Agilent Technologies 4395A - Page 351

Reection
Uncertainty
Equations
Reection Uncertainty
Equations
T
otal
Reection Magnitude
Uncertainty (E
rm
)
An
analysis
of the
error model
yields an
equation for
the reection
magnitude uncertainty
. The
equation
contains
all
of
the
rst
order terms
and the
signicant second
order terms
.
The
error
term
related
to
thermal
drift
is
combined on
a worst
case basis
with the
total
of
systematic
and
random
errors
.
The
four
terms
under the
radical are
random in
character and
are
combined
on
an
RSS
basis.
The terms
in the
systematic error
group
are
combined
on
a
worst
case
basis
.
In
all
cases
,the
error terms
and the
S-parameters are
treated
as
linear
absolute
magnitudes
.
E
rm(linear)
=V
r
+S
11
T
rd(magnitude)
and
E
rm(log)
=
20log

1
6
E
rm
S
11

where
V
r
=
S
r
+
p
W
2
r
+
X
2
r
+
Y
2
r
+
Z
2
r
S
r
=
systematic
error
=
(1
+
T
sw
)(D
+
S
r1
)
+
(T
sw
+
T
r
)S
11
+
(M
sw
+
M
s
+
S
r1
)S
2
11
+
(M
l
+
S
r2
+
M
sw
)S
21
S
12
+
(A
m
+
U
m
)S
11
W
r
=
random
low-level
noise
=
3N
l
X
r
=
random
high-level
noise
=
3N
h
S
11
Y
r
=
random
port1
repeatability
=
R
r1
+
2R
t1
S
11
+
R
r1
S
2
11
Z
r
=
random
port2
repeatability
=
R
r2
S
21
S
12
Total
Reection Phase
Uncertainty (E
rp
)
Reection phase
uncertainty is
determined from
a comparison
of
the
magnitude
uncertainty
with the
test signal
magnitude.
The worst
case phase
angle
is
computed.
This
result
is
combined
with
the
error
terms
related
to
thermal
drift
of
the total
system,
port
1
cable
stability, phase dynamic accuracy
, and phase multiplexer switching uncertainty
.
E
rp
= ar csin

V
r
0 ( A
m
+ U
m
) S
11
S
11

+ T
rd
( phase )
+2
S
t 1
+ A
p
+ U
p
Specications and Supplemental Characteristics 11-35