Network synthesis filters

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 wavelengths while rejecting waves of other wavelengths. 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 image method. The image method considers the characteristics of an individual filter section in an infinite chain (ladder topology) of identical sections. The filters produced by this method suffer from inaccuracies due to the theoretical termination impedance, the image impedance, not generally being equal to the actual termination impedance. With network synthesis filters, the terminations are included in the design from the start. The image method also requires a certain amount of experience on the part of the designer. The designer must first decide how many sections and of what type should be used, and then after calculation, will obtain the transfer function of the filter. This may not be what is required and there can be a number of iterations. The network synthesis method, on the other hand, starts out with the required function and generates as output the sections needed to build the corresponding filter. In general, the sections of a network synthesis filter are of identical topology (usually the simplest ladder type) but different component values are used in each section. By contrast, the structure of an image filter has identical values at each section, as a consequence of the infinite chain approach, but may vary the topology from section to section to achieve various desirable characteristics. Both methods make use of low-pass prototype filters followed by frequency transformations and impedance scaling to arrive at the final desired filter.