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

Abstract

The calibration of immittance bridges and reflection-coefficient meters over the complete radio-frequency spectrum requires a wide range of fixed standards of complex immittances or reflection coefficients. This can be accomplished with a relatively small number of fixed standards by connecting them in series or parallel and computing the value of the composite standard. The series connection is readily achieved by using precision coaxial connectors which form an integral part of the standards, and has already been described in a previous paper. Parallel connection, however, requires a multiport coaxial junction, the parameters of which enter into the immittance characteristic of the composite standard. The symmetrical 3-port coaxial junction is analysed, and it is found that the most convenient method of characterising it at the highest level of standardisation is in terms of scattering parameters normalised to its complex characteristic impedance. The low-frequency scattering matrix, comprising real numbers only, is evaluated in terms of d.c. concepts. It is then shown that the general matrix applicable at all frequencies is given by multiplying the d.c. matrix by e~2( a+ J0'*, where 1 is the length of each arm. Formulas are given for the input reflection coefficient of one arm of the junction in terms of the reflection coefficients of the fixed standards connected to the remaining two ports. Various techniques are discussed for evaluating the scattering parameters of the junction to an accuracy that would not significantly degrade the accuracy of the fixed standards, assumed to be in the order of 0 -l°/£,. The technique is considered to be equally as applicable to low frequencies as to microwave frequencies, thus enabling a unified computing program to be employed. Extension of the technique to cascaded 3-port junctions is also considered, whereby more than two fixed standards can be connected in parallel. For less-accurate standardising work, as performed by certain calibration laboratories, it is shown that adequate accuracy can be achieved by adopting a simpler procedure, whereby the scattering parameters of the junction and the reflection coefficients of the standards are all normalised to an ideal real characteristic resistance R n . LIST OF PRINCIPAL SYMBOLSa a,b bi.,b (3oo Cd l + 1 P R()0 Rn Pi P2"P7 St d(n)> t( n ) S d(z)> S t(z)= attenuation constant of junction arms of characteristic impedance Zj,Np/cm = £J3QO = inner-and outer-conductor radii of coaxial line, respectively = incident waves = reflected waves = phase constant of junction arms of characteristic impedance Zj, rad/cm = w/v = /3oo(l + 0 = phase constant of junction arms of real characteristic resistance Roo, rad/cm = w/voc