A phase/frequency estimator-based phase locked loop (PFE-PLL) may be use to obtain a phase and frequency estimation by using an algebraic summer, a gain block and a (co)sine waveform generator. The apparatus and methods of the present invention may provide the phase estimation of an input signal from which a frequency of the signal is estimated by a derivative function. Unlike conventional phase lock loop systems, which may use a multiplier to perform complex calculations on an input and a feedback signal to develop a demodulated voltage output, the present invention may use a simple algebraic summer to provide an error signal and output a phase and a frequency estimation of the input signal.