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The broadband measurement of complex permittivity of materials based on transmission line methods has been attracting more and more interests in scientific research and industrial applications. In this paper, by removing the transition section in conventional implementations and applying high-order mode-matching theory of axisymmetric coaxial discontinuity, we propose a single-cavity coaxial transducer for broadband measurement of complex permittivity of lossy media. With an ultra simple structure, the sample holder can be designed to install any coaxial connector, and its radial and longitudinal dimensions can be arbitrarily designed to fit variant capacity demands. Full-wave simulation and experimental measurement show that the proposed transducer can obtain the same precision as previous designs. The proposed approach also applies for two-port transducers. We expect a wide range of practical applications of this general approach in scientific research and industrial applications. [ABSTRACT FROM AUTHOR]