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Homework Help: Quarter Wave; no reflection

  1. Jan 9, 2014 #1
    1. The problem statement, all variables and given/known data

    Part(a): Show relation between impedance of dielectric and impedance of material:

    Part (b): Show the ratio between reflected and incident amplitude is:

    Part (c): Three layers now from left: vacuum, dielectric 2 sandwiched inbetween, and dielectric 1.

    Part (d): Give reasons why dielectric coatings are painted on glass transmission devices.


    2. Relevant equations

    3. The attempt at a solution

    [tex] Z_{in} = \frac {E_{(-l)}}{I_{(-l)}} = \frac {E_i e^{jkl} + E_r e^{-jkl} } {E_i e^{jkl} - E_r e^{-jkl} - E_r e^{-jkl} }Z = \frac { (Z_1 + Z_2)e^{jkl} + (Z_1 - Z_2)e^{-jkl} } {(Z_L + Z) e^{jkl} - (Z_L - Z)e^{-jkl} } Z_2 [/tex]
    [tex] Z_{in} = \frac {Z_2^2}{Z_1} [/tex]
    [tex] n_2^2 = n_1 [/tex]

    To calculate ratio:
    Consider boundary at z=0 between Z2 and Z1:
    [tex]\frac{E_T}{E_I} = \frac {2Z_1}{Z_1 + Z_2} = \frac {2\sqrt{n_1}}{\sqrt{n_1} + n} [/tex]

    Consider Boundary at z = -λ/4 between Z0 and Z2:
    [tex]\frac{E_T}{E_I} = \frac {2Z_2}{Z_0 + Z_2} = \frac {2}{\sqrt{n} + 1} [/tex]

    Then they are the same! Which is strange because there should be a standing wave in the sandwiched layer, which destructively interferes to poduce a smaller transmitted wave onto boundary z>0..

    For impedance matching, so that maximum power is transmitted; no reflection.
  2. jcsd
  3. Jan 11, 2014 #2
  4. Jan 15, 2014 #3
  5. Jan 16, 2014 #4
  6. Jan 21, 2014 #5
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