Receivers Antennas and Signals Lecture Notes - lecture22 - Wave Propagation by YAdocs

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									                              Wave Propagation
 Molecular line absorption by gases:
                                  • permanent electric dipole
     C       O
                                    (H2O, CO)
                        H
                                  • permanent magnetic dipole
     O     O               O        (O2)
                        H         • unpolarized (N2) (collision­
     N      N
                                    induced dipoles)
 Quantized energy levels: Ei – Ej = hf
                         electronic states
                                vibrational states
                                         rotational states
                                                    nuclear spin states



             visible, UV, x-ray           IR - µW
                                                    r.f. → audio
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                       Molecular Lines in Gases
 Quantized energy levels: Ei – Ej = hf

 Probability of radiation = A + B ρf
               “Einstein ‘A’ coeff.”               radiation intensity (energy density)
                           “Einstein ‘B’ coeff.”

 Probability of absorption = Bρf
               3       3                             Atmospheric absorption of
 A B = 8πhf        c                  dB
                                                     radio waves at zenith (clear air)
                                    100                                 O2     H2 O
                                                               O2
  Collisions and radiation
  compete to control level     10
  populations. In equilibrium,
  kinetic and radiation                       H2 O
                                1
  temperatures are equal.

                                          0                                           f (GHz)
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                                              22.235      60        118      183           A2
                       Molecular Line Shape
  Broadening: intrinsic, collisional, Doppler
        Einstein “A” yields spontaneous emission, limiting state
        lifetime T; intrinsic linewidth ≅ 1/T
   Absorption             Electric                           random collisions
                          field                              change dipole
                                                             phase, orientation
                                                         t

                            f
             ∆ω = linewidth ∝ number of collisions/sec



  “Pressure broadening” or “collision broadening” ≅ 2 GHz at
  standard temperature and pressure (STP) for O2, H2O < 1 THz

                                              2    (
             Doppler broadening has thermal 1 mv 2 ≅ 3 kT ,
                                                     2              )
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             turbulent (random), and systematic components                        A3
                   Overlapping Spectral Lines
   Superposition characterizes the cumulative absorption by independent
   spectral lines, except for certain single molecules.

   For a single molecule with collision-coupled states, total absorption is
   generally greater than sum of line absorptions between coupled lines, and
   less outside. Such coupled lines coherently “interfere” (e.g. 60-GHz oxygen
   band).

                            interference-
  α(f)       A+B
                            enhanced absorption          α(f)
                             A alone
                               B alone
                                                         0      ωo          f
                                interference-
                                reduced absorption


                                      f
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                                   Refractive Effects
      ε(f)
                              α(f), resonance
                              absorption      The permittivity ε(f) of a medium is
                 ε εo                         related in part to the absorption
                                              coefficient α(f) by the Hilbert transform;
                                              α(f) is related to the imaginary part of ε(f).
             1           fo               f

                 Atmospheric water vapor scale height = ~2 km
                 Atmospheric density scale height ≅ ~8 km
                 So humidity-based refractive effects are mostly a lower tropospheric
                               ~
                 phenomenon (< 8 km).
                 Thermal inhomogeneities are turbulent in the boundary layer (first
                 few hundred meters or more) and near convective instabilities, and
                 are more layered at higher altitudes.
                 Humidity variations often dominate radio refraction, while density
                 variations dominate optical propagation.
                 Optical telescopes have ~1 arc-sec “seeing” on good nights (2” – 10”
                 in Boston is typical); the best mountain days may yield ~0.4 arc sec.,
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                            Refractive Effects
The radio index of refraction n is given by: (n − 1) 10 = ( 79 T ) (p + 4800 e T )
                                                       6

   where T is °K, and p and e are total and partial water vapor pressures (mb).
          refraction           less dense
                                                        “duct” of humid air
 ionosphere
                             dense                          dry
                                                      humid
                          over the horizon
  Ducting can occur in cold or humid layers of air, or in under-ionized
  ionospheric layers. Acoustic ducting can occur in cool or salty ocean layers.

