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Theoretical investigation and experimental verification of the nonanalytic form of the conversion equations in a frequency divider by two
Author(s) -
Di Paolo Franco,
Leuzzi Giorgio,
Schreurs Dominique,
Serino Antonio
Publication year - 2006
Publication title -
international journal of rf and microwave computer‐aided engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.335
H-Index - 39
eISSN - 1099-047X
pISSN - 1096-4290
DOI - 10.1002/mmce.20130
Subject(s) - nonlinear system , local oscillator , microwave , signal (programming language) , frequency conversion , frequency divider , barkhausen stability criterion , physics , matrix (chemical analysis) , power dividers and directional couplers , optics , computer science , electrical engineering , materials science , engineering , quantum mechanics , phase noise , magnetization , magnetic field , composite material , programming language
The conversion matrix, usually represented in a conventional complex‐number form, assumes a nonanalytic, real‐imaginary form when the frequency of the small signal f s is equal to one‐half the local oscillator (LO) frequency f 0 . This is due to interference phenomena between the input small signal at f s = f 0 /2 and the converted signal again at f 0 − f s = f s = f 0 /2; the interference is dependent on the phase relation between the input small signal and the LO. The conversion matrix with f s = f 0 /2 is used in the design of frequency dividers by two. The conversion equations have been rewritten for the case of f s = f 0 /2, and the conversion matrix has been found to assume a real‐imaginary form. Consequently, Barkhausen's criterion has been reassessed for this case. Experiments are performed that confirm this formalism, and computer simulations based on a nonlinear model for the nonlinear device are presented, showing similar results. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.