A study of some line methods for the measurement of impedance at ultra-high frequencies

The standard circuits for the measurement of impedances at frequencies up to about 50 Mc/s are bridge networks although special design incorporating shielding and earthing devices is necessary in the radio-frequency range. The theory of the various bridge methods assumes that the current flowing in any arm of the bridge is constant throughout its path and depends only on the potential difference applied across the arm and the impedance of the arm. Since the current at any point in a circuit depends on the magnetic field of the electro-magnetic wave in the vicinity and is not constant throughout the whole of its path, this assumption is only permissable for wavelengths which are large compared with the linear dimensions of the apparatus. In fact the current varies from a maximum to a minimum value in a distance where is the wavelength of the electro-magnetic wave associated with the current. At a frequency of 100 Mc/s, say 300 cms and 4. =75 cms. It is impracticable to design bridges of the dimensions of a few centimetres and other methods have to be employed at these higher frequencies. An outline of these methods is given in Section I followed by a more detailed study of two of the methods in Sections II and III. The difficulty of obtaining a satisfactory short-circuit in order to find the critical separation of the Williams' method was then investigated. This was eliminated by plotting the graphs differently. This work is described in Section IV. Next an impedance was measured on the same apparatus by the Williams method (using this modification) and the Chipman method. These results are described and compared in Section V. Finely in the conclusion it is suggested that the Williams method may prove more useful on a coaxial transmission line than on open Lecher wires