We develop and demonstrate an on-chip resonator working at 15 GHz with a high quality factor (Q-factor) of 93.81 while only requiring a small chip size of 195 mu m x 195 mu m on Si by using our new design methodology. In our design, unlike previous approaches, we avoid the need for any external capacitance for tuning; instead, we utilize the film capacitance as the capacitor of the LC tank circuit and realize a fully on-chip resonator that shows a strong transmission dip of > 30 dB on resonance as required for telemetric-sensing applications. We present the design, theory, methodology, microfabrication, experimental characterization, and theoretical analysis of these resonators. We also demonstrate that the experimental results are in excellent agreement with the theoretical (both analytical and numerical) results. Based on our proof-of-concept demonstration, such high-Q on-chip resonators hold great promise for use in transmissive telemetric sensors.