Using the binomial transformer to approximate the Q distribution for maximally flat quarter-wavelength-coupled filters
With the binomial transformer as a basis, a closed-form expression is derived for the Q distribution used to design maximally flat quarter-wavelength-coupled transmission-line filters. The derived expression is shown to be valid for filters with small values of total Q. Also, an existing Q-distribution expression derived from the lumpedelement prototype (LEP) circuit is discussed, and is shown to be valid for filters with large values of total Q. By combining the derived binomial transformer Q distribution and the LEP Q-distribution expressions, a piecewise closed-form Q-distribution expression is developed, which is applicable over a wide range of total Q values. Index Terms-Bandpass filters, binomial transformer, Butterworth filters, maximally flat magnitude filters, quarter-wavelength-coupled filters, Q distribution. © 1998 IEEE Publisher Item Identifier S 0018-9480(98)07236-6.
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