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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 7, JULY 20063127

Wideband Measurement of the Dielectric

Constant of an FR4 Substrate Using a

Parallel-Coupled Microstrip Resonator

Eric L. Holzman, Senior Member, IEEE

Abstract—We have made a wideband measurement of the real

part of the dielectric constant of flame retardant #4 epoxy (FR4),

a common high-frequency printed-circuit-board insulator. We

designed a novel test circuit, an electrically long parallel-cou-

pled microstrip resonator, which was etched on a 0.014-in FR4

substrate, manufactured by NELCO, Melville, NY. We used a

computer model of the resonator to extract the dielectric constant

at the frequencies of zeroes in its measured transmission response.

By adjusting the model’s dielectric constant, we tuned the fre-

quency of each zero to match the measured frequency, yielding the

dielectric constant at that frequency. To validate our method and

results, we present a simple, but original proof that the frequencies

of zeroes in the resonator’s transmission response are insensitive

to input and output mismatches. Additionally, we compare the

measured and predicted response of a two-stub filter designed

with our measured data. The fabricated filter’s measured return

loss and insertion loss from 3 to 12 GHz are within 1% of the

predictions of Agilent Technology’s Momentum.

Index Terms—Dielectric materials, measurement, microstrip

resonators, permittivity measurement, printed circuits.

I. INTRODUCTION

F

microwave printed circuit boards (PCBs). Its dielectric constant

is knowntovarywithfrequencyand manufacturer[1].FR4data

sheets generally do not list dielectric-constant data over a wide

frequency range, and we found only one set of broadband data

in the literature [1]. Unfortunately, these data are presented in

a relative sense only (normalized to unity), not well validated,

and the vendors are not identified. Further to this, four different

measurement techniques were used to obtain the data. A simple

means to measure the real part of the dielectric constant is de-

sirable, particularly if it can serve as a process control monitor

during production.

Many methods for measuring the dielectric constant of mate-

rialshavebeendevelopedand usedsuccessfully. Fora PCBma-

terial such as FR4, a practical approach is to fabricate a circuit

havingeasy-to-measurecharacteristicsthatcanbeusedtodeter-

mine the material’s dielectric constant. If such a circuit is mod-

eled accurately with computer-aided design (CAD) software,

one can determine the substrate’s dielectric constant by com-

paring the predictions of the software with the circuit’s mea-

LAME-RETARDANT #4 epoxy (FR4) is a low-cost di-

electric material that finds use as a substrate for RF and

Manuscript received February 2, 2006; revised April 7, 2006.

The author was with YDI Wireless, South Deerfield, MA 01373 USA. He is

now with Northrop Grumman Electronic Systems, Baltimore, MD 21240 USA

(e-mail: eholzman@ieee.org).

Digital Object Identifier 10.1109/TMTT.2006.877061

sured characteristics. The extracted dielectric-constant data can

then be used to design other circuits.

This type of empirical/analytical approach has been demon-

strated by a number of researchers in the microwave field.

Das et al. used two microstrip lines of unequal length to mea-

sure the effective dielectric constant of microstrip [2]. With

a computer model of microstrip, they extracted the substrate

dielectric constant and were able to achieve a measurement

accuracy of 1% over a broad bandwidth. Their method required

care in assembling the test fixture, long microstrip lines, and

well-matched and repeatable coaxial transitions according

to Lee and Nam [3]. Shimin [4], and Verma and Verma [5]

