The relevance of odd, and in particular loss-less, frequency transformations is well established in analog filter design. A loss-less frequency transformation s←F(s), in fact, allows to design multi-bandpass multi-bandstop filters as transformed systems G̃(s)=G(F(s)) from an original prototype lowpass filter G(s), by properly selecting F(s). In this paper the invariance of the shape of the Nyquist plot for linear time-invariant continuous-time systems under a class of odd frequency transformations is proved. This result allows to determine closed-loop stability conditions for this class of transformed systems on the basis of the Nyquist's criterion referred to the original, lower order, system.

Nyquist plots under frequency transformations

Buscarino, Arturo;Fortuna, Luigi;Frasca, Mattia
2019

Abstract

The relevance of odd, and in particular loss-less, frequency transformations is well established in analog filter design. A loss-less frequency transformation s←F(s), in fact, allows to design multi-bandpass multi-bandstop filters as transformed systems G̃(s)=G(F(s)) from an original prototype lowpass filter G(s), by properly selecting F(s). In this paper the invariance of the shape of the Nyquist plot for linear time-invariant continuous-time systems under a class of odd frequency transformations is proved. This result allows to determine closed-loop stability conditions for this class of transformed systems on the basis of the Nyquist's criterion referred to the original, lower order, system.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/361969
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