Instrumentation & Measurement Magazine 26-5 - 48

Component
Tolerance
Test Frequency
Manufacturer
Loffset Component
α
Loffset Wire
01005
Table 2 - Tested components and extracted parameters
0402
0201
0.1 - 0.3 nH
500 MHz
0.1 - 0.3 nH
5%
Murata, Sunlord Wurth
0.45
1.137
-
0.636
1.208
-
0.1 - 0.3 nH
5%
100, 500 MHz 100 MHz
0.923
1.136
0.785
0603
0.1 - 0.3 nH
5%
100 MHz
TDK, Taiyo Wurth
1.075
1.139
0.888
0805
1008
0.3 nH
5%
100 MHz
0.3 nH
5%
100 MHz
Eaton, Abracon TDK
1.661
1.062
0.877
3.242
1.0063
1.011
average deviation obtained by linear regression analysis as the
parasitic inductance of the test fixture.
To account for the correction to the actual inductance value
due to low frequency, we used the following expression to extract
the actual inductance from the measured value:
L LL
measured =α actual offset
+
(1)
The expression for extracting the actual inductance from
the measured value takes into account a correction factor due
to low test frequency. The symbols used in the expression
have obvious meanings. The coefficient α in the expression
reflects this correction factor and depends on the component
type, manufacturer technology, and test frequency used by
the manufacturer for their data sheet measurements. To extract
both the coefficient α and the parasitic inductance offset
Loffset, linear regression analysis is performed on the measurement
data for a number of components for each of the 6
different sizes.
We make the assumption that the measured inductance
is proportional to the actual (measured at high frequency)
inductance value, and in order to limit the effect of larger
tolerances for larger inductors on the accuracy of extracted
parameters, we restricted our measurements to smaller
inductors. The values of the coefficients α and Loffset were extracted
using linear regression analysis of measurement data
for each of the 6 different sizes, and are presented in Table 2.
To extract the actual inductance values for higher test frequencies,
we use equation (1) along with linear regression
analysis.
Inductance Offset Extraction Using Single
Wire Inductors
Larger size low value inductors (below 10nH) are not available
and therefore we used made in house single wire
inductors instead. They were made of 0.65 mm copper wire.
Our very limited capabilities allowed to achieve 0.05 mm
length accuracy. For inductors with lengths larger than 1
mm, that is 0402 component size equivalent, this accuracy
level (under 5%) was acceptable. By subtracting the theoretical
value of a linear wire inductance calculated according
to [4] from the value measured using HP4284A LCR-meter
48
we extracted the inductance offset of the fixture. The values
obtained for Loffset for single wire inductors are presented
in Table 2.
The experiments used various components, mainly multilayer
chip inductors from manufacturers such as Wurth
Elektronik, TDK, Taiyo Yuden, Murata, Eaton, and Abracon.
The extracted inductance offsets for both methods are compared
in Fig. 3, and they are similar for component sizes
0402 and 0603. However, the difference between the two
methods increases significantly for sizes 0805 and especially
1008.
A possible reason of the significant difference of the extracted
Loffset is a contribution of the inductor pads that are
significantly bigger for larger component sizes and therefore
affect the geometry of the fixture. This discrepancy in the extracted
inductance offsets for larger component sizes may also
be attributed to the fact that smaller inductors with this size
are not available. As inductance values increase, the component
tolerance also increases, especially for 0805 components,
which typically have a tolerance of 5%, resulting in a tolerance
of 1 nH. For 1008 components, the tolerance leads to a
typical tolerance of 2 nH. As a result, the effect of component
value fluctuation and the absence of lower inductance value
components when using regression analysis may lead to an
Extracted Inductance Offset
4
3
2
1
Wire
Component
01 2
Component length (mm)
3
Fig. 3. Extracted inductance offset for the two methods of Loffset extraction:
using SMD inductors and single wire inductors, from [5] (© IEEE 2022, used
with permission).
IEEE Instrumentation & Measurement Magazine
August 2023
nH
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