Estimation of Optical Link Length for
Multi Haul Applications
M V Raghavendra1, P L H Vara Prasad2
Research Scholar Department of Instrument Technology1, Professor & Chairman (BOS) Department of Instrument Technology2
College of Engineering, Andhra University1 College of Engineering, Andhra University2 Vishakapatnam Andhra Pradesh, India
Abstract--In a fiber-optic system at long distances or high data rates, the system can be limited either by the losses (attenuation-limited transmission) or, assuming that the link is not limited by the source or detector speed, by the dispersion of the fiber (dispersion-limited transmission).In this paper we demonstrate how the optimum link length can be determined in different aspects like Dispersion & attenuation.
Key Words: Link Length, attenuation limited transmission, & Dispersion limited transmission.
I.INTRODUCTION
Optical Communication mainly depends on the following aspects.
Source Selection
Power Budget
Dynamic Range
Timing Analysis
Attenuation-Limited Transmission Length
Dispersion-Limited Transmission Distance These are explained in the following sections.
II .SOURCE SELECTION
The starting point for a link design is choosing the operating wavelength, the type of source (i.e., laser or LED), and the fiber type (single-mode or multimode). In a link design, one usually knows the data rate required to meet the objectives. From this data rate and an estimate of the distance, one chooses the wavelength, the type of source, and the fiber type.
A silica-based fiber operating with an LED source in the 800 to 900 nm region has a data rate-distance product of about 150 Mbps.km. The same fiber operating with a laser source in the same region of the spectrum has a product of approximately 2.5 Gbps.km.
In the region near 1300 nm, an LED can achieve a product of 1.5 Gbps.km and a laser can achieve products in excess of 25 Gbps.km. These benchmarks are summarized in Table 1
The choice of fiber type involves the decision to use either multimode or single-mode fiber, and, if multimode, whether to use graded-index or step-index profiles. This choice is dependent on the allowable dispersion and the difficulty in coupling the optical power into the fiber.
If an LED is chosen, then the obvious choice of fiber is a multimode fiber because the coupling losses into a single-mode fiber are too severe. For a laser source, either a multimode or single-mode fiber can be used. The choice depends on the required data rate, as losses in both types of fiber can be made quite low.
TABLE 1
Source data rate-distance performance limits.
Type Short λ Long λ
III.POWER BUDGET
With a tentative choice of source, we know the power PT available to be coupled into the fiber. If receiver power
PR is necessary to achieve the required performance, then the ratio PT/PR is the amount of acceptable loss that can be incurred and still meet the specifications. This is expressed by
Losses (dB) + lM = 10 log (PT/PR) (1)
Where lM is the system margin.
The losses can be allocated in any desired fashion by the system designer. Generally, the probable losses will be as follows:
• The source-to-fiber coupling loss lT(dB).
• The connector insertion loss lC, or the splice insertion loss lS.
• The fiber-to-receiver losslR. This loss is usually negligible.
• Allowance lA for device aging effects and future splicing requirements.
• Fiber losses, expressed as the unit loss times the link length L. Equation 1 can then be written as
10 log(PT/PR) = losses + lM
= L + lT + nlS + lR + lA + lM . (2)
After we solve Eq. 2 for the system margin, we find lM = PT(dBm) - PR(dBm) - L - lT - nlS - lR - lA . (3)
A positive system margin ensures proper operation of the circuit; a negative value indicates that insufficient power will reach the detector to achieve the BER.
For the source we will select an LED that produces 2 mW (PT(dBm) = 3 dBm) in a spot that is 225 m in diameter.
For the fiber, we will use a parabolic graded-index fiber (g = 2) with a 50 m core and a 125 m outer diameter that has a numerical aperture of 0.25.
The effective source radius (rs = 112.5 m) is larger than the fiber radius (a = 25.0 m), so we use Eq. 5.53 to calculate the coupling efficiency.
= [NA(0)2] (a/rs)2 [g/(g+2)]
= (0.25)2(25/112.5)2[2/(2+2)] (4) = 0.001543 = 0.1543% lT = 28.1 dB.
