Understanding the Variables of Dielectric Constant for PCB Materials used at Microwave Frequencies

Understanding the Variables of Dielectric Constant for PCB Materials used at Microwave Frequencies John Coonrod Rogers Corporation Advanced Circuit Materials Division Chandler, Arizona, U.S.A. Abstract PCB (Printed Circuit Board) materials are used extensively in the microwave industry. Understanding the details of electrical properties for these materials can improve the designer s models and circuit performance. The r (relative permittivity or dielectric constant) for PCB laminates is often assumed to be a fixed value; however there are times this can be wrong and be a costly assumption. An r value of a laminate can vary with thickness or with the type of copper used. Some laminates can have issues with a higher or lower dielectric dispersion, which can cause the value to vary with frequency. Many designers are aware of the potential for PCB laminates to have anisotropic r values, which is often assumed to be attributed to the glass fiber reinforcement layer/s, however some PCB materials with no glass reinforcement are highly anisotropic. The details of the variables associated with r in many microwave PCB materials will be discussed and its supporting data will be given. The most common test methods which are used to characterize r of these materials will be examined along with their capabilities and limits. Finally guidance will be given for improved use of r values regarding common microwave PCB materials, which will enable the designer to have increased accuracy in models and circuit performance. Keywords dielectric constant, effective dielectric constant, design dielectric constant, PCB dielectric constant I. INTRODUCTION Microwave designers have a wide choice of tools these days for predicting the performance of circuits by software modeling techniques. These tools can help the designer optimize a circuit performance prior to having the actual circuit built. However, these tools are only as good as the input given, due to the many variables to be considered in microwave circuit analysis. The PCB (Printed Circuit Board) materials used in microwave circuitry have many attributes that are not, and sometimes can not be captured in electromagnetic modeling. The dielectric constant (or relative permittivity, r ) of a PCB material has several attributes that should be considered in the design stage and are often ignored until the actual circuit performance demands attention. Most times disregarding these subtle properties is unintentional and is founded on the lack of information or a misunderstanding of material interactions with microwave structures. There have been several cases where a microwave circuit is modeled properly, according to the datasheet properties of the material, only to find the actual circuit performs quite differently. Of course there can be many reasons for this, however when using the r from the material datasheet, it is important to understand that the value was determined by a very specific test method which may or may not correlate to the microwave application of interest. Also the r value was probably determined at a specific frequency and a certain substrate thickness. There are material attributes where the apparent r value can be dependant on the substrate thickness, the testing frequency, the type of copper used and the microwave structure. Anisotropic r properties of a laminate may be a concern as well and can cause the microwave circuit to perform different than modeled. The anisotropic effects of r for a PCB laminate is often assumed to be due to the glass reinforcement layers that are used within the substrate. This can be a valid concern, however there are other components of circuit material which can be as significant or more than the glass effect. It will be shown that when a laminate has a higher degree of anisotropic characteristics, where the r is higher within the surface plane of the laminate as compared to the thickness axis, coupled features may experience a very different value of r as compared to what the material datasheet would suggest. And when using that same material, a transmission line may experience the exact same r as suggested in the datasheet. So it is possible and it has been proven that two different microwave circuits using the exact same material will experience two different r values due to how the electromagnetic fields are using the different planes of the material. II. BASIC ELECTROMAGNETIC PROPERTIES OF PCB MATERIAL The interaction between PCB materials and electromagnetic fields can be described from Maxwells equations: D = ρ v (1.1) B = 0 (1.) X H = D/ t + J (1.3) X E = - B/ t (1.4) Where E is the electric field intensity, D is the electric displacement vector, ρ is charge density, B is magnetic flux density, H is the magnetic field strength and J is the current density vector. There are the following constitutive relationships to consider as well: PREPRESS PROOF FILE 1 CAUSAL PRODUCTIONS

