Comprehensive Information of Dielectric Constants for Circuit Design using Rogers High Frequency Materials

Transcription

1 Comprehensive Information of Dielectric Constants for Circuit Design using Rogers High Frequency Materials Abstract The text is an extension of a paper titled General Information of Dielectric Constants for Circuit Design using Rogers High Frequency Materials. The paper will expand on the same information given in that text, with added engineering rigor for the various topics. This text is intended to promote better understanding of the Specification Dk and the Design Dk as shown on the Rogers Corporation datasheets and Product Selector Guide. Several common test methods will be discussed and their capabilities and limits outlined. Attention will be given to the apparent Dk determined by circuit performance with regards to some material interactions. A testing scheme which has been adopted to define the Design Dk, which is the dielectric constant suggested for circuit design and modeling, will be summarized with results. Lastly the Design Dk values will be given for the various Rogers high frequency materials. Introduction There are a multitude of different test methods that can be used to determine a Dk value for a laminate. Each of these test methods has their own set of limits and capabilities. In general a test method is used to characterize a material, but not necessarily to characterize the material for a particular application. The X-band clamped stripline test will give results of Dk and Df (dissipation factor) for a material under test. These results may or may not correlate well to the same material used in a microstrip application, as an example, where the electromagnetic environment of the circuit performance is very different from the stripline test. The X-band stripline test has been proven very repeatable for quality control of high frequency laminates, however it has limits, as do all test methods. Some limits mentioned in the test method document itself are noted here: Test method IPC-TM c 1.3 Limitation: The following limitations in the method should be noted. 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 fabricator boards The measured effective permittivity for the resonator element can differ from that observed in an application. Where the application is in stripline and the line width to ground plane spacing is less than that of the resonator element in the test, the application will exhibit a greater component of the electric field in the X, Y plane. Heterogeneous dielectric composites are anisotropic to some degree, resulting in a higher observed K for narrower lines. Microstrip lines in an application may also differ from the test in the fraction of substrate electric field component in the X, Y plane.

2 Bonded stripline assemblies have air excluded between boards, thus tend to show greater K values. Other test methods that will be discussed are the Full Sheet Resonator (FSR), Split Post Dielectric Resonator (SPDR) and differential phase length method. Industry standard test methods used to determine Dk As previously mentioned the X-band clamped stripline resonator test is used most often for the specification Dk or the Processing Dk of a high frequency circuit material. A simple graphic representation of this test method is given in figure 1. Resonator element gap coupled area Top view of resonator (circuit) card Stripline resonator Stripline resonator Side view of resonator card clamped into test fixture Figure 1. X-band clamped stripline resonator test showing dielectric material under test The dielectric material under test is sandwiched between two clamping plates that are held under pressure. These plates act as the ground planes for the clamped stripline structure. The resonator circuit is relatively thin, designed to be loosely coupled (gap coupled) and the element is 2 wavelengths, in physical length, at 10GHz for a particular material. The electric fringing fields in the gap coupled area are where the concern for X-Y plane anisotropy can be an issue. There is also the concern for accuracy due to entrapped air with this test method.

3 A broadband look at several resonant peaks can be seen in figure 2. Figure 2. Example of a typical broadband response for the clamped stripline test. In Figure 2 the markers labeled 1 through 6 are shown at the various resonant peak nodes. By the nature of this test method, the fixture, connectors used and cabling, the resonant peak nodes that can be measured accurately are 1 through 5 which typically translates to approximately peaks at 2.5 GHz through 12.5 GHz respectively with 2.5 GHz spacing between nodes. The following formula is used to determine the dielectric constant for this test method. Where n is the resonant peak node, c is the speed of light, f r is the center frequency for the resonant peak, L is the physical length of the resonator element and ΔL is the added length of the resonator element due to E-field fringing effects in the gap coupled area. The ΔL variable can be an issue regarding accuracy of determining dielectric constant. The fringing can vary with the overall ground-to-ground thickness, the dielectric constant and anisotropic effects of the material under test. The ΔL value for a particular material test set up is determined one of two ways. One way is by empirical means of measuring resonators of varying lengths and gaps and

