Coaxial 2-port resistor and its application to r.f. measurements and standards

The cylindrical resistor mounted coaxially in a cylindrical outer conductor has already received considerable attention in the literature as a 1-port circuit element for terminating a coaxial line. Various methods have been described which minimise the reactance and the change of the resistance with frequency. In all cases, a compromise solution has to be adopted. These difficulties are overcome by employing a tractorial profile for the outer conductor of a cylindrical resistor or by using a conical resistor with a cylindrical outer conductor. In contrast, the cylindrical resistor as a coaxial 2-port circuit element has received little attention in spite of its application, in association with precision coaxial connectors, to radio-frequency measurements and standards. The theory of 1-port coaxial resistor design is reviewed and extended to the 2-port resistor. It is shown that the techniques previously employed to minimise the reactance and change of resistance with frequency for 1-port resistors no longer apply in the 2-port case. However, other techniques are possible which extend the frequency range over which the effective series susceptance is zero and the effective series conductance is substantially equal to the d.c. conductance. A preliminary analysis is carried out using lumped-circuit theory followed by a more rigorous treatment in terms of transmission-line theory. A comparison between the 1-port and 2-port parameters is made at all stages of the analysis, because the 1-port admittance is always equal to the sum of the series admittance and one shunt admittance of the 2-port´s equivalent ¿ network. An outline is given of the application of 2-port resistors to the range extension of fixed immittance standards, also to checking system accuracy generally in the fields of immittance measurement and standardisation.