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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 under given conditions reflects 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 by an

applied voltage, relative to that stored in a vacuum. Similarly, it is also the ratio of the capacitance of a

capacitor using that material as a dielectric, compared to a similar capacitor which has vacuum, or air, as its

dielectric1.

In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming

an electric field in a medium, e.g, a dielectric such as a laminate or film. In other words, 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 (more correctly, flux) is 'generated' per unit charge. Less electric flux exists in

a medium with a high permittivity (per unit charge) 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.

Thus, permittivity relates to a material's ability to transmit (or "permit") an electric field2.

The dielectric constant (DK) is an essential 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 are used in RF

transmission lines.

Electrical signals on wires and traces travel at the speed of light:

186,280 miles/second! 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. So, for example, a stripline trace in FR4 with an r of 4.0 would travel at the speed of light divided by

the square root of 4 (which is 2) or about 6 in/ns. This is valid in a stripline or multilayer application where all

the flux lines are going through materials having the same or similar DK. In a microstrip 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 those types of

circuits3.

In physics, the dissipation factor (DF) is a measure of loss-rate of

energy of a mode of oscillation (mechanical, electrical, or

electromechanical) in a dissipative

system. It is the reciprocal of Quality

factor, (Q) which represents the

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, to the right, the dissipation factor is equal to the tangent of the angle

between the impedance vector and the negative reactive axis, as shown in the

diagram to the right. This gives rise to the parameter known as the loss tangent

δ, or tan delta. DF will vary depending on the dielectric material and the

frequency of the electrical signals.

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As DF is an indication of power, let’s discuss dB briefly. The term dBm is an abbreviation for the power ratio

in decibels (dB) of the measured power referenced to one milliwatt (mW). It is used in radio, microwave and

fiber optic networks as a convenient measure of absolute power because of its capability to express both very

large and very small values. Zero dBm equals one milliwatt. A 3 dB 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 milliwatt5. 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. One was co-opted by

someone connected to IPC, into designing the IPC-TM-650 2.5.5.5.1 method.

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.

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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.

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 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 1. 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 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 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).

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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.

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.

In the example shown to the left, 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 the figure to the right.

The test itself is pretty direct. After calibrating the VNA for the FSR test,

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, where the measured

dimension and mode have already been entered, and the DK value is

generated. Repeat. For thinner laminates [<10 mils] the resolution of the

VNA is increased from a Scale Reference of 2 dB/div to 1.0 or 0.5/div as

the “peaks” are smaller.

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How does the FSR compare to the 1 MHz test? Very well, as shown in the two charts below. 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 R2 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

shows a comparison of DK values obtained

by FSR and Bereskin of RF-35A.

FSR testing has been performed at higher

frequencies. Shown 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

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. 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];

although the majority of applications are in

the UHF, L, S, & C-bands [all <8 GHz].

Here is a link to the IPC test method: http://www.ipc.org/4.0_Knowledge/4.1_Standards/t

est/2-5_2-5-5-5.pdf .

The calibration of the VNA for this method

is extensive. Unlike the Two Fluid Cell

Method which can test multiple DKs at the

same time of the same DT, this test method

can only test one DK at a time. Why?

Because the resonant frequency is achieved

by exciting a pattern card with a circuit

designed on a discrete material. That is, to

test 3.5 DK materials requires the use of a

pattern card made from 3.5 DK material,

8.5 mils thick. As changing cards is

cumbersome, each card requires its own

fixture.

According to the latest revision in the

online IPC-TM-650 test method manual,

only 9 different DKs can be tested with

this method. Or at least, that’s all they have

dimensions for. [See in the procedure: Table 1 Dimensions for Stripline Test

Pattern Cards in Millimeters] Taconic

offers 68 different DKs [As of 11.11.11]!

Additionally, according to the procedure,

the resonator pattern card can be +/- 2.5%

of the nominal DK! That’s +/- 0.075 for a

3.0 nominal card and +/- 0.085 for a 3.5

card. This is important when you consider

the next issue in the following paragraph.

A drawback to this method is that the 8.5

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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. 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

resonant frequency is derived from the two – 3dBm points. 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.

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 through the z axis of the sample and a resonant frequency is found. Using the resonant frequency

found from the -3dBm points, as described above, Εr is derived from the equation:

Εr = C / (2.54*F0*Leq)2

Where C= speed of light,

F0 = resonant frequency and

Leq = conductor length including field fringing.

This 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

earch-adv.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

earch-adv.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

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:

“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 technique3 at the 3M Laboratory

4.

These data were compared to historical

data obtained at MIT using a waveguide

technique5. The results summarized in

Table 3, indicate very good correlation

between the Bereskin method and the

other two techniques for pure

polysulfone.” [For the footnotes see

original paper.]

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Here is the data from “Table 3” graphed, above, to easily see the relationship. [Polysulfone ([C27H22O4S]n) is a

thermoplastic, like PFTE, without its 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 ADD Data Sheet

Data Testing file [Tpnt1\public\Keep\ADD

DATA SHEETS\ADD Data Sheet Data.xlsx] is

graphed and shown. The Bereskin

DK @ 1.9 GHz displays excellent

correlation with both the X-Band

and 1 MHz DKs.

The 4th

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 FRS

method; the RF-41s, -43s, -45s, -

60As, & Cr-10; the Bereskin

method does well as seen by the

high R2 value.

The Bereskin method has been used

to perform DOA testing [Degree of

Anisotropy]. The relatively small

sample size, 2-1.1625” X 4”, make

testing in all three axis [X,Y, & Z]

just a matter of making a suitably

thick laminate.

These are the four DK tests

performed at Taconic’s Advanced

Dielectric Division.

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David L. Wynants, Sr. has been with Taconic for over 35 years. He has designed

or revised over 1,300 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, 2 http://en.wikipedia.org/wiki/Relative_permittivity

3 http://www.ultracad.com/mentor/microstrip%20propagation.pdf

4 http://en.wikipedia.org/wiki/Dissipation_factor

5 http://en.wikipedia.org/wiki/DBm

All accessed on 11.11.11.