Synthesis of a Finite, Four‐Terminal Net‐Work from its Prescribed Driving‐Point Functions and Transfer Function

Synthesis of Reactance 4‐Poles Which Produce Prescribed Insertion Loss Characteristics: Including Special Applications To Filter Design

“…(13) In this case, J' must be real and any complex p;'s must occur in conjugate pairs but any of the p;'s are permitted to have positive real parts. These conditions can always be satisfied because of the fact that (6) and (7) require (N -(R~~~2)2 p2) to be non-negative at real frequencies. In general, there are actually a number of solutions for A I and B' because of the arbitrariness of the signs of the p;'s as well as that of J'.…”

“…Under certain conditions this can be accomplished by modifying the first part of the non-dissipative design procedure in such a way as to obtain the open-and short-circuit impedances corresponding to the removal of the dissipation from the final network. 6 This permits the element values to be computed from the impedances on a strictly non-dissipative basis.…”

“…The various sets corresponding to a single loss function, for instance, usually occur in inverse pairs leading to inverse configurations. 6 The possibility of doing this depends upon the following situation. When the dissipation required in a network satisfies certain restrictions as regards its variation from element to element the effect of the dissipation on complex impedances and complex voltage ratios corresponds to simple transformations of the functions of frequency representing the impedances and voltage ratios, these transformations being independent of the specific network configuration and element values.…”

Synthesis of RC Transfer Functions as Unbalanced Two Terminal-Pair Networks

“…The design of networks to produce transfer functions having prescribed behavior is a relatively new art. This is especially true in the case of the insertion loss methods employed by Darlington (2) which are based upon the theory of network synthesis as developed principally by Cauer (3), Brune (1), Gewertz (6), and Guillemin (7). The most common form taken by a network designed according to these methods is a network of pure reactances terminated at one or both ends in a resistance.…”

“…Guillemin (6) has shown that it is possible to design a passive network containing only resistances and capacitances which produces any specified minimum-phase insertion-loss characteristics to within any specified tolerance, except, of course, a characteristic calling for a pole on the finite part of the imaginary axis. (The restriction to minimum-phase functions is not essential; but a function having zeros in the right half-plane is realizable in unbalanced form only if the polynomial defining the totality of its zeros has all positive coefficients.)…”