The dielectric constant, or permittivity, is a fundamental property that characterizes a material's electromagnetic behavior, crucial for diverse applications in agriculture, healthcare, industry, and scientific research. In microwave engineering, accurate permittivity measurement is essential for advancements in fields such as biomedicine, aerospace, and microwave chemistry. However, conventional waveguide resonator methods face challenges when measuring high-loss materials, often leading to reduced accuracy and increased cost. This paper introduces a lightweight, compact system for dielectric constant measurement using a negative-resistance voltage-controlled oscillator (VCO) integrated within a frequency synthesizer. The proposed system employs phase response variations of a planar sensor embedded in the VCO's gate network to detect changes in oscillation frequency, enabling precise measurement of high-loss materials. The experimental validation demonstrates the system's capability to accurately measure dielectric constants of lossy organic liquids, with applications in distinguishing liquid mixtures. The contributions include the design of a resonant-network-attached oscillator, comprehensive sensor performance simulations, and successful characterization of organic liquid mixtures, showcasing the potential of this approach for practical dielectric property measurements.