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Varactor-based circuits, used for frequency conversion, have the advantages of a simple topology, high efficiency, reasonable bandwidth, and good isolation of the input signal. However, they often exhibit spurious oscillations, which complicate the design and limit their applicability. In the case of frequency dividers, the operation bands are bounded by bifurcation phenomena. In this paper, the behavior of these circuits is investigated with stability-analysis and bifurcation-detection capabilities through harmonic-balance techniques. The techniques are applied for the design of a frequency tripler, a frequency divider-by-3 and a fractional-order frequency divider-by-3/2. Good experimental behavior has been obtained in all cases. The discrepancies with the simulated results have been found to be due to the high tolerances of the lumped elements.