Filters with equi-ripple transmission characteristics in the pass-band as well as the stop-band have, for a long time, been considered as optimum with regard to performance and economy of elements. These were first synthesized by Darlington by the use of Jacobian elliptic functions. This method necessitates the use of double-entry tables, but with the tables commonly available, the values are not sufficiently accurate, especially if the number of poles is greater than four. Other methods based on potential analogy, and using electrolytic tanks, are equally cumbersome.
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