IPC-TM-650 EN 2022 试验方法.pdf - 第440页
with specimen thickness, increasing as specimen thickness increases. Ignoring this effect by use of a fixed ∆ L value for calculating test results will bias the permittivity values upward for thicker specimens, downward …
Cartesian
screen display shows the S21 parameter and the
transmission/incident power ratio in negative dB vertical scale
units versus frequency on the horizontal scale. Select the start
and stop frequency range to sweep across the resonance
peak and at least 3 dB below the peak. Adjust the start and
stop frequency values as narrowly as possible, but still include
the resonant peak and the portions of the response curve on
both sides of it that extend downward 3 dB.
6.4.1
The
first option is to get the three points (f
r
,f
1
,
and f
2
)
as
described in 6.2 and 6.3. Determine the resonant dB
r
and
frequency
f
r
values
for the highest point (maximum) on the
response curve. With manual operation, instrument program
features are available to do this very quickly. On the response
curve to the left and right of f
r
,
locate the f
1
,d
B
1
and
f
2
,d
B
2
points
as near as possible to 3 dB below dB
r
.
These may then
be used in the calculations shown in 7.2.
6.4.2
A
second option requires a computer external to the
instrument. Collect from the network analyzer all of the f,dB
data points represented by the response curve between f
1
,
dB
1
and
f
2
,d
B
2
and
apply non-linear regression analysis tech-
niques to statistically determine values for Q, f
r
,
and dB
r
that
best
fit the F
i
,d
B
i
paired
data points to the formula.
dB
i
=d
B
r
-
A log
e
(
1+4Q
2
((f
i
/f
r
-1
)
2
)
where
A=1
0log
e
(10)
= constant for converting from log
e
to
dB
This formula may be derived from combining equation 4 and
equation 6 as corrected in 7.2, with the reasonable assump-
tion that f
r
-f
1
equals
f
2
-f
r
.
The statistically derived values for
f
r
and
Q would then be used in equation 2 of 7.1 and equa-
tion 4 of 7.2 respectively.
This has been found to fit the collected data points very well
at all regions across the entire f
1
to
f
2
range.
It is a simplified
version of the non-linear regression method for complex S21
parameters
5
.
7.0
Calculations
7.1 Stripline Permittivity
At
resonance, the electrical
length of the resonator circuit is an integral number of half
wavelengths. The effective stripline permittivity, ε
r
,
can be cal-
culated from the frequency of maximum transmission as fol-
lows:
ε
r
=[
nC/(2f
r
(L
+ ∆L))]
2
[1]
Where
n is the number of half wavelengths along the resonant
strip of length L, ∆L is the total effective increase in length of
the resonant strip due to the fringing field at the ends of the
resonant strip, C (the speed of light) is 3.000z10
11
mm/s, and
f
r
is
the measured resonant (maximum transmission) fre-
quency.
The more exact value for C of 2.9978z10
11
mm/s
would give a
lower permittivity value, differing for example by 0.003 for 2.5
permittivity material. This method does not use the more exact
value to avoid confusion with specifications for materials and
proven component designs based on older versions of this
method where 3.000z10
11
has
been in use.
For example, for a specified 38.1 mm long resonator, the
parameters at X-band aren=4,L=38.1 mm. For a given
material with ∆L = 1.397 mm, the formula for ε
r
becomes:
ε
r
=
2.30764z10
20
/f
r
2
[2]
7.1.1
Determination of L
∆L,
a correction for the fringing
capacitance at the ends of the resonator element, is affected
by the value of the ground plane spacing and the degree of
anisotropy of permittivity of the material being tested. The
degree of anisotropy is affected by the amount and orientation
of fiber and the difference between permittivity of fiber and
matrix polymer. Because of this, a ∆L value for use with a
particular type of material must be determined experimentally
by the following procedure.
7.1.1.1
Prepare
a series of resonator circuit cards having
patterns in which only the resonator element length is varied
to provide n values of 1, 2, 3, and 4 at close to the same fre-
quency. For example, lengths of 9.5 mm, 19.0 mm, 28.6 mm,
and 38.1 mm may be used.
7.1.1.2
For
each of at least three sets of typical specimen
pairs of the material to be measured, measurements of f
r
are
obtained
at each L value. Plot L f
r
/n
on the Y axis versus f
r
/n
on
the X axis or preferably use a numeric linear regression
analysis procedure to determine the slope of the least squares
fit through the four data points. The slope is equal to the
negative value of ∆L.
