Passive filters are mainly networks using inductors, capacitors and resistors. The classical theory employed was based on the image parameter theory which in turn was based on the filter’s characteristics and performance. Its component values were calculated by considering a source having a specified source resistance and feeding it into a constant load impedance called the termination impedance, resulting in constant — K type filter or prototype filter. This filter is a T or π section in which the series arm Z1 and shunt Z2 are connected by the relationship Z1 • Z = R02 where Ro is a real constant called the design impedance.
The constant — K filter section cannot have an idealised attenuation versus frequency characteristic. Hence the response characteristics in the attenuation band can be modified to an almost ideal respone curve by suitable changes in the shunt or series arm without affecting the design impedance of the filter circuit. Such derived filter circuits of the prototype filter section are called m-derived filters, where m is the design parameter, which is a constant. Constant-K filters were often modified with m-derived end sections both at the input and output side, to obtain better impedance matching between the source and filter network on the input side and between the filter and load on the output side.
One of the main difficulties with these passive filters was the necessity of always using the specified source and termination impedance. The cascading of these filters was also not straight forward, in spite of designing the filters so that their source and termination impedance were equal. Additional isolation amplifiers often had to be used between cascaded sections. This was done to prevent severe distortion of the filter characteristics due to non-ideal matching of impedance between the filter end sections and the source, as well as the terminating load. Another disadvantage was the necessity of using bulky and often nonlinear inductances for low and very low frequencies. Due to the relatively low values of inductive reactance at low frequency, in addition to the non-linearity at high current levels (due to saturation of cores), the circuit was designed to keep the signal levels low.
The availability of opamps in integrated form has changed the saturation significantly, giving rise to active filters.
Today, a majority of low frequency filters are of this type, particularly for frequencies below 100 kHz. The special advantage of the active circuit for use in low frequency filters is the fact that inductors can be totally eliminated. In addition, active capacitance multiplication enables the use of capacitors of low practical values even for cutoff frequencies down to a fraction of 1 Hz. However due to the limited gain-BW produCt of the ICs and their effect on the filter characteristics, and due to the advantages of the inductor in high frequency range, passive filters are preferred for frequencies above a few 100 kHz.