Synthesis of Interference Filters

A method of synthesizing electrical circuit filters to transmit prescribed functions of frequency in a specified pass-band is applied to dielectric interference filters containing up to four half-wave layers. The method relies on an approximation that the half-wave layers are the only parts of the filter which are sensitive to frequency. The reflecting quarter-wave multilayers are described by a single parameter whose values are deduced in the synthesis. The transmission functions are either maximally flat in the pass-band or contain equal ripples. The rate of transition from the pass-band to the stop-band is increased rapidly by increasing the number of half-wave layers. The synthesis is applied to filters specified to transmit an 8% bandwidth within which the transmissivity is not less than 0.91. The exact transmission characteristics of these examples show excellent agreement in the pass-band with the simple functions. The method can be applied to the design of filters of moderate bandwidth for any spectral region.