In this paper, analysis and design of an ultra-low-voltage low-power voltage controlled oscillator (VCO)-based comparator operating in subthreshold region is presented. It is composed of a pseudo differential VCO and a phase-frequency detector (PFD). An analytical design approach is developed resulting in closed-form expressions for important properties of the comparators such as resolution, comparison time, comparison energy and input-referred noise. Using the developed expressions, the design of phase-frequency detector (PFD) and its limitations is fully addressed and the possibility of using a signal premapping strategy allowing for rail-to-rail operation is investigated. To comprehensively verify the operation of the proposed comparator, it has been adopted in an 8 bits, 13 kS/s SAR ADC suitable for biomedical applications. Using a 0.18 mu m standard CMOS process under a 0.5-V supply voltage, the total power consumption is about 153 nW. The simulated SNDR and SFDR are 49.15 dB and 57.76 dB, respectively. The DNL is +0.12/-0.13 LSB and the INL is +0.24/-0.51 LSB.