used a microstrip patch antenna as the test circuit, and by

comparing the resonant frequency predicted by an analytical

model with the measured resonant frequency, they determined

the dielectric constant of the substrate. For the best results, the

substrate had to be 3 –4

larger than the patch. Akhavan and

Mirshekar-Syahkal replaced the patch with a microstrip fed slot

antenna to overcome some of the limitations of the resonant

patch method [6]. In both cases, a different test circuit was

required for each frequency of interest. Bernard and Gautray

used a ring resonator fabricated on alumina as their test circuit

[7]. They placed a test sample of the material of interest on

top of the ring resonator. The ring’s resonant frequency was

perturbed by the sample, enabling the authors to determine the

dielectric constant of the material using an analytical model

of the ring. Measurements of several substrates were within

15% of those from a cavity resonator. Similarly, Kantor used

microstrip, stripline, and disk resonators to determine the di-

electric constant of several microwave PCB materials [8]. Yue

et al. measured the characteristic impedance of the stripline,

and determined the dielectric constant of the substrate from

equations for the impedance [9]. Their technique required a

precision coaxial load to terminate one end of the stripline and a

full two-port calibration of the vector network analyzer making

the measurements. Gruszczynski and Zaradny made measure-

ments of a sample of dielectric of fixed width, metallized on

both sides [10]. The primary source of error in their technique

was also the coaxial transition.

Each of the above techniques, to a varying degree, depends

on having well-matched coaxial transitions attached to the sub-

strate sample under test. With increasing frequency, such tran-

sitions become difficult to produce, and it is at higher frequen-

cies that accurate knowledge of the dielectric constant of most

substrates is most critical and often is not known. A measure-

menttechniquethatisinsensitivetotransitionmismatchisdesir-

able. Toward that end, Amey and Curilla [11] and Peterson and

Drayton [12] used the transmission response of microstrip and

0018-9480/$20.00 © 2006 IEEE

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3128 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 7, JULY 2006

Fig. 1. Two-port network situated between a source and load. (a) With imped-

ances ? . (b) With impedances ?

and ? .

coplanar lines with series stubs to extract the dielectric constant

ofthesubstrate.PetersonandDraytondemonstratedempirically

that their measurement is insensitive to impedance mismatch at

the transitions. Another advantage of the stub is that a single

circuit has multiple transmission zeroes over a wide frequency

band, with each zero yielding a value of the substrate dielec-

tric constant. A limitation of the coplanar version is that higher

order modes are excited at the tee junction.

In this paper, we extend the work of Peterson and Drayton,

first by presenting in Section II a simple proof that theoretically

validates their observation that the frequencies of the transmis-

sion zeroes of a passive two-port circuit are independent of port

mismatch. In Section III, we describe an alternative to the tee

circuit, the parallel-coupled resonator, which inherently is well

matched. We use this resonator to measure the real part of the

dielectric constant of NELCO FR4 over a broad range of fre-

quencies. In modeling our test circuit, we take advantage of the

high level of accuracy that commercial circuit simulators can

achieve. In particular, we use Agilent Technology’s Advanced

Design System (ADS), which includes a standard circuit sim-

ulator, based on analytical models, and Momentum, which is

based on the method of moments (MoM). We know the dielec-

tric constant of FR4 sufficiently well to design the test circuit.

We then fabricate it, measure its insertion response accurately,

and compare the data with the predictions of ADS. Due to our

confidence in the simulator, we can attribute any difference be-

tween the measured and predicted performance primarily to the

error in our knowledge of the dielectric constant. With a rela-

tively high-

circuit element such as our microstrip resonator,

we can accurately adjust the dielectric constant in the simulator

until its prediction matches the data at the zero frequencies. In

Section IV, we use our measured FR4 dielectric constant data

to design an evaluation circuit. We perform a precision thru-re-

flect-line (TRL) calibration to enable us to measure the

rameters of the circuit at its microstrip inputs, and compare the

results with the predictions. Our measured and predicted reso-

nantfrequencyagreementis within1%,whichis excellent,con-

sideringthevariationsinetchtolerance,metallizationthickness,

substrate thickness, and dielectric constant typical of most PCB

manufacturing processes.

-pa-

II. THEORY

Fig. 1 shows a generic two-port network embedded between

amicrowavesourceandload.WefollowtheanalysisofHa[13],

and assign the two-port network a scattering matrix S, normal-

ized to the port impedance

at which the

determined [see Fig. 1(a)]. S’ is the generalized scattering ma-

trix of the same two-port network situated between a source and

loadhavingimpedances

and

positiveforallfrequenciesinthebandofinterest[seeFig.1(b)].

