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Introduction
This section discusses various aspects involved in designing a fiber optic system link.
The process of designing a successful fiber optic link can be broken down into three separate sections. The first requirement is to determine all the fundamental design parameters of the link.
This would include such parameters as the services to be provided, data speed requirements, link distances, cable routes, etc. Included in this are the performance objectives of the fiber optic system. Some of these design parameters and considerations have been discussed in depth in previous sections. The first part of this section will discuss other important design considerations.
The next requirement is to calculate the anticipated operational performance of the link.
This is often referred to as 'link budgeting', 'power budgeting', or 'loss budgeting'. The different operating parameters of the link, including transmit powers, receiver sensitivity, fiber link losses and performance objectives are used to determine the theoretical performance expectations of the optic fiber system. It is also required to calculate the maximum operating bandwidth of the fiber optic system, that is, the maximum data rate the system will support. The second section of this section discusses how to calculate the loss budget and bandwidth budget for a fiber optic link. A software package is available from the author's website that can be used to automatically calculate the power budget and bandwidth budget for each link, by entering the required parameters into the spreadsheet.
The third requirement is to determine the cost of the system that has evolved from the design steps discussed above. Once a budgetary cost has been calculated, then a cost/performance analysis can be carried out. There will always be trade offs between the cost of the system and its preferred level of performance. The main issues involved in determining the most cost-effective system design and the compromises that are available are incorporated in the discussions of the first section of this section. A costing package is included in the software that is available from the author's website.
1. Initial design considerations
A number of design considerations have been discussed in previous sections. This section will briefly review these requirements and will examine some new considerations.
1.1 Data transmission technology
The fiber optic system design will be developed and prepared around the initial data services proposal and planned requirements. The transmission system technology that is chosen will depend on the user's application, transmission speed, and capacity requirements. An overview of the different types of technologies that are available is provided in Section 10. It is vital that all the data requirements of the organization are extracted from the personnel concerned before design begins. This will ensure that the systems that are installed will cater to all the organization requirements.
1.2 Transmission parameters
Considerations during the design phase include the data rate requirements, the bandwidth requirements and the transmission distances. These parameters have been discussed at length in other sections of this guide.
1.3 Future data transmission capacity growth
During the design of a fiber optic system, it is extremely important that the expected future system growth of data transmission at a site be determined. It is the author's experience that if there is availability of communications capacity, no matter how large, someone will find a reason to use it.
It is far cheaper to accommodate the future fiber optic cable requirements in the initial installation phase than to upgrade the cable installation at a later date. The cost per meter of fiber in a fiber optic cable can be lower than one hundredth of the cost of digging the trench to bury it. For example, if it cost 20 cents per meter for a single fiber within a cable, it could cost up to $20.00 per meter to dig a trench, bury a conduit and pull a cable through it (though the cable itself may contain 96 fibers and cost $25.00 per meter). Therefore, the cost of adding extra fibers in a cable run is often almost insignificant in the total cost of the project. For this reason, it is considered prudent to over design the fiber optic system transmission capacity and bandwidth and avoid enormous cost blowouts at a later date.
For cable runs of hundreds or thousands of kilometers, the cost of the cable/fiber will become a much larger percentage of the total system cost. This is usually the case for systems put in by large telecommunications companies. The typical proportional cost for a cable in a system is illustrated in FIG. 1.
FIG. 1 A comparison of cable costs and distance
1.4 Reliability
One of the most difficult design considerations to account for is the system reliability. The most fundamental consideration in system reliability is the manufactured quality of the transmitting and receiving equipment, data network/processing equipment, and the fiber optic cable. This is often a subjective problem, especially when every supplier will tend to claim that they have the best quality equipment! Seeking advice from independent consultants, talking to a number of other users and reading the appropriate trade magazines will provide a good idea of what are the relative merits of each make of equipment.
Reliability will also depend on the level of the physical design that is implemented. For example, the two extremes of cable installation would be, firstly, a very high reliability system where the cable is steel armored, buried in conduit in 0.5 m of concrete at a depth of 5 m. Secondly, a very low reliability system requirement would be where a standard plastic sheathed cable is simply just laid across the ground without any protection. Other factors to be considered here include the quality of pit boxes, splice encasings, termination cabinets and the degree of locking and environmental protection that is required of them.
