High Frequency Electronics

High Frequency Design

MICROWAVE MATERIALS

Understanding DielectricConstant for MicrowavePCB Materials

By John Coonrod and Allen F. Horn IIIRogers Corporation

One of the mostimportant proper-ties of a laminate

used in microwave PCBtechnology is the dielectricconstant, also known asrelative permittivity or εr.Many electrical engineer-ing courses teachingmicrowave technology will

use this property as a constant for a givenmaterial when discussing a PCB related topic.Because of that experience, some engineersare under the impression that the dielectricconstant (Dk) of a laminate is a fixed value forall microwave scenarios. In reality this is notthe case. The Dk value found on datasheets forlaminates is a number that was generated bya specific test method, which may or may notapply to a specific microwave application.

This article discusses several topics andbegins with the basic theory as to why the Dkvalue of a PCB material can vary for differentmicrowave scenarios. Some of the common testmethods used for determining the Dk ofmicrowave laminates will be explained aswell. Lastly, analogies will be given betweenthe various test methods and some generalmicrowave applications.

It is well known that the relative permit-tivity of free space is defined as a fixed num-ber of 1. In this case the relative permittivityvalue doesn’t depend on the applied electricfield (E), frequency or the field properties of anelectromagnetic wave in question. However,when a material is subjected to an electricfield, the field causes polarization of themolecules, which establish electric dipolemoments and augments the electric flux. This

reaction to the applied field is unique for amaterial and is dependent on frequency aswell as other electromagnetic properties. Freespace obviously will not react to the appliedfield in this manner. When a material is acomposite that is made up of several othermaterials, then the dipole moment reaction tothe applied field can be complicated. This isbecause each of the raw materials making upthe composite may form dipole moments dif-ferently with the applied electric field. Thematerials used in the PCB industry are typi-cally a composite, therefore their reaction toapplied electric fields may be more complexthan one would initially imagine. The basicequation which accounts for the material reac-tion to the applied electric field is:

D = εE

Where D is the electric field flux or dis-placement vector, E is the electric field inten-sity and ε is the permittivity. To be more spe-cific with the interaction of materials and theapplied electric field there is a polarizationvector (P) that is to be added to the formula.

D = ε0 E + P

In a linear medium, which most dielectricmaterials used in the PCB microwave indus-try are, the polarization is linear and relatedto the applied electric field by:

P = ε0 χ E

Where χ is the electric susceptibility, canbe complex and ε0 is the permittivity of freespace.

This article discusses howthe dielectric constant (Dk)

of microwave PCBs mayvary for different applica-

tions, and describes thetypical test methods usedin determining Dk values

for these materials

From July 2011 High Frequency ElectronicsCopyright © 2011 Summit Technical Media, LLC

July 2011

Expanding the definition of complex permittivity toinclude the effects of susceptibility and polarization:

D = ε0 E + P = ε0 (1 + χ) E = ε E

ε = ε' – jε" = ε0 (1 + χ)

ε' is the real value of the complex permittivity and isassociated with the Dk of the material, and ε" is the imag-inary part and related to material losses or dissipationfactor.

When the polarization vector (P) is in the same direc-tion as E, then the material is said to be isotropic. MostPCB materials are not isotropic (they are typicallyanisotropic) and there is usually a complicated relation-ship between P and E as well as D and E. An anisotropiclaminate is one in which the Dk in the z-axis (thickness)is different than the Dk in the x-y plane.

By the nature of how the material reacts to theapplied electric field, that will dictate how sensitive theDk value is with a change in frequency. It will also deter-mine the isotropic or anisotropic behavior of the material.Of course when the material is heated, the molecularstructure will change and this change combined with thepolarization properties of the material will have an influ-ence on the TCDk (thermal coefficient of Dk) of the mate-rial. All of these considerations are unique for a particu-lar microwave PCB material. When these considerationsare combined with the many different possible electro-magnetic field scenarios of microwave applications, itbecomes apparent why determining the proper Dk of aPCB material for a particular application is not trivial.

