Continuation methods and filter design

A geometric interpretation is given of the effect described by H.J. Orchard (IEEE Trans. Cir. Syst., vol.CAS-32, p.1089-96, 1985), which can be considered as bifurcation in the progress of a continuation process. The principles of a design method are described. Testing their design method for active filters, the authors have designed a low-pass filter of degree 4 and a bandpass filter of degree 9 and have realized these filters in practice. They show that their design approach leads to stable active filters in the higher frequency range. The authors emphasize that their results are not restricted to their design problem. In many situations of network analysis and design it is necessary to solve equations of the form f(x)=0. In most cases the authors´ approach is a natural interpretation as a parameterized family of problems where things like bifurcations and turning points may occur