(1.5) ) j - D = E = ( (1.6) ) jμ - μ B = μh = ( J = σe (1.7) Equations 1.1 to 1.7 indicate that the responses of the material due to the electromagnetic fields are determined basically by three constitutive parameters;, μ and σ. is complex, j permittivity of the material and is represented by = the complex permeability is μ = μ jμ and σ is the conductivity of the material. When an electric field is applied to a dielectric material, the field causes polarization of the atoms and molecules of the material to create electric dipole moments, which augment the total displacement flux, D. This effect is suggested in equation 1.5 where D is equated to the product of and E. The additional polarization is a vector P where the definition of D is expanded to: The imaginary part of complex permittivity is related to dielectric loss and is due to the damping of vibrating dipole moments. Microwave materials are typically specified using the real component of the permittivity which is: = r 0 (1.13) It is this real component of permittivity that is our main point of interest. The r value is the permittivity which is typically shown on material datasheets and more commonly referred to as dielectric constant is actually a multiplier of 0. When a material is specified to have an r value of 3.66 for example, then the actual real component of permittivity is 3.66 multiplied by 0 ; where 0 is the permittivity of free space and 0 = 8.854x10-1 F/m and in this example the real permittivity would be 3.41x10-11 F/m. The permittivity of a material is related by several physical interactions and is frequency dependent []. Figure 1 shows a typical behavior of permittivity as a function of frequency. D = 0 E + P (1.8) In a linear medium, which most dielectric materials used in the PCB microwave industry are, the polarization is linear and related to the applied electric field by: P = 0 χ E (1.9) Where χ is the electric susceptibility and can be complex. Expanding the definition of complex permittivity to include the effects of susceptibility and polarization: D = 0 E + P = 0 (1 + χ ) E = E (1.10) = j = 0 (1 + χ ) (1.11) Most dielectric materials used in the PCB microwave industry are paraelectric and the polarization of the material is linear. Paraelectric materials have polarizations that return to the original position when an external E field is removed. When the polarization vector (P) is in the same direction as E, then the material is said to be isotropic. Most PCB materials are not isotropic (they are typically anisotropic) and there is usually a complicated relationship between P and E as well as D and E. A commonly used general linear relationship between these vectors is a tensor [1] : Dx xx D = y yx Dz zx xy yy zy xz yz zz (1.1) Figure 1. Frequency dependency of a typical microwave PCB substrate []. Within the range of frequencies for microwave applications, the permittivity behavior is mainly attributed to dipolar moments and relaxation. The curve shown in figure 1 is regarding a hypothetical material since different dielectric materials will have different properties related to the dipole relaxation time. The relaxation time is the time it takes for an electric dipole moment to establish or relax due to the electric field variation with frequency. The materials used as substrates in the microwave PCB industry are classified as dielectrics where the permeability is very near unity and the conductivity is extremely low or acts as an excellent insulator. Due to this, the main focus here will be permittivity. III. EXAMPLE COMPARISON OF TWO DIFFERENT MICROWAVE CIRCUITS It has been found that there is a dependency on the apparent value of r of microwave PCB laminates and the interactions of the electromagnetic fields of a circuit design. When using the exact same material, two different microwave circuit designs can realize different values of r. For some materials the difference in apparent r is minimal and can be ignored;

however, in other materials, the differences can be significant. The reasons are typically related to anisotropic behavior of the laminate combined with the electromagnetic field patterns and directions for the microwave circuit design. Two simple examples will be given to demonstrate this potential issue. The first will be a microstrip transmission line and the second will be a microstrip edge coupled resonator. Both circuits will use the same microwave PCB substrate, which is a ceramic filled PTFE (polytetrafluoroethylene) substrate using 18 micron (1/oz) electro-deposited copper. This material has an r of 10. when tested according to a standard test method used in the microwave PCB industry, which is the X-Band Clamped Stripline Resonator test per IPC-TM-650.5.5.5 [3]. The microstrip transmission line is a simple structure with the dimensions and specifications shown in figure. Where ΔΦ is the differential phase angle and ΔL is the differential physical length of the transmission lines. Rearranging 1.15 to solve for effective r : ΔΦc eff = πfδl (1.16) After the effective r is found the r of the circuit substrate is back calculated with the given circuit dimensions, phase angle at the specific frequency with a computer routine using the well proven Hammerstad and Jenson [5] microstrip equations; an EM field solver software could be used as well. After this calculation, the frequency is incremented, phase angle measured and the calculation of r at that frequency is determined. This is done repetitively over a wide range of frequencies and the results are shown in figure 3. Figure 3. Microstrip transmission line differential phase length measurement for r. Figure. Microstrip transmission lines The test method that is used to determine the r is a differential length method where two microstrip transmission line circuits of significantly different lengths are evaluated [4]. This test method uses the microstrip transmission line phase response formula: Φ = πf eff c L (1.14) The two circuits are measured for a differential phase angle at a specific frequency and the differential physical lengths are considered as well. The phase response formula is modified accordingly: ΔΦ = πf c eff ΔL (1.15) The reason two microstrip transmission line