Electronic circuits for locking an oscillator in phase with an arbitrary input signal. A phase-locked loop (PLL) is used in three fundamentally different ways: (1) as a demodulator, where it is employed to follow (and demodulate) frequency or phase modulation; (2) as a tracker of a carrier or synchronizing signal which may vary in frequency with time; and (3) as a frequency synthesizer, where an oscillator is locked to a multiple of an accurate reference frequency. When operating as a demodulator, the phase-locked loop may be thought of as a matched filter operating as a coherent detector. When used to track a carrier, it may be thought of as a narrow-band filter for removing noise from the signal and regenerating a clean replica of the signal. When used as a frequency synthesizer, a voltage-controlled oscillator (VCO) is divided down to a reference frequency that is locked to a frequency derived from an accurate source such as a crystal oscillator.