White Paper #4. Scaling Copper Interconnects. Main Contributors

Transcription

1 1 White Paper #4 Scaling Copper Interconnects Main Contributors Lionel Kimerlng, MIT George Celler, SOITEC/Rutgers Jeff Sinsky, Alcatel-Lucent Bill Bottoms, ITRS Terry Bowen, Tyco Electronics Rich Grzybowski, Corning Petre Popescu, AMD Madeleine Glick, Intel Tremont Miao, ADI WhitePaper#4, ScalingCopperinterconnects

2 2 DRAFT White Paper # 4 Scaling Copper Interconnects Executive Summary See Appendix A Introduction The Issue The issue addressed is the suitability of copper 1 vs optical technology as data transmission rates increase. More specifically, as data rates increase how does the distance for which copper can serve as the data transmission media decline before cost and capability favor switching to optical technology. The Demand Driver This tradeoff arises due to the ~40%+/yr growth in the amount of data transmitted over the world s telecommunications networks due to the internet. This growth rate is expected to continue for at least 5 years and probably longer. The data rate demand increase is being driven by two phenomena. The first is applications such as YouTube, Netflix, Video on Demand applications, etc. that require transmitting large video files. The second source of demand is from users for higher data rates to minimize the delay the user experiences between requesting info from the net and its appearance on the screen. Economic Impact Providing infrastructure to support this ever growing data rate demand is now seen as crucial to economic growth. Data transmission access rates are now viewed as basic infrastructure for a nation just as the number of miles of railroad and highway were in the 19 th and 20th century. In response, the US government has initiated a program through the Federal Communications Commission to increase broadband access to the country. Background 1 Theterm copper asusedthroughoutreferstotransmittingdataoveranelectricalconductoreventhoughthe conductorisoftenanothermaterialsuchasaluminum,analloy,oreven,atleastpotentially,atotallynew conductormaterialsuchascarbonnanotubesorgrapheme. WhitePaper#4, ScalingCopperinterconnects

3 3 Optical methods started replacing copper in long haul telecommunications in the late 70 s and now dominate that application at distances down to the metro (1 to 10 kilometers) application. Optical methods continue replacing copper at shorter and shorter distances with the leading edge of replacement now in specialized, high data rate applications at distances as short as 5 centimeters. As both the number of links and the data rate of links increases photonic technology becomes more attractive vs copper. Copper will Survive Photonic methods will not totally displace copper data transmission methods; the two will coexist indefinitely. Copper use will continue in applications where it is best by some criteria such as cost, bandwidth density 2 and power consumption. In addition, copper data transmission will continue improving just as the less mature photonic methods improve although copper methods are unlikely to improve at as great a rate as optical methods without some fundamental breakthrough. The tradeoffs of copper vs photonic data transmission are between data rate capability, distance, power consumption, cost, electromagnetic interference and, sometimes, physical size, ease of installation, maintainability, weight, availability and other properties in very specific applications. Copper No longer Viable in Long Haul Telecommunications Since optical methods are well established in long haul telecommunications applications, the issues is not whether copper is sustainable or not; copper no longer has a role. The issue is increasing the amount of data that can be sent through fiber, especially existing provisioned fiber plant, to minimize and delay incurring the cost of installing additional fiber. The solution is largely technical involving developing multiplexing, coding, modulation and integrated photonic chips at the lowest total cost. Focus on Distances Less than 1000 meters 2 Bandwidthdensityisthedataratedividedbyeither,a.,thecrosssectionofthemedia,suchasfiber,b.,thesize oftheconnectorforthemedia,c.,thecircuitboardfootprintofthedeviceor,d.,thelinearwidthofthemedia. Eachofthesedensitiescanbealimitingfactorinspecificapplications. WhitePaper#4, ScalingCopperinterconnects

4 4 Since optical methods have replaced copper in long haul communications and copper is no longer a sustainable solution this white paper will not address these applications but will concentrate on copper sustainability in distances less than 1,000 meters. 3 The Limits of a Channel Transmitting information through any communications channel, either copper or optical, is limited by a fundamental parameter called the channel capacity. Channel capacity is determined by the Shannon-Hartley Limit as described in detail in Appendix B. 4 The capacity, C, is where B = bandwidth in Hertz S= Signal power in any units N = Noise power in same units as S The energy required to increase the capacity of a channel scales linearly with bandwidth but only with the log 2 of the signal-to-noise ratio. Thus, less energy is required to increase capacity by increasing bandwidth than by increasing the signal to noise ratio. For example, raising the S/N ratio from 7 (where 7+1 has log 2 of 3) to 15 (where 15+1 has log 2 of 4) increases the capacity 33.3% from 3 bits/hz to 4 bits/hz but increases the energy by 8/7 or 114%. Conversely, keeping the S/N ratio of 7 and doubling the bandwidth requires 100% more energy and increases the capacity 100%. The amount of data that can be transmitted through most data transmission channels falls far short of the Shannon Limit. Implementing a channel to approach the Limit requires utilizing 3 Thecoppertofibertransitionoccurredfortelecommunicationsatthevalueofthebitratexdistancemetricof about10mb/sxkm;ifthesamecriteriahold,thecoppertoopticaltransitionshouldoccurat10gb/sfordistances ofonemeterand1tb/sforonecentimeter. 4 "Whenopticalfiberisdrivenwithhighenoughintensity,non lineareffectscausetheshannonchannelcapacity topeakatasignal to noiseratio(snr)of25to30dbat~9bits/symbol/hzfora500kmspan,virtually independentofdriverlevel( 5dBmisoptimal),androll overanddeclineathighersnr.forshorterdistances,this roll overpointincreases.seereference#1,page687,figure38,fordetailsofthisconclusion. WhitePaper#4, ScalingCopperinterconnects

