Variations of characteristic impedance along short coaxial cables

A method is described for determining the local characteristic impedance at any point on a high-frequency coaxial cable. Measurements are made of the deviations from a harmonic series of the resonant frequencies of a short length of open or short-circuited cable. It is shown how these deviations can be used to calculate the coefficients of Fourier series describing the impedance variations along the length. Since the measurements are performed at microwave frequencies, the resolution of the impedance changes is considerably better than for lower-frequency methods. Measurements on an artificially discontinuous cable have allowed the experimental accuracy of the method to be determined, and close agreement has been obtained between the experimentally predicted and the actual impedance changes. Results from short cable samples indicate that the local variations of characteristic impedance are largely due to changes in the diameter over the dielectric filling.