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In this paper, dielectric constants of lossy organic liquids are measured using oscillation frequency shifts of a negative-resistance voltage-controlled oscillator (VCO). The design and working principle of the oscillator and the effect of material loss are presented in detail. The proposed method provides relatively large frequency shifts of 10-110 MHz for lossy test sample volumes of 50-200 μL whose dielectric constants are between 2-13 at 4.5 GHz, thereby allowing good resolution in dielectric-constant measurement. To make the system self-sustained, the VCO is used as part of a frequency synthesizer system for frequency-to-voltage conversion and digital extraction of the frequency shift using a unique detection algorithm. The dielectric constant of several organic liquids have been extracted to an accuracy better than 2% using sample volumes of 50-200 μL , and has excellent agreement with reported values. The applicability of this system for sensing dielectric mixtures has also been shown, and volume fraction estimation has been demonstrated to an accuracy of around 1%.