Over designing a system will add significant cost to the overall project. Therefore, there has to be a trade off between an acceptable level of reliability and a cost-effective system. The majority of system failures are caused by human error. The two all time classics are someone digging the cable up with a shovel or a backhoe and secondly, a technician cutting the wrong cable when carrying out maintenance on the system. To help avoid these problems, run the cables through areas where they are less likely to be tampered with, clearly mark the cables at all termination points and ensure that the system is thoroughly documented and that the documentation is kept up to date.
As part of this cost analysis equation, it is essential that other types of transmission technologies be considered. For example, it may be more cost effective to install a microwave link or use public telecommunications facilities for all or certain sections of the communications route. In this case, data rates and leasing costs need to be taken into account. FIG. 2 provides an example comparison of technologies with an illustration of some of the advantages and disadvantages of using microwave radio or fiber optic cable over a 30 km route.
FIG. 2 Some comparisons between radio and fiber cable systems
1.5 Selecting an operating wavelength
One of the first decisions to be made before detailed system design can begin in earnest is the selection of the system operating wavelength. Generally, the fiber wavelength used is dictated by the application that it is to be used on the system. For example, the fiber distributed data interface (FDDI) standard (refer to Section 10) requires transmission at the 1300 nm wavelength.
Once a wavelength is chosen, it is recommended that it may be used throughout the entire network. This will avoid problems with compatibility of the transmitter and receiving equipment as well as having to double up on spares and the test and maintenance equipment.
The 850 nm wavelength is often used for slow speed short distance links. For example, data rates up to approximately 20 Mbps and distances up to approximately 3 km are possible.
The 1300 and 1550 nm wavelength will provide the high data rates and the longer transmission distances discussed in previous sections. But as a result, the system costs increase significantly.
As a general design rule, it is always preferable to choose the shortest possible wave length of operation that will still provide satisfactory data rates and transmission distances for the application in which it is to be used simply because of the cheaper costs.
1.6 Cable type selection and installation route
The next step in the design process is to select the cable type to suit the application and the route that the cable will follow. These aspects of system design are discussed in detail in Section 7. The following provides details of a number of additional requirements.
It is worth noting that due to the economics of scale in production (there is far more singlemode fiber produced than multimode), coupled with the extra material costs, multimode fiber is generally more expensive than singlemode fiber.
Low loss, high bandwidth fiber will accept less light than higher loss, lower bandwidth fibers. This is because the latter fibers have larger NAs. Therefore, over relatively short distances, it is generally more cost effective, and will provide less signal attenuation, to use the multimode fiber, which has the higher intrinsic loss. The cost might slightly be more but multimode fiber collects the light far more efficiently from the significantly lower cost LED light sources.
The topology of a data network (the physical layout), is generally determined by the type of network that is to be installed. The topology that is chosen (star, bus or ring as illustrated in FIG. 3) can significantly affect the overall cost of the project. Different types of networks will use different lengths of cable and different types and numbers of transmitter and receiver devices. This needs to be carefully evaluated during the design phase.
FIG. 3 Illustration of star ring and bus topologies
It is also advisable to consider the relative merits of route duplication and/or alternative routing. This subject can become very complex and is beyond the scope of this guide. It is advisable to seek professional advice for this level of design, as it will have a significant affect on the overall cost and reliability of the network.
During system design, remember to add the extra costs of cable slack requirements, splice enclosures, termination cabinets and patch panels that were discussed in Section 7.
1.7 Repeaters and amplifiers
For long cable runs where the attenuation introduced by the cable, connectors and splices drops the transmitted signal level below the minimum level required by the receiver, an insitu repeater, or an amplifier is required. The amplifier can be placed directly between the transmitter and the cable or between the receiver and the cable or can be placed at any distance along the cable. The amplifier simply increases the level of the incoming signal.
Because the amplifier does nothing to the incoming signal, except amplifying it, the amplifier will inherently add noise to the outgoing signal.
The repeater, on the other hand, is installed at a distant point along the cable where the signal has dropped to the near minimum acceptable level. It takes the weak incoming light pulse, which will also have suffered from dispersion; it regenerates this pulse into a new square shaped pulse and then amplifies it and transmits it onto the next section of cable. This will inherently remove noise from the signal. To determine whether repeaters and amplifiers are required, loss budgets must be calculated. This procedure is discussed in section 2 below .