circuits, using the same material at different lengths are employed for this test is the ability to eliminate the affects of the signal launch and isolate the results to the r of the circuit material only. This assumes the use of the same connectors and in this case it was.4mm end launch connectors [6]. These connectors were used due to the ability to accurately and consistently align the connector pins to the circuit conductors as well as excellent performance over broadband frequencies. The elimination, which in reality may just be a very significant minimization of the signal launch affects, are due to the cancelation of the reactance s and / or mismatches associated with the signal launches. It can be seen that the r (Dk) values for this substrate shown in figure 3 do not match the reported r value of 10. which is noted on the material datasheet. This is due to several issues and mostly due to the difference in the testing procedures. Later in this paper the details of several test methods will be discussed, however a quick comparison between the stripline test used for the r value found on the datasheet and the differential phase length test are shown in table I. 3

TABLE I COMPARISONS BETWEEN THE STANDARD IPC CLAMPED STRIPLINE RESONATOR TEST AND THE MICROSTRIP DIFFERENTIAL PHASE LENGTH TEST METHOD. The next circuit example to consider will use this same material in a different microwave circuit configuration and its performance will demonstrate another aspect to consider in circuit design. This circuit is a long edge coupled microstrip resonator called a RA Resonator with a unique and accurate test procedure. The real utility for the RA Resonator is the ability to accurately determine the r in the z axis (substrate thickness) and the x-y plane (width length). This is done using a specialized field solving technique and extracting the electrical characteristics of the circuit isolated to the axis or plane of interest. An excellent paper regarding this topic was presented at COMCAS 009 [7] and the interested reader should refer to this paper for more detailed information. Figure 4 shows the results of the RA Resonator test method using the same material previously mentioned in the microstrip differential phase length test. (SPDR) and it evaluates the r properties in the x-y plane of the material only. The SPDR testing of this same material yielded an r value of 1.1. IV. OVERVIEW OF COMMON MICROWAVE PCB MATERIAL ELECTRICAL CHARACTERIZATION TECHNIQUES There are two general categories of electrical testing procedures and they are resonant and non-resonant techniques. Resonant methods are used to get accurate knowledge of the dielectric properties at a single frequency or several discrete frequencies. Non-resonant methods are used to get a general understanding of the electromagnetic properties of the material over some frequency range. Resonant methods typically have higher accuracies and sensitivities than non-resonant methods and are more suitable for low-loss material characterization. These methods generally use resonant or resonant-perturbation methods. The resonant methods are based on the fact that the resonant frequency and quality factor are based on the materials permittivity, given the resonator dimensions are well known. This is used for low-loss material and assuming the material has a permeability of μ o. The resonant-perturbation methods are considering a resonator with given electromagnetic boundaries which are changed when a sample is introduced. When the change in the resonant frequency and the quality factor are noted, the properties of the sample can be determined. Non-resonant methods generally use impedance or wave propagation characteristics. Non-resonant methods mainly use transmission / reflection methods and analyze how the substrate alters the wave propagation properties. Figure 4. RA Resonator results where the Meas Erel Vert is the r in the z axis of the substrate (thickness) and the Meas Erel Horz is the x-y plane. The r results of the microstrip differential phase length method shown in figure 3 is the r values for the z axis of the substrate. It can be seen in figure 4 that r in the z axis (labeled Meas Erel Vert) compares well to the microstrip differential phase length. The two test procedures are different however yield relative similar results. Data from another test method that will be discussed in more detail agrees well with the x-y plane r values shown in figure 4. The other test method is the split post dielectric resonator The microstrip differential phase length method uses TEM (transverse electromagnetic) waves and is a non-resonant method. It assumes the circuits are performing as a transmission line. Transmission line characteristics are such that the physical length (L) of the circuit has to be comparable to the wavelength λ g ; where L/λ g 1. For this test method there are two microstrip transmission lines of two different lengths. In the case of the shorter circuit and at lower frequencies, it may not be performing as a transmission line where L/λ g is not 1 and at those frequencies the collected data is ignored when determining r. This test method will generally yield valid data above 8 GHz; however substrates with a high r value, will frequently yield data that is not as accurate. The industry standard IPC clamped stripline test previously mentioned is a good test method for testing raw substrates in large volume; which is what most material manufacturers will do for quality and process control. The test method is well understood and very repeatable, however, this method may not 4