4 determining the optimum ΔL value [1]. The other method is given in [2] by assuming a proportionality to the published prediction in [1]. The significance of the accuracy of the ΔL value is lessened for testing of lower Dk materials, where the resonator element is longer. The high Dk materials, such as materials with a Dk of approximately 10, which will use a shorter resonator element, will cause the ΔL value to be more important. When considering gap coupling of a stripline resonator there are generally three categories of interest; Overcoupled, critically coupled and undercoupled. With many resonator designs the critically coupled design is desired to where the unloaded Q and the loaded Q are matched and maximum energy is achieved at the resonant peak. In the case of this stripline test it is desired to have the gap coupled stripline resonator to be undercoupled (loosely coupled) in order for the test procedure to detect the Q of the material and not the Q of the circuit image. A value for the loss tangent (dissipation factor) of the substrate is obtained by subtracting the appropriate conductor loss value, 1/Q c from the total loss value 1/Q. The total loss is obtained from the resonant peak measurement of the 3 db frequency bandwidth. f 1 is the 3 db frequency down from the resonant center frequency (f r ) which is lower in frequency. f 2 is the 3 db frequency down from f r on the high side of the center frequency. f 1 and f 2 are noted as markers 2 and 3 in figure 3, respectively. Marker 4 is f r. Figure 3. Node 4 testing of a sample in the clamped stripline resonator test

5 α c is the attenuation constant and c is the speed of light. Another concern with this method is how well the material under test will conform to the resonator circuit image. The copper circuit image on the resonator circuit has some height above the substrate. If the material under test is very rigid, the material will not conform around the resonator circuit features well and more entrapped air will cause the Dk value to differ. A very soft material, as is the case for most of the Rogers PTFE substrates, conforms quite well to the circuit image with minimal amount of entrapped air. Copper surface roughness also has an effect on the issue of potential entrapped air in the stripline test. Initially, the material under test had been a copper clad laminate and just prior to this test all of the copper was etched off. The mirror image of the copper surface roughness is now the substrate surface roughness. When a copper is used to make the laminate which has a rough surface this will translate to more surface area for the material under test. More surface area has the potential to have more entrapped air which can lower the reported Dk value. A worse case scenario for this consideration is a very rigid substrate that will not conform to the resonator circuit well and has used a very rough copper. This is the case for some of the materials in the Rogers RO4000 family of circuit materials. A paper has been written specifically about the Design Dk of the RO4000 circuit materials [1] where the stripline and other tests are considered. Another test method that is often used is IPC-TM Full Sheet Resonance test. This method does not have the issue of entrapped air or sensitivity to anisotropic material properties, as does the stripline test. This method uses the copper clad laminate as a parallel plate waveguide and determines the dielectric constant from resonant peaks established by standing waves corresponding to the physical size of the laminate. These standing waves typically occur at low frequencies due to the size of the panel under test. Therefore the FSR test is usually considered a low frequency test, which evaluates the Dk properties of the laminate in the Z axis (thickness axis) only. A graphic representation of this test method is shown in figure 4.

6 Figure 4. copper clad laminate under test using the FSR test method The FSR test method is a quick, non-destructive test method which gives relatively accurate Dk results. Some limitations of this test are that the Dk results are given for low frequency only and thin laminates are more difficult to get valid data. The frequency of the test is determined by the size of the panel and is typically less than 1 GHz. A thin laminate will naturally have the copper edges closer together which can alter the coupling; however a bigger concern for accuracy would be the risk of copper stringers bridging the two copper layers. Also minor dents, scratches or handling damage in the signal launch area can alter the FSR results. A screenshot of a panel under test using the FSR method is shown in figure 5.

7 Figure 5. Screenshot of a panel under test using the FSR test method In Figure 5 the nodes are the resonant peaks that will be used for measurement. These nodes are noted by the ½ wavelength designators for the length and width axes. For example, node 2,1 would state that the peak is 2 ½ wavelengths in the length axis and 1 ½ wavelength in the width axis. The dominate mode for this structure is TE δ10 or node 1,0. The panel with the node information shown in Figure 5 has two clearly defined peaks at frequencies where only standing waves will occur in the length axis. The panel is rectangular in shape and in this case the length is 1.5X as long as the width. Beyond a certain frequency there is a possibility of standing waves in both the length and width axes. In this range of frequency there can be distortion of the resonant peaks due to wave interference patterns and these peaks are typically not measured for determining Dk. The formula used to determine the Dk of a material in the FSR test is shown below. m and n are the integer node designators in the length and width axis respectively. L and W are the physical length and width measurements. f r is the center frequency of the resonant peak and c is the speed of light.

