The chaotic dynamics observed for the second-order phase-locked loop (PLL) operating as a frequency-modulated (FM) demodulator are studied theoretically as well as experimentally. The existence of horseshoe chaos in this circuit is proved using Melnikov's method. It is demonstrated that chaos can indeed occur in a practical FM demodulator circuit made of an integrated circuit module and using realistic parameter values. Explicit expressions that specify the possible region of chaos are derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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