be a good representation of an actual circuit due to some limits of the testing procedure. The outer plates of a clamping mechanism are acting as the stripline ground planes. In between these plates is a very thin circuit which has a gap coupled resonator pattern. The circuit pattern is typically designed to be wavelengths long at 10 GHz. The material to be tested will be a copper clad laminate with the copper etched completely off leaving the raw substrate. Two pieces of this substrate are put into the clamped stripline fixture; one piece between the resonator circuit and a ground plane in front and back. The testing scheme is shown in figure 5. and ΔL is the added length due to the fringing effects in the gap coupled areas. Another test method that is common for PCB microwave material characterization is the Full Sheet Resonance (FSR) method per IPC-TM-650.5.5.6 [3]. This test method is a resonant method. It is a non-destructive test, unlike the clamped stripline method that requires the sample to have the copper etched off. The FSR test uses the copper clad laminate as an open walled parallel plate waveguide. A graphical representation of this method is shown in figure 6. Figure 5. Graphic representation of the IPC X-Band Clamped Stripline Resonator test. One concern for this test method is the potential to have some amount of entrapped air during the testing. The entrapped air will cause the test to report a lower r than expected. If the substrate is a copper clad laminate with a high profile copper, there will be more entrapped air. This is due to etching off the copper prior to testing and the exposed substrate surface will have the mirror image of the copper surface roughness. A high profile copper will leave a sample with a rougher surface or more surface area, which will increase the amount of entrapped air. If the substrate is soft, such as PTFE substrates, the potential for entrapped air is lessened due to the material compressing while it s under pressure during the test. A rigid substrate with a rough surface will be the worse case scenario for entrapped air. Another concern for the stripline test is the gap coupling of the resonator. In the gap coupled areas, the fringing fields will increase the resonator length and that variable is difficult to accurately account for with materials that have some natural variation of r and thickness. Also in the gap coupled areas, the surface r properties can effect the resonant peak and therefore the r value. With materials that are more anisotropic, the effect of the surface r can be significant. The determination of r is found by: nc r = f0( L + ΔL) (1.17) Where n is the node, c is the speed of light in free space, f 0 is the resonant frequency, L is the physical length of the resonator Figure 6. Graphical representation of the FSR test method, showing a copper clad panel under test with established standing waves. Basically a standing wave/s is established within the laminate and the resonant peak measured. The r value is determined by: c m n r = + f0 L W (1.18) Where m is the node number in the length axis and n is the node number in the width axis. L is the length and W is the physical width of the copper clad panel under test. The FSR test does not have the limits of the clamped stripline test such as potential for entrapped air and the gap coupled concerns. The FSR also does not have any concern with anisotropic behaviors altering the results. This test will only evaluate the r of the substrate in the z axis. The limit to this test method is that due to the size of the panel under test, the testing frequency is relatively low. Typically copper clad panels are tested as 4 x18 and that size dictates a long wavelength which translates to a low frequency test. Depending on the r of the substrate, the resonant frequency is typically within the range of 100 to 300 MHz. The last test method being discussed here is the SPDR (Split Post Dielectric Resonator) test and this method has been quickly gaining popularity. This is also a resonant test method that has an advantage of being very fast with minimal human interface. To be specific, this method is a resonant perturbation method, where the empty resonant frequency is measured 5

initially, then the sample inserted and the resonant frequency measured again. The change in the resonant frequency is used to calculate the r value. A graphical representation of this test method is shown in figure 7. and is not a change in the intrinsic r property of the laminate. It has been proven that a laminate using a copper with a very smooth surface, will report a lower r value for thinner laminate constructions. The copper surface of interest here is the copper surface at the interface between the copper and the substrate. A rougher copper has been known to affect the conductor losses, however it also has an effect on the propagation constant and thereby effecting the apparent r value. Data collected using a homogeneous thin laminate and only varying the copper surface roughness is shown in figure 8. Figure 7. Graphical representation of the SPDR test procedure; cross-sectional view of the testing fixture. This method uses a circular polarized TE 01δ propagation mode with the reason being that the electric field is parallel to the different dielectric boundaries. In doing so, the dielectric boundary between the air gap and the sample under test has minimal impact on the calculation of the r value. The limit to this test is the accuracy of determining r is directly related to the accuracy of the thickness measurement of the sample. The sample needs to lay relatively flat and