5 5 signal processing techniques, such as equalization and coding, that can introduce latency, require more power, and increase cost. Thus those techniques are used only when necessary. In summary, the limit, C, applies to data transmission channels using any transmission method including copper and photonic methods. Data Transmission with Copper Energy Loss Phenomena Transmitting a data signal requires receiving transmitted energy. The sources and rate of loss of energy with distance determine how much data and how far data can be transmitted through a link. Copper conductors lose energy due to a variety of physical phenomena including: bulk electrical resistance the skin effect the loss tangent of nearby dielectrics electron scattering in small conductors radiation a few other phenomena such as scattering from rough edges and grain boundaries The major losses in the applications of interest are the first 3; bulk resistance, the skin effect and the loss tangent associated with dielectrics. The loss through radiation is typically not high, but the effect on other conductors of a related or nearby system manifest themselves as electromagnetic interference (EMI). That effect is often highly detrimental and important to minimize if it cannot be eliminated entirely. Skin Effect Loss The skin effect occurs at high frequencies and forces the current in a conductor to flow only near the surface with an effective depth called the skin depth. Higher conductivity materials have higher skin depth. In addition, the skin depth decreases with the inverse of the square root of the frequency of the signal. Thus, increasing the frequency by 4 X reduces the skin depth by ½. For example, in copper, the skin depth at 10 MHz is 21 microns while at 10 GHz the skin depth is 0.65 microns. WhitePaper#4, ScalingCopperinterconnects

6 6 The result is that as the signal frequency increases, the skin depth decreases forcing the current to flow is less cross sectional area increasing the electrical resistance and the energy loss per unit distance. The Tan delta Loss Tan delta loss in transmission lines takes place in the dielectric surrounding the conductors and is proportional to the signal frequency. Doubling the frequency doubles the loss. An important property of materials used as dielectrics and insulators for transmission lines is that they have low tan delta loss. Sum of the Skin Effect and Tan delta Losses At the frequencies of interest for copper data transmission with copper, the skin depth loss dominates at low frequencies and the tan delta loss dominates at high frequencies. The figure below illustrates the result. The figure shows the loss due to the skin effect and tan delta loss, and also the sum of the two, vs frequency for a 50 ohm microstrip transmission line in WhitePaper#4, ScalingCopperinterconnects Chartconceptandbasicdatafrom"SignalIntegritySimplified",EricBogatin2004,PrenticeHall,pg.380

7 7 an FR-4 circuit board. Thermal Noise as an Ultimate Limit for Copper Under ideal conditions, the Shannon Limit using copper is set by thermal noise, KTB 5, at the receiver. If S, the signal level in a link, drops to KTB, the Shannon limit is B x 1 or 1 bit per cycle of bandwidth. One example to illustrate the implications of the KTB limit is shown below. 5 KTBwhereKisBoltzmann sconstantof1.38x10 24 Joule/ o K,TistheabsolutetemperatureindegreesKelvinand BisthebandwidthinHertz. WhitePaper#4, ScalingCopperinterconnects

8 8 This example illustrates the distance at which the S/N ratio drops to 1 as a function of bandwidth. The copper transmission link in the example assumes skin depth 6 attenuation only of a value from the Bogatin chart data on page 5, namely a stripline with air dielectric. The example also assumes 20 mw of power (1 volt into 50 ohms), the Boltzman constant and a T of 290 K. The chart illustrates that the maximum distance 20 mw of power can transmit information before the S/N ratio drops to 1 depends on the Bandwidth of the signal. As the Bandwidth increases, the Noise power increases as KTB grows, so less Signal attenuation can occur before the S/N drops to 1. Thus, with the S/N at 1, the capacity, C, is ~ 1Gb/s over a distance of 30 meters and ~40Gb/s over ~4 meters over an idealized stripline structure. 6 Inthisexample,alllossesexcepttheunavoidableskindepthlossareassumedtobezero.Thuslossesfromtan delta,radiation,roughedges,grainboundaryscattering,etc.areallignored.whilethisisnevertrueinpractice, theselatterlossmechanismscanbelargelyeliminatedbydesignwhereasskindepthlosscannot. WhitePaper#4, ScalingCopperinterconnects

