Digital filter realization based on simulation of the node equation of lc filters

One method of synthesizing a digital filter involves the simulation of an LC analog filter. This method retains the low element sensitivity that is characteristic of an LC filter and is generally attractive in that it requires only a small number of bits in the multiplier that is used to produce the filter coefficients. The web digital filter is a typical application of this design method and is known to possess low-element sensitivity, but it involves a somewhat complex configuration and the transfer functions which can be realized are therefore limited. This paper discusses a method of designing digital filters by simulation of the node equation of LC filters. Using this method, the transfer function of an analog filter which can be implemented by means of LCR elements, including transformers, can always be realized. With this method, we first transform the LC filter into an equivalent circuit and determine the applicable node equation. Then bilinear transformation is used to transform the s-variable into the z-variable and, to prevent the occurrence of a delay-free loop within the circuit, after rearranging the circuit equation it is realized as a digital filter. In addition, a study is made of methods reducing the number of multipliers without degrading the coefficient sensitivity. Finally, the effectiveness of this design method is verified by means of computer simulation.