there is a thickness limit. Being a resonant test the r value obtained will be at one specific frequency. The Rayleigh-Ritz method is used to compute the resonant frequencies and the other related parameters of the SPDR. The r is found using the following [8] : 1 + f r = hf K 0 f s (, h) 0 s r (1.19) Where h is the sample thickness, f 0 is the empty SPDR resonant frequency, f S is the resonant frequency with the sample, K S is a function of the sample r and thickness which is specific to the individual SPDR fixture. V. OTHER MATERIAL PROPERTIES TO BE CONSIDERED WHICH IMPACT APPARENT DIELECTRIC CONSTANT VALUES It has been long known in the PCB material industry that the r value can be dependent on the substrate thickness for some materials. With certain substrates where the building blocks of the laminate were not well controlled, it was not a surprise to have varying r with different thicknesses. However, multiple experiments were ran and verified that a homogeneous material made at different thicknesses could show different r values with certain construction considerations. The test method used was representative of a real microwave circuit where the microstrip differential phase length method was used. Also the FSR test method has shown this same phenomenon where a different r value is reported when testing the exact same material with the only difference being the substrate thickness. The thickness dependency of r is not related to the substrate. For a microwave material where the building blocks of the laminate have well controlled r, the thickness dependency of r is based on the effects of the copper used to make the laminate Figure 8. Microstrip differential phase length testing showing copper roughness of the substrate has an effect on the effective r. Early in the investigation it was theorized that the effects of the copper roughness on r were due to an increased path length for wave propagation. This would have a slower phase velocity which is inversely related to the effective r of a microstrip and that seemed to make sense. However, the FSR test method which also shows the same trend of rougher copper yielding higher r values, does not have an effective r ; FSR is a parallel plate waveguide operating in a standing wave resonant mode. Figure 9 shows the results of FSR testing several different PCB copper clad laminates which were using the same dielectric material, using the same copper, however the substrate was different thicknesses. Figure 9. Center frequency variation of FSR test results for 4 microwave PCB copper clad laminates using the same nearly pure PTFE substrate, the same copper however the substrate thicknesses vary from 0.17mm to 3.175mm. In figure 9 the shift in the center frequency is inversely related to the r value. The center frequency of each laminate is color coded and can be seen in the upper right of the chart in figure 9. 6

An excellent paper that gives details of the effects of copper roughness on r as well as conductor losses was given at DesignCon 010 [9] and is suggested for the interested reader. VI. RECOMMENDED DIELECTRIC CONSTANT VALUES FOR CIRCUIT DEISGN USING MICROWAVE PCB MATERIALS It is recommended the microwave designer engage the supplier of the PCB materials early in the design stages, to better understand the r properties of the material being considered. Each material, test method and application has their own unique considerations. VII. CONCLUSION With the advance of CAD systems aiding the microwave designer to have improved circuit designs and more efficient performance, understanding the many aspects of the microwave PCB material r properties is critical. This paper has shown that the r value which is reported for a material can be dramatically different by the test methods which are used to determine the dielectric properties. Also some materials with higher anisotropic properties will need to be well understood in order to get optimum performance from the microwave circuit design. And lastly some material properties such as the copper roughness can have more affect on the circuit than just conductor losses, where a rougher copper surface can alter the r value and cause an apparent dependency of r on substrate thickness. Understanding the many aspects of electrical characterization of microwave PCB materials is essential for the microwave designer to optimize the performance of their designs. REFERENCES [1] David M. Pozar, Microwave Engineering, John Wiley & Sons, Inc. 005, pp. 9-11. [] L.F. Chen, C.K. Ong, C.P. Neo, V.V. Varadan and V.K. Varadan, Microwave Electronics, Measurement and Materials Characterization, John Wiley & Sons, Ltd 004 [3] IPC-TM-650 Standard Test Methods, http://www.ipc.org [4] Nirod K. Das, Susanne M. Voda and David M. Pozar, Two Methods for the Measurement of Substrate Dielectric Constant, IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-35, No. 7, July 1987. [5] E. Hammerstad and O. Jenson, Accurate models of microstrip computer aided design, 1980 MTT-S Int. Microwave Symp. Dig., May 1980, pp. 407-409. [6].4mm End Launch Connectors from Southwest Microwave, Inc.; Model: 149-0A-5, http://www.southwestmicrowave.com/ [7] James C. Rautio, Measurement of Uniaxial Anisotropy in Rogers RO3010 Substrate Material, COMCAS 009. [8] Agilent, Split Post Dielectric Resonators for Dielectric Measurements of Substrates, Agilent Application Note, 5989-5384EN, July 19, 006 [9] J.W. Reynolds, P.A. LaFrance, J.C. Rautio & A.F. Horn III, Effect of conductor profile on the insertion loss, propagation constant, and dispersion in thin high frequency transmission lines, DesignCon 010. 7