An intentionally approximate bilinear based transform

Over the last few years the bilinear transform has become established as the major transform for SC filters synthesis. Mathematically exact realizations of bilinearly transformed passive template filter have been developed. But these realizations, while having the advantage of being exact (and thus correct by design) generally suffer from unnecessarily complex topologies. For example, the standard ladder transform, assumes an external sample and hold circuit (which practically can be costly to realize), and for many circuits, results in much higher than necessary capacitor ratios. This paper seeks to address these problems by presenting a modified `non-exact´ bilinear transform, which can be used to produce mathematically exact SC filters (by preshaping the passband of the passive template filter). It can be viewed as a step towards direct z-plane synthesis of SC filters, in that, the s-plane function is distorted to simplify the z-plane realization