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

Abstract

A new general method for the synthesis of RC transfer functions is presented.Based on an extension of Brune's procedure for the synthesis of driving-point impedances, it makes use of canonical sections for controlling transmission zeros in much the same way as canonical sections are used by Darlington in synthesizing lossless two terminal-pair networks.The characteristic process of the method makes use of the following theorem, proof of which comprises the principal result of the report.Given a function F 1 () of suitable degree, realizable as an RC impedance or admittance, it is always possible to design an unbalanced two terminal-pair network that: (a) produces a transmission zero or single pair of conjugate zeros at any given point or points, respectively, not in the right half-plane; and (b) produces the prescribed function F 1 (k) when terminated in a second function F 2 (X), also RC, the degree of which is less than the degree of F 1 ().The networks obtained by the new method take the form of ladder networks cascaded with bridge sections similar to the well-known twin-T null network. The "zero sections"are obtained one at a time, each by a single application of the theorem, and this process is repeated until the original function is completely developed.When used in combination with existing synthesis techniques the method provides a highly flexible procedure which allows limited control over impedance levels and insertion loss.

Zur Synthese von RC-Gyrator-Vierpolen

“…garantiert. (6a, b, c, d) erhält man die Gesamtschaltung nach BildS, wobei der RC-Vierpol B nach [5] bzw. [16]).…”

“…Der linke RC-Vierpol hat nach[5] in gewissen F llen eine andere Struktur M glichkeit b: Mit γ > 0 und 0 < ε < l wird ') Bei einer Realisierung nach [7] sind auch Xullstcllcn rechts zul ssig. Bild 2.…”

Distributed RC Networks with Rational Transfer Functions

“…Assuming a product type of solution in which the time dependent component is 4 eSt, the general solution of Equation (18) is expressed in Equations (19) and (20). …”