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Concept# Network synthesis filters

Summary

In signal processing, network synthesis filters are filters designed by the network synthesis method. The method has produced several important classes of filter including the Butterworth filter, the Chebyshev filter and the Elliptic filter. It was originally intended to be applied to the design of passive linear analogue filters but its results can also be applied to implementations in active filters and digital filters. The essence of the method is to obtain the component values of the filter from a given rational function representing the desired transfer function.
The method can be viewed as the inverse problem of network analysis. Network analysis starts with a network and by applying the various electric circuit theorems predicts the response of the network. Network synthesis on the other hand, starts with a desired response and its methods produce a network that outputs, or approximates to, that response.
Network synthesis was originally intended to produce filters of the kind formerly described as wave filters but now usually just called filters. That is, filters whose purpose is to pass waves of certain frequencies while rejecting waves of other frequencies. Network synthesis starts out with a specification for the transfer function of the filter, H(s), as a function of complex frequency, s. This is used to generate an expression for the input impedance of the filter (the driving point impedance) which then, by a process of continued fraction or partial fraction expansions results in the required values of the filter components. In a digital implementation of a filter, H(s) can be implemented directly.
The advantages of the method are best understood by comparing it to the filter design methodology that was used before it, the . The image method considers the characteristics of an individual filter section in an infinite chain (ladder topology) of identical sections. The by this method suffer from inaccuracies due to the theoretical termination impedance, the , not generally being equal to the actual termination impedance.

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