A design methodology of lossy transconductance filters

Transconductance filters use LC ladder filters as prototypes. Unfortunately real LC filters and transconductance filters have losses and the resultant filter characteristics are often very different than the desired one. The purpose of this study is to redesign filters in such way that, despite of nonideal elements, the filter characteristics is very close to ideal ones. This can be done by changing values of Ls and Cs in such way that the filter regains close to ideal characteristics. As the measure of correctness several criteria can be used. First, sum of square distances between poles of ideal and lossy filters. Second, the sum of the square of differences in the coefficients of ideal and lossy transfer functions. Third, the differences between the filters´ magnitude plot are minimized. The first and second method work, but only for simple low pass filters. In the case of more complex designs, the number of poles in ideal and lossy filters are different, so the first method can´t be used. Also, if there are a different number of poles, then the filter´s orders are different, so the second method of coefficient comparison will not work too. The most universal approach is the third method where the frequency magnitude plots of ideal and lossy filters are being matched. As a result of this approach, a lossy filter obtained in this way can have exactly the same frequency response as the ideal filter, designed using the classical algorithm.