Error analysis for dielectric spectroscopy using shielded open-circuited coaxial lines of general length

The shielded open-circuited coaxial line of genera! length is studied in detail as a sample cell for broad-band measurements of the dielectric permittivity. This cell is a section of transmission line with the center conductor abruptly terminated. The dielectric material to be measured fills the coaxial section of the cell and extends beyond the center conductor into the tube formed by the outer conductor of the transmission line The inverse function for obtaining the permittivity of the sample from the measured input admittance of the cell is multivalued. The error in the measured permittivity caused by passing onto the wrong branch of the inverse function is analyzed, and a procedure that can prevent passage onto the wrong branch is developed. The error in the measured permittivity due to the inaccuracies in the instrumentation is also analyzed. Contour graphs are constructed that quantify the effects of this error on the measured permittivity. This error is shown to be largest when the combination of frequency, sample length, and sample permittivity place the measured normalized admittance near a branch point of the inverse function. The permittivities of several primary alcohols were measured with the open-circuited sample cell. The measured relaxation spectra for these alcohals are used to demonstrate the usefulness of the error analysis.