Keysight Technologies 16454A, Operation And Service Manual

Page: 30 / 41

As alternating current causes inductance loss , the self-inductance L of the measurement circuit
is expressed as complex impedance , as shown in Equation 3-12.
Equation 3-12. Self-Inductance of Measurement Circuit Expressed as Complex Impedance
L =
Z
3
j !
Substituting \L" from Equation 3-12 to Equation 3-8 yields Equation 3-13.
Equation 3-13. Complex Relative P ermeability of DUT
3
r
=
2 (Z
3
0 j ! L
ss
)
j !
0
hl n
c
b
+ 1
Structure of 16454A T est Fixture
As shown in Figure 3-5, 16454A has a residual impedance Z
*
res
.
Figure 3-5. 16545A Residual Impedance
Given the ideal impedance Z
*
ss
of the 16454A text xture with no DUT mounted, the residual
impedance Z
*
res
can be calculated from the measured impedance Z
*
sm
with no DUT mounted in
16454A (in SHORT state).
Equation 3-14. 16454A Residual Impedance
Z
3
r es
= Z
3
sm
0 Z
3
ss
Errors due to residual impedance can be minimized by SHORT compensation. The impedance
after error compensation Z
*
comp
can be calculated from the measured impedance Z
*
m
with a
DUT mounted in 16454A, as shown in Equation 3-15.
Equation 3-15. Compensated Impedance
Z
3
comp
= Z
3
m
0 Z
3
r es
Assuming that Z
*
ss
consists only of inductance elements (Z
*
ss
= j! L
ss
), the complex relative
permeability of the DUT can be calculated using Equation 3-13 and compensated impedance ,
Z
*
comp
= Z
*
, as shown in Equation 3-16.
Equation 3-16. Complex P ermeability of DUT
3
r
=
2 (Z
3
m
0 Z
3
sm
)
j !
0
hl n
c
b
+ 1
3-4 Theory on Material Measurement