Power ratio

Impedance matching

• consider a system of two parallel interfaces, from left to right the medium impedances are respectively , and . The distance between the two interfaces to be

• 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

  

• we define the effective impedance to be , thus acquiring a similar reflective coefficient as for a single interface system with and

Quarter wave matching (i.e. the interface spacing with impedance has length )

• Satisfied under the condition ,
• this gives the zero reflection condition for quarter wave matching