| Popis: |
This thesis presents an active Complex Filter implementation that that creates a transfer function with with a single real pole and a complex zero. The two-input/two-output network developed in in this thesis responds differently based upon upon the relative phase difference of of the two inputs. If a negative ninety-degree phase difference occurs between the two inputs, the filter will exhibits a bandstop response. While a positive ninety-degree phase difference exhibits a bandpass response. This topology is relatesd to to Gingell’s RC-CR polyphase topology but because of of the use of of op-amps, can be cascadedd without without suffering loading effects. This thesis will focusfocuses primarily on on the bandstop response characteristics of of the filter. In a several stage cascade, each stage contributes a notch to broaden the attenuation bandWhen several sections are cascaded, multiple notches will be created from each stage that forms a broader attenuation band. Closed form design equations were were derived to to give expressions for for the “attenuation floor”. These equations can be used by a designer to predict the attenuation provided by by a cascaded system. The closed form expressions derived in in this thesis are used to implement an example five-stage topology that that operates from from 147 Hz to to 3.34 KHz. The thesis also investigates the robustness of of multi-stage cascades to to component variations. Monte Carlo analysis is used to determines the effects of of cascading the filter in in different orders, component tolerances, and a comparison to to an idealized polyphase RC-CR topology. |
