The
self-inductance
of
the
measurement
circuit
including
the
DUT
is
derived
as
Equation
3-5
from
Equation
3-2,
Equation
3-3,
Equation
3-4,
and
the
physical
shape
of
16454A.
Equation
3-5.
Self-Inductance
of
Measurement
Circuit
L
=
1
I
Z
B
ds
=
Z
e
a
Z
h
0
0
2
r
dr
dz
By
unfolding
Equation
3-5
with
0
as
permeability
of
free
space
and
r
as
relative
permeability
of
the
DUT
,
Equation
3-6
can
be
obtained.
Equation
3-6.
Self-Inductance
of
Measurement
Circuit
L
=
Z
e
c
2
Z
h
0
0
0
2
r
dr
dz
+
Z
c
2
b
2
Z
h
0
0
r
2
r
dr
dz
+
Z
c
2
b
2
Z
h
0
h
0
2
r
dr
dz
+
Z
b
2
a
Z
h
0
0
0
2
r
dr
dz
By
further
unfolding
Equation
3-6,
Equation
3-7
can
be
obtained.
Equation
3-7.
Self-Inductance
of
Measurement
Circuit
L
=
0
2
f (
r
0
1)hl n
c
b
+
h
0
l n
e
a
g
By
transforming
Equation
3-7
to
calculate
the
relative
permeability
(
r
)
of
the
DUT
,
Equation
3-8
can
be
obtained.
Equation
3-8.
Relative
P
ermeability
of
DUT
r
=
2
(L
0
L
ss
)
0
hl n
c
b
+
1
L
ss
in
Equation
3-9
indicates
the
self-inductance
when
a
DUT
is
not
mounted
in
the
test
xture
.
Equation
3-9.
Self-Inductance
When
DUT
Is
Not
Mounted
in
T
est
Fixture
L
ss
=
0
2
h
0
l n
e
a
Figure
3-4.
Loss
of
Magnetic
Material
The
impedance
Z
of
the
circuit
(i)
in
Figure
3-4
is
expressed
as
Equation
3-10,
and
the
complex
impedance
Z
*
of
the
circuit
(ii)
is
expressed
as
Equation
3-11.
Equation
3-10.
Impedance
of
Circuit
(i)
Z
=
j
! L
Equation
3-11.
Complex
Impedance
of
Circuit
(ii)
Z
3
=
R
s
+
j
! L
s
=
j
!
R
s
j
!
+
L
s
Theory
on
Material
Measurement
3-3
Summary of Contents for 16454A
Page 1: ...Operation and Service Manual Keysight 16454A Magnetic Material Test Fixture ...
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Page 12: ...APC 7 R is a U S registered trademark of the Bunker Ramo Corporation viii ...
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