Transcript ENE 429 Antenna and Transmission Lines

DATE: 04/09/06
08/09/06
ENE 429
Antenna and
Transmission lines
Theory
Lecture 9 Optical fiber
Review (1)
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TE wave in rectangular waveguides (Hz = 0)
For lossless TE rectangular waveguides,
m x
n y  j z
cos
e
A/ m
a
b
A dominant mode for TE mode is TE01
A dominant mode for TM mode is TM11
Rectangular cavity resonator
H z  H 0 cos





To minimize the field radiation due to comparable size of
component to the wavelength.
To confine field inside the enclosed cavity.
Review (2)

Magnetic field representation for TEmnp mode is

m x
n y
p z
H z ( x, y, z )  H 0 cos
cos
sin
A / m.
a
b
d
Electric field representation for TMmnp mode is

m x
n y
p z
sin
cos
V / m.
a
b
d
Resonant frequency is
Ez ( x, y, z )  E0 sin
f mnp
u p  m 2  n 2  p 2
 resonant frequency 
   


2  a  b d 
Hz
Optical fiber
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operates at optical frequency (1014 Hz)
Three primary transmission windows are
centered around 850, 1300, 1550 nm.
telephone system
cable TV
interconnects in computer
How does it work?
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
wave travels using total internal reflection at the
core-cladding boundary.
core and cladding are typically made of silica.
jacket is typically made of polyethelene
interconnects in computer
Dimension

50/125 fiber means 50 m diameter core and
125 m diameter cladding.
Pros and Cons
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
advantage: carry much more info than coaxial
cable, smaller, lighter, more flexible, and less
attenuation than coax.
disadvantage: hard to repair when it breaks
Types of the optical fiber
1.
2.
3.
step-index fiber – abrupt change in n-refractive
index
single-mode fiber – supports only one
propagating mode
multi-mode fiber – supports several modes.
step-index fiber
Graded-index fiber (for multi-mode)
Propagating mode (1)

There will be a propagating mode if the wavelength
2 a n 2f  nc2

k01
m
where k01 = first root of the zeroth-order Bessel function =
2.405
a = radius of the core.

If we can control n2f  nc2 to be small, we can support
more modes.
Propagating mode (2)

For a step-index multimode fiber, the total number of
propagating modes is approximately
a  2
2
N  2
(
n

n
f
c ).

  
2
Typical Characteristics of Glass
optical fiber
See table 7.2
Numerical aperture (1)

To initiate mode propagation, use Snell’s law.
n0 sin  a  n f sin b
Note that
that gives
c  (i )cri
sin( i ) cri
nc
 .
nf
Define the maximum acceptance angle a = a cone of
Acceptance over which light will propagate along the fiber.
Numerical aperture (2)
Let
c  (i )cri
and by geometry,
sin c  cos b
then from
sin 2 b  cos 2 b  1
we have
n0 sin a  n f 1  cos2 b  n f 1  sin 2 c .
n 2f  nc2
 NA or Numerical
Therefore at c  (i )cri , sin  a 
n0
Aperture (given by the manufacturer)
Ex1 Which optic fiber would be better
to use for wave guiding?
1)
Fiber 1, core index = 1.465, cladding index =
1.463
2)
Fiber 2, core index = 1.465, cladding index =
1.450
Signal degradation
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Intermodal dispersion
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Chromatic dispersion
 Waveguide dispersion
 Material dispersion
Attenuation due to interaction inside fiber
material
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Graded-indexed fiber (GRIN)
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Single-mode step-index fiber has a small cone of
acceptance.
Multimode fiber suffers from intermodal dispersion.
GRIN is one approach to minimize dispersion in a
multimode fiber.
Common size: 50/125 and 85/125
Fiber optic communication systems

Basic components of a fiber optic
communication system:
To boost up the signal
due to the limited coverage of the fiber
Optical sources: LED

Light emitting diodes (LEDs)

