Theoretical investigation and experimental verification of the nonanalytic form of the conversion equations in a frequency divider by two

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.