DK or Dielectric Constant or Relative Permittivity or Er - Taconic

DK or Dielectric Constant or Relative Permittivity or r
What is it, Why is it Important, and How Does Taconic Test for It?
By David L. Wynants, Sr. Process Engineer, Taconic ADD
The relative permittivity of a material always depends on how it’s tested. So, under given conditions, the DK
of a material is a reflection of the extent to which it concentrates electrostatic lines of flux. Technically, it is the
ratio of the amount of electrical energy stored in a material, relative to that stored in a vacuum. It is also the
ratio of the capacitance of a particular material as a dielectric, compared to a similar capacitor which has
vacuum, or air, as its dielectric 1 .
Absolute permittivity is the measure of the resistance that is generated when forming an electric field in a
medium, e.g, a dielectric such as a laminate or film. So, permittivity is a measure of how an electric field
affects, and is affected by, a dielectric medium. The permittivity of a medium describes how much electric field,
or more correctly, flux, is 'generated' per unit charge. Less flux exists in a medium with a high permittivity due
to polarization effects. Permittivity is directly related to electric susceptibility, which is a measure of how easily
a dielectric polarizes in response to an electric field. This influences the capacitance of the material and the
speed of light within the dielectric. Thus, permittivity relates to a material's ability to transmit (or "permit") an
electric field 2 .
The dielectric constant (DK) is an important piece of information
when designing capacitors and in other circumstances where a
material might be expected to introduce capacitance into a circuit.
The layers beneath etched conductors in printed circuit boards (PCBs)
also act as dielectrics. Dielectrics, of course, are used in RF
transmission lines. DK is a dimensionless number.
Figure 1
Electrical signals on wires and traces travel at the speed of light (c).
That works out to 11.8 in/nanosecond. Electrical signals slow down in any other medium by the square root of
the relative dielectric coefficient of the medium. As an example, a stripline trace in FR4 with an r of 4 would
travel at “c / √4” or about 6 in/ns. This is valid in a stripline [Figure1] or multilayer application where all the
flux lines are going through materials having the same or similar DK. In a microstrip [Figure 2] application
(such as in a double sided board, or on the outer layer of a multilayer board), some part of those flux lines travel
in air, so the effective dielectric constant will be slightly less.
Software programs take this into account when designing
microstrips 3 .
The dissipation factor (DF) is a measure of loss-rate of energy of a
mode of oscillation. For our interest the mode would be electrical. It
is the reciprocal of Quality
factor, (Q) which represents the
Figure 2
quality of oscillation. For
example, electrical potential energy is dissipated in all dielectric materials,
usually in the form of heat.
When representing the electrical circuit parameters as vectors in a complex
plane (Figure 3), the material’s dissipation factor is equal to the tangent of
the angle between the impedance vector and the negative reactive axis.
This gives rise to the term known as the loss tangent δ, or tan delta. The
DF will vary depending on the dielectric material and the frequency of the
electrical or RF signals 4 .
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Figure 3

As DF is an indication of power, let’s discuss dBm (sometimes referred to as just dB) briefly. The term dBm is
an abbreviation for the power ratio in decibels (dB) of the measured power referenced to one milliwatt (mW).
Microwave, radio, and fiber optic networks use dBm as a convenient measure of absolute power because it has
the capability to express both very large and very small values. Why? Because it is logarithmic in nature. Zero
dBm equals one mW. A 3 dBm increase represents roughly doubling the power, which means that 3 dBm
equals roughly 2 mW. For a 3 dB decrease, the power is reduced by about one half, making −3 dBm equal to
about 0.5 milliwatt 5 . The -3 dBm frequencies are used in determining the DF of a material in some of the test
methods for DK we’ll be discussing.
Presented below are discussions of the four DK test methods we do at Taconic, Petersburgh [TP]. Three of them
are IPC methods, listed as a DK test method for all 17 legacy data sheets in IPC 4130A.
