Maximal Flatness and Filters Transitional Between Butterworth and Inverse Chebyshev Ones

The paper describes the family of filters which are transitional between Butterworth and inverse Chebyshev ones. Introducing a polynomial of squared frequency in the numerator of squared modulus of the Butterworth filter requires that a similar polynomial is added to the denominator of this squared modulus function if one wants to preserve the flatness property. After these two modifications are made the restoration of transfer function gives a transitional filter. If the polynomial introduced in the numerator includes all zeros of inverse Chebyshev filter then the restored filter will be the inverse Chebyshev filter. In case of partially restored flatness one obtain a transitional filter. An example of transitional filter for the fifth order Butterworth and inverse Chebyshev filters is calculated.

[1]  P. Halpern,et al.  Optimum Monotonic Low-Pass Filters , 1969 .

[2]  P. Aronhime,et al.  Transitional Butterworth-Chebyshev filters , 1971 .

[3]  Allen L. Hollister,et al.  Wideband Amplifier Design , 2007 .

[4]  Igor M. Filanovsky,et al.  A New Design Method Of Transitional Polynomial Filters , 2018, 2018 16th IEEE International New Circuits and Systems Conference (NEWCAS).

[5]  A. Papoulis,et al.  Optimum Filters with Monotonic Response , 1958, Proceedings of the IRE.

[6]  S. C. Dutta Roy,et al.  Transitional Butterworth--Chebyshev filters , 1978 .

[7]  Thomas H. Lee,et al.  The Design of CMOS Radio-Frequency Integrated Circuits: RF CIRCUITS THROUGH THE AGES , 2003 .

[8]  H. Hindin,et al.  Impulse Response and Transfer Phase of Transitional Butterworth-Thompson Filters , 1968 .

[9]  G. Aiello,et al.  Transitional Legendre Thomson filters , 1974 .

[10]  P. Geffe.  Flatness and symmetric low-pass lossless filters , 1959 .

[11]  H. W. Bode,et al.  Network analysis and feedback amplifier design , 1945 .

[12]  Peter Starič,et al.  Wideband Amplifiers , 2006 .

[13]  Igor M. Filanovsky.  A generalization of filters with monotonic amplitude-frequency response , 1999 .

[14]  C. Chang.  Maximally Flat Amplitude Low-Pass Filter with an Arbitrary Number of Pairs of Real Frequency Transmission Zeros , 1968 .

[15]  Rui Seara,et al.  Transitional filters based on the classical polynomial approximations , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[16]  Igor M. Filanovsky,et al.  Maximally flat property and bandwidth enhancing by transfer function zeroes , 2017, 2017 15th IEEE International New Circuits and Systems Conference (NEWCAS).

[17]  M. Fukada.  Optimum Filters of Even Orders with Monotonic Response , 1959 .

[18]  Igor M. Filanovsky,et al.  Enhancing amplifiers/filters bandwidth by transfer function zeroes , 2015, 2015 IEEE International Symposium on Circuits and Systems (ISCAS).

[19]  Louis Weinberg,et al.  Network Analysis and Synthesis , 1962 .