7.1.1.3
The ∆L
values for each of the specimen pairs may
then be averaged to provide a suitable working ∆L value. For
a given material type, a ∆L value should be agreed upon as
standard for testing to a specification.
7.1.2
Determination of Effect of Specimen Thickness on
L
The ∆L
correction for end fringing capacitance will vary
IPC-TM-650
Number
2.5.5.5
Subject
Stripline
Test for Permittivity and Loss Tangent (Dielectric Constant
and Dissipation Factor) at X-Band
Date
3/98
Revision
C
P
age7of25
电子技术应用 ｗｗｗ．ＣｈｉｎａＡＥＴ．ｃｏｍ
with
specimen thickness, increasing as specimen thickness
increases. Ignoring this effect by use of a fixed ∆L value for
calculating test results will bias the permittivity values upward
for thicker specimens, downward for thinner ones. For low
permittivity materials where the resonator is longer, this bias is
quite small and only of interest for close tolerance applica-
tions. For high permittivity materials, the smaller resonator
length makes this correction more important.
There are two ways in which this thickness effect may be
handled: by an empirical determination of ∆L for various thick-
nesses or by assuming a proportionality to the published pre-
diction of ∆L
(4)
.
7.1.2.1
For
the empirical method, use the 7.1.1 procedure
to obtain ∆L with specimens at extremes of thickness variation
expected in day to day testing. Use numerical linear regres-
sion of the collected ∆L-specimen thickness data pairs to
derive a linear formula of the form
∆L=B0+B
1
(thickness)
Specification
values for B
0
and
B
1
for
a given material must be
agreed upon for a particular material type.
7.1.2.2
A ∆L
correction factor can be derived for a given
material type in a range of permittivity values by determining
for specimens of known thickness the ratio of ∆L derived
according to 7.1.1 to that predicted by equation 3 when R=1.
An average of ratios so determined must be agreed upon as
the specified correction factor for the formula. From this, ∆Lis
calculated by:
∆L= R (K
2
+2KW
)/(2K+W) [3]
where
R = the average ratio of observed to predicted ∆L
K = B log
e
(
2)/pi
= 0.2206356 B
W = width of resonator in mm
B = 2 (specimen thickness) + (test pattern card thickness)
= total ground plane spacing in mm
7.2
Calculation of Effective Dielectric Loss Tangent
A
value
for loss tangent for the dielectric is obtained by subtract-
ing the appropriate conductor loss value, 1/Q
c
,
in Table 1
from the total loss value, 1/Q, as shown
tan δ = 1/Q - 1/Q
c
[4]
or
tan δ =[
(f
1
-f
2
)/f
r
] - 1/Q
c
[5]
where
1/Q or (f
1
-f
2
)/f
r
is the total loss due to the dielectric, copper,
and copper-dielectric interface.
A more exact calculation can be used that does not require
that the values of f
1
and
f
2
be
at exactly half the power level of
the maximum at resonance. This is especially suited for auto-
mated testing. The formula is
tan δ = (1-(f
1
/f
r
))
(10
(dB
1
/
10
)-1
)
-0.5
+
((
f
2
/f
r
)-1
)(10
(dB
2
/
10)
-1
)
-0.5
-
(1/Q
c
)
[6]
dB
1
is
the dB below the peak power level at f
1
and
dB
2
is
the dB below the peak power level at f
2
7.2.1
Calculation of 1/Q
c
The
following calculation scheme is used
(1)
1/Q
c
= α
c
C/(π f ε
r
0.5
)
[7]
where
α
c
=4
R
s
ε
r
Z
0
Y
/ (377
2
B)
=
attenuation constant, nepers/mm
R
s
=
0.00825 f
0.5
=
surface resistivity of copper, Ohm
Z
0
=
377/(4 ε
r
0.5
(C
f
+
(W/(B - T))))
= characteristic impedance of resonator, Ohm
377 = 120 π. = free space impedance, Ohm
C
f
=
(2 X log
e
(X+1)-(X-1)log
e
(X
2
-1))/ π
Y
= X+2WX
2
/B
+X
2
(
1+T/B)log
e
[
(X+1)/(X-1)]/π
X = B/(B-T)
ε
r
=
nominal permittivity
B = ground plane spacing, mm
C = 299.796 mm/ns = speed of light
f = nominal resonant frequency, GHz
IPC-TM-650
Number
2.5.5.5
Subject
Stripline
Test for Permittivity and Loss Tangent (Dielectric Constant
and Dissipation Factor) at X-Band
Date
3/98
Revision
C
P
age8of25
电子技术应用 ｗｗｗ．ＣｈｉｎａＡＥＴ．ｃｏｍ
NOTE: GHz
is equivalent to cycles/ns to keep units consis-
tent in this section 7.2.1.
