IPC-TM-650 EN 2022 试验方法.pdf - 第501页

For each frequency repeat the following procedure: 1. Compute the complex permittivity using Equations (2b) and (2c). This is an initial trial solution of the iterative process for k =0, where k is the iterative step: ε …

100%1 / 824
obtained
directly from Equations (2b) and (2c) respectively
Reference [2]:
Z
in
s
=
1
jωC
p
ε
r
*
(2a)
ε’ =
−2
|
S
11
|
sin φ
ωZ
0
C
p
(1+2
|
S
11
|
cos φ +
|
S
11
|
2
)
(2b)
tan δ’ =
ε’’
ε’
=
1 −
|
S
11
|
2
−2
|
S
11
|
sin φ
(2c)
where
|
S
11
|
is
the magnitude and φ is the phase of the scat-
tering coefficient, ω =2πƒ is the angular frequency, and C
p
is
the
specimen geometrical (air filled) capacitance (in units of
farads),
C
p
=ε
0
(π a
2
/ 4d)[
F
]
(3)
a is
the specimen diameter, and d is the dielectric thickness
of the specimen (in units of meters). Permittivities ε
0
and ε
r
*
are
defined in 3.1 and 3.2. In Equation (3), the specimen
diameter a =3.0x10
-3
m
(3.0 mm), should match the diam-
eter of the central conductor pin (see 4.1, Figure 1). Note that
the actual diameter of the top electrode may be between 2.85
x10
-3
mt
o3.0x10
-3
m
(2.85 mm to 3.0 mm in 4.1).
In practice, the conventional formulas (2a - c) are accurate up
to a frequency at which the input impedance of the specimen
decreases to about one tenth (0.1) of the characteristic
impedance of the coaxial line, i.e., about 5 Ω. In the example
given in Figure 3, this upper frequency limit is about 1.5 GHz.
Some practical considerations regarding this limitation are dis-
cussed in References [4 and 5].
At higher microwave frequencies, the specimen section filled
with a high-k material represents a network of a transmission
line with capacitance C
p
ε
r
*.
The input impedance, Z
in
s
,
of such
network is given by Equation (4) (see Reference [6]).
Z
in
s
=
x
cot (x)
jωC
p
ε
r
*
+ jωL
s
[Ω]
(4)
L
s
is
the specimen residual inductance,
L
s
= 1.27
10
−7
[H / m]
*
d [m]
(5)
and
the propagation term x is given by (6):
x =ωl
√
ε
r
*
/ 2c
(6)
where, l =2
.47x10
-3
m
(2.47 mm) represents the propaga-
tion length in the specimen section and c is speed of light
(c = 2.99792 10
8
m/s).
At low frequencies, below series reso-
nance frequency, ƒ
LC
,
the propagation term x cot (x)
approaches 1, L
s
can
be neglected and Equation (4) simplifies
to well known formula (2a) for a shunt capacitance, C
p
ε
r
*,
ter-
minating a transmission line.
7.3
Computational Algorithm for Permittivity
Combin-
ing
Equations (1) and (4) leads to Equation (7) that relates the
dielectric permittivity, ε
r
*,
of the test specimen with the mea-
surable scattering parameter S
11
.
ε
r
*
=
xcot (x)
jωC
p
(Z
0
(1 + S
11
) / (1 − S
11
)−jωL
s
)
(7)
Because
the propagation term x depends on permittivity
(Equation (6)), Equation (7) needs to be solved iteratively.
Description of a suitable procedure can be found in the Ref-
erence [7].
According to the Reference [7], the right-hand-side of (7) can
be labeled as ϕ and rearranged into a compact form (7a),
which is more convenient in describing the iterative procedure
shown below.
ε
r
*
= ϕ(
ε
r
*
)
(7a)
IPC-25510-3
Figure
3 Impedance magnitude (circles) and phase
(triangles) for a 25 µm thick dielectric film with ε’ of 10
and tan (δ) of 0.01.