If possible, avoid repeaters because they require maintenance and are generally expensive capital items. Optical amplifiers are not very effective and may also be very expensive.
It is important that a thorough cost analysis is carried out of various alternatives to using repeaters and amplifiers. For example, it may be cheaper to use a single long cable run of high quality singlemode fiber with laser sources than to use multiple hops of multimode fiber cable with repeaters and LED sources. On the other hand, the reverse of this scenario may be true.
1.8 Transmitter and receiver equipment selection
Once the design is complete for the parameters discussed in the previous sections, it is then possible to select the required transmitters and receivers to match these design parameters of the system.
If a particular standard of data transmission is being installed, for example, gigabit Ethernet, then the transmitter and receiver modules will be designed to operate to a very stringent set of standards that all manufacturers are required to adhere to. In this case, it should be possible to interface equipment from different manufacturers and they should communicate successfully.
If the system to be installed does not conform to a particular standard, then it is wise to have matched transmitter and receiver module sets from one source of manufacturer for each route. Unfortunately, although the transmit and the receive modules from different manufacturers may claim to adhere to a single physical standard, quite often, they will not communicate with each other at a physical level. It is recommended that the same type and model of transmitter and receiver modules from a single manufacturer be used throughout, until the completion of installation. This will assist in simplifying maintenance procedures and will reduce the spares holding requirements.
The parameters that must be considered before selecting a transmitter and receiver module set are:
• The maximum data transmission rate requirement
• The wave length of operation
• The maximum transmission distance requirement
• The losses introduced along each route
• The maximum dispersion expected along the link
• The maximum permissible rise time for each component and for the system as a whole
• Whether a LED or a laser source is preferred
• The NA and diameter of the fiber to be used and the required NA and diameter of the source and detectors to match
• Matching the transmitter and receiver modules to the chosen fiber
• The required data encoding to be used, if it is carried out by the transmitter and receiver modules (NRZ, Manchester etc)
• Whether it is a commercial or industrial application
• The required reliability of the equipment
• The required availability of each link (including anticipated BER) Wherever possible, it is preferable to use LEDs rather than lasers as they are significantly cheaper; they require less protection from the environment and are more stable and less sensitive to physical stress and vibration.
At present, the 1300 nm light sources are cheaper than the 1550 light sources. If 1550 nm sources are to be used, they must have a very narrow spectral width and should be used with dispersion compensated fibers.
2. Design loss calculations
The next step in designing a fiber optic system is to determine whether each separate section of cable link in a system is going to operate or not, and what level of performance it is going to provide. The main objective here is to determine whether there will be enough power left in the transmitted signal for it to activate the receiver when it reaches the end of the cable, and will the signal be sufficiently free of noise and dispersion so as to be interpreted correctly. The following section provides a detailed description of the procedures and calculations required to carry out a loss budget and a bandwidth budget. Firstly, it will look at the definition of and derivation of the parameters that are used in calculating loss budgets.
2.1 Definition of parameters
• Transmitter power The accepted method for measuring transmitted power out of an optical light source is a de facto arrangement, where a piece of fiber approximately 2 m in length is attached to the light source and the output power is measured at the end of the fiber. Using this method accounts for mismatches between the fiber and the light source such as fiber core/light source size and NA differences and any other sources of power loss at the source to fiber interface. An optical transmitter specification is therefore generally specified with a matching cable size and type.
• Minimum transmit power
The manufacturer will generally quote the minimum transmit power that can be expected from the light source over its operating lifetime. This figure should be used in the calculations to ensure that the calculated loss budget is within the acceptable limits.
The output power figure that is specified will be either peak power or average power and will be specified in dBms. The important point to remember here is to use the same power measurement type (peak or average) for the transmitter and receiver in the calculations. If the measurement types are different, then the loss budget figures could be incorrect by 3 dB or more.