-parameters were

,whoserealcomponentsare

We can write the transmission response or insertion loss as

[12]

(1)

If the source and load impedances are equal to

is perfectly matched,

Now let us assume

has a zero at a frequency

becomes

, the two-port

, and.

and, and that

. At , the bracketed term in (1)

which is finite valued. Thus,

quency

as

natorofthebracketedtermin(1)isnonzero.Therefore,theonly

zeroes that appear in

are those appearing in

canselectatwo-portcircuitwithtransmissionzeroeswhosefre-

quencies are dependent on the substrate dielectric constant. If

we build and test such a circuit, the frequencies of those zeroes

will be insensitive to port mismatches. A calibration of the test

equipment should not even be necessary, as verified empirically

by Peterson and Drayton [12]. We can use an accurate model of

the circuit to extract the value of the dielectric constant at each

measured zero frequency.

has a zero at the same fre-

. At frequencies away from, the denomi-

, and we

III. TEST CIRCUIT DESIGN AND MEASUREMENT

A. Test Circuit

Circuits fabricated on FR4, a relatively lossy material, typi-

cally have passbands that do not extend above 6 GHz, but they

may have reject requirements at higher frequencies. Thus, it

would be useful to have accurate dielectric-constant data from

approximately 2 to 12 GHz. We know that FR4’s dielectric con-

stantvariesslowlyoverthatfrequency.Ifwedesignatestcircuit

with half a dozen transmission zeroes over that bandwidth, we

will have sufficient data to interpolate values at other frequen-

cies with good accuracy. Fig. 2 shows such a circuit, i.e., a mi-

crostrip parallel-coupled resonator. This particular example has

zeroes in transmission starting at approximately 2.7 GHz, and

repeating approximately every 2.7 GHz. To select the resonator

dimensions, we assumed the dielectric constant of the FR4 sub-

strate is 4.5 for all frequencies. Fig. 3 plots the insertion loss

of the resonator as predicted by ADS’s circuit simulator and by

Momentum. All Momentum analyses used a mesh with at least

15 cells/wavelength at the highest frequency of simulation. Mo-

mentum’s edge mesh feature was enabled also. We generated a

photo-mask and printed the filter on 14-mil FR4. We confirmed

the filter dimensions to be within 0.5 mil of the design and ad-

justed our model’s dimensions accordingly. The only important

circuit dimension is the resonator length, which, along with the

dielectricconstantofthematerial,setsthezerofrequencies.The

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HOLZMAN: WIDEBAND MEASUREMENT OF DIELECTRIC CONSTANT OF FR4 SUBSTRATE3129

Fig. 2. Microstrip parallel-coupled resonator. Dimensions are in inches.

FR4 substrate thickness ? ????? in. Metallization thickness ? ????? in

(1/2-oz copper).

Fig. 3. Insertion loss of microstrip parallel-coupled resonator—ADS circuit

simulator,Momentum,andmeasurement.Simulationsuse4.5forFR4dielectric

constant.

separation of the resonator and main transmission line only af-

fects the depth of the transmission zero at each frequency.

Our test setup consisted of a Hewlett-Packard 8510 vector

network analyzer, a Wiltron 3680 K Universal Test Fixture with

twoK-connectorcoaxialinputports,andaground-planebacked

FR4 substrate metallized with the test circuit shown in Fig. 2.

Since calibration is not critical, we only calibrated the analyzer

with a K-connector coaxial calibration. We then placed the test

circuit in the test fixture and measured its transmission response

over frequency.

Fig. 3 plots the measured insertion loss, and it is obvious that

our assumed value of 4.5 for the dielectric constant is in error,

with the error increasing with increasing frequency.

B. Dielectric-Constant Computation

To extract the correct frequency-dependent dielectric con-

stant, we adjust manually its value in our ADS circuit simulator

and Momentum models at each of the measured reject frequen-

cies until the predicted zero matches the measured zero. We

then know the dielectric constant at the reject frequency null.

