On the Design of a Multiple Pass-band Filter by Frequency Transformation

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It is shown that the use of reactance functions for frequency transformation of a normalized low-pass filter (NLPF) to a multiple passband filter (MPBF) is straightforward and simpler than the methods using repeated low-pass to band-pass transformation or a combination of such transformations. The method gives the band edges of the MPBF corresponding to the positive and negative cutoff frequencies of the NLPF unambiguously. The transformation function is found explicitly in terms of the band edges of the MPBF and the NLPF elements are converted to those of the MPBF with ease. Furthermore, the center frequencies of the passbands are also found with ease. Dual and triple passband filters are considered for illustrating the use of the method.