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Unformatted text preview: G.2 Filter Design 785 coefficient at the 1-2 interface can be calculated using (G.3), and the power transfer function of the filter can be determined. G.2 Filter Design Although the power transfer function of any given stack of dielectrics can be deter- mined using the preceding procedure, designing a filter of this type to meet a given filter requirement is a more typical problem encountered in practice. The multiple dielectric slab structure exemplified by Figure G.1(c) is quite versatile, and a number of well-known filter transfer functions, such as the Butterworth and the Chebyshev, may be synthesized using it [Kni76]. However, the synthesis of these filters calls for a variety of dielectric materials with different refractive indices. This may be a difficult requirement to meet in practice. It turns out, however, that very useful filter transfer functions can be synthesized using just two different dielectric materials, a low-index dielectric with refractive in- dex n L and a high-index dielectric with refractive index n H [Kni76]. Assume we want to synthesize a bandpass filter with center wavelength . Then, a general structure for doing this is to use alternate layers of high-index and low-index dielectrics with thicknesses equivalent to a quarter or a half wavelength at...
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- Spring '09