Phase noise in a phase-locked-loop (PLL) is unwanted and unavoidable. It is a main concern in oscillation system especially PLL. The phase noise is derived in term of power spectrum density by using a reliable phase noise model. There are four noise sources being considered in this paper, which are generated by reference oscillator, voltage controlled oscillator, filter, and main divider. The major concern for this paper is the noise from the filter. Two types of second order low pass filter are used in the PLL system. Applying the mathematical phase noise model, the output noises are compared. The total noise from the passive filter is lower than the active filter at the offset frequency range between 1 Hz to 33 kHz.