W = resonator width, mm
T = resonator conductor thickness, mm
Where combinations of resonant frequency, resonator width,
ground plane spacing, and nominal permittivity are encoun-
tered other than those listed in Table 1, a calculated 1/Q
c
must
be agreed upon. Data is not currently available for cor-
recting this calculated value to account for increased conduc-
tor loss due to surface treatments or type of copper foil used.
7.2.2
Corrections to the Loss Factor
Corrections
in the
total loss value, 1/Q, may be needed for materials of high
anisotropy of ε
r
as
mentioned in 1.2.2. The Q actually mea-
sured is Q
loaded
,
but is often assumed to be Q
unloaded
.
The
probe gap given in Table 1 is intended to provide insertion
loss at a resonance high enough to make Q
loaded
approxi-
mately
equivalent to Q
unloaded
.
When
materials with high anisotropy of permittivity are mea-
sured, probe coupling is affected and the insertion loss
becomes small, making a correction useful before applying
the above calculations. Insertion loss is determined by com-
paring transmitted power at resonant frequency of the fixture
and specimen with the resonator pattern card and with a simi-
lar card having a straight through 50 Ohm line. The dB
r
differ-
ence
as dB
r
is
related to the power ratio by
P
2
/P
1
=e
(log
e
(10)
dB
r
/
10)
[8]
and
the unloaded Q is determined from the measured Q by
Q
unloaded
=Q
loaded
/ [1-
√
P
2
/ P
1
] [9]
The
following values illustrate this relationship:
dB
r
60
50 40 30 20 15 10 5
Q
unloaded
/
Q
loaded
1.00
1.00 1.01 1.03 1.11 1.22 1.46 2.28
8.0 Report
The
report shall contain the following:
• The measured length of the resonator and ∆L value.
• The measured thickness of specimen stacks.
• The maximum transmission (resonant) frequency, f
r
.
•
If the three point method of 6.2, 6.3 or 6.4.1 is used, report
the frequencies of the two 3 dB points on the resonance
curve or the frequency and actual dB value of the two
points.
• If the non-linear regression (NLR) method of 6.4.2 is used,
then optionally report the number of data points used, NLR
uncertainty values for f
r
,Q
loaded
,d
B
r
•
The calculated effective stripline permittivity.
• The calculated effective dielectric loss tangent.
• If the test was not done in the X or machine direction, give
the direction in which test was performed. That is, orienta-
tion of the resonator with respect to the X or Y axis of the
specimen.
• The temperature of the test fixture during the test.
• The grade of copper foil used in the test pattern card.
9.0 Notes
9.1
Permittivity
The
dielectric of a stripline circuit affects
the electrical response of all the circuits printed on it. Velocity
of propagation, wavelength, and characteristic impedance all
vary with permittivity. If the permittivity varies from the design
value, the performance of such circuits is degraded.
Throughout this document, the term ‘‘permittivity’’ refers to
relative permittivity of the dielectric material, a dimensionless
ratio of the absolute permittivity of the material to that of a
vacuum.
9.2
Loss Tangent
The
attenuation and Q (figure of merit) of
stripline circuits are a function of combined copper and dielec-
tric loss. An excessively high loss tangent leads to loss in sig-
nal strength and to degraded performance of frequency selec-
tive circuits such as filters. In this method, a great saving in
time and cost of testing is achieved by using a permanent
stripline resonator, which is part of the test fixture. With this
fixture, variations in loss tangent due to the dielectric can be
monitored but not the additional loss due to the type of metal
and bonding treatment used in laminating.
9.3
Measurements at Other Frequency Bands
The
test
equipment of 4.1 can be modified for L, S, and C band mea-
surements at some additional cost. The test equipment of 4.2
will be able as is to handle other bands.
9.4
Frequency Ranges
Accepted
frequency ranges for the
various bands are:
IPC-TM-650
Number
2.5.5.5
Subject
Stripline
Test for Permittivity and Loss Tangent (Dielectric Constant
and Dissipation Factor) at X-Band
Date
3/98
Revision
C
P
age9of25
电子技术应用 ｗｗｗ．ＣｈｉｎａＡＥＴ．ｃｏｍ