The calibration of modern automatic RLC bridges requires a set of
impedance standards. Each standard needs in turn a calibration, i.e.
the knowledge of its four-terminal-pair impedance Z4TP
at frequencies up to 10–100 MHz—frequencies beyond the capabilities of standard
metrological setups for impedance traceability (transformer bridges). It is possible
to think of an impedance standard as a multiport linear radiofrequency network;
the properties of the network can be mathematically related to its Z4TP. In
the literature, such a connection is made using the relation between the impedance matrix
Zij and
Z4TP,
and with careful identification of an ad hoc lumped-parameter electrical model of the
standard. A vector network analyser is employed to measure diagonal elements of
Zij
directly; non-diagonal elements are measured in an indirect way. Here
we derive a new relation between the scattering parameter matrix
sij and Z4TP of the impedance
standard. All sij
elements can be directly measured with a network analyser: we measure scattering
parameter spectra of a set of commercial gas-dielectric capacitors. Computed Z4TP
spectra are compatible with those obtained with the Zij
technique, but the new method proves much more sensitive, permitting estimates
of the frequency behaviour of an impedance standard even when electrical
modelling is inconvenient or impossible.
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