• Receiver sensitivity
For a particular optical detector, the manufacturer will quote the minimum level of signal power that is required at the receiving end of the fiber to activate the receiver. This minimum allowable receive signal level is referred to as the receiver sensitivity. The quoted receiver sensitivity will be the minimum receive signal level that is required to provide a data output from the receiver with a worst bit error rate (BER) of 10^-9 or 10^-12. There are two important points to be noted concerning receiver sensitivity. As the data rate increases, a receiver will require an increase in the minimum input power (receiver sensitivity) to maintain the same BER. Secondly, if the data rate remains the same and the transmitter input level drops only slightly, the bit error rate can increase significantly. For example, if the received signal level drops 1 dB below the receiver sensitivity the bit error rate could drop to 10^-6.
• System gain
The system gain is a figure that represents the total available optical power between the optical source and the optical detector. Therefore, the system gain can be represented as the numerical difference between the transmitter output power and the receiver sensitivity.
• System losses
Losses to the optical signal (attenuation) over a fiber optic link are caused by natural fiber attenuation, splicing losses, connector losses, coupling losses, dispersion losses, losses due to component aging and variations over time of environmental losses. (For example, temperature, physical stress, damaged fibers.)
• Safety margin
The component losses due to aging and variations over time of the environmental losses are not directly calculable and are accounted for by leaving a safety margin in the design. This margin also helps to account for small design errors and for additional splices that may be required at a later date if the cable is broken. Manufacturers also sometimes specify a figure referred to as the receiver power penalty. This is a power safety margin figure that is to compensate for jitter, bandwidth limitations, dispersion and clock recovery problems that may be encountered by the receiver and reduce its effective receiver sensitivity.
This power margin should also be covered by the system safety margin.
The author recommends that the designed safety margin be somewhere between 5 and 10 dB.
• Dynamic range
The receiver detector will have a maximum limit to the signal power that it can receive without going into distortion. The difference between the maximum power that it can receive and the receiver sensitivity is referred to as the dynamic range.
When designing a system, it is important that the dynamic range of the receiver is not exceeded. Sufficient attenuation must be available in the fiber route to ensure that it does not occur. In some cases, it may be required to insert additional attenuation into the fiber section.
• Transmitter to fiber coupling loss
Coupling from LEDs into fibers results in a significant amount of the power from the LED being lost because the LED has a very large surface area compared to the surface area of the fiber core. For example, an LED coupled to a 50 µm core diameter fiber will lose about 15 dB of the transmitted power to coupling loss. If the LED is producing 0 dBm. (1 mW) of output power, then only -15 dBm (32 µW) of power is getting into the core of the fiber for transmission. Losses from an LED into a single mode fiber are significantly higher (approximately 35 dB) and are therefore almost never used as a combination.
Lasers generally have a surface area that is much smaller than the core of a singlemode fiber and therefore, the coupling losses are relatively small. Several milliwatts of power can be coupled into a singlemode fiber from a laser.
As mentioned earlier, the manufacturer will generally specify the output power of an optical source as the power that is available after several meters of fiber and not the power directly from the source itself.
• Fiber to receiver coupling losses
For both singlemode and multimode fibers, the detectors have a much larger surface area than the optical fiber cores and therefore, there is only a very small coupling loss incurred (mostly due to internal Fresnel reflection).
• Link loss budget
If the safety margin is subtracted from the system gain, the remaining figure is the link loss budget. This figure represents the maximum amount of signal loss available during the design process for cable attenuation, splicing losses and connector losses. Some manufacturers will provide a link loss budget figure with their transmitter and receiver equipment which will take into account safety margin and system gain. This concept is illustrated in FIG. 4.
• Fade margin
Given that the length of the cable run is known, then the total known loss can be calculated (for connectors, splices, cable length). If this figure is subtracted from the link loss budget, then there should be a positive value. This is known as the fade margin and it represents the amount of unused system gain.
FIG. 4 Illustration of link loss budget and safety margin
2.2 Methodology for loss budget calculations
The following is a step by step approach to designing the power loss budget of a fiber optic link:
• Power into fiber
Generally, the transmitter power that is quoted by the manufacturer is the power into the fiber. If not, then the coupling loss must be determined.
• Calculate the system gain Subtract the receiver sensitivity, for a given bit error rate from the minimum transmit power. Both values must be in the same type of units (the most common being dBm) and must be of the same measurement type (average power or peak power). The system gain will then be represented in decibels.
• Determine the safety margin
Either calculate the safety margin or allow a suitable figure. The safety margin is represented in decibels.