Photon (light) is emitted when excited electrons are
relax and fall back to lower energy state.
 Gallium Arsenide (GaAs) is popular.
 The wavelength of light emitted can be adjusted by
adding some compounds.
LED configurations (1)

Surface-emitting configuration
 Mount
the fiber on the surface close to p-n junction
 A beamwidth is approximate 120.
LED configurations (2)

Edge-emitting configuration
 Photon
propagate out the side of the device.
 A beamwidth is approximate 30.
Optical sources: Laser diode (1)

Semiconductor laser diode
doped layers (p+ and n+)
 Diode layers (p-AlGaAs and n-AlGaAs)
 Lasing region is where photon production occurs.
 Heavily
Optical sources: Laser diode (2)
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narrow beamwidth
can be modulated at an order of frequency higher than
LEDs
higher drive currents than LEDs
wear out faster than LEDs
Property comparison for LEDs and
Laser diodes
See table 7.3
Optical detectors: PIN photodiode

PIN photodiode
 An intrinsic layer of semiconductor is sandwiched by p-type
and n-type regions.
 When a photon is captured,
it generates an electron-hole
pair thereby producing a weak
current proportional to the light
intensity.
 an avalanche photodiode (APD)
is a heavily doped structure with a
large reverse-bias voltage.
Comparison of Optical detectors
See table 7.4
Repeater
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
The optical system is limited by the operating distance.
Repeaters or optical amplifiers are needed to boost a
signal.
Repeaters are costly and need their own source of
power.
Optical amplifier

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Erbium-doped fiber amplifier (EDFA) enable direct
amplification of an optical signal.
The EDFA features high gains and high output power
capability with low noise.
Connections
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Made from the optical source to fiber, fiber to the optical detector,
and between lengths of fiber.
12 dB loss is produced between an LED and a mulitmode fiber, > 32
dB loss if connected to a single mode fiber while it only produces
about 2 dB loss with laser diodes.
Efficient coupling between a fiber and a detector produces only 1.5
dB loss.
Attenuation arisen from joining a pair of fiber produce less than 1 dB
loss, with 0.7 dB being typical.
Splices are considered a permanent connection, generally no more
than 1 dB, with 0.05 dB being typical loss.
A matching refractive index epoxy is usually applied to attach the
source-to-fiber and fiber-to-detector connections.
Typical losses associated with
connections
See table 7.5
Optical link design (1)

Power budget
 to ensure enough power at the receiver end.
 The optical source must supply enough power to
overcome source-to-fiber loss, connector and splice
loss, and fiber-to-detector loss.
Optical link design (2)

Rise-time budget: to verify the received signal has not
been distorted
 For
high information rates and long operating
distance, digital transmission is more reliable than the
analog one.
 Return-to-zero format is a popular digital signals
Rise-time budget
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The rise time of the source and the detector as well as
the effects of dispersion in the fiber cause the spreading
of the pulse.
The accepted bit error rate (BER) is 1 error in 109 bits.
Rise-time budget calculation (1)
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A time period T is related to the data rate (bit per second or
bps) such that
1
S.
T
bps
The total system response time ts is typically require such
that
1
S.
ts  T
2
The total system response time can be determined.
ts  tt2  t 2f  tr2
S.
where tt = transmitter response time (s)
tf = fiber response time (intermodal + chromatic) (s)
tr = receiver response time (s)
Rise-time budget calculation (2)

The pulse width of the output signal (Tpw)out can be
expressed as
(t pw )out  (t pw )in2  ts2 S.

Total rise time of the fiber can be expressed as
2
2
t f  tint


t
er mod al
chromatic S.
Ex2 What is the proper optical detector to detect the
receiving power from an optical link that transmits data over
a 1 km distance, given an 850nm LED source with 1 mW (0
dBm) power that launches a signal into 850 nm step-index
multimode fiber and a system margin for unexpected
losses of 8 dB?
Ex3 Calculate the system rise time from Ex2 , is
this rise-time budget satisfied?