How To Say What You Want

1
How To Say What You Want

• Describing Signals

2
Review

• Light is trapped in an optical fiber if it
  strikes the sides of the fiber at angles greater
  than the critical angle for the core-cladding
  interface
• The core must have a higher index of refraction
  than the cladding for total internal reflection
  to occur.
• The numerical aperture (NA) of a fiber relates
  the maximum angle of incidence on the front of
  the fiber to the indices of refraction of the
  fiber
• NA n0 sin qm (n12 - n22)1/2.

3
Review (cont.)

• Any periodic function of frequency f0 can be
  expressed as a sum over frequency of sinusoidal
  waves having frequencies equal to nf0, where n is
  an integer. The sum is called the Fourier series
  of the function, and a plot of amplitude
  (coefficient of each sin/cos term) vs. frequency
  is called the Fourier spectrum of the function.
• Any non-periodic function (so frequency f0 ?0)
  can be expressed as an integral over frequency of
  sinusoidal waves having frequencies. The
  integral is called the Fourier transform of the
  function, and a plot of amplitude vs. frequency
  is called the Fourier spectrum of the function.
• The Fourier spectrum of a wider pulse will be
  narrower than that of a narrow pulse, so it has a
  smaller bandwidth.

4
How do we send signals?

• Radio antenna (AM frequencies around 1000 kHz, FM
  frequencies around 100 MHz)
• TV antenna (VHF frequencies are around 100 MHz,
  on either side of FM frequencies, UHF frequencies
  around 500 MHz)
• These are public transmissions, and so the
  carrier frequencies are set and regulated
• Coaxial cable
• Optical waveguides
• ISDN

These are private transmissions, and sent over
range of frequencies
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Optical waveguides pros and cons

• Message remains private
• Flexibility
• Low Loss
• Insensitive to EM interference
• Very high bandwidth
• BUT
• Expensive to connect to every house
• Require electricity-to-light converters
• Either multi-modal, or less efficient (better
  coupling makes this less relevant)

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Chromatic Dispersion

• Index of refraction is dependent on wavelength.
• Typical materials exhibit higher indices of
  refraction for lower wavelengths (higher
  energies)
• Thus violet light bends the most through a prism
  or water and appears on the outside of a rainbow.

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Optical Fiber Dispersion/Attenuation

• Dispersion means spreading
• Signals in a fiber will have several sources of
  dispersion
• Chromatic
• Material index of refraction depends on
  wavelength (prism)
• Waveguide some of wave travels through cladding
  with different index of refraction (primarily
  single-mode) leads to wavelength-dependent
  effects
• Modal different modes travel different paths
  and so require different amounts of time to
  travel down fiber (CUPS)
• Also have attenuation/loss due to
  scattering/absorption by fiber material, which
  depends on wavelength/frequency

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Modes in Optical Fibers

• Modes in a fiber are specific field distributions
  that are independent of the length traveled down
  the fiber. However, these modes travel at
  slightly different speeds which matters more with
  longer fibers.
• Fields of modes look like harmonics of standing
  waves

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Modes Combine to Give Path of Light

• To add Mode 1 and Mode 2, must add fields.
• BUT, modes travel at different speeds, so sum of
  fields changes as go down the fiber
• Result is one of the paths light will take

2
Mode 2
Mode 1
Intensity Pattern of Sum

• (Figures adapted from Photonics not to scale)

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Modes in Optical Fibers (cont.)

• Modes are like sines and cosines in Fourier
  series each path that light takes down a fiber
  can be expressed as a sum of modes.
• Can make a single-mode fiber by
• reducing diameter of fiber so smaller cone of
  light enters
• reducing NA of fiber so smaller cone of light is
  trapped

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What Exactly Is Bandwidth, and Why Do We Care?

• A range of frequencies
• Generally found by taking the frequencies with
  amplitudes more than half the maximum amplitude
  (e.g., on a Fourier spectrum)
• Bandwidth for a medium is the range of
  frequencies which can pass through that medium
  with a minimum of separation
• Sampling theory says that a signal transmitting N
  different amplitudes per second requires a
  bandwidth of at least N/2 BgtN/2
• Usually this ideal is not achieved, and the
  required bandwidth is larger
• Grant says B approx N

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Some ways to modulate signals

• Amplitude modulation
• A signal with a constant carrier frequency is
  sent
• The original signal becomes the amplitude of the
  transmitted signal
• Since the transmitted signal is not a simple sine
  wave, it has a bandwidth of Fourier components
• Frequency modulation
• A signal with a constant carrier frequency is
  sent
• The original signal becomes the change in
  frequency of the transmitted signal
• Since the transmitted signal is not a simple sine
  wave, it has a bandwidth of Fourier components
• FM is easier to amplify, since only the frequency
  determines the signal.

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Schemes for Encoding

• ASCII - The American Standard Code for
  Information Interchange is a standard seven-bit
  code that was proposed in 1963, and finalized in
  1968. ASCII was established to achieve
  compatibility between various types of data
  processing equipment.
• ASCII is the common code for microcomputer
  equipment. The standard ASCII character set
  consists of 128 decimal numbers ranging from zero
  through 127 assigned to letters, numbers,
  punctuation marks, and the most common special
  characters. The Extended ASCII Character Set also
  consists of 128 decimal numbers and ranges from
  128 through 255.

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(No Transcript)
15
Pulses and Data

• Can represent binary data with pulses in a
  variety of ways
• 10110 could look like . . .

Notice that the NRZ takes half the time of the
others for the same pulse widths
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Distortion

• No physical change is instantaneous
• If change is too slow, wont have time to rise
  before needs to fall
• Results in data loss

• Since rise is generally exponential, we define
  rise time to be time from 10 of max value to
  90 of max fall time is time from 90 to 10
• To be able to resolve data, the rise time and
  fall time must be less than 70 of the bit width

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What exactly is a decibel?

• A ratio, often of power
• BUT, in logarithmic form
• dB 10 log (P2/P1)
• e.g., if my received signal is 1/10 as big as my
  transmitted signal, my gain would be
• gain dB 10 log (1/10) -10
• The minus sign denotes loss, or a second power
  less than the initial power

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Why care about decibels?

• Signal-to-noise ratios are often given in
  decibels
• You want the signal to be larger than the noise,
  so the ratio (in dB) should be positive
• For digital data, we use bit error rate, not
  signal-to-noise
• Bit error rate is ratio of wrong bits to total
  bits - it should be small, whereas SNR should be
  large
• Bit error rate can be expressed as a plain
  number, or in decibels

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Before the next class, . . .

• Read On-Line Reading on Interference and
  Diffraction
• Do Reading Quiz
• Finish Homework 7 (start 8)
• Do Activity 06 Evaluation by Midnight tonight.