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2018-11-05

2018-11-05

作者: carpediemmlf | 来源:发表于2018-12-21 06:41 被阅读0次

Power ratio

R = (\frac{Z_2 - Z_1}{Z_1 + Z_2})^2

T = (\frac{2 Z_1 }{Z_1 + Z_2})^2

R + T = 1

Impedance matching

  • consider a system of two parallel interfaces, from left to right the medium impedances are respectively Z_1, Z_2 and Z_3. The distance between the two interfaces to be \frac{1}{4} \lambda

  • by the continuity equations of the displacement and velocity at the two interfaces, we conclude the total reflective coefficient of the double layer system to be

    r = \frac{Z_1 - \frac{{Z_2} ^ 2}{Z_3}}{Z_1 + \frac{{Z_2} ^ 2}{Z_3}}

  • we define the effective impedance to be Z_{eff} = \frac{{Z_2} ^ 2}{Z_3}, thus acquiring a similar reflective coefficient as for a single interface system with Z_1 and Z_{eff}

Quarter wave matching (i.e. the interface spacing with impedance Z_2 has length \frac{1}{4} \lambda)

  • Satisfied under the condition Z_2 = \sqrt{Z_1 Z_3}, r = 0
  • this gives the zero reflection condition for quarter wave matching

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