Two Fluid Cell Method [@ 1 MHz] IPC-TM-650 2.5.5.3
As the definition of DK is a ratio of capacitances, and this method measures capacitance, this method excels at
DK. The ratios are that of an empty cell [air as the fluid] without and with the material under test (MUT), and a
wet cell [Dow 200 silicone fluid] without and with the MUT. It is a destructive test since a discrete sized sample
[~3X3] is required.
But at 1 MHz? What’s the use? Well, if the DK of the material doesn’t change with frequency, as with PTFE,
then the Two Fluid Cell test is as valid as a test at 10 GHz. In addition, the Two Fluid Cell Method is easier to
perform, and multiple tests of the same dielectric thickness (DT) can be performed nearly simultaneously.
Figure 4 DK & DF relationships between the Two Fluid Cell & X-Band, stripline test. These charts represent 17 years worth of PTFE/Glass
laminate testing @ TP. DK, on the top shows excellent correlation, while the DF on the bottom has no correlation, based on the R 2 value.
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Virtually any DK can be measured using this method.
Speaking of DTs: From the very thin to the very thick [~0.0001” to 0.2500”] can be tested. So the actual
material that customers are buying is being tested. This is an important advantage for Taconic.
The DF, in my opinion, is worthless however. Why? Very thin materials have an extremely high tested DF,
while very thick samples with the same DK exhibit very low DFs. Correlations of measured DF between the
Two Fluid Cell method and other test methods are non-existent, while the DK obtained by the Two Fluid Cell
correlates well with the other two DK test methods that IPC references on all 17 legacy slash sheets of IPC
4103. Notice the excellent relationship between the DKs and the non-existent correlation of the DFs done with
the Two Fluid Cell and the X-Band test, as shown in the charts above [Figure 4].
The temperature of the laboratory environment, or fixture, needs to be well controlled. The lab cannot get too
hot or the DK will be too low. This is typical PTFE behavior. Chilling the fixture [Figure 5, below] can
remediate potential temperature issues within the lab. Some porous, highly filled, ceramic products can absorb
the silicone fluid and be problematic to test, since the capacitance raises as the air is displaced by the fluid,
seemingly increasing the DK. Values need to be recorded immediately upon entry of the MUT in those
instances.
Figure 5 Not-to-Scale Schematic of 2-Fluid Cell fixture. Readings are taken with the cell empty, then with the MUT inserted. The MUT is taken
out, the fixture is filled with Dow 200 silicone fluid. Readings are taken; the MUT is re-inserted and final readings taken. A spreadsheet spits out
the DK.
Here is a link to the IPC test method: http://www.ipc.org/4.0_Knowledge/4.1_Standards/test/2.5.5.3c.pdf
Full Sheet Resonance [FSR] Method [TP Stnd @ 130 to 500 MHz] IPC-TM-650 2.5.5.6
FSR is a non-destructive test and faster to perform than the Two Fluid Cell method. Given a clean-cut sample
edge, and sufficient floor space, virtually any sized panel can be tested, from a 6X6 to an 18X102.
What happens in an FSR test? A signal is launched from the output port of the VNA from the edge of a cut
panel. The clad panel acts as a wave guide. The edges behave as “opens” and so reflect the signal back into the
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panel. The DK and the panel dimension determine how the reflected signals behave inside the panel to create
the resonant pattern seen on the CRT screen of the vector network analyzer (VNA).
Notice the patterns, in the figures below, created by a TLX-9 & a TLX-6. They should look almost identical.
But the TLX-6 is a square 12X12, while the TLX-9 is a rectangular 12X18. Square panels generally show an
unambiguous, single peak [actually a “valley”] in the frequency range tested. Rectangular panels show a
“noisier” wave form due to all the possible resonances from the uneven length sides. Note the relatively simple
display of the 12X18 of the TLX-9 to the many peaks generated by the CEr-10’s 12X18 in Figure 6, below.
Figure 6 CRT representations from an HP VNA #8720B showing FSR tests of 2.65, 2.5, & 9.70 [30mil] DK materials, respectively.