9 9 Interestingly, current, real systems 7 approach sending 40Gb/s a distance of ~1 meter vs this ~4 meters. The chart shows an absolute limit, C, of what is theoretically possible in copper for the conditions assumed. It illustrates that if the tan delta, radiation and other losses are eliminated by design and methods to extract data from a signal as low as KTB are implemented, in principal, copper can be utilized to transmit data ~ 4 X further (or at 16 X the data rate for the same distance) than current methods enable. Tolerable Energy Loss in Current Copper Data Transmission The chart on page 5 from Bogatin, shows that the total attenuation at 1GHz is ~7.0 db per meter and over 40 db per meter at 10GHz. In a typical data communication application, the attenuation budget is ~ 20 db. (This corresponds to injecting a 1 v signal into a channel and receiving 0.1 v.) Using the attenuation data above and 20 db budget, data can be sent 2.9 meters in FR-4 microstrip using a 1GHz carrier and ~0.5 meters with a 10GHz carrier. 90%+ of the loss is energy absorbed in the copper media. 8 Added circuitry can enhance the attenuation budget, of course, to 40 db or even 60 db. Allowing 40 db doubles the distance; 60 db triples the distance, etc. Increasing distance by adding circuitry is only cost effective to a point. The attenuation budget can only be increased until the signal to noise ratio at the receiving end decreases to a value compatible with the sophistication of the receiver. While the Shannon Limit shows that a very low S/N ratio can still be used to transmit data, implementing the necessary techniques is often not practical or cost effective. Thus, most data transmission through physical media, such as copper and optical fiber, utilizes an attenuation budget of ~ 20 to 40 db or less. 9 If we take the total attenuation from the chart above (Bogatin s Figure 9-19), assume the attenuation budget is 20 db and further assume transmitting 1 bit per Hertz, the table below results. 7 SeetheChartonpage17,particularlythegreentrianglesforbackplanes,circuitboardsasassumedinthe exampleabove,andflexcircuitry. 8 This90+%losscontrastswithopticaldatatransmissionwhereverylittleofthelossisattributabletoenergy absorbedinthefibermedia. 9 Wirelessisanexception,ofcourse,wheretheratioofpowertransmittedtopowerreceivedisoften100dbor higher. WhitePaper#4, ScalingCopperinterconnects

10 10 Multiple assumptions underlay the results in the table. Nonetheless, for the conditions assumed, the table gives an indication of the limits of copper as a data transmission medium in circuit boards. Limit of Copper In FR-4 Circuit Boards as a Data Transmission Media Frequency & data 1 bit/cycle Distance in meters for 20 db attenuation Distance X Bandwidth, Hz- Meters Energy per bit in pj/bit (1 volt into 50 ohms all cases) <100MHz Practically unlimited <1.5 x 10 9 > MHz 20/1.3 = ~ x GHz 20/6.7 = ~3 3.0 x GHz 20/40 = ~ x GHz 20/310= ~ x The 2 nd column from the right shows an increase in the product of Bandwidth X Distance as frequency increases. The relationship is not simple, however, and tends toward a constant at the higher frequencies where tan delta loses dominate. Thus, at very high frequencies, the distance x frequency is a constant for a given amount of attenuation. This seems to be a general approximation for copper data transmission. Copper Data Transmission Compensation For Power Loss and Distortion In addition to the frequency dependent power loss with distance discussed above, signals also experience frequency dispersion which further distorts the signal. If the power level drops too far, and noise in the receiver or, more likely, electromagnetic interference (EMI) from a nearby conductor/s, is high compared to the signal, the signal is lost in noise and cannot be recovered. Electronic techniques to at least partially compensate for the power loss, frequency dispersion, EMI and noise are available. While these techniques are sometimes highly effective, they are never 100% effective. Thus, copper is always limited in its data carrying capacity. The compensation techniques include pre-emphasis, encoding and decoding, shielding, echo cancellation, phase compensation, etc. Fortunately, the cost of silicon chips to perform the WhitePaper#4, ScalingCopperinterconnects