A considerable loss is incurred in coupling the light from the source into the fiber. This loss is subtracted from the optical power to produce
(PT)fiber = PT - lT = 3 - 28.1 = - 25.1 dBm. (5)
The only losses at the receiver are the Fresnel reflection losses at the fiber-air and air-detector interfaces. These losses are approximately 0.2 dB per interface for a total loss of 0.4 dB at the receiver. Including a representative 6 dB allowance to compensate for aging effects, the required power at the receiver is, then,
(PR)fiber = - 40 + 0.4 + 6 = - 33.6 dBm. (6)
A representative loss of graded-index fiber cable might be 5 dB/km. The fiber losses are found from
L = (PT)fiber-(PR)fiber = -25.1-(-33.6) = 8.5 dB. (7) The length of the fiber is
L = [(PT)fiber-(PR)fiber]/ = 8.5/5 = 1.70 km. (8)
For the 1.7 km distance calculated, three additional joints might be assumed as typical since fiber cables might typically be available in lengths up to 1 km. If we assume splices with a loss of 0.1 dB per splice, then the 1.7 km distance is not changed very much since we have
L + 3lS =(PT)fiber - (PR)fiber (9) L = (PT)fiber - (PR)fiber – 3lS
L = [(PT)fiber - (PR)fiber - 3lS] /
= (8.5 - 0.3)/5 = 1.64 km.
For connectors with a loss of 1 dB, we have
L = [(PT)fiber - (PR)fiber - 3lC] /
= (8.5 - 3.0)/5 = 1.10 km.
We note now that we are below 1 km and only two pairs of connectors are required. Redoing the calculation for two pairs of connectors, we have
L + 2lC = (PT)fiber - (PR)fiber (11) L = (PT)fiber - (PR)fiber – 2lC
L = [(PT)fiber - (PR)fiber – 2lC] /
= (8.5 - 2.0)/5 = 1.30 km.
The assumption of two pairs of connectors being needed leads to a length of 1.30 km, a length that requires three pairs of connectors. If we are required to use connectors with 1 dB loss per connection, we can achieve 1 km of link length with two connectors.
IV.DYNAMIC RANGE
Using a "best case/worst case" set of calculations; we can see whether our link has sufficient dynamic range. From Eq. (2), we can write the system margin LM as
lM = lTR - lsystem, (12)
where lTR is the ratio of the transmitter power to the required receiver power, expressed in dB, and lsystem is the
summation of the system losses, given by
lsystem = L + lT + nlS + lR + lA. (13)
The dynamic range of the system is found by computing the maximum and the minimum system margins. The two computations are summarized by
(lM)max = (lTR)max – (lsystem)min (14)
(lM)min = (lTR)min – (lsystem)max . (15)
The system dynamic range DR (dB) is given by the difference in these values:
DR(dB) = (lM)max - (lM)min . (16)
The receiver must have an equivalent dynamic range in order for the system to work properly.
We are basically concerned with keeping the power at the receiver above the minimum detectable power of the detector (PR)min and below the maximum-rated power of the detector (PR)max. From Eq.2, the received power is deduced to be
PR(dBm) = PT(dBm) - lsystem . (17)
If me assume that we hane transmitted a logical 1 then
Case I: Maximum power output combined with minimum fiber attenuation. The maximum transmitter power allowed in this case is
(PT)max = PR(1)max + min(L - 0.5) (18) = -12.5 + (0.3)(2.0 - 0.5) = -12.05 dBm.
Case II: Minimum power output combined with maximum fiber attenuation. The minimum transmitter power allowed in this case is
(PT)min = PR(1)min + max(L - 0.5) (19) = -21.0 + (0.63)(2 - 0.5) = -20.1 dBm.
For the source specified, we can produce a maximum output of -8.4 dBm (144 W) at the maximum drive current of 60 mA. The output power of an LED is linearly dependent on the drive current,
P / Pmax = I / Imax (20)
To produce the maximum allowed transmitter power of -12.05 dBm (62.3 W), the required drive current is I = Imax(P/Pmax)
Imax = (60 x 10-3) (62.3/144) = 26.0 mA. (21)
The lowest rated output power at the 60 mA maximum-rated drive current is -14.8 dBm (33.1W). Hence, to produce the minimum output of 9.77 W, we require a minimum drive current of
I = Imin (P/Pmin) (22) Imin = (60 x 10-3) (9.77/33.1) = 17.71 mA.
