# IEEE Instrumentation & Measurement - September 2023 - 30

```Examination of (13) shows that the slope x′ is used for
extrapolating the open-circuited line Q-factors Q2
short-circuited line Q-factor Q0
(7) and (9), the slope x′ is specific to the extrapolations of
the open-circuited line Q-factors such as Q2
and the
. However, as indicated by
. Consequently,
it is an error to use the slope x′ for extrapolating the shortcircuited
line Q-factor Q0
is directly calculated with (4). That can be
. In this last case, according to
(8) and (10), the slope x must be used. This error is impossible
when rf
demonstrated by substitution of (7) and (8) in (4). After rearrangement,
we find:
r Z ff Q f
1 0 
f
π 0 /4
1
=()() ()() −()()

/ // //1 Q ff
0 10 2 1 2
f
−−′
xx


(14)
Examination of (14) shows effectively that the opencircuited
line Q-factors Q2, and the short-circuited line Q-factor
Q0 are correctly extrapolated with respectively the slopes:
x′ and x.
From (13) and (14), the ASTM method produces the relative
error:
```

# IEEE Instrumentation & Measurement - September 2023

Contents
IEEE Instrumentation & Measurement - September 2023 - Cover1
IEEE Instrumentation & Measurement - September 2023 - Cover2
IEEE Instrumentation & Measurement - September 2023 - Contents
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