8 Other common test methods used to determine Dk The split post dielectric resonator (SPDR) test has been becoming more popular recently. This test method is a quick test with minimal potential for human errors. By the nature of this test, it will only determine the Dk of the material under test within the X-Y plane of the material. There has been some work that would suggest the combination of the FSR test (Z axis Dk) and the SPDR test can give some indication as to the anisotropy properties of a material. The SPDR method is very sensitive to the thickness measurement of the sample under test and because of that, the Dk measurement is only as good as the thickness measurement. A cross-sectional view of the SPDR is given in figure 3. Figure 3. Cross-sectional view of the SPDR fixture and material under test. The SPDR fixtures are designed to have a resonant peak at a specific frequency. The distance between the dielectric resonators help to establish the resonant peak and accordingly the thickness of the sample under test is limited. In general as SPDR fixtures are designed for higher frequencies, the sample must be thinner. A SPDR fixture with a resonant peak at 20 GHz will only test a substrate that is or thinner. More information regarding SPDR can be found from an application note detailing this technology [2]. The SPDR will test the material for X-Y plane Dk values only. There is another test methodology that has been recently introduced which will test the Dk values in the Z axis as well as the X-Y plane of the circuit material. This test uses a microstrip circuit with an edge couple resonator called a RA Resonator [3]. This test methodology appears to be very accurate; however at this point in its development it is a very time consuming test method. There have been several different waveguide and resonant cavity tests developed for determining Dk of circuit materials. Each of these test schemes has their own set of

9 capabilities and limits. In general the waveguide and resonant cavity tests are typically more time consuming and requires more sophisticated engineering knowledge for these test methods. A well defined cylindrical cavity method was developed to determine Dk for circuit materials over a wide range of frequencies by Damaskos Inc [4]. Microstrip circuits are the most common circuit construction currently used in microwave applications. Because of this, there have been many test methods developed for determining Dk of the circuit material for a variety of microstrip circuits. One common circuit used for material characterization is the microstrip ring resonator [5]. This type of circuit has several advantages, where a very clear resonant peak can be achieved and an accurate Dk number calculated. However, the disadvantages would be that the resonant peaks are at very specific frequencies and not over a range of frequencies and the coupling to the resonator can alter the Dk value. Ideally a loosely coupled ring resonator will allow the Q factor of the material to be realized and not necessarily the Q of the copper circuit. There are tradeoffs with the coupling [6] for a ring resonator; tightly coupled ring resonators can cause an error in the reported Dk value and too loosely coupled can yield a distorted peak which also can give error to the Dk value. A microstrip test method that has been widely adapted and offers several benefits over other methods is the differential phase length method [7]. Basically two microstrip transmission lines of significantly different length are fabricated using the same material and the same signal launch (reusable connectors or fixture). The circuits are tested on a network analyzer and the phase response of each circuit is measured. The microstrip phase response formula will yield an effective Dk from these measurements and the Dk of the material is back calculated using the well proven Hammerstad and Jenson [8] methods or other microstrip calculators. Besides the benefit of using the most common microwave circuit, this method offers the significant benefit of reporting the Dk over a very wide range of frequencies and not at specific frequencies such as a resonator circuit. An example of the microstrip differential phase length method is shown in figure 4.

10 Figure 4. Example of microstrip differential phase length test results. Material and circuit performance interactions that can alter apparent Dk There are some scenarios where the nature of the circuit design can cause one to assume a different Dk of a circuit material than would be expected. Most laminates used in the PCB industry are anisotropic, so the Dk value for the Z axis is different than the X-Y plane values. An example: if the exact same laminate is used to fabricate and evaluate circuits of a microstrip transmission line and an edge coupled filter, the evaluation will likely yield a different Dk value for the same material. The reason is due to how the electromagnetic fields of these circuits utilize the Dk properties of the laminate. The microstrip transmission line will use the Z axis Dk properties mostly and the edge coupled filter will use some of the Z axis properties too, however it will certainly use some of the X-Y plane properties as well. Since most PCB laminates are anisotropic the filter will probably realize a different overall Dk value than the transmission line. A simple comparison is shown in figure 5.

