Wave digital adaptors for Brune, Darlington C and D, and twin-t sections

Abstract

This thesis is concerned with the derivation of new wave adaptors for the Brune section, the Darlington C and De sections, and an adaptor for the Twin-T structure. These wave adaptors have been derived by applying Martens' and Meerkötter's n-port voltage scattering matrix representation to the corresponding reference network interconnections. The following results have been obtained: a) The Brune, C and D adaptors are realized without any unit elements. b) The adaptors in a0 are canonical in the number of delays. c) All the adaptors considered may have a reflection-free port which makes cascade synthesis possible. d) The Brune and C adaptors require six multipliers, four of which are independent and two of which are identical. e) The D adaptor requires a total number of eleven multipliers, seven of which are independent and two pairs of which are identical. f) The Twin-T adaptor requires ten multipliers of which seven are independent. g) In a hardware realization, all the adaptors considered are made to have zero output after a finite time for zero input by means of a simple arithmetic procedure. Illustrative examples of filters using these structures have been designed, and simulated on a minicomputer. Their respective impulse responses are obtained and show no granularity and/or overflow oscillations, as expected.