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

Abstract

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 -n 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.List of symbols a = attenuation constant, Np/cm a,b = radii of inner and outer conductors of coaxial system a if a 2 , Ai, A 2 = incident waves b x , b 2 , B u B 2 = reflected waves P = phase constant for lossless coaxial line, rad/cmphase constant for lossy coaxial line discontinuity capacitance capacitance per unit length of coaxial system shunt capacitance of equivalent TT network of resistor internal capacitance of cylindrical resistor pi, rad permittivity of free space, F/m relative permittivity d.c. conductance of resistor propagation constant of lossy coaxial line formed by resistor = a + j'P renormalising reflection coefficient = (Z z -R n )J (Z z + R n ) renormalising reflection coefficient = (R n -Z z )/ length, cm inductance per unit length of coaxial system wavelength, cm angular frequency, rad/s propagation factor of lossy coaxial line formed by resistor = F c / propagation factor related to complex characteristic impedanze Z z = {(a + jp)l}( z ) d.c. resistance of resistor characteristic resistance of ideal lossless coaxial line resistance per unit length of coaxial system = 5" parameters normalised to R n and Z z , respectively surface resistivity, Q.Paper 6566 S, first received ...

Application of 3-port coaxial junction to r.f.-immittance standardisation and measurements

“…The [1] in eqn. 9 is the reflection coefficient of the open circuit which is now present at the junction end of the 1-port.…”

“…1 These composite standards would be characterised in terms of an input reflection coefficient normalised to either Zj or R n , depending on the accuracy required.…”

“…A method that is equally as applicable at low frequencies as at microwave frequencies has already been described. 1 The parallel connection of standards requires a multiport coaxial junction, the parameters of which enter into the immittance characteristic of a composite standard. This technique has already been applied at relatively low frequencies (a few megahertz), in lumped-parameter immittance measurement.…”

“…They are given below, where the subscript j has been added to indicate the junction parameters. j = R a) (l + C -K -K) (1) (2)…”