* Power into fiber (dBm) = TX power (dBm) - coupling loss (dB)
* System gain (dB) = TX power (dBm) - RX sens. (dBm)
* Safety margin (dB) = Environmental factor (dB) + Aging factor (dB)
+ Dispersion factor (dB) + Jitter factor (dB) + Repair factor (dB) + Design error margin (dB)
• Calculate the link loss budget Determine the maximum allowable loss for the end-to-end optic fiber cable link section by subtracting the safety margin from the system gain.
• Calculate the total connector losses
Calculate the total connector losses in a link section of optic fiber by multiplying the number of connectors in that section by the loss per connector (in dBs).
• Calculate the total splice losses
Calculate the total splice losses in a link section of optic fiber by multiplying the number of splices by the loss per splice (in dBs).
• Calculate other possible losses
Calculate other losses to the system by adding together losses due to passive components in the optic fiber route. For example: passive stars, combiners, splitters, etc.
• Calculate the maximum allowable cable attenuation
Each section of fiber link should be analyzed to determine the maximum allowable fiber optic cable attenuation. This is calculated by subtracting the connector losses, splice losses and other losses from the link loss budget.
• Calculate the maximum normalized cable attenuation
For each section of optic fiber, determine the maximum allowed decibels per kilometer (dB/km) attenuation rating. This calculated figure is then compared to the manufacturer's attenuation figures to determine which cables are suitable for each section. The figure is calculated by dividing the maximum allowable cable attenuation by the total cable length.
• Choose the required fiber grade
Once the maximum normalized cable attenuation figure has been calculated, choose the appropriate fiber optic cable grade to match. The fiber grade (db/km) should be equal to or less than that calculated earlier in this section.
• Calculate the fiber loss for each cable section
Calculate the expected signal attenuation from each section of optic fiber, by multiplying the cable length for a section by the specified normalized cable attenuation of the chosen cable.
* Link loss budget (dB) = System gain (dB) - Safety margin (dB) Total Connector Losses (dB) = Connector Loss (dB) × number of connectors
* Total Splice Losses (dB) = splice loss (dB) × number of splices
*Allowable cable attenuation (dB) = Link loss budget (dB) -
Connector losses (dB) - Splice losses (dB) - other losses (dB)
* Max. norm. cable atten. (dB/km) = (max. allowable cable atten.(dB)) (total cable length (km))
• Calculate the received signal level
Determine the power level of the signal at the end of the fiber that is entering the receiver. This is calculated by subtracting all the losses along the cable section from the transmit power into the fiber.
• Check dynamic range
Ensure that the receive signal level at the end of the fiber section does not exceed the maximum permitted signal level allowed into the receiver. This is calculated by adding the dynamic range to the receiver sensitivity and ensuring that the receive signal level is less than this result.
2.3 Example calculation
The specifications for the system are as follows:
* Fiber loss (dB) = fiber length (km) × norm. cable atten. (dB/km)
*Received signal level (dBm) = transmit power (dBm) - fiber loss (dB) - connector losses (dB) - splice losses (dB) - other losses (dB)
* Received signal level (dBm) < Receiver sensitivity (dBm) + Dynamic range (dB)
Following is the procedure that was discussed in section 2.2:
a) power into fiber = -17 dBm
b) system gain = (-17 dBm) - (-40 dBm) = 23 dB
c) Let :
environmental factor = 1 dB
aging factor = 2 dB
repair factor = 1 dB
design error factor = 2 dB
and :
dispersion factor = 0.5 dB
jitter factor = 0.2 dB
therefore:
safety margin = 1 + 2 + 1 + 2 + 0.5 + 0.2 = 6.7 dB
d) link loss budget = 23 dB - 6.7 dB = 16.3 dB
e) total connector losses = 4 × 0.8 dB = 3.2 dB
f) total splice losses = 3 × 0.5 dB = 1.5 dB
g) no. of other losses
h) maximum allowable
cable attenuation = 16.3 - 3.2 - 1.5 = 11.6 dB
i) maximum normalized
cable attenuation = 11.6 dB/3.48 km = 3.33 dB/km
j) Using the result in (i) as a reference, the cable chosen was a Belden model 227417, which has a maximum normalized attenuation of 3 dB/km and a bandwidth of 600 MHz. km at 850 nm.
k) Fiber loss = 3.48 km × 3 dB/km = 10.44 dB
l) Received signal level = -17 dBm - 10.44 - 3.2 - 1.5 = - 32.14 dBm
m) Check dynamic range - 32.14 dBm < (- 40 dBm + 14 dB) = - 26 dBm
3. Design bandwidth calculations
The next requirement in fiber optic system design is to determine whether the link system has sufficient bandwidth to support the data speed requirement of the system. As the greater majority of fiber optic links are used for digital transmission, this discussion will look at the bandwidth requirements for standard digital transmission.
