise 5 (Long-Haul)

Calculate the dispersion penalty associated with the use of each fibre. By preparing a two standard deviation statistical power budget using each fibre type in turn decide whether fibre type A or B should be used and why. State clearly any assumptions made.

Estimate the bit rate for the two standard deviation case at which the power margin falls below 2 dB for fibre A and B, Discuss your result in the context of the dispersion performance of the different fibres. (Should be able to change the bit rate in your dispersion formula to achieve this)

Exercise 5 DataFibre typeTotal dispersionAttenuation Attenuation Standard DeviationA7 ps/km0.36 dB/km0.05 dB/kmB9.5 ps/km0.33 dB/km0.04 dB/kmTable 1Joint TypeAverage attenuationAttenuation Standard deviation Fusion splice0.03 dB0.012 dBConnector0.25 dB0.04 dBTable 2

Power Budgeting in Distributed Systems

Overview Single transmitter signal distributed to two or more receivers via optical splittersTransmitterReceiver #1Receiver #2Receiver #3Receiver #432 km18 km54 km41 kmOptical Splitter

Equal power splitterSingle transmitter signal distributed to N receiversUp to 32 waysInsertion loss of splitter main source of lossTransmitterReceiver #1Receiver #2Receiver #3Receiver NN way Optical Splitter

1% tap splitterSingle transmitter signal distributed to N receiverAgain insertion loss of splitter main source of lossTransmitterReceiver #1Receiver #2Receiver #3Receiver N1% Tap1% Tap1% Tap1% Tap

Exercise: Distributed systemsTransmitter32 way Optical Splitter10km1kmReceiver #1Receiver #32Transmitter10km1% Tap 11% Tap 21% Tap 32Receiver #1Receiver #2Receiver #32Option 1Option 2Using only one transmitter we wish to distribute an optical video signal to 32 residential customers. Using the specifications and questions investigate both options.

Exercise: Distributed systemsG.652 fibre 0.2dB/km @ 1550 nmWorst case splice loss 0.07dB per spliceWorst case connector loss 0.4dB32 way splitter4 of 1*8 splitter and 1 of 1*4 splitter1*4 splitter maximum insertion loss 7.2 dB1*8 splitter maximum insertion loss 10.8 dBSplitters are spliced into network1% Tap1/99 split ratio, insertion loss 19-21 db / 0.2 dB50 m between tapsTap is spliced into networkPON (passive optical network) typical Tx and Rx specsTerminated with connectorsTransmitter output power 0 dBmReceiver sensitivity -24 dBmDetermine the power margin for option one. Determine the power margin for the first receiver in option two.Investigate if any improvements can be made to option two by changing the splitter type.

Power Budgeting in SDH Systems

ITU Rec. G.957Optical Interfaces for Equipments and Systems relating to the SDH

ITU System Classification (I)SDH system interfaces are classified by an ITU coding schemeITU Code is defined as: Application Code - STM level.Suffix numberApplication Code: I (intra-office), S (Short haul), L (Long haul), V (very long Haul)STM level: 1, 4, 16, 64Suffix number: (blank) or 1 indicating nominal 1310 nm wavelength sources on G.652 fibre; 2 indicating nominal 1550 nm wavelength sources on G.652 fibre for short-haul applicationsand either G.652 or G.654 fibre for long-haul applications; 3 indicating nominal 1550 nm wavelength sources on G.653 fibre.

ITU classification table for Optical Interfaces

REC. G.957 Reference PointsG.957 is very specific about the optical path:The S reference point is just after the Transmitter optical connector CTXThe R reference point is just before the receiver optical connector CRXAdditional connectors on the Optical Distribution Frame (ODF) are considered to be part of the fibre plant

STM-16 Transmitter Specifications as per ITU G.957

STM-16 Receiver Specifications as per ITU G.957The optical path penalty accounts for degradations due to reflections, intersymbol interference (caused by dispersion), mode partition noise and laser chirp.Overload is an important parameter on short range systems

REC. G.957 Design ApproachThe optical path penalty is effectively added to receiver sensitivityThe maximum and minimum T/X powers are at the S reference pointThe receiver sensitivity is at the R reference pointWorst case design and statistical design approaches used.Manufacturers data may exceed G.957 specs Optical path penaltyAttenuation minimumAttenuation maximumMaximum T/X powerMinimum T/X powerR/X overload powerR/X Sensitivity

STM-16 Optical Path Specifications as per ITU G.957Note: Dispersion limits are under study or cannot be agreed in some cases

Power Budgeting in DWDM Systems

Power Budgeting in DWDM SystemsPower budgeting in DWDM is much more complex due to:Multiple channelsLimits on power caused by FWM and other effectsPresence of amplifiers, multiplexers and demultiplexersOverall end-to-end budgets are typically a lot higher eg. 160 dBMost manufacturers comply with ITU-T standards G.692 and G.957 (single channel systems)As with SDH involves classifying the system by an ITU methodology

Overview of the G.692 StandardRecommendation deals with optical line systems that include the following features:Maximum number of channels: 4, 8, 16 , 32 or more;Signal channel types: STM-4, STM-16, or STM-64;Transmission over a single fibre: unidirectional or bi-directional.As with G.957 the standard defines:A reference model for DWDM systemsApplication codes with/without LINE optical amplifiersG.692 draws heavily from G.957 for many parameter values, e.g.. transmitter output power etc.

G.692 Reference PointsS and R reference points refer to Transmitter outputs and receiver inputs at connectors as in G.957 (See next overhead)

REC. G.957 Reference PointsG.957 is very specific about the optical path:The S reference point is just after the Transmitter optical connector CTXThe R reference point is just before the receiver optical connector CRXAdditional connectors on the Optical Distribution Frame (ODF) are considered to be part of the fibre plant

G.692 Application Codes without Line AmplifiersSTM-4, STM-16 etc.Fibre type: 2 = G.652, 3 = G.653, 5 = G.655

Attenuation Ranges without Line Amplifiersper span target distance up to 80 kmper span target distance up to 120 kmper span target distance up to 160 km

G.692 Application Codes with Line AmplifiersSTM-4, STM-16 etc.Fibre type: 2 = G.652, 3 = G.653, 5 = G.655

Attenuation Ranges with Line Amplifiersper span target distance up to 80 kmper span target distance up to 120 km

System design is an iterative process Will vary from system to system System Planning Tools Initial...

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