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Flip-flop based phase-frequency detectors are widely used in phase-locked loop circuits. These devices are usually assumed to behave linearly although they consist of non-linear parts. In this work, a flip-flop based phase-frequency detector circuit is analysed. Analytic output signal models are derived for arbitrary input signal frequencies and phases. Exact and approximate closed-form solutions are found for different frequency ratios. The model is validated by numerical time-domain simulations.
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