Agilent Technologies 4395A - Page 352

Transmission
Uncertainty
Equations
Transmission Uncertainty
Equations
T
otal
Transmission Magnitude
Uncertainty (E
tm
)
An
analysis
of the
error model
in Figure
11-23 yields
an equation
for the
transmission
magnitude
uncertainty
.
The
equation
contains
all of
the rst
order terms
and some
of
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
are
treated
as
linear
absolute
magnitudes
.
E
tm(linear)
=
V
t
+
S
21
T
td(magnitude)
and
E
tm(log)
=
20log

1
6
E
tm
S
21

where
V
t
=
S
t
+
p
W
2
t
+
X
2
t
+
Y
2
t
+
Z
2
t
S
t
=
systematic
error
=
C
+
(T
sw
+
T
t
)S
21
+
(M
sw
+
M
s
+
S
r1
)S
11
S
21
+
(M
sw
+
M
l
+
S
r2
)S
21
S
22
+
(A
m
+
U
m
)S
21
W
t
=
random
low-level
noise
=
3N
l
X
t
=
random high-level
noise
=
3N
h
S
21
Y
t
=
random
port1
repeatability
=
R
t1
S
21
+
R
r1
S
11
S
21
Z
t
= random
port2
repeatability
=
R
t2
S
21
+
R
r2
S
22
S
21
T
otal
Transmission
Phase
Uncertainty
(E
tp
)
Transmission
phase
uncertainty
is
calculated
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 phase
dynamic accuracy
,
cable
phase
stability
,
thermal
drift
of
the
total
system,
and
phase
multiplexer switching
uncertainty
.
E
tp
= ar csin

V
t
0 ( A
m
+ U
m
) S
21
S
21

+ T
td (
phase )
+ S
t 1
+ S
t 2
+ A
p
+ U
p
11-36 Specications and Supplemental Characteristics