Calculation practice: fill, loss budgets and sizing

Calculation items are the ones Daniel fears and the ones Roz thinks he should welcome. A calculation item has one right answer, the method can be practised until it is automatic, and the distractors are usually the results of predictable mistakes: a forgotten term, a wrong unit, a rounding step in the wrong direction. A candidate who drills the common methods can turn those items into reliable marks. This lesson collects the calculations that appear across RCDD design work and gives a method, a worked example and the usual traps for each. The numbers used are typical values for practice; on the exam and in design, use the values in the current standards and the reference material.

Roz's drill format is the same for every method: write the formula or rule from memory, set out the given values with units, compute step by step, check the result for reasonableness, and state the answer with its unit. The check step catches most errors. A loss budget of 24 dB for a short campus link, a conduit that holds 300 cables or a rack that needs a cooling unit the size of a car are signs of a slip, not answers.

Conduit and pathway fill

Fill calculations compare the total cross-sectional area of the cables with the usable area of the pathway. For a single cable in a conduit, the area of a cable of diameter d is π times d squared over four. For a group of cables, add the areas. The usable area is the internal area of the conduit multiplied by a fill factor. A design fill of about four tenths (0.40) of the internal area is commonly used for three or more cables in communications conduit, and many owners specify less to leave room for growth; check the factor in the governing standard and the owner's requirements.

Here N is the number of cables, k is the fill factor, A is the internal area of the conduit and d is the cable diameter. Always round N down; a fraction of a cable cannot be installed. Bends reduce how much cable can be pulled through a conduit section, and pathway standards limit the number and total angle of bends between pull points and the length of each section. The usual design rule is no more than two 90 degree bends, or 180 degrees in total, between pull points, and a section length of no more than about 30 metres. Confirm both in the current standard.

Cable tray fill is calculated the same way, using the tray's usable cross-section. A common design limit is that cable fill should not exceed half of the usable cross-section, and cables should not be stacked deeper than about 150 mm; check both in the pathway standard and the manufacturer's data. Tray load is a separate check: the weight of the cable per metre must not exceed the tray's rated load for the span between supports.

Horizontal lengths and work area cords

Horizontal length items test the 90 metre permanent link and the 100 metre channel, measured as installed, including slack and vertical runs, not as a straight line on the plan. Add the routed length, the drops to the outlet and the service loop in the room. Where a multi-user telecommunications outlet assembly serves an open office, the work area cord may be longer than usual if the horizontal cable is shorter, using the formula from the cabling standard.

Here H is the horizontal cable length, D a de-rating factor for the cord's construction, commonly 0.2 for 24 AWG cords and 0.5 for 26 AWG cords, C the combined length of work area cord, equipment cord and patch cord, T the length of the cords in the telecommunications room, and W the maximum work area cord. The standard also caps the work area cord length; check the cap in the current edition.

Optical loss budgets

An optical loss budget adds up the expected loss of a link: cable attenuation, connector pairs and splices. The total is compared with the loss the application allows, and with a test limit. The method is the same for multimode and singlemode; only the values change.

Here α is the cable attenuation in decibels per kilometre at the test wavelength, L the length in kilometres, n_c the number of mated connector pairs, a_c the allowance per pair, n_s the number of splices and a_s the allowance per splice. Typical maximum values for practice are 3.5 dB per km for multimode at 850 nm, 1.0 dB per km for indoor singlemode, 0.5 dB per km for outside plant singlemode, 0.75 dB per connector pair and 0.3 dB per splice. Two traps account for most errors: counting connectors instead of mated pairs, and forgetting to convert metres to kilometres.

Decibels and power

Decibel arithmetic underlies loss budgets, wireless link budgets and amplifier gains. A ratio in decibels is ten times the base-ten logarithm of a power ratio. Three decibels is about a doubling or halving of power, ten decibels a factor of ten. Power in dBm is decibels relative to one milliwatt, so 0 dBm is 1 mW, 10 dBm is 10 mW, 20 dBm is 100 mW and 30 dBm is 1 W. Gains and losses in decibels are added and subtracted, which is why budgets are kept in decibels.

Free-space path loss for a radio link, with distance d in metres and frequency f in megahertz, is twenty times the logarithm of d plus twenty times the logarithm of f, minus 27.55. It grows by six decibels each time the distance doubles. Effective isotropic radiated power is the transmitter power plus the antenna gain minus the cable and connector losses.

Bonding conductor sizing

The telecommunications bonding backbone conductor is sized from its length, using the table in the bonding standard. A widely quoted rule of thumb approximates that table as about 2 kcmil of conductor area for each linear foot of conductor, with a minimum of 6 AWG and a maximum of 750 kcmil. Use the rule to check your answer and the table in the current standard for the design. The telecommunications bonding conductor that joins the primary busbar to the building's electrical grounding system must be at least as large as the largest backbone conductor.

PoE and power

Power over Ethernet calculations ask how much power reaches a device, how much is lost in the cabling and how much power and cooling the telecommunications room needs. The IEEE types give, in round numbers, 15.4 W at the source for Type 1, 30 W for Type 2, 60 W for Type 3 and about 90 W for Type 4, with less available at the device because of cable losses. The difference is heat, in the cable bundle and in the room. A switch's power supply must deliver the PoE budget plus the switch's own consumption.

Room load in watts converts to cooling in British thermal units per hour by multiplying by about 3.412, and to tons of refrigeration by dividing the British thermal units per hour by 12,000. One ton is about 3.517 kW. Cooling items often give the load in watts and ask for one of the other units, or the reverse.

Rack and data centre sizing

Rack power density drives cooling and power design in data centres. Total IT load divided by the number of racks gives average density; a few dense racks can need special cooling even when the average is modest. Uninterruptible power supply capacity is sized from the load with a margin, and battery runtime depends on the load, the battery capacity and its efficiency. Items usually give the values needed and test the method and the units.