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A new method is discussed for the systematic synthesis, design and performance optimization of varactor-based parametric frequency dividers (PFDs) exhibiting an ultra-low power threshold ($P_{th}$). For the first time, it is analytically shown that the $P_{th}$-value exhibited by any PFD can always be expressed as an explicit closed-form function of the different impedances forming its network. Such a unique and unexplored property permits to rely on linear models, during the PFD design and performance optimization. The validity of our analytical model has been verified, in a commercial circuit simulator, through time-domain and frequency-domain algorithms. To demonstrate the effectiveness of our new synthesis approach, we also report on a lumped prototype of a 200:100MHz PFD, realized on a printed circuit board (PCB). Although inductors with quality factors lower than 50 were used, the PFD prototype exhibits a $P_{th}$-value lower than $-$15dBm. Such a low $P_{th}$-value is the lowest one ever reported for passive varactor-based PFDs, operating in the same frequency range.