Prove that the scaled transfer function of bandpass filter is H ′ ( s ) = ( 1 Q ) ( s k f ) ( s k f ) 2 + ( 1 Q ) ( s k f ) + 1 .

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Chapter 15, Problem 14P

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Prove that the scaled transfer function of bandpass filter is H′(s)=(1Q)(skf)(skf)2+(1Q)(skf)+1.

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A plane wave propagating in the +z direction in medium 1 is normally incident to medium 2 located at the z=0 plane as below. Both mediums are general, characterized by ( ε i, Mi, Ơi ). tot = [ ει μη σ] [ε, μη σε ] Ex Ex tot E₁₂ (z) = Ee Ex z=0 From conservation of energy: P₁AV'(z=0) + Piav'(z=0) = P2av²(z=0). Using the above show for lossless media that: ( 1 - ||²) = (1/M2 )|T|² .

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