We conclude that a drive current between the values of 17.71 and 26.0 mA will ensure proper operation of the 2 m link if the source and receiver meet specifications and if the other sources of system losses are negligible.
V.TIMING ANALYSIS
The rise time of an fiber-optic system tsys is given by
where ti is the rise time of each component in the system. The four components of the system that can contribute to the system rise time are as follows:
• The rise time of the transmitting sourcetS.
• The rise time of the receivertR.
If B3dB is the 3-dB frequency bandwidth of the receiver, the rise time can be calculated as
tR = 0.35/B3dB . (24)
• The material-dispersion time of the fibertmat. Equation 3.24 gives the dispersion relation as
tmat = -(L/c).().(2 d2n/d2) . (25) • The modal-dispersion time of the fiber link tmodal.
For a step-index fiber with length L, the modal-dispersion delay is given by
tmodal = L (n1 - n2) / c. (26) The delay time is a function of the index profile g. For a parabolic-index fiber (g = 2), the delay is estimated as
tmodal = (L/c).(NA2(0) / 8n12) (27)
FIGURE 1 Plot of λ2
(d2
n/dλ2
) vs. wavelength for typical silica glass.
If we consider the 100 Mbps link previously described in the power-budget analysis. The postulated LED might have a rise time of 8 ns and a spectral width of 40 nm.
Then the pin diode might have a typical rise time of 10 ns. For a silica fiber operating at 830 nm, the value of
2
(d2n/d2) is approximately 0.024 (from Fig.1). For a link distance of 2.5 km, the material-dispersion delay time is
tmat = - (L/c).().(2.d2n/d2)
= - (2.5 x 103/3.0 x 08)(40/830)(0.024)
= - 9.64 x 10-9 s = - 9.64 ns. (28)
A typical intermodal dispersion for graded-index fibers is 3.5 ns/km. Hence, a 2.5 km link has
tmodal = 8.8 ns. (29) Calculating the system's rise time, we have
tsys = [(tS)2+(tR)2 + (tmat)2+(tmodal)2]1/2 (30) = (82 + 102+ 9.642 + 8.82)1/2 ns = 18.3 ns.
If the system rise time of the previous example was 18.3 ns. Using this value, if we calculate the data rate that the system can suppor for NRZ coding as
tsys < 0.7 TB (31) TB > tsys / 0.7,
BR < 0.7/tsys < 0.7/(18.3 x 10-9)
< 38.3 Mbps For RZ coding, we have
BR = 0.35/tsys
=[0.35/(18.3x10-9)]=19.1Mbps (32)
Neither coding will support the desired 100 Mbps data rate. Inspection of Eq. 30 reveals that: the receiver speed and the material dispersion are too large; the modal dispersion contribution is small because the distance is so short; and we need to use a faster detector. To reduce the material dispersion, inspection of Eq. 25 reveals that one should reduce . Two methods of doing this would be
VI.DISPERSION-LIMITED TRANSMISSION DISTANCE
(a) Material Dispersion-Limited Transmission
Consider material dispersion in a link using RZ coding. We require
tmat < 0.35TB. (33) Hence
0.35TB > (Lmax/c) () (2d2n/d2) (34) Lmax = (0.35TBc) ()[1/(2d2n/d2)]
(b)Modal Dispersion-Limited Transmission
For modal dispersion in a step-index fiber, we have Lmax = 0.35cTB / (n1 - n2)
= 0.35c / (n1 - n2)BR = 0.7cn1/NA2BR (35) For modal dispersion in a graded-index fiber, we have Lmax = 2.8TBcn12/[NA(0)]2
= 2.8cn12/[NA(0)]2BR. (36)
These latter three equations are useful for estimating the dispersion-limited transmission distances when waveguide dispersion is not significant.