               Refractive seeing beyond the horizon can be ~ 30
                                                            >
               arc minutes on RF, and less at optical frequencies.

             Fading caused by interfering multipath: paths of different
             length cause different frequencies to cancel out or “fade.”




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                  Ionospheric and Space Plasmas
  Plasmas can have both neutral and ionized components.
                                             (
  The ionosphere has ne ≅ 107 − 1012 m−3 from ~50        )
  to 5000 km altitude. Electron density ne (max) is ~100 - 400 km.
  Plasma frequency:

                     ωp =
                          neq2 −1
                          m εo
                               rs  ( )
                                  where m =
                                             memi
                                            me + mi
                                                    ≅ me

                     ε = εo (1 − ωp ω2 )
                                  2
                                                 q = electron charge

                          Evanescent waves only, if ω < ωp

  Propagation delay:

                                       1 − ( ωp ω) > c
                                                     2
             phase velocity   vp = c                         for f > fp

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             group velocity   v g = c 1 − ( ωp ω) < c
                                                 2           (v g vp = c 2 here   )
 1/12/01                                                                      C3
             Refraction and Absorption by Plasmas
  Refraction by plasmas:                                          y
                                                                           vp
        ω > ωp   refraction is governed by Snell’s Law                θt            t

                 sin θi sin θt = vpt vpi                                                z
        ω < ωp   evanescent waves, total reflection           θi θi        vp
                                                                                i

  Absorption by plasmas:
                                      transient electric dipole
                                      emits and absorbs




                  # collisions ∝ n2 (weak in ionosphere)
                                  e
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                    Magnetized Plasmas
                                Faraday rotation, bi-refringence
                                    x                x

         ⎡ K'     jK '' 0 ⎤     E          B
  ε = εo ⎢− jK '' K '   0⎥⇒                                 -e
         ⎢                ⎥                                        z
         ⎢ 0
         ⎣         0 Ko ⎥ ⎦

                            y                   y



     The EM interaction and Faraday rotation become strong near
     the electron and ion cyclotron resonances, ωc = qBo m


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  Scattering and Absorption by Dielectric Spheres
                                 ε, sphere (e.g. raindrop)
 EM
                                                λo     εo
wave                                     D <<                    ⇒      "Rayleigh scattering"
                          D                     2π     ε
              E                               λo
                                         D>
                                                                ⇒      "Mie scattering"
                                             2π
                                              λo
                                         D >>                    ⇒      Geometric scattering
                                              2π
    induced electric dipole                                    null
                                                                             dipole re-radiation
   EM                                                                        pattern
   Mie is multimode:
                 log (σs)                                              induced electric dipole

                                                                      4πa2
                                 πa2
                  slope = 4
                                                     0.25πa2           Geometric
                                                   Mie                   f
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                              Rayleigh                                                             C6
  Scattering and Absorption by Dielectric Spheres
 Rayleigh regime             ( λ >> 2πDε εo ) :             (constant ε)
        σs ∝ ( a λ ) λ scattering cross-section, α scattering dBm
                         6   2
                                                                           (    )
                                                                               −1
                                                                                    ∝f
                                                                                         4


        σa ∝ ( a λ ) λ absorption cross-section, α absorption
                         3
                                                                           (dBm ) ∝ f
                                                                               −1        2

                  
 Cloud absorption < 85 GHz (Rayleigh region):
                                                         [0.0122( 291− T )− 6]
                                    (
                            γ CLD nepers cm      ≅      )
                                                   m • 10
                                                   -1

                                                             λ
                                                               2

                    where m = g/m3 liquid water, λ = wavelength cm, T = K°

         strong                         ice               
                                                   Albedo < 0.8, fmax scat. ≈ 100 − 150 GHz
         scattering                                ∴ TB > 70K as seen from space
                                                        
                                                                  ∆
              updraft                              (Albedo = reflectivity, all angles)

                                              cumulonimbus
                                              cloud
                  rain
                                                  Rain attenuation > 30dB sometimes
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