Lecture 4b

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Lecture 4b  Fiber Optics
Communication Link 1. Introduction  2.
Optical Fiber, Physical Background 3.  The
Light Transmitters and the Receivers as a
Components of the Fiber Optic
Communication Links 4. Light Emitting
Diodes 5. Transmitters 6. Driving
Circuits 7. Receivers 8. p-i-n
Photodiode 9. Transceivers and Repeaters
10. Fiber Optic Communication Link Rise Time
and Bandwidth Bandwidth 11.
Communication Link Power Budget 12.
Connectors 13. Conclusion
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• 1. Wide bandwidth Fiber optic system uses light
  as a carrier with
• 1013 to 1014 Hz. Radio waves are 106 to
  1010 Hz. Electrical signals have frequencies up
  to 108 Hz. The maximum bandwidth of the
  transmitted signals is 10 of the carrier.
• 2. Low loss The typical attenuation of a 1 GHz
  bandwidth digital signal in an optical fiber is
  0.1 dB per km. A 100 MHz bandwidth signal in
  RG-58/U coaxial cable has attenuation of 130 dB
  per km.
• 3. Electromagnetic immunity Electrical fields do
  not affect light signals.  
• 4. Light weight and small size 1 km of optical
  fiber cable weighs about 10 kilograms. A 1 km
  copper wire with the same signal carrying
  capacity would weigh 700 kg.
• 5. Safety There is no possibility of a short
  circuit in a fiber optic system, eliminating the
  hazard of sparks in an electrical cable.
• 6. Security Optical fiber is harder to tap than
  electrical wire. Unwanted tapping over the
  length of the fiber can usually be detected.

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• A. Index of Refraction
• C 3108 meters per second, but it is reduced
  when it passes through matter. The index of
  refraction n

c
speed of light in a vacuum, 3108 m/s
speed of light in the given material
wavelength
of light in a vacuum
wavelength of light in the given material
X ray,
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Index of refraction and speed of light for
various materials.
Index of Refraction Speed of Light
Free space (vacuum) 1.0 3108 m/s
Air at sea level 1.003 2.99108 m/s
Ice 1.31 2.29108 m/s
Water 1.33 2.26108 m/s
Glass (minimum) 1.45 2.07108 m/s
Glass (maximum) 1.80 1.67108 m/s
Diamond 2.42 1.24108 m/s
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?1 The incident angle (from the
surface normal)?2 The angle of refracted light
(from the surface normal)n1 index of
refraction in the incident mediumn2 index of
refraction in the refracting medium Light that
is not absorbed or refracted will be reflected.
The incident ray, the reflected ray, the
refracted ray, and the normal to the surface will
all lie in the same plane.
B. Refraction with Snell's Law
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D. Multimode Step Index Fiber
We want to find the critical case of total
internal reflection at the core-cladding
boundary. Using Snells Law with ?2 90º, we
can find the critical angle ?CR
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  C. Total internal reflection
Total internal reflection when ?1 gt ?CR .
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Critical angle refraction90
0
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• Since we can relate ?r, CR to angle ?CR by
  simple geometry, and we can make the approximate
  n0   1, this equation can be simplified
• The negated and shifted sine function is
  identical to the cosine, and we can relate this
  cosine to the sine by the trigonometric identity
• In equation (3.4), this sine was found above in
  terms of n1  and n2 

For n1  ? n2 , we can simplify the numerical
aperture calculation
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E. Modal Dispersion

• Dispersion means the difference in arrival time
  of the light rays at the output end of an optical
  fiber.
• Modal dispersion is caused by the difference in
  rays path (with equal wave length) due to
  variation in light incidence angles at the input
  end. It occurs only in multimode fibers
• Material dispersion is related to the variation
  of light velocity in a given fiber material due
  to the difference in propagated light wave.

Number of modes
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A
Input pulse
Output pulse
LMax
t
Critical angle
LMin
For instance, if n1   1.5 and ?  0.01, then
the numerical aperture is 0.212 and the critical
angle ? r,cr,  is about 12.5 degrees.
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• ?i   0 and path lengthL (fiber length).
• The longest path occurs for ? i ?i, CR and can
  be estimated as

For ?  0.002 in a small-step index optical
fiber
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B Mbps
150
1
L km
1
150
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F. Bandwidth of a Multimode Optical Fiber

• To estimate the bandwidth of an optical fiber, we
  can convert from a bit transfer rate to a
  bandwidth. In one signal period, two bits can be
  transferred, so the maximum signal frequency is
  simply one-half the bit transfer rate.

• Light frequencies used in fiber optic systems
  use a carrier frequency between 1014 and 1015 Hz
  (105 to 106 GHz). The theoretical bandwidth of a
  fiber optic system is about 10 of the carrier
  frequency, or up to 10,000-100,000 GHz!

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G. Attenuation

• Attenuation ranges from 0.1 dB/km (single-mode
  silica fibers) to over 300 dB/km (plastic fiber).
  
• There are two reasons for attenuation
  Scattering Absorption

Attenuation (dB)

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3. Classification of optical fibers and their
characteristics
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? multimode step inde ? multimode graded
index? single-mode step index
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4. Light Emitting Diodes
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Sources of losses of light power due to
mismatches
A source, with an output diameter of 100?m and an
NA of 0.30 is connected to a fiber with a core
diameter of 62.5?m and NA of 0.275. The  and
the are as follows
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LED driver circuits
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p-n Photodiode, (p-i-n)
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The important characteristics of receivers are

• Signal-to-noise ratio (S/N) is expressing the
  quality of signal in a system. In decibels, S/N
  is equal to the signal power in decibels minus
  the noise power in decibels.
• S/N (dB) 10 log10( S/N )
  10 log10( S ) - 10 log10( N ).
• If the signal power is 50 ?W (-13 dBm) and
  the noise power is 50 nW (-43 dBm), the S/N is
  1000, or 30 dB.
• Bit-error rate (BER) is related to S/N. The BER
  is the ratio of the incorrectly received bits to
  correctly transmitted bits. A ratio of 10-9
  means that one wrong bit is received for every 1
  billion transmitted bits.
• Responsivity (R) is the ratio of the photodiode's
  output current to the input optical power it is
  expressed in Amperes /Watt (A/W). A p-i-n
  photodiode typically has a responsivity of around
  0.4 to 0.6 A/W. A responsivity of 0.6 A/W means
  that incident light having 50 ?W of power results
  in 30 ?A of current.
• Rise time For most components, rise time and fall
  time are assumed to be equal. The response time
  of the receiver characterizes its bandwidth.
• Sensitivity specifies the weakest optical signal
  that can be detected. Sensitivity can be
  expressed in microwatts or dBm. A sensitivity of
  1 ?W is the same as a sensitivity of -30 dBm.

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Receivers
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Transceivers and Repeaters
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System Rise Time and Bandwidth
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Communication Link Power Budget
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Connectors