How is the proper peak selected? Generally familiar products with a long history of FSR data are being tested.
However, if a different panel size or an unfamiliar DK is being measured, the expected frequencies can be
generated through the use of the Mode Table file in Excel . The panel size and expected DK are entered into
the Mode Table and the fist 4 modes are calculated.
Figure 7 Mode Table: Generating expected frequencies.
In the example shown to the left[Figure 7], a CEr-10-0250 panel
with the dimensions of 18X24 and an expected DK of 9.5 shows
that the first peak available in the frequency range is 213 MHz or
0.213 GHz. We always put the shorter dimension first as that is the
direction that the signal will be launched into the panel. [See
below] The frequency of 0.213 GHz represents the 2:0 mode. TP
always chooses to measure the M (X) :0 modes since this simplifies
the calculations when N=0. For an explanation, here is a quote
from the IPC procedure for the FSR method [
http://www.ipc.org/4.0_Knowledge/4.1_Standards/test/2.5.5.6.pdf ]:
“5.4 Selection of Unambiguous Resonant Modes In a conventional waveguide cavity, reflections at the metal bounded sides show a
current maximum, while in the parallel plate waveguide, reflections at open edges or corners show a voltage maximum. When the
waveguide is a rectangle, as for clad panels, each resonance mode is a grid array pattern of maxima and may be designated (M:N),
where M is the integer number of times (nodes) the pattern repeats along the length and
N along the width.”
Taconic uses a simplified text fixture, as seen in Figure 8, to the right. The
test itself is pretty direct. After calibrating the VNA for the FSR test, [an
open response for the S 22 parameter , which is the output port voltage
reflection coefficient], a panel is placed in the orientation shown. The
signal launching pin is lowered down to the surface of the panel. The
correct “valley” in the spectrum shown on the CRT screen of the VNA is
chosen. The frequency of interest is then entered into an FSR spreadsheet,
Figure 8 Simplified FSR Fixture
where the measured dimension and mode have already been entered, and
the DK value is generated. Repeat. For thinner laminates [

How does the FSR compare to the 1 MHz test? Very well, as shown in the two charts below [Figures 9&10].
Figure 9 Lab Press FSR Results vs Two Fluid Cell
Figure 10 Production laminate FSR results vs Two Fluid Cell
The one on the right shows TP production testing data. The chart on the left is from Lab Press panels that were
FSR tested using 7X10 sample sizes. Since the 3X3 sample used for the Two Fluid Cell test represents a much
greater percentage [3X to 6X] of the
original FSR tested panel, the R 2 value is
higher for the Lab Press samples than the
production panels.
The FSR method compares well with the
Bereskin method also. The graph to the left
[Figure 11] shows a comparison of DK
values obtained by FSR and Bereskin of
RF-35A.
Figure 11 FSR vs Bereskin testing
Figure 12 FSR tested over a range of frequencies on the same panel
FSR testing has been performed at higher
frequencies. Shown in Figure 12 is FSR
data measured between 15.5 & 17.5 GHz,
performed on a verification panel of RF-60
for the FSR test. Modes from 79 to 88,
inclusive, were measured. Frequencies
above 12 GHz require a different cable and
recalibration to achieve a clean signal.
Since the cladding remains on the dielectric,
in FSR testing, unlike other tests where the
cladding is removed, there are no air pockets
which could lower the DK values, as is
observed other test methods. So, the FSR
DK value may be slightly higher than other
test methods. The holes left in the surface by
copper dendrites may trap microscope air
pockets and lower the DK in the Two Fluid
Cell test and wherever retains are
“squeezed” in a test fixture such as in the X-
Band & Bereskin test methods.
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X-Band Test Method [@ 8 – 12 GHz] by Stripline Using a Resonant Element Pattern Card
Figure 13 Resonant peak to determine DK
Figure 14 Schematic of X-Band fixture from IPC-TM-650 2.5.5.5
Figure 15 Resonator Pattern Card template from IPC-TM-650 2.5.5.5
This is the “test” elephant in the room.