11 Figure 5. Microstrip transmission line and filter segment showing E-fields (red) and how the different circuits use the same material differently. Something that could make this example even more dramatic would be if the filter circuit was aligned to where the E-fields were also in the glass layer (blue in figure 5). The Dk of the glass in the laminate may be significantly different than the Dk of the resin areas of the laminate. By the nature of different edge coupled filter designs, some will utilize the X-Y properties more than other filters. This could cause some filters to report a different Dk value than another filter design when built on the exact same material. The effects of different circuit design and how it corresponds to the apparent Dk was also discussed in a recently presented paper [9]. Recently, it has been found that the copper surface roughness can have an effect on the Dk value of a laminate. This is more pronounced with thinner laminates where the effects of copper roughness become more dominate. Figure 6 shows an exert from a paper [10] which discusses this phenomenon in greater detail. In this figure, it can be seen that the Dk value will increase with an increase in copper surface roughness. This experiment used the same homogeneous substrate with the only difference being the copper.

12 Figure 6. Dk vs. frequency, with varying copper roughnesses while using the same substrate. Roughness is given as microns RMS. In previous years it was known that when evaluating the same material at different thicknesses in the FSR test, a different Dk value would be reported. At one time this difference was believed to be due to a difference in coupling which was affected by the different laminate thickness. However, with the recent insight of how copper roughness affects the Dk value, it is now obvious that the thickness dependency of Dk in the FSR test is actually due to the copper effects becoming more dominate as the laminate gets thinner and thus the copper roughness having more effect on the Dk value. The laminate thickness and copper roughness affect upon Dk is also compounded by another variable and that is frequency. It was found in microstrip transmission line testing over a wide frequency range, the reported Dk value of a particular laminate did not correspond well with the FSR measurement. However, when the FSR test was forced to a higher frequency and more closely matching the microstrip test, the Dk numbers converged to the microstrip Dk numbers. Test method defined for Design Dk In an effort to establish a good test method for the suggested Dk of microwave circuit design and modeling, Rogers Corporation evaluated many different test methods. When considering the vast diversity of microwave and millimeter wave circuit designs and how these designs interact with the material, it became obvious that a generalization had to be made. Rogers decided to use a test vehicle that was the most common high frequency circuit, which is a microstrip transmission line. The electric fields in this circuit primarily utilize the Z axis of the material and the desired test method should also be capable of testing over a wide range of frequencies.

13 Considering a summary of some of the test methods discussed; the FSR test method has several benefits and does not have the entrapped air and anisotropic issue associated with the clamped stripline resonator test. However, FSR is limited to lower frequency and this makes the test less sensitive to the copper roughness issue, due to skin effects being less significant at low frequencies. The SPDR test has good capabilities, however it tests the material in the X-Y plane only and it will test at very specific frequencies for the resonant peaks and not over a wide range of frequencies. The test method that was determined to be most appropriate for circuit design and modeling (Design Dk) is a differential phase length method using microstrip transmission lines of different lengths. This method uses the common microstrip transmission line circuit, capable of testing over a wide range of frequencies, is primarily evaluating the Z axis of the material and there is minimal effects due to anisotropic behavior. Supplemental information Some PTFE materials with higher Dk values (approximately 10 or more) can have other issues to consider when regarding testing and Design Dk. Please refer to the Rogers Corporation paper titled Design Dielectric Constant for RT/duroid LM and RO3010 TM High Frequency Circuit Materials for more details. This paper can be found at Conclusion The industry standard IPC test methods are very good for testing the raw circuit material. However, the numbers reported for Dk may or may not correlate well to an actual circuit application. There are numerous other test methods and each of these has their own set of capabilities and limits. Also, by the nature of some circuit designs, the circuit can utilize the material in such a way as to cause the apparent Dk to be other than what would be expected. Rogers Corporation s High Frequency Circuit Materials are used in an extreme amount of different microwave applications. In order to give a Dk number which is appropriate for a microwave circuit design and modeling, some assumptions had to be made. It was determined that actual circuits should be used as part of the testing methodology. The microstrip transmission line circuit is the most common microwave circuit used in the PCB industry and it seemed appropriate to use this construction as part of the testing procedure. The microstrip differential phase length test methodology has been employed for years and is capable of determining accurate Dk values of the circuit material over a very wide range of frequencies. It is this test method which Rogers Corporation has adopted to determine the suggested Dk values for RF circuit design and modeling. The following tables of information are the Dk values for various Rogers High Frequency Circuit Materials when tested using many of the mentioned test methods. Also, the suggested Dk value for circuit design and modeling (Design Dk) of many Rogers laminates are given as well.