3.1 Time response
The simplest method of evaluating the bandwidth requirements of a transmission link system is to examine and compare the time responses of the signal and the transmission system. This avoids (some mathematicians would argue 'incorrectly') the requirement to analyze the system and the signals from a frequency perspective, which can become quite complex.
The light signal that emanates from the transmitter will be in the form of a square wave. If it is a non return to zero (NRZ) waveform then it will have a signal period equal to one bit period. Therefore for a data transmission rate of R and a pulse duration of T:
T = 1/R This is illustrated in FIG. 5 below.
FIG. 5 Illustration of pulse duration and time response For example, if
the signal has a period of 1 µs (1 × 10^-6 seconds) then the data transmission
rate is 1 Mbps for an NRZ signal.
In theory, the link system (the link system includes the transmitter, receiver and optic fiber cable) time response must be faster (shorter response period) than the signal response time (signal rise time) for the signal to pass through it successfully. The fiber optic link can be conceptualized as a low pass filter, whose cutoff frequency must be higher than the highest frequency component of the signal that is attempting to pass through it. If the transmission link system time response is too slow, then the pulses coming out of the receiving end of the link system will have their rise times slowed down by the system response time and will be overlapping each other.
The low pass filtering effect of the link system on the square input pulse produces a curved pulse at the receiver output as illustrated in FIG. 5 (like the charging and discharging of a low pass filter or capacitor). In order to define a limit to the time response of the link system, an often used rule of thumb is to assume the worst case (slowest response time of the system). It means, where the pulse coming out of the receiver has risen to either equal to or greater than 90% of the input pulse amplitude in 70% of the input pulse period. That is, the rise time of the link system should be no more than 70% of the input pulse duration.
where:
Tr is the system rise time
T is the input pulse period
The allowable rise time then becomes the maximum allowable link system time response. For example, if the link system is required to be able to transmit a data rate of 1 Mbps, where the pulse duration of the input signal for an NRZ pulse is 1 µs, the required link system maximum time response is:
Tr = 0.7T = 0.7/R
0.7 × 1 µs = 0.7 µs
The 0.7 µs time response represents a fiber link system minimum bandwidth requirement of 1/(0.7 µs) = 1.43 MHz to successfully transmit the 1 Mbps signal.
If the signal is a return to zero signal, then the pulse period is half that of the non return to zero signal. This is illustrated in FIG. 5b. The required system link time response is:
Tr = (0.7 × T)/2 = 0.35 T = 0.35/R
3.2 Overall system time response
To calculate the overall time response for a fiber optic transmission link system, take the square root of the sum of the squares of the time response of each individual component. This is represented as:
Ts = vS(Ti 2 )
where:
Ts= the system time response
Ti= time response of each individual component
The only components that affect the time response of a system to any degree are the transmitter, receiver and the length of optic fiber. Passive devices such as couplers, stars, connectors and splices do not cause any noticeable effect to the system time response. Therefore, the system time response becomes:
Ts = √Σ (Tt 2 + Tr 2 +Tf 2)
where:
Tt = time response of the transmitter
Tr = time response of the receiver
Tf = time response of the optic fiber
3.3 Optical fiber time response
The optical fiber rise time:
Tf is affected by two factors; modal dispersion and chromatic dispersion. The total effect of both dispersions is found by using the sum of squares formula on the separate time responses that result from each dispersion.
The time response that is caused by modal dispersion is given by:
Tfm = Dm × L
where:
Tfm = time response from modal dispersion (ns)
Dm= modal dispersion (ns/km)
L = fiber length (km)
To determine a value for modal dispersion, we can assume that the maximum bandwidth of a fiber correlates directly to the minimum modal dispersion that can be attained from that fiber.