11 11 electronic signal processing is relatively low. 10 The chip itself, almost no matter how complex, is relatively inexpensive to fabricate. The bulk of the cost to add the chip is in testing the chip, providing board space, performing assembly, testing the final assembly, maintaining the functionality over the lifetime of the copper link, paying for the additional power to drive the chips and sometimes incurring increased latency. Overall, extensive and complex data processing can be performed to minimize distortions and power loss in copper to maximize the data rate through a channel. This capability is likely to lead to extensive and imaginative extensions of copper data transmission. Data Transmission with Photonics Multimode vs Single Mode Data can be transmitted through optical fiber using both multimode (MM) and single mode (SM) technology. MM utilizes a fiber that is usually 125 microns in diameter with a 50 or 62.5 micron inner core diameter. This core has an index of refraction that is higher than that of the outer cladding. SM fiber has the same outer diameter but utilizes a 5 micron diameter core The image 11 to the left illustrates graphically the multiple paths of light through a MM fiber including a ray, in yellow, that escapes because it strikes the cladding at too steep an angle to be totally internally reflected. The larger core diameter allows MM fiber to transmit light that bounces from side to side of the fiber as it travels along the fiber. The resulting variations in path length are called modes which result in dispersion as light travels down the fiber. The longer the fiber the greater is the dispersion or smearing in time of light. When information is transmitted by modulating the light intensity, too much dispersion causes the intensity variations to overlap so much that the modulation is lost and the signal cannot be recovered. A rule of thumb is that data can be transmitted with 10 Commercialchipstoperformthesefunctionsarewidelyavailablewithadditionalchipscontinuallyintroducedto addressevolvingneeds.developinganewchipofthistypetypicallycostsafewmilliondollarssoachievinglow partcostrequireshighvolumewhichimpliesthesaleofmultiplemillionsofchips.atlesservolumethecostwill behigherduetorecoveringthesedevelopmentcosts. 11 TheimagesoftheMMandSMfiberarefromhttp:// optictutorial. WhitePaper#4, ScalingCopperinterconnects

12 12 multimode fiber if the product of the data rate and distance is 1Gb/s x 1 km or less. Thus, MM is suitable for relatively short distances of less than 1 Kilometer. 12 Gb/s using SM technology. The small core of SM fiber allows only one path for the light that is straight down the middle. Thus, a SM fiber does not exhibit dispersion due to variations in path length as MM does 13. The result is that light can be transmitted 100 s of Kilometers at 10 s of The cost of the components that launch and retrieve light and of aligning these components for MM technology is lower than the cost for SM technology. This is largely due to the greater tolerances associated with the MM 50 to 62.5 micron core vs the SM 5 micron core. This cost difference makes MM technology the technology of choice IF, and it s a big IF, MM technology will support the data transmission application. When the data transmission capability of copper is no longer adequate in an application, the distance x data rate of MM technology is usually adequate to fill the immediate needs. SM technology could fill the need too, but at higher cost. Thus, in many of the applications where optical methods are being considered because copper is no longer sustainable, MM technology rather than SM technology, is chosen. For this reason this White Paper tends to focus on MM technology. Nevertheless, in the long run, MM technology will not be adequate to provide the data rate required in all applications. In those cases, SM technology can be utilized. 14 MultiMode and Single Mode Compared Multimode Single Mode Pros Cons Pros Cons 12 MMfiberislimitedindistanceforanotherreason,too;thelosspermeterishighcomparedtoSMfiber. 13 Singlemodeopticalsignalsdoexperiencedispersionbutforadifferentreason;variationinthevelocityof propagationwithwavelength.modulationofanopticalsignalintroduces sidebands ontheopticalcarrierwhich havewavelengthsthatvaryslightlyfromthatofthecarrier.sincetheindexofrefractionofglassissomewhat dependentonwavelength,themodulatedsignalundergoessomedispersion(smearing)overdistance. 14 AnothersituationwhereSMispreferredoverMMiswhenaverylargeamountofdatamustbetransmitted througharelativelysmallarea.smtechnologyenablesmuchhigherdataratespermm 2,forexample,thandoes MM.ThisresultsfromSM5micronsvs50micronmedia(core)plusSMmultiplexingofmanywavelengths. WhitePaper#4, ScalingCopperinterconnects

13 13 Large core minimizes the cost and complexity of terminating the fiber to launch and receive light Data transmission capacity is limited to distance data rate product of ~ 1Gb/s x 1 Km. Transmits light 100 s of kilometers at Gb/s data rates per wavelength. 5 micron core diameter requires sub micron tolerances in the optical chain that launches and receives light. Results in high termination costs. Low cost when many terminations are required vs single mode. Typically only one wavelength per fiber; multiplexing is not easily used. Able to transmit many wavelengths at once (100+) Complex technology required to multiplex and demultiplex multiple wavelengths. Can utilize low cost light sources such as LEDs and VCSELs. The large area detectors required have high capacitance so 10Gb/s and noise become issues. Single mode fiber is less expensive than multimode fiber. Single mode components are more expensive than multimode. Optical Fibers vs Optical Waveguides While the bulk of current applications of optical data transmission utilize optical fiber, waveguides with a square or rectangular cross section can also guide light. Waveguides built with a variety of technologies have been demonstrated that support both MM and SM technology. These media are of interest in applications where light is transmitted < 1 meter, often less than 1 cm. While optical fiber is the focus of this discussion vs copper, many of the points are relevant to waveguides and other optical transmission media. Photonic Data Transmission Energy Requirement An important issue in photonic data transmission is the amount of energy required to convert data between the electrical and optical domains. Currently, many products, such as Active Optical Cables (AOCs), that are on the market require about 10 milliwatts per Gbs, or 10pJ/bit, for these two conversions. (See Prior whitepaper from the MIT CTR). 15 Transmitting data through single mode fiber allows data to be transmitted 100 meters with 10pJ/bit of energy at data rates of 40Gbs with a 20 db loss budget. That budget must cover: 15 Weneedareferenceandtitleandmaybeweblink. WhitePaper#4, ScalingCopperinterconnects