0.1
1 10
0.01
0.1
1
10
100
-
1
00
-80
-60
-40
-20
0
20
40
60
80
1
00
|Z|= 0.05 Ω
|Z|= 5 Ω
Frequency, GHz
Phase (degree)
|Z|= (Ω)
IPC-TM-650
Number
2.5.5.10
Subject
High
Frequency Testing to Determine Permittivity and Loss
Tangent of Embedded Passive Materials
Date
07/05
Revision
P
age4of8
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For
each frequency repeat the following procedure:
1. Compute the complex permittivity using Equations (2b) and
(2c). This is an initial trial solution of the iterative process for
k=0, where k is the iterative step:
ε
r
*
[
k = 0
]
=ε’ −
j
ε
’’
(7b)
2.
Compute successive approximations for subsequent itera-
tive steps k.
ε
r
*
[
k + 1
]
=ϕ(
ε
r
*
[
k
]
)
(7c)
(k = 0,
1, 2, 3...)
3. The iteration procedure is terminated when the absolute
value of Equation (7d) is sufficiently small, for example
smaller than 10
-5
.
|
ε
r
*
[
k
]
−ε
r
*
[
k − 1
]
|
/
|
ε
r
*
[
k
]
|
<10
−5
(7d)
Typically
it may require five to about twenty iterations to reach
the terminating criterion.
Commercially available software can be used to program and
automate the computational steps 1 through 3 and solve
Equation (7) numerically for ε
r
*
and the corresponding uncer-
tainty values. The software should be capable of handling
simultaneously both real and imaginary parts of complex S
11
,
x
cot (x) and ε
r
*, (for
example Visual Basic, C or Agilent VEE
and National Instruments LabView programming platforms
can be employed).
8
Report
The
report shall include:
• Dimensions of the specimen.
• Plot of magnitude and phase of the measured impedance
as a function of frequency, (similar to Figure 3) or Smith
Chart.
• Plot of ε’ and ε’’ or ε’ and tan δ as a function of frequency.
9
Notes
9.1 Measurements at Frequency Range Above 12 GHz
The
presented APC-7 test fixture design may be utilized in the
frequency range of 100 kHz to 18 GHz. The computational
algorithm and in particular Equations (4) and (5) have been
validated up to the first cavity resonance frequency, ƒ
cav
,
which
is determined by the propagation length l, and the
dielectric constant of the specimen:
ƒ
cav
=
c
l Re (
√
ε
r
*
)
≈ 121/(
√
ε
r
[
GHz
]
(8)
where
Re indicates the real part of complex square root of
permittivity and l = 2.47 mm, which is the propagation length
for the test fixture presented in Figure 1, [5]. For example, in
the case of a specimen having the dielectric constant of 100
ƒ
cav
is
about 12 GHz.
9.2
Accuracy Considerations
Several uncertainty factors
such as instrumentation, dimensional uncertainty of the test
specimen geometry, roughness and conductivity of the con-
duction surfaces contribute to the combined uncertainty of the
measurements. The complexity of modeling these factors is
considerably higher within the frequency range of the LC reso-
nance. Adequate analysis can be performed, however, by
using the partial derivative technique [1] for Equations (2b) and
(2c) and considering the instrumentation and the dimensional
errors. The standard uncertainty of S
11
can
be assumed to be
within the manufacturer’s specification for the network ana-
lyzer, about ± 0.005 dB for the magnitude and ± 0.5° for the
phase. The combined relative standard uncertainty in geo-
metrical capacitance measurements is typically better than
5%, where the largest contributing factor is the uncertainty in
the film thickness measurements.
Equation (5) for the residual inductance has been validated for
specimens 8 µm to 300 µm thick. However, since residual
inductance becomes smaller with thinner dielectrics, mea-
surements can be accurately made for sample thicknesses
down to 1 µm.
Measurements in the frequency range of 100 MHz to 12 GHz
are reproducible with relative combined uncertainty in ε’ and
ε’’ of better than 8% for specimens having ε’ <80 and thick-
ness d <300 µm. The resolution in the dielectric loss tangent
measurements is <0.005.