Fig. 4 shows an example at 11.21 GHz. In this case, a dielectric

constant of 4.00 in the circuit simulator and 4.03 in Momentum

matched the frequencies of the zeroes predicted by the models

to the measured results. The values differ slightly because the

two analytical methods are different.

We extracted the real part of the dielectric constant in this

manner at every measured zero frequency through 16.7 GHz,

and the results are summarized in Table I. The rise in dielectric

constant above 14 GHz, though surprising, has been observed

by others [1].

Each set of data can be fit to a third-order polynomial. The

polynomial for the circuit simulator, which can be inserted di-

rectly into the ADS MSUB block, is

(2)

Fig. 4. Adjustment of substrate dielectric constant (ADS—4.00, MoM—4.03)

to match predicted and measured insertion loss at 11.21 GHz.

TABLE I

DIELECTRIC CONSTANT OF FR4 VERSUS FREQUENCY FOR ADS’S CIRCUIT

SIMULATOR AND MOMENTUM. FR4 MANUFACTURER: NELCO

where

After designing a preliminary circuit with the circuit sim-

ulator, one should perform an analysis in Momentum, which

models the circuit more accurately. Since Momentum does not

allow parameterization of the dielectric constant as a function

of frequency, one must analyze the circuit over frequency bands

narrow enough such that the dielectric-constant variation is

small. For instance, if we design a circuit to operate from 3 to

8 GHz, we might use two frequency bands based on the data in

Table I for analysis in Momentum, say, from 3 to 5.5 GHz and

from 5.5 to 8 GHz. Over these bands, the dielectric-constant

variation will be no more than 0.06, approximately 1(1/2)%.

For those designers who want to interpolate the Momentum

data in Table I, we have generated a third-order fit

is the frequency in gigahertz.

(3)

It is important to keep in mind that (2) and (3) and the data in

TableImaynotbevalidforFR4producedbyvendorsotherthan

NELCO. New data should be measured.

IV. VALIDATION CIRCUIT

To confirm the accuracy of our dielectric-constant data, we

designed a microstrip two-stub reject filter on FR4. This filter

was designed to pass the band at 5.7–5.9 GHz while rejecting

signals at 3.3 and 11.5 GHz. The design was optimized with

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3130 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 7, JULY 2006

Fig. 5. Microstrip two-stub reject filter for validating the measured dielectric

constant of FR4. All dimensions are in inches. Substrate: NELCO 14-mil FR4.

Fig. 6. Microstrip reject filter—comparison of measured and predicted (Mo-

mentum) rejection, return loss, and insertion loss.

ADS’s circuit simulator using (2) for the dielectric constant. It

wasthenfurtheradjustedwithMomentum,using(3).Thelayout

of the filter is shown in Fig. 5.

We fabricated the filter along with TRL calibration standards

covering the 2–12-GHz frequency range. With these standards,

we deembedded our Wiltron test fixture’s coax-to-microstrip

transitions and microstrip lines up to the input and output ports

of the filter. As shown in Fig. 6, the measured insertion loss and

return loss are within 1% of the performance predicted by Mo-

mentum.

V. CONCLUSION

FR4’s known variability is best managed with a circuit-board

process control monitor. The efficient shape and noncritical test

conditionsofourparallel-coupledresonatormake itagoodcan-

didate. Its insertion response can be an important part of a spec-

ification provided to a circuit-board vendor. These resonators

can be placed on the edge of or between the circuits on a stan-

dardpanel.Afterthepanelhasbeenprocessed,onecanmeasure

the frequency response of the filter to determine if the dielec-

tric constant of the substrate is sufficiently close to the desired

value by comparing the frequencies of the transmission zeroes

with the specification. The verification test can be used to de-

cide whether or not to separate and assemble the production

circuit-boards, which may include costly surface-mount com-

ponents.