14 Testing Results X-band Clamped Stripline resonator (Processing Dk): Table 1. Random sampling of materials using the X-band clamped stripline resonator test. The Specification Dk uses this test method and is typically done at 10GHz.

15 Full Sheet Resonator (FSR) test results: Table 2. FSR test results of random sampling of materials with varying material thickness. The Dk numbers for the RO4400 TM prepregs is an average of 2 and 3 ply constructions.

16 Differential Phase Length Test method results (Design Dk):

17 Table 3. Random sampling of materials with different thickness. These are the suggested Dk values for RF circuit design and modeling. Estimated anisotropic effects of some laminates, from FSR and SPDR test comparisons Table 4. FSR and SPDR Dk test results that may suggest some anisotropic effects of the selected laminates. The FSR and SPDR tests were done at different frequencies and there are other differences as well, so this should be viewed as an approximate estimated behavior of the materials.

18 [1] Stripline Test for Permittivity and Loss Tangent (Dielectric Constant and Dissipation Factor) at X-Band, IPC-TM Revision C, March [2] Discontinuities in Center Conductor Strip Transmission Line, Altschuler, H. M. and Oliner, A. A IRE Transactions MTT 8, May 1960, p [1] Design Dielectric Constant for RO4003 TM and RO4350 TM High Frequency Circuit Substrates, John Reynolds, Pat Larrow, Al Horn, Rogers Corporation Technical Report No. 6006, March 2006, can be found at [2] Agilent Split Post Dielectric Resonators for Dielectric Measurements of Substrates, Application Note, [3] Measurement of Planar Substrate Uniaxial Anisotropy, James C. Rautio, IEEE Transactions on Microwave Theory and Techniques, Vol. 57, No. 10, October [4] Measuring dielectric constants of low loss materials using a broadband cavity technique, N.Damaskos & B. J. Kelsall, Microwave Journal, p. 140 September [5] Design of Ring Resonator Mode Spacing and Bandwidth using the Phase Response of Composite Right/Left Handed Transmission Lines, Catherine A. Allen, Kevin M.K.H Leong and Tatsuo Itoh, Department of Electrical Engineering, University of California at Los Angeles, 405 Hilgard Avenue, Los Angeles, CA , U.S. [6] Review of Different Ring Resonator Coupling Methods, Athanasios Vitas, Vassiliki Vita, George E. Chatzarakis, lambros Ekonomou, Proceedings of the 9 th WSEAS International Conference on Telecommunications and Informatics [7] Two Methods for the Measurement of Substrate Dielectric Constant, Nirod K. Das, Susanne M. Voda and David M. Pozar, IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-35, No. 7, July [8] Accurate models of microstrip computer aided design, E. Hammerstad and O. Jenson, 1980 MTT-S Int. Microwave symp. Dig. pp , May 1980 [9] Determining Dielectric Properties of High Frequency PCB Laminate Materials, John Coonrod, Rogers Corporation, APEX Expo, IPC 2010, April [10] Effect of conductor profile on the insertion loss, propagation constant, and dispersion in thin high frequency transmission lines, J.W. Reynolds, P.A. LaFrance, A.F. Horn III, Rogers Corporation and James C. Rautio Sonnet Software, DesignCon 2010, Feburary The world runs better with Rogers., the Rogers' logo, RT/duroid, RO3000, RO3003, RO3006, RO3010, RO3035, RO3203, RO3206, RO3210, RO3730, RO4000, RO4003C, RO4350B, LoPro, RO4360, RO4730,

19 RO4450B, RO4450F, RO4460, XT/duroid, ULTRALAM, RO4400 and TMM are licensed trademarks of Rogers Corporation The information in this presentation is intended to assist you in working with Rogers' High-Frequency Materials. It is not intended to and does not create any warranties, express or implied, including any warranty of merchantability or fitness for a particular purpose or that any results show in this presentation will be achieved by a user for a particular purpose. The user is responsible for determining the suitability of Rogers' High Frequency Materials for each application.