Additional limitations may arise from the systematic uncer-
tainty of the particular instrumentation, calibration standards
and the dimensional imperfections of the actually imple-
mented test fixture. Results may be not reliable at frequencies
where
|
Z
|
decreases
below 0.05 Ω, which in Figure 3 is
shown as a frequency range of 11.9 GHz to 13.5 GHz.
9.3
Test Software
Test
software enabling this technique to
be performed is available in the Agilent VEE platform. Please
contact Dr. Jan Obrzut at NIST-Gaithersburg, MD
(jan.obrzut@nist.gov) to obtain such.
9.4
Metric Units of Measure
This
test method uses only
metric units of measure, as is the case with nearly all such
high frequency test methods. Conversion to English/Imperial
units has not been done in this document, as any conversions
IPC-TM-650
Number
2.5.5.10
Subject
High
Frequency Testing to Determine Permittivity and Loss
Tangent of Embedded Passive Materials
Date
07/05
Revision
P
age5of8
电子技术应用　　　　　　　ｗｗｗ．ＣｈｉｎａＡＥＴ．ｃｏｍ
from
metric units will lead to inherent accuracy and/or preci-
sion errors.
10
References
[
1] Fundamental Physical Constant, Permittivity,
http://
physics.nist.gov/cgi-bin/cuu/V
alue?ep0|search_for=permittivity
[2] M. A. Stuchly, S. S. Stuchly, ‘‘Coaxial line reflection meth-
ods for measuring dielectric properties of biological sub-
stances at radio and microwave frequencies: A review,’’
IEEE Trans. Instrum. Meas., vol. 29, pp. 176-183, 1980.
[3] N. Marcuvitz, Waveguide Handbook. McGraw-Hill, New
York: 1951.
[4] H. J. Eom, Y.C. Noh, J.K. Park, ‘‘Scattering analysis of a
coaxial line terminated by a gap,’’ IEEE Microwave Guided
Wave Lett., vol. 8, pp. 218-219, 1998.
[5] N.-E. Belhadj-Tahar, O. Dubrunfaut, A. Fourrier-Lamer,
‘‘Equivalent circuit for coaxial discontinuities filled with
dielectric materials - frequency extension of the Marcu-
vitz’s circuit’’ J. Electromagnet. Wave, vol. 15, pp. 727-
743, 2001.
[6] J. Obrzut, A. Anopchenko, ‘‘Input Impedance of a Coaxial
Line Terminated with a Complex Gap Capacitance -
Numerical and Experimental Analysis’’ IEEE Trans.
Instrum. Meas., vol. 53(4), Aug. (2004).
[7] ‘‘Mathematical Handbook for Scientists and Engineers,’’
G. A. Korn and T. M. Korn, McGraw-Hill, 2
nd
edition
(1968),
page 719.
11
Test Fixture Drawings
IPC-25510-4
6
1 Center conductor pin
a
= 3.05 mm
2 Supporting dielectric in the APC-7 section
3 Center conductor in the APC-7 to APC-3.5
4 Supporting dielectric in the APC-3.5 section
5 APC-3.5 section of the adaptor
6 Section A outer conductor (
b
=7.00 mm)
7 Section B outer conductor (
b
=7.00 mm)
8 APC-7 mount
8
1
2
a
d
b
b
Section B
Section A
Section A details
Test Fixture for HF Permittivity of Embedded Passive Materials
Originator: IPC Embedded Passives Test Methods
3
4
5
50 Ω
Calibration Plane
METRIC, dimensions are in mm
7
APC-3.5 female mount
IPC-TM-650
Number
2.5.5.10
Subject
High
Frequency Testing to Determine Permittivity and Loss
Tangent of Embedded Passive Materials
Date
07/05
Revision
P
age6of8
电子技术应用　　　　　　　ｗｗｗ．ＣｈｉｎａＡＥＴ．ｃｏｍ