There is no shortage of test methods for determiningthe Dk value for microwave PCB materials. The mostcommon test method is the X-band clamped stripline res-onator. This test is typically done in accordance with anIPC test method, which details the test; IPC-TM-6502.5.5.5c and can be found at http://www.ipc.org. The test istailored to the needs of a laminate supplier where a largenumber of samples are tested on a daily basis. This test is

excellent for repeatability regarding the testing of rawlaminate, however, there are aspects of the test that arenot real-world for an actual microwave application. Thetest will essentially clamp two samples of the raw lami-nate on both sides of a resonator circuit and form aclamped stripline resonator as shown in Figure 1.

The material being tested was initially a copper cladlaminate, and the copper was etched off prior to the test.The mirror image of the copper treatment is the surfaceroughness of the samples and with the sample havingmore surface area that will relate to an increase inentrapped air in the clamped fixture. The addition of airin the sampling area of the fixture will cause the test tounder estimate the Dk value of the material being tested.This is one concern with this test method, which will notrelate to a “true” stripline circuit. Another issue with thistest is related to the loosely coupled stripline resonatorcircuit. The resonator is purposely designed to be looselycoupled, and in the gap coupled area there are strong Efields that are sensitive to the x-y plane properties of thematerial under test. This test is intended to determinethe Dk value of the material in the z-axis (thickness),however, if the material under test has a high degree ofanisotropy then the x-y properties detected in the gapcoupled area can alter the calculated Dk value.

Another test that is common in the microwave PCBlaminate industry is the Full Sheet Resonance (FSR) test.This test is also detailed on the IPC website and is testmethod IPC-TM-650 2.5.5.6. The FSR test uses the copperclad panel as an open walled parallel plate waveguide,establishes a standing wave, measures the resonant peakand determines the Dk value of the material. A graphicalrepresentation is shown in Figure 2.

The FSR test offers some advantage over the clampedstripline test. This test does not have the potential issuewith entrapped air and is not sensitive to the anisotropicnature of the material being tested. Another possible

Figure 1 · Drawing of clamped stripline resonator testfixture.

Figure 2 · Graphical representation of the FSR testmethod.

High Frequency Electronics

High Frequency Design

MICROWAVE MATERIALS

advantage is that this test can give the circuit fabricatora copper clad panel with its own distinct Dk value as com-pared to the sampling Dk value, which is necessary withthe destructive stripline test. The drawback for the FSRtest is that it is a low frequency test. Because the reso-nant peak of the standing wave being evaluated for Dk isrelated to the physical size of the panel by wavelength,this test is a low frequency test. The clamped striplinetest is typically done at 10 GHz where this test will gen-erally be less than 1 GHz. The low frequency Dk value canbe an issue for microwave applications using the materi-al at higher frequencies. It has been found [1] that thecopper roughness can have an effect on the Dk value of alaminate and the lower frequency testing of FSR does notfully capture these effects.

Another test that has gained much interest over theyears is the split post dielectric resonator (SPDR) test.This test is not currently defined per IPC, however, therehave been several application notes written [2]. TheSPDR test is a fast test with minimal operator influence.It uses a fixture that is a resonator tuned to a specific fre-quency. The empty resonator is measured first, then thesample is introduced into the resonator and the centerfrequency shift noted. The Dk is determined from the cen-ter frequency shift along with an accurate measurementof the sample thickness. A drawing of a typical SPDR fix-ture is shown in Figure 3.

The accuracy of this test is directly related to the accu-racy of the measurement of the sample thickness. TheSPDR test determines the Dk value for the sample undertest in the x-y plane only, and because of this it is some-times used in combination with other tests to understandthe anisotropy nature of a material. The SPDR test wouldbe used to understand the x-y plane Dk properties whileFSR or some other test that evaluates the z axis proper-ties is used. It should be understood when comparingSPDR to other tests, such as FSR, there are many differ-ences in these test methods so the comparisons for Dkdata related to anisotropic properties of a laminate

should be viewed as approximate only.There are many different types of

microwave applications. How the elec-tromagnetic fields for a particularapplication will use the microwavePCB laminate is important to considerwhen using a Dk value from a specifictest method. As it has been mentioned,some test methods will report the Dkvalue of a microwave laminate in thez-axis only, and other methods willreport x-y plane only.

