430
Appendix E
Theory on Material Measurement
Magnetic Material Measurement
When a DUT (toroidal core) is mounted in a 16454A, an ideal (no magnetic flux leak)
inductance with a wire rolled once is formed, as shown in Figure E-8.
Figure E-8
Measurement Principle When Using 16454A Test Fixture
The self-inductance of a measurement circuit including the DUT is derived as Equation
E-11 from Equation E-8, Equation E-9, Equation E-10, and the physical shape of the
16454A.
Equation E-11
Self-Inductance of Measurement Circuit
By unfolding Equation E-11 with
as permeability of free space and
as relative
permeability of the DUT, Equation E-12 can be obtained.
Equation E-12
Self-Inductance of Measurement Circuit
By further unfolding Equation E-12, Equation E-13 can be obtained.
Equation E-13
Self-Inductance of Measurement Circuit
By transforming Equation E-13 to calculate the relative permeability (
) of the DUT,
Equation E-14 can be obtained.
Equation E-14
Relative Permeability of DUT
L
1
I
---
B s
d
μ
2
π
r
---------
r
d z
d
0
h
0
a
e
=
=
μ
0
μ
r
L
μ
0
2
π
r
---------
r
d z
d
0
h
0
c
2
---
e
μ
0
μ
r
2
π
r
-----------
r
d z
d
0
h
b
2
---
c
2
---
+
μ
0
2
π
r
---------
r
d z
d
h
h
0
b
2
---
c
2
---
+
μ
0
2
π
r
---------
r
d z
d
0
h
0
a
b
2
---
+
=
L
μ
0
2
π
------
μ
r
1
–
(
)
h c
b
---
h
0
e
a
---
ln
+
ln
=
μ
r
μ
r
2
π
L L
ss
–
(
)
μ
0
h c
b
---
ln
---------------------------- 1
+
=
Summary of Contents for E4991A
Page 6: ......
Page 24: ...18 Contents ...
Page 80: ...74 Chapter3 Setting Measurement Conditions Averaging Measurement Results ...
Page 220: ...214 Chapter9 Setup and Use of Control Management Functions System Recovery ...
Page 338: ...332 AppendixB Probe Station Connection Kit Option 010 OPEN SHORT LOAD Calibration ...
Page 428: ...422 AppendixD Menu References Menu References ...
Page 482: ...476 AppendixI Messages Wait measuring comp standard ...
