Model of a damped electrical oscillator for analyzing the temperature-dependent admittance of brake fluid in the high-frequency range

This study presents the development and experimental validation of an advanced methodology for electromagnetic spectroscopy applied to DOT 4 brake fluid, aiming to characterize the temperature-dependent behavior of complex admittance across a broad frequency range—spanning 50 kHz to 300 MHz. Measurements were conducted over a temperature interval from –5 °C to +55 °C, capturing the thermally induced evolution of the fluid’s electrical properties under near-operational conditions. To interpret the data, the admittance spectra were modeled using a damped harmonic oscillator framework, enabling decomposition of the system’s response into three physically meaningful parameters: effective inertia (m), dissipation (β), and elastic stiffness (k). A comprehensive inverse fitting procedure was applied to over 6000 frequency profiles, yielding high-precision identification of the temperature-dependent resonance features. Notably, the damping parameter β exhibited exponential growth with temperature, in accordance with the Arrhenius law. This behavior allowed for the first electromagnetic estimation of the activation energy for viscous dissipation in DOT 4 fluid, determined to be approximately 21.25 kJ/mol. In contrast, the temperature dependence of effective mass and stiffness revealed nonlinear trends, suggesting potential phase transitions or microstructural rearrangements within the fluid matrix. The proposed methodology offers a pathway to non-invasive diagnostics of brake fluid quality by analyzing its electromagnetic response characteristics. This opens opportunities for the integration of autonomous sensing systems—for example, those based on vector network analyzers—capable of real-time fluid evaluation without extraction from the hydraulic circuit.