Instrumentation & Measurement Magazine 25-7 - 26

Measurement of Extreme
Impedances with the S Parameters
Francis Rodes and Xavier Hochart
H
igh frequency measurement of extreme impedances,
such as the Equivalent-Series-Resistance
(ESR) of an ultra high-Q capacitor, can be performed
with specific and costly instrumentation whose
principle is generally based upon a coaxial resonant line or
a resonant cavity [1]. A cost-effective solution for measuring
impedances at high frequencies is the classical One-Port reflection
technique that can be performed with a Vector Network
Analyzer (VNA). In [2], only this technique was considered,
and the analysis was limited to a relative error of 10%; nevertheless,
this work showed that the reflection technique is
unsuited for measuring extreme impedances. In [3], all of the
impedance measurement techniques that can be performed
with a VNA are presented and compared. This analysis confirmed
the limitations of the reflection technique and showed
the abilities of the transmission technique for measuring extreme
impedances. Unfortunately, these comparisons were
based on absolute errors of the measured impedance (ΔZ) that
are not significant for an engineer who needs to select the best
method. Moreover, in [2], [3], the analyses are not extended to
the negative resistances, and the resistance's sign inversion error
is not considered.
The present paper pursues these works and overcomes
their limitations as follows. In the first section, the limits of
the One-Port reflection technique are computed for any resistance's
sign and any relative error objective. This analysis
demonstrates particularly that the reflection technique can
be plagued by a resistance's sign inversion error. To avoid
such an unacceptable error, the principle of the Two-Port
transmission technique is deduced in the second section. The
theoretical expressions of an impedance measured with this
technique are then established. Using these expressions, an
error analysis is performed for computing the extreme impedances

Instrumentation & Measurement Magazine 25-7

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