Companies which sold mainly to the
military market, which required, for certain
laminates, testing at X-Band, are especially
attached to this method. This method can
spit out a DK and an adequate DF loss
number. It determines the loss based on - 3
dBm from the resonant frequency [See
Figure 13]. Since loss relates to power and
this method is using the - 50% power from
resonant, the result is valid for this set-up.
This method is often preferred because it’s
in the X-Band frequency range [8 to 12.4
GHz]; though the majority of TP’s
customers have applications are in the
UHF, L, S, & C-bands [all

A drawback to this method is that the 8.5 mils of the resonator card becomes part of the MUT. This is even
mentioned in the IPC test procedure. [Limitations 1.3.3] So, if a 3.0 card is used to test a 2.95 nominal material,
the DK and DF will be shifted slightly higher. Conversely, testing a 3.2 DK with the same card will pull the DK
and DF lower. If the DK tolerance of the product being tested is narrower than the DK tolerance of the
resonator card, materials can be rejected.
Another issue is that the test is not able to accommodate all thicknesses of product that a company might offer.
The specimens required are 2 pieces or sets of pieces from 58.3 to 66.9 mils thick. That is, except for the
highest DK; this requires specimen sets or pieces of 46.5 to 53.5 mils. So only DTs divisible into ~ 60 mils: 2-
30s, 3-20s, 4-15 mils or for the 10.5 DK 1-50, 2-25 mils may be tested. Period. Of course, anything thicker than
the set sizes cannot be tested with this method. The procedure warns that using built-up specimens can
introduce up to 5% error due to air gaps [See the Note at the end of 3.1 under Test Specimens]. Interestingly, the
old MIL-S-13949 slash sheets [Cancelled in November 1998] for GY & GX laminates, Taconic’s TLY & TLX
laminates, states that “Materials other than 0.030 and 0.060 inch thick are not testable at 10 GHz.” Therefore, if
a customer orders, for example, a 45 mil, or anything thicker than 67 mils, it cannot be tested with this method.
The very good DK correlation with the 2-fluid cell test was given above in Figure 4. The major purpose of this
test method, which can be applied to any test method is stated in the procedure itself:
“1.3 Limitations … Users are cautioned against assuming the method yields permittivity and loss tangent values that
directly correspond to applications. The value of the method is for assuring consistency of product, thus reproducibility of
results in fabricated boards.”
Bereskin Test Method [@ ~1 to ~ 22 GHz] [Modified into IPC-TM-650 2.5.5.5.1]
This method excels at DF. Why? Because: power is being measured. Power in versus power out. Even the
Figure 16 Schematic of the Bereskin fixture from his patent #5,187,443; Fig.1
resonant frequency is derived from the two – 3dBm points. This is unlike the X-Band test where the resonant
frequency is found and used for the DK, the Bereskin test takes the average frequency after determining the -3
dBm frequencies. That average frequency is used to determine the DK. This is why Bereskin excels for DF. The
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limiting factor for this method is that 11 mils is the thinnest to be tested, without stacking. The 11 mil limit is
due to the fringing length addition to the center copper strip [See Figure 16, above].
A range of frequencies can be tested, depending on the DK and DF of the material. Low loss materials can be
tested to higher frequencies. This may be due to the connectors attached to the fixture itself. Also, the fixture
currently in use [not the longer, 7” fixture, mentioned in the second patent] seems to have a self resonance
around 4 GHz, obscuring measurements between ~3.7 and ~5 GHz.
In the procedure, two samples [or sets] of identical thickness are placed in the test fixture under pressure with
the standardized copper strip compressed in between to create an imbedded stripline resonator. A signal is
propagated [excited] through the z axis of the sample and the resonant frequency is detected by finding the most
power. Using the resonant frequency found from the -3dBm points, as described above, Ε r is derived from the
equation:
Ε r = C / (2.54*F 0 *Leq) 2
Where C= speed of light,
F 0 = resonant frequency and
Leq = conductor length including field fringing.