If we calculate the modal-dispersion-limited transmission distance for a 50 Mbps data link using SI and GI fibers with = 1% and n1 = 1.45. The coding is return-to-zero, then
We begin with
n1 - n2 = n1 = 0.01(l.45) = 0.0145. For the SI fiber,
(Lmax)SI = 0.35c/[(n1 - n2)BR]
= [(0.35)(3.0 x 108)] / [(0.0145)(50 x 106)]
=1.448 x 102 m. (37) For the GI fiber,
(Lmax)GI = 2.8cn12 / [NA(0)]2 BR
=2.8cn12 / 2n1(n1-n2)BR = 1.4cn1 / (n1-n2)BR (38) = [(1.4)(3.0 x 108)(1.45)] / [(0.0145)(50 x 106)]
= 840 m.
The small transmission distances are caused by the use of a multimode fiber for a fairly high-data-rate signal instead of a single-mode fiber.
(c) Attenuation-Limited Transmission Length
For comparison purposes we frequently want to calculate the maximum link distance for a system limited only by the fiber attenuation. The formula for this is
Lmax = [PT(dBm)- PR(dBm)] / fiber (39)
Here PT is the power of the transmitter, PR is the power that the receiver requires to maintain the bit-error rate or the signal-to-noise ratio, and is the fiber attenuation value.
Let us consider a graded-index fiber with n1 = 1.45 and = 1% and a loss of 1 dB/km. It is used with an 850 nm source that produces an output power (in a fiber) of -10 dBm. The source line width is 60 nm. The receiver is a pin-diode receiver that requires a power given by
PR(dBm) = -65.0 + 20 log BR [Mbps] (40)
To maintain a BER of 1 x 10-9, where BR is the data rate in Mbps. The coding is RZ coding. We set up the equations to find
(a) The material-dispersion-limited distance,
The equation for the material-dispersion-limited distance is Lmax = 0.35cBR2 d2n/d2. (41)
The value of 2(d2n/d2 is estimated to be 0.022 from Fig. 1. Hence, we have
Lmax = [(0.35)(3.0 x 108 )(850 x 10-9)] / [(BR)(60 x 10-9)(0.022)] = (6.76 x 1010) / BR. (42) (b) The modal-dispersion-limited distance.
This distance is
Lmax = 2.8cn12/[NA(0)]2BR = 1.4cn12/n12BR (43) = 1.4c/BR = 1.4(3.0 x 108)/(0.01)(BR)
=4.14 x 1010/BR
Lmax = [PT(dBm) - PR(dBm)]/
= [-10 - (-65.0 + 20 log (BR))]/1.0 (44) = 55.0 - 20 log (BR).
Plotting the results for a data rate range extending from 1 kbps to 1000 Mbps.
2(A)
2(B)
2(C)
2(D)
FIGURE 2(A), 2(B), 2(C) & 2(D) Graph between Link Length & Data Rate.
VII.RESULTS:
Figure 2 shows the plot of the curves & is noted that for data rates below about 17 Mbps, the link length is attenuation-limited. Above 17 Mbps, the link is limited by the modal dispersion. The material-dispersion limit is slightly longer than the modal-dispersion limit.
VIII.REFERENCE
[1] Gerd Keiser, “Optical Fiber Communication”, McGraw-Hill International Editions.
[2] C K Sarkar, D C Sarkar “Optoelectronics & Fiber Optic Communication” New Age International Pvt.Ltd.
[5] Nosu. K, “Advanced Coherent Lightwave Technologies”, IEEE Communications Magazine, Vol.26, No.2, Feb. 1988. [6] J.R.Barry and E.A.Lee, “Performance of coherent optical receivers”, Proceedings of IEEE, Vol. 78, No. 8, August 1990. [7] H.R.Burris, A.E.Reed, N.M.Namazi, M.J.Vilcheck, M.Ferraro, “Use of kalaman filtering in data detection in optical
communication systems with multiplicative noise”, Proceedings of IEEE, April 2001.
About the authors
M.V.Raghavendra is a Research Scholar Department of Instrument Technology College of Engineering, Andhra University Vishakapatnam Andhra Pradesh, India. He has received his M.Tech Degree from ECE Dept, College of Engineering, Andhra University. His main research includes signal estimation of optical communication.
P.L.H.Vara Prasad received his PhD degree in Instrumentation, & his areas of specialization are Surface Science, Ellipsometry, Control Theory, He is currently working as Professor &
