non dissipative ladder filters

calculate the inductances and capacitances of a non-dissipative analog ladder filter

This set of *.m files is useful to calculate the elements (inductances and capacitances) of non-dissipative, ladder structured, analog filters. It follows the first step of filter design which can be implemented with the help of functions available in the "Analog Lowpass Filter Prototypes", "Analog Filter Design" and "Analog Filter Transformation" categories of the "Signal Processing Toolbox". This first step consists in finding the transfer function, namely the transmission coefficient s21 of the scattering matrix of a quadrupolar circuit, expressed as the ratio of two polynomial of the "s" variable, the numerator "f" and the denominator "g" in the case of a normalized transfer function. Then, the following functions can be used :
- hurwitz.m calculate the Hurwitz conjugate of a polynomial.
- unitarh.m calculate the third polynomial, labelled "h", from the two polynomials "f" and "g" of the transmission coefficient s21.
- z11sb.m ; z11sh.m ; z22sb.m ; z22sh.m ; y11sb.m ; y11sh.m ; y22sb.m ; y22sh.m are labelled with the diagonal elements of the impedance and admittance matrix of the quadrupole circuit respectively. These functions calculate the numerator and denominator of these normalized diagonal impedance or admittance, the inductances and the capacitances of the normalized filter from polynomials "g" and "h". The non-dissipative elements are arranged in a ladder, the first one being an inductance in series for diagonal impedances while it is a capacitance in parallel for diagonal admittances.
Normally, one of these last eight functions is sufficient to fully determine the elements. However, it is better to try two or three of them, and choose the result which has the largest number of elements.
In the case of elliptic filters, it is necessary to displace a fraction of each capacitance which has been found to form a parallel "stop" circuit with the adjacent inductance in order to get the right zero circular frequencies of the numerator of the lowpass transfer function.

Reference :
"Les filtres électriques", Traité d'Électricité, volume XIX, École Polytechnique Fédérale de Lausanne, H.
Dedieu, C. Dehollain, M. Hasler, J. Neirynck, Presses Polytechniques et Universitaires Romandes, 1996
(3ème édition), CH-1015, Lausanne, Suisse.