The supplier will normally quote the 3 dB bandwidth of the fiber. In that case, a rule of thumb formula is used to calculate Dm is:
Dm=350/Bandwidth(3dB)
where the bandwidth is in MHz /km.
If the supplier provides a figure for 'modal bandwidth,' it is simply a matter of inverting this value:
Dm=1 /(Modal) Bandwidth
Another method is the calculation modal pulse spreading using the following formula:
Where:
NA = Numerical aperture
L = Length
N = RI of core
C = 3 × 10^8
Optical pulse spreading can be converted into electrical rise time through the following:
Tfm = 0.44 Tps
The first of the two methods is preferred because it is being calculated from an actual measured figure provided by the supplier, of a complete 1 km length of the cable. The second method is based on many assumptions and tends to give rather spurious results.
The time response that is caused by chromatic dispersion is given by:
Tfc = Dc × Δ λ × L
where:
Tfc = time response from chromatic dispersion (ps)
Dc = chromatic dispersion (ps/nm-km)
Δ λ = spectral spread (range of wavelengths) of the optical source (nm)
L = length of fiber optic cable (km)
The manufacturer in the optical fiber specification provides the chromatic dispersion figure.
Therefore the time response Tf of the fiber is given by:
T = √Σ(T 2 + T 2 )
For multimode fibers, note that modal dispersion is the significant problem and chromatic dispersion to a lesser extent but for singlemode fibers, modal dispersion becomes negligible and chromatic dispersion becomes the major factor.
3.4 Transmitter and receiver time response
The time responses for the optical transmitters and receivers are provided in the manufacturers' specification sheets. For LED transmission systems, which are generally short distance, the source and detector time responses are slow compared to the optical fiber time response. For example, a typical time response for a transmitter is approximately 6 ns and for a detector, approximately 10 ns. Over 1 km of fiber the time response may only be 2 ns.
For laser transmitters and receivers, the time responses are generally less than 0.5 ns and for a singlemode fiber, the time response would generally be significantly less than 0.01 ns over a 1 km link.
3.5 Example of bandwidth calculation
A fiber optic transmission system has the following specifications:
a) The first step is to calculate the modal dispersion for the fiber using the first rule of thumb formula.
Dm 350 /600= 0.58 ns/km
b) Calculate the time response caused by modal dispersion:
Tfm = Dm × L
= 0.58 × 3.48
= 2.02 ns
c) Calculate the time response due to chromatic dispersion for the fiber:
Tfc = Dc × √Σ × L
= 110 × 45 × 3.48
= 17226 ps = 17.226 ns
d) Calculate the overall time response for the fiber:
Tf = vS(Tfm 2 + Tfc 2 )
= √Σ ((2.02) 2 + (17.226) 2 ) = 17.34 ns
e) Calculate the overall time response of the link system.
Ts = vS(Tt 2 + Tr 2 +Tf 2 ) = √Σ((6) 2 + (9)2 + (17.34) 2 ) = 20.44 ns
f) The figure calculated in (e) represents the minimum time response from a signal that would successfully pass down the link system. That is, the 20.44 ns is the fastest time response that is possible from the link system. The signal must have a slower time response than the system to pass through it successfully. Therefore, to calculate the maximum data rate that the link system can support, this time response figure shall be a minimum of 0.7 of the pulse duration of the digital signal.
Ts = 0.7T = 0.7/R (T = 1/R )
20.44 10-9 = 0.7 T = 0.7/R
where:
T = 29.2 × 10-9 = 1/R
R = 34.25 Mbps (NRZ)
R = 17.12 Mbps (RZ)
With the maximum data speed calculated for this link segment, it can now be determined if this matches the requirements of the proposed technology. For example, this link would be suitable for an Ethernet FOIRL. It is also worth noting from the figures used in (d) and (e) that the major limiting factor here is the chromatic dispersion. This is more significant than modal dispersion because an LED is being used at 850 nm, which has a very wide spectral width and high chromatic dispersion at the 850 µm wavelength, over a relatively long distance. If an LED operating at 1300 nm (which is closer to the zero dispersion wavelength with a chromatic dispersion approximately 5 ps/nm/km) then modal dispersion would become the major limiting factor. It would be so if laser were to be used (which has a spectral width of approximately 3 nm) or the link were operating over a shorter distance, (but of course, the modal dispersion will also be very low due to the very small number of modes emitted by a laser).