14 14 o the electrical to optical conversion efficiency of the VCSEL or other light source o fiber launch losses (stripping of higher order modes) o losses in the fiber or other waveguide o detector inefficiency Among these loss sources, losses in the fiber are minimal after the launch losses in the first few meters of fiber are incurred. Single mode fiber has a loss of ~ 0.2 db/km, for example, and allows a reach (distance) of over 100 Kilometers. Typical MM Electrical and Optical Power Budgets The two tables below expand the comments above by illustrating typical electrical and optical power budgets for a MM link similar to Light Peak. Typical Electrical Power Budget for a MultiMode Optical Link Stage Convert data stream to a signal to drive the VCSEL Electrical power level into this stage of a MM link +20dbm or 100 mw 16 Comments A purely electrical loss. Depends on the application. Power to drive a VCSEL +16 dbm or ~ 11ma x 3.3 volts Simply voltage x current driving = 36 mw 17 VCSEL. Included in the above 100 mw. Photon to electron conversion in the photodetector. -11dbm 18 with an additional ~3 db conversion loss, so -14dbm of electrical output from the photodetector. -11dbm is a typical minimum optical input power to the photodetector. Photodetector conversion efficiency is typically 50%. 16 FromtheEnsphereSolutionsdatasheetfortheESI XVR10100chip 17 FromtheEnsphereSolutionsdatasheetfortheESI XVR10100chip 18 FromtheEnsphereSolutionsdatasheetfortheESI XVR10100chip. WhitePaper#4, ScalingCopperinterconnects

15 15 Amplify the photodetector electronic signal into a double ended data stream. ~+19 dbm or 70mw 19 Power consumption by the transimpedance amplifier (TIA) & output drivers. Power out of receiver. +2dbm 400 mv differential signal into 100 ohm at 10Gb/s 20 Total Electrical Power = 100 mw + 70 mw or +28dbm for a 10Gb/s link This does not include power to code or decode the data stream. Typical Optical Power Budget for an 850nm MultiMode Optical Link Stage Optical Power Level and Losses Comments VCSEL Optical power +4 dbm 21 Typical VCSEL Optical Power Output Loss between VCSEL and MM fiber < 1db Coupling loss due to mismatch of the VCSEL radiation pattern and fiber acceptance aperture. Launch Loss in MM <1 db Loss results from stripping higher order modes. Connector Loss 1.0 db Typical MM connector Loss. Attenuator Loss Variable In some cases, the VCSEL puts out too much power for optimum detection so power is reduced. Transmission loss ~0 db 3.5db/km 22. Loss within fiber. 19 FromtheEnsphereSolutionsdatasheetfortheESI XVR10100chip. 20 FromtheEnsphereSolutionsdatasheetfortheESI XVR10100chip. 21 InformationprovidedverballybyEnsphere. 22 PerTIA/EIAspecifications. WhitePaper#4, ScalingCopperinterconnects

16 16 Connector loss 1.0 db Typical MM loss. MM fiber to photodetector <1 db Coupling loss due to mismatch of the fiber radiation pattern and the detector aperture. Link Margin 6db Amount by which power can decline before the link does not function properly. Minimum Optical power into the photodetector. Total Optical Power budget -11dbm 23 15db Typical photodetector output. The input to a TIA. Difference between the VCSEL +4dbm output and -11dbm detector sensitivity. Optimizing Optical Power Link Energy Consumption To minimize optical data transmission power consumption, the system the technology is used in can be customized to achieve that end. Power can be reduced in the optical data transmission link by turning off not only the light source but the pre-processing chip functions and some post detection functions as well. The receiving photodetector bias and TIA can be turned off until their functionality is needed. At least one receiving channel, however, must be fully functional to detect a turn-on signal from the transmitting end and turn-on the other receivers. Including this power reduction capability depends on either designing the chips and software to achieve that function or incorporating commercially available power saving devices and software that do so. In many applications, additional power might be saved by designing the entire system assuming optical data transmission. Shannon Limit for Photonic Data Transmission A second important characteristic of photonic data transmission is the maximum amount of data that can be transmitted through an optical fiber. The fundamental limit is again the Shannon Limit 24, specifically, the capacity in bits per second is equal to the bandwidth times the log base 2 of 1 plus the power signal-to-noise ratio. The bandwidth of optical signals is ~290 TeraHertz (from 650 nm to 1610 nm). With a typical power 23 FromtheEnsphereSolutionsdatasheetfortheESI XVR10100chip. 24 SeeAppendixB. WhitePaper#4, ScalingCopperinterconnects