Figure 17 is the set-up showing a 26.5 GHz
synthesized sweep oscillator on the left; the two,
stacked, power meters in the center; and the fixture
itself in the press that applies a 200 psi force, on
the right. The test itself is explained in the two
patents; 5,083,088 & 5,187,443 available at the
USPTO website: http://patft.uspto.gov/netacgi/nph-
Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fs
earchadv.htm&r=1&f=G&l=50&d=PALL&S1=05083088&OS=PN/05083088&R
S=PN/05083088 & http://patft.uspto.gov/netacgi/nph-
Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fs
earchadv.htm&r=1&f=G&l=50&d=PALL&S1=05187443&OS=PN/05187443&R
S=PN/05187443
How does this test method compare? Allied Signal
Figure 17 The Bereskin set up @ TP
Laminate Systems presented this discussion of the
Bereskin test method at the IPC Expo ’99 in 1999 in Long Beach, CA under the tile “New Developments in
High Frequency Dielectric Measurements of PWB Materials Part II: Applications of the Bereskin Method to
PWB Materials.” Under the subheading
“Comparison to Other Techniques” it stated:
Figure 18 Charted test values for various methods @ various frequencies
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“A pure polysulfone sample tested for DK and
DF at various frequencies in our laboratory by
the Bereskin Method was also tested by the
Resonant Re-Entry Cavity technique 3 at the 3M
Laboratory 4 . These data were compared to
historical data obtained at MIT using a
waveguide technique 5 . The results summarized
in Table 3 [Figure 18, to the left], indicate very
good correlation between the Bereskin method
and the other two techniques for pure
polysulfone.” [For the footnotes in the
quotation, see the original paper.]

Figure 19 Graphed data from Allied Signal’s 1999 presentation at the IPC Expo in Long Beach, CA
Here is the data from “Table 3” graphed, above in Figure 19, to easily see the relationship. [Polysulfone
([C 27 H 22 O 4 S] n ) is a thermoplastic, without PTFE’s high temperature robustness. Polysulfone melts at 371°F!]
How does the Bereskin Method
compare with the other DK tests
performed by Taconic? Data from
Taconic’s internal testing is shown
in Figures 20 & 21. The Bereskin
DK @ 1.9 GHz displays excellent
correlation with both the X-Band
and 1 MHz DKs.
Figure 20 The Bereskin test method vs the X-Band & Two Fluid Cell [1 MHz] test methods
The other DK test performed at
Taconic, the FSR method, was
already shown in the section
devoted to that method above, as a
good predictor of RF-35A DK.
When graphed with the products
Taconic certifies to the FSR
method; the RF-41s, -43s, -45s, -
60As, & Cr-10; the Bereskin
method does well as seen by the
high R 2 value.
The Bereskin method has been
used to perform DOA testing
[Degree of Anisotropy]. The
relatively small sample size, two
1.1625” X 4” pieces, make testing
in all three axis [X,Y, & Z] just a
matter of making a suitably thick
laminate 6 .
These are the four DK tests
performed at Taconic’s Advanced
Dielectric Division.
Figure 21 Bereskin test method vs the FSR test method
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David L. Wynants, Sr. has been with Taconic for over 35 years. He has designed
or revised over 1,600 dielectric offerings of Taconic ADD since being assigned to
that division. He is a former supervisor of Taconic’s QA Lab, and was
instrumental in bringing the Bereskin Test Method to Taconic, being trained by
Dr. Alexander Bereskin himself. He is an ASQ recognized Green Belt.
References:
1 http://en.wikipedia.org/wiki/Relative_permittivity
2 http://en.wikipedia.org/wiki/Permittivity , http://en.wikipedia.org/wiki/Electric_susceptibility
3 http://www.ultracad.com/mentor/microstrip%20propagation.pdf
4 http://en.wikipedia.org/wiki/Dissipation_factor
5 http://en.wikipedia.org/wiki/DBm
6 \\Tpnt1\public\Keep\A.D.D\TSM-30 Anisotropy Report.docx
All accessed on 11.11.11.
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