Immittance transformation using precision air-dielectric coaxial lines and connectors

By utilising a small number of fixed immittance standards and precision air-dielectric coaxial lines, it is possible to realise a relatively large number of complex immittance standards by connecting the lines in different combinations and terminating them with fixed immittance standards. The realisation of immittance standards in this manner demands a precision coaxial connector system embodying features that are lacking in most precision connectors. Previous methods are reviewed for the precise transformation of immittance through rigid air-dielectric lines. One of these methods employed the concept of a reciprocal velocity factor (1+¿) to account for the reduced velocity caused by current penetration in a line of real characteristic impedance. It is shown that the same propagation correction term ¿ can also be used to express all the residual parameters of a line having complex characteristic impedance and propagation constant. A simple method is described for the transformation of immittance through a line of complex characteristic impedance employing the operator e±2(¿+jß)l, in which ¿ and ß are also expressed in terms of the parameters of an ideal line of infinite conductivity and the propagation correction term ¿. The transformation error is negligible compared with the accuracy of immittance measurement realisable with the most precise methods so far developed, provided lines of suitable material and appropriate mechanical tolerances are employed. Certain conclusions are drawn regarding the limitations of current forms of precision coaxial connectors.