17 17 signal-to-noise ratio of 32 (which has a log base 2 of 5) gives a bandwidth multiplier of ~5 for a total theoretical Shannon Limit data capacity of ~1,450 terabits/second. Adding Quadrature Amplitude Modulation (QAM) and Polarization Multiplexing each double the capacity of a fiber to give 5,800 terabits/second. Achieving that result requires not only utilizing the entire optical band, but signal processing that is beyond the current state of the art. The capacity of optical data transmission channels is several orders of magnitude larger than is utilized by current technology. Current Practical Limit A more practical today maximum can be estimated based on current capabilities such as: maximum number of wavelengths sent through a single mode fiber; 160 maximum bandwidth of each wavelength with 2 polarizations; 100Gb/s Multiplying these to determine the data rate gives 160 x 100 Gb/s = 160 x or 16.0 Terabits/s per fiber. While this is far short of the Shannon Limit of ~ 5,800 Terabits/s, this is still very high compared to typical copper transmission lines and even typical optical links. Resulting Photonic Data Density This 16Tb/s capacity is available in a single mode fiber over long distances (>1Km) with a cross section of 125 microns x 125 microns or mm 2 giving a data transmission density of 839 Terabits/mm 2. This is far in excess of anything achievable with copper data transmission over even short (< 10mm) distances. These limits are applicable to all optical transmission media. They apply to waveguides built on silicon or quartz or glass, plastic optical fiber, as well as multimode and single mode fiber. The massive amount of capacity arises primarily from the high frequency of optical signals. Building hardware that operates at these frequencies to achieve this capacity requires complex technology, not only theoretically, but practically as well. Real World Experience The chart below is based on data and a graphical concept originally described by David Neilson, et al., of Alcatel-Lucent 25, with points added by Jeff Sinsky also of Alcatel-Lucent 25 D.T.Neilson,D.StiliadisandP.Bernasconi, Ultra highcapacityopticaliproutersforthenetworkoftomorrow: IRISProject,presentedattheEuropeanConferenceonOpticalCommunication(ECOC),Glasgow,UK,Sept.2005 PaperWe WhitePaper#4, ScalingCopperinterconnects

18 18 The points in the chart illustrate the maximum data transmission rate of a single link in a Standard. The points are from Standards and a few other points that have been reported for short distance (<1.0 meter) transmission using circuit boards or flex circuitry. Appendix D has the same data in a table format along with additional notes including, most importantly, both the data rate of the Standards and the data rate of a link from that standard. The difference results because many of these Standards, including IEEE ba and 10Gbase T, utilize multiple links such as individual twisted pair in a CAT 6 cable and complex circuitry at both the transmitting and receiving ends to transmit at the data rate of that Standard. IEEE 802.3ba, for example, utilizes 10 twin-ax 26 cables for copper transmission up to 7 meters, 10 MM fibers for transmission up to 150 meters and 4 SM fibers for transmission up to 40km. See Appendix E for more details of the combinations covered by the 400 page IEEE 802.3ba Standard. The key point is that the data rate per conductor pair or per fiber is often a quarter or a tenth of the data rate of the Standards. 27 The chart has 5 types of transmission media; copper conductors including PCB traces and flex circuitry (green triangles); twisted pair (purple triangles); coax cables (red triangles); MultiMode (MM) fiber (gold squares); and Single Mode (SM) fiber (blue squares). Coax tends to overlap twisted pair. PCB and flex circuitry tend to overlap twisted pair at short distances. MOST is the Plastic Optical Fiber (POF) standard used in automotive applications. The lines at 45 o are of constant data rate x distance. The limit of the various transmission methods tends to follow these lines. 26 Twin axisacoaxiallikeconstructionthathas2parallel center conductorsinadielectricwithanoutercircular shieldsurroundingbothconductors.theconductorsareusuallydrivenwithadifferentialsignal. 27 IEEE802.3bafor100Gb/sdatatransmissionisthehighesttransmissiondatarateStandardasofthedateofthis WhitePaper.However,400Gb/s,800Gb/sand1Tb/smethodsandcomponentsareindevelopmentandunder discussion.thesehigherratesenvisionasmanyas72,12.5gb/sparallelsmlinkstoreachtheserates. WhitePaper#4, ScalingCopperinterconnects