Many microwave PCB applicationswill have E fields, which primarily usethe z-axis of the material. An example

may be a simple microstrip transmission line circuit. Ifthe circuit is used at relatively low frequency (less than 1GHz), then the Dk data generated from the FSR testshould be appropriate. If the circuit is used at higher fre-quencies, the stripline test may be of interest, however,knowing the material would be very important. If thematerial does not have a rough copper treatment and/ora high degree of anisotropy, then the stripline test may beappropriate. If the material uses rough copper and/or hasa high degree of anisotropy, then it should be understoodthat the clamped stripline test will report a lower Dkvalue than an actual circuit. In this case, it may be best touse Dk data from a microstrip differential phase lengthmethod [3]. This method uses microstrip circuits of twodifferent lengths and calculates the Dk value over a widerange of frequencies. An example of a microwave PCBlaminate using this test method is shown in Figure 4.

Some microwave PCB applications will have E fieldswhich are in the x-y plane only, however, this is unusual.For these applications, the Dk values of microwave mate-rials generated by the SPDR method would be appropri-ate. The SPDR fixtures can be made for testing at differ-

Figure 3 · Simple drawing of a typical SPDR test method fixture.

Figure 4 · Microstrip differential phase length methodfor determining Dk values.

ent frequencies, so the application fre-quency should match the SPDR dataas close as possible.

There are several applicationswhere the E fields are in the x-yplane as well as the z-axis. Most edgecoupled applications will fall in thiscategory, and this type of circuit is alittle more difficult to pick the appro-priate test method for the proper Dkvalue. Understanding the x-y planeDk value of the material is impor-tant, and in that regard, the SPDRtest data will be helpful. The z-axisDk is also important. As previouslymentioned, if it is a lower frequencythen a Dk value from the FSR testwould be appropriate, and if higherfrequency then the differential phaselength method results would be suit-able. The challenge with this applica-tion is that the overall Dk value to beused is a combination of the z-axisnumber and the x-y plane number.What ratio of which number to usewill vary by the nature of the circuit.An edge coupled circuit that is tightlycoupled will not use as much of the x-y properties of the material as a loose-ly coupled design. In this case, thebest scenario is to collect the Dk datafrom the appropriate test methodsand use a field solver that can accom-modate anisotropy in the design.

It has been a surprise to someengineers when they learn that a

particular microwave PCB laminatehas a Dk value that is different thanwhat is given on the datasheet. Thisoften comes after the engineer hasbuilt a circuit on a laminate, back cal-culated the Dk value from the circuitperformance and determined the dif-ference in the Dk value from the lam-inate datasheet. Understanding thedifferent test methods and how thefields are used in the test will helpthe engineer pick the Dk value fromthe test method that is most appro-priate to his circuit.

NoteRO3000™ and RO3003™ are

licensed trademarks of RogersCorporation.

References1. J. W. Reynolds, P. A. LaFrance,

J. C. Rautio, A. F. Horn III, “Effect ofconductor profile on the insertionloss, propagation constant, and dis-persion in thin high frequency trans-mission lines,” DesignCon 2010.

2. “Split Post DielectricResonators for Dielectric Measure-ments of Substrates,” AgilentApplication Note 5989-5384EN, July19, 2006.

3. Nirod K. Das, Susanne M. Voda,and David M. Pozar, “Two Methodsfor the Measurement of SubstrateDielectric Constant,” IEEE Trans-

actions on Microwave Theory andTechniques, Vol. MTT-35, No. 7, July1987.

Author InformationJohn Coonrod is a Market

Development Engineer for RogersCorporation, Advanced CircuitMaterials Division. About half of his23 years experience in the printedcircuit board industry was spent inthe flexible PCB industry doing cir-cuit design, applications, processingand materials engineering. The pastten years have been spent supportingcircuit fabrication, providing applica-tion support and conducting electri-cal characterization studies of highfrequency rigid printed circuit boardmaterials made by Rogers. John hasa BSEE degree from Arizona StateUniversity. He can be reached at:john.coonrod @rogerscorp.com

Allen F. Horn, III received aBSChE from Syracuse University in1979, and a Ph.D. in chemical engi-neering from M.I.T. in 1984. Prior tojoining the Rogers Corporation LurieR&D Center in 1987, he worked forDow Corning and ARCO Chemical.He is an inventor/co-inventor on 15issued US patents in the area ofceramic or mineral powder-filledpolymer composites for electronicapplications. He can be reached by e-mail at: al.horn@rogerscorp.com

July 2011