Instrumentation & Measurement Magazine 25-7 - 29

If the S21
becomes:
parameter is specified by its magnitude in dB, (13)

Y 2Y .10

C
S2 1 dB
20
(14)
These approached expressions demonstrate that the measurement
of very low magnitude S21
produce any admittance sign indetermination.
Nevertheless, such an error could occur if the phase error
of the measured S21
parameters do not
parameter reaches 180°. An examination of
the curves of phase uncertainty represented in Fig. 1b shows
that a sign indetermination is impossible, since, for instance
at 1 GHz, the maximum phase uncertainty is about 10°. Consequently,
the Two-Port transmission technique is not affected
by the sign inversion error that plagues the One-Port reflection
technique.
It is important to note that this interesting property is no
longer valid when the shunt admittance insertion is used for
measuring some very low admittances. In this case, (9), (10)
can respectively be approximated as:
S 21  1
and:  
y 21 S21 YY S 
    21
2 C 1
(15)
(16)
With a S21 parameter magnitude close to unity and taking
into account the magnitude uncertainty specified in Fig.
1b, expressions (15), (16) demonstrate that the measurement
of very low admittances becomes affected by a sign
indetermination similar to the one that plagues the reflection
technique.
Hence, the shunt insertion mode is strictly reserved for
measuring very high admittances and must be avoided for
measuring high impedances. By virtue of the duality principle,
it is the serial insertion mode that must be selected for measuring
high impedances. For these reasons, the error analysis that
follows, is limited to the two most useful boundaries:
◗ The high admittance boundary of the shunt admittance
insertion mode.
◗ The high impedance boundary of the series impedance
insertion mode.
Error Analysis

Instrumentation & Measurement Magazine 25-7

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 25-7

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