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The use of resonant injection-locked frequency dividers in frequency synthesizers has increased in recent years due to their lower power consumption compared to conventional digital prescalers. Numerous circuit ideas have been proposed, but there are few and sometimes contradictory estimates of the locking ranges (LRs) in these dividers. Despite several attempts, there is still no accurate analytical method to predict the LR. In this paper, we present a nonlinear approach based on the application of bifurcation theory to predict where the LR is wider rather than to say precisely how wide it is. The results presented have been derived by numerical bifurcation analysis using AUTO and have been verified by circuit simulations and experiments. In Part II, we will show how the insights developed in this paper lead to a rigorous design methodology.