REFERENCES

[1] J. R. Aguilar, M. Beadle, P. T. Thompson, and M. W. Shelley, “The

microwave and RF characteristics of FR4 substrates,” in IEE Low Cost

Antenna Technol. Colloq., Feb. 1998, vol. 24, pp. 2/1–2/6.

[2] N. K. Das, S. M. Voda, and D. M. Pozar, “Two methods for the mea-

surementofsubstratedielectricconstant,”IEEETrans.Microw.Theory

Tech., vol. MTT-35, no. 7, pp. 636–642, Jul. 1987.

[3] M.-Q. Lee and S. Nam, “An accurate broadband measurement of sub-

strate dielectric constant,” IEEE Microw. Guided Wave Lett, vol. 6, no.

4, pp. 168–170, Apr. 1996.

[4] D. Shimin, “A new method for measuring dielectric constant using the

resonant frequency of a patch antenna,” IEEE Trans. Microw. Theory

Tech., vol. MTT-34, no. 9, pp. 923–931, Sep. 1986.

[5] Y. K. Verma and A. K. Verma, “Accurate determination of dielectric

constant of substrate materials using modified Wolff model,” in IEEE

MTT-S Int. Microw. Symp. Dig., Jun. 2000, vol. 3, pp. 1843–1846.

[6] H.G.AkhavanandD.Mirshekar-Syahkal, “Slotantennasformeasure-

mentofpropertiesofdielectricsatmicrowavefrequencies,”inIEENat.

Antennas Propag. Conf. Dig., 1999, pp. 8–11.

[7] P. A. Bernard and J. M. Gautray, “Measurement of dielectric constant

using a microstrip ring resonator,” IEEE Trans. Microw. Theory Tech.,

vol. 39, no. 3, pp. 592–595, Mar. 1991.

[8] Y. Kantor, “Dielectric constant measurements using printed circuit

techniques at microwave frequencies,” in 9th Electrotech. Conf. Dig.,

May 1998, vol. 1, pp. 101–105.

[9] H. Yue, K. L. Virga, and J. L. Prince, “Dielectric constant and loss

tangent measurement using a stripline fixture,” IEEE Trans. Compon.,

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[10] S.GruszczynskiandM.Zaradny,“Asimpleresonancemethodofmea-

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NewYork:Wiley,

Eric L. Holzman (S’86–M’89–SM’95) received the

B.S., M.S., and Ph.D. degrees from the University of

California at Los Angeles (UCLA), in 1984, 1987,

and 1989, respectively, all in electrical engineering.

In 2004, he joined Northrop Grumman Electronic

Systems, Baltimore, MD, as a Consulting Engineer

with the Advanced RF Product Technology Depart-

ment. His research involves design and analysis of

active arrays and other antennas operating from UHF

to millimeter-wave frequencies. From 1999 to 2004,

hewasaSeniorMicrowaveEngineerwithYDIWire-

less, South Deerfield, MA, where he designed antennas and transceiver cir-

cuits for a variety of fixed wireless applications. From 1993 to 1999, he was

a Principal Engineer and Manager with Lockheed Martin Government Elec-

tronic Systems, where he was involved in the design of advanced, solid-state

phased arrays. He began his career designing power oscillators, low-noise am-

plifiersandantennasfortheHughesMissileSystemsCompany.Hehasauthored

approximately 35 publications. He authored Essentials of RF and Microwave

Grounding (Artech House, 2006) and Solid-State Microwave Power Oscillator

Design (Artech House, 1992). He holds seven patents in the microwave field.

He is listed in Who’s Who in Young America (1992).

Dr. Holzman a member of Tau Beta Pi and Eta Kappa Nu. He is a reviewer

for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He

is past chairman of the Philadelphia Chapter of the IEEE Antennas and Prop-

agation (AP)/Microwave Theory and Techniques (MTT) societies. He was a

member of the Organizing Committee for the Benjamin Franklin Symposium

(1995–1997). He was the recipient of the 1997 Lockheed Martin Engineer of

the Year award for his research on antennas and transmit/receive modules. He

is a former Howard Hughes Fellow.