Network synthesis filters

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.

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.

Generally speaking, the higher the order of the filter, the steeper the cut-off transition between passband and stopband.

[4] A Chebyshev filter has a faster cut-off transition than a Butterworth, but at the expense of there being ripples in the frequency response of the passband.

There is a compromise to be had between the maximum allowed attenuation in the passband and the steepness of the cut-off response.

[6][7][8] The Bessel filter has a maximally flat time-delay (group delay) over its passband.

This gives the filter a linear phase response and results in it passing waveforms with minimal distortion.

[1] Not every possible mathematical function for driving point impedance can be realised using real electrical components.

Wilhelm Cauer (following on from R. M. Foster[10]) did much of the early work on what mathematical functions could be realised and in which filter topologies.

The full design calculations from the relevant mathematical functions and polynomials are carried out only once.

The actual filter required is obtained by a process of scaling and transforming the prototype.

[16] Values of prototype elements are published in tables, one of the first being due to Sidney Darlington.

For instance low-pass, high-pass, band-pass and band-stop filters can all be produced from the same prototype.