19 19 WhitePaper#4, ScalingCopperinterconnects

20 20 The table below summarizes several views that emerge from this Chart, the underlying data of Appendix D and the characteristics of the link media. Capability of Various Copper Data Transmission Media 28 Copper Media Gb/s x meters Typical Applications Typical Typical Max Max data Distance rate Circuit board traces, microstrip, stripline, 40 On card, within SiPs, backplanes 1 meter 40Gb/s Single twisted pair of Cat Ethernet standards for LANs 100 and Cat 5e cabling 29 meters 25Mb/s to 250Mb/s Braided shielded coax; RG-59 1,200 CATV 30 with 256QAM and 550 MHz bandwidth. 300 meters 4Gb/s Cat 6 cabling. 31 A single channel of twin-ax cable. 70 The 40G Base T and 100G BaseT LAN per IEEE ba meters 10Gb/s Semi-rigid coax 1000 Instruments, Communications 10 meters 100Gb/s Multimode fiber 1000 Data communications, Single ba channel, Cars 100 meters 10Gb/s Single Mode fiber 16 x 108 = 1.78Tb/s Telecommunications 250,000+ meters 10Gb/s 28 ManyofthestandardapplicationsincludingtheEthernetstandards,themaximumdistanceanddatarateis limitedbycrosstalkandinterferenceratherthanattenuationanddistortion. 29 TheCat3,5and5ecablesutilizes4pairtotransmitdata.Theratehereisperpairandthusdividedby4fromthe standard. 30 Requiresamplifiers. 31 Cat6cableutilizes4or10linkstotransmitdata.SeeAppendixE.Therateshereareperlinkandthusdivided by10fromthestandard. WhitePaper#4, ScalingCopperinterconnects

21 21 Cost of Copper vs Optical Data transmission Cost is an important, but difficult to compare metric. The chart below compares the cost of copper vs optical fiber data transmission vs distance with the notes providing additional metrics. The distance between copper repeaters depends on the media and the actual data rate. Power Consumption of Copper vs Optical Technology Semiconductors Limited by Power Consumption The increasing economic and social cost of energy has focused attention on the power consumption of electronic equipment, especially the increasing amount of power required to support internet activities. 33 In addition, the semiconductor industry has found that dissipating the power consumed by modern chips, especially microprocessors, is limiting the performance of these devices. In short, economics and the required technically methods of eliminating heat resulting from power consumption are limiting the performance of many chips. The result is that on-chip clock frequencies are no longer increasing and have been limited to about 4GHz. In addition, power 33 WeshouldreferenceearlierMITCTRworkhere. WhitePaper#4, ScalingCopperinterconnects

22 22 supply voltages are being reduced to accommodate a new design constraint. This new constraint is maximize the amount of computing per unit of power rather than maximizing the computing capability independent of the amount of power consumed. Transmitting Data Optically Can Reduce Power Optical technology is a potentially important contributor to power reduction. As noted above, transmitting data utilizing optical methods reduces the power required in many situations. Some of the applications that are at least partially driven by power saving are: 1. Telecommunications 2. Hybrid fiber Coax in CATV 3. Active Optical Cables 4. On-card MicroPOD 5. Consumer audio & HDMI 6. Automotive & transportation These applications are discussed more fully below. Other Copper Limits In addition to the physical and economic basics discussed in earlier sections, additional, practical characteristics of copper data transmission need to be considered and addressed in specific applications. Latency Sometimes the latency of electronic data processing is higher than that for optical technology. That is particularly true when signal conditioning, signal recovery, modulation and demodulation, coding and decoding are needed to achieve high data rates through electrical channels that have distortions or low signal to noise that must be compensated for at the transmitter and/or receiver. Approaching the Shannon Limit electrically, especially at low signal to noise ratios, requires coding methods that inherently introduce latency. Data density A greater amount of information can be transmitted off-chip or through a given area using optical methods than with copper technology. The same is not true on-chip where conductors carry 10Gb/s data rates over distances of ~1 mm with conductors that have a 45 nm width and spacing. An optical waveguide must be at least 0.5 microns wide spaced over 1 micron apart. WhitePaper#4, ScalingCopperinterconnects

23 23 The ratio of 1.5 microns/0.045 microns, or 30:1, favors electrical density. Dense conventional chip electrical IO methods transmit < 10Gb/s per IO utilizing wire bonds on 35 micron pitch. Standard optical methods utilize fiber or waveguides that are typically 5 microns in diameter spaced at least 5 microns apart. While the ratio of 35/(5+5)= 3.5 may not be compelling, the optical waveguides can easily carry 100 wavelengths, each of which can easily carry 10Gb/s of data. The result is a 350:1 advantage in data transmission per unit length or width. A similar argument can be made for optical methods vs electrical per unit area; optical data density due to the ability to multiplex optical wavelengths is far greater than the amount of data that can be transmitted electrically through a given cross-section. Cross Talk Elimination of cross talk between optical waveguides is much easier than between electrical conductors. The strength of an optical signal outside of the main waveguide in the cladding (the so-called evanescent field falls off exponentially at a rate of 1/e per wavelength. More importantly, in most applications of optical data transmission, the evanescent field falls to essentially zero within the cladding of the waveguide. Electrical signals, however, fall off in intensity only as 1/d 2, where d is the distance from the conductor. While shielding can be used to effectively eliminate electrical radiation, the size increase, complexity and cost of shielding is significant. Backplanes and Connectors At frequencies above ~10 GHz, daughter-card to backplane connectors tend to introduce signal distortion. Much work 34 shows that the limit for backplanes is about 18 to 40 Gb/s over a distance of 1 meter. Optical Limits The most important issue, and frequently the barrier, to economically implementing optical data transmission technology is the availability of a light source that can be modulated. A second barrier is the added cost, space and power associated with the electrical to optical and optical to electrical conversion inherent in what is predominantly an electronic environment. Lossless optical transmission overcomes exponential electrical losses over relatively short distances, especially as the electrical losses increase with frequency. 34 Forexample,see ScalableComputeInterfaces:Requirements,TrendsandElectricalSolutions,BryanCasper, IntelLabs.PresentedtotheMITCTR,April2010andIEEE802.3BA,40GBase KR4 WhitePaper#4, ScalingCopperinterconnects

24 24 Potential Light Sources The ideal light source to support optical data communications would be built into CMOS die when the silicon wafer is fabricated. Unfortunately, silicon does not support lasing, so additional parts of alternate methods or materials must be introduced. The methods that are under investigation are: A final characteristic of VCSELs is continuing concern about their reliability. Even though VCSELs have been in use in optical data communications for over 10 years, questions concerning their reliability remain unanswered. The wear out lifetime is indeed good enough to say that it does not contribute to the observed field FIT rate. It is, however, hard to measure the true random failure rate. That rate is low enough that you cannot practically measure it in a controlled lab setting. Studying field data is challenging because, depending on the product type and customer, you may not receive a return. In any case if you choose "right" and "measure" WhitePaper#4, ScalingCopperinterconnects 1. Hybrid approaches in which a laser made in a III-V compound is bonded to a silicon die that has a waveguide. 2. Building the source using a SiGe layer on top of the CMOS chip 3. Using an off-chip photon power source and building only modulators on the CMOS die 4. Driving VCSELs placed near CMOS chips. VCSELs as Light Sources When considering changing from copper to optical methods for most of the applications of current interest, the best light source available today is the Vertical Cavity Surface Emitting Laser (VCSEL). That source is compatible with MM fiber and can be directly modulated. VCSELs are available both as single devices and in arrays with precise dimensions that facilitate use with ribbon fiber, a common MM media. Most current VCSELs emit -3 dbm to + 4 dbm at 850+/- nm of light in a cone whose primary axis is perpendicular to the surface of the VCSEL chip. The voltage is typically 3.3 V; the drive current varies depending on the size but is in the range of 10 to 30 ma. The most important characteristic of the VCSEL is its stability and reliability. The light output varies with temperature so in some applications circuitry monitors the VCSEL temperature and compensates electrically to so the optical output stays in an acceptable range. Another characteristic of some VCSELs is that they have to be run at high intensity to turn off and on at high speed. That not only requires more drive power but sometimes the addition of an optical attenuator to reduce the light intensity to the ideal range for the photodetector.

25 25 based on field data you can get some very low upper bounds on FIT rates lower than single digits. The FIT rate aside, the big concerns are: 1. reliability issues that affect only a sub-population and cannot be detected by standard sample screening. 2. hazards the VCSEL is exposed to in assembly. The industry is caught between having small volumes and low margins which inhibit development of the process control required to deal with a sub-populations. VCSEL FIT rates have improved over the last 10 years as the industry has made progress on the two above issues. Nonetheless, the rate has not yet improved as much as needed. VCSEL users continue to be concerned for, and demanding, lower infant slip-through rates because the markets cannot tolerate failed channel disruptions. When Copper Is Displaced by Optical Technology Application Trends In general, as data rates go up optical methods are used at shorter distances. More specifically, the trends in applications are: to higher data rates smaller size & greater density lower energy consumption increased functionality Beyond these observations and generalizations, some specific reasons why copper is replaced by optical data transmission are these. Primary Power Reduction An important driver for optical methods is the reduced power required to transmit the same amounts of data using optical methods vs electrical. The crossover point where energy is saved is calculated to be no more than about 3 centimeters. Optical is not used at these short distances now because the economic cost is too high. Secondary Power Reduction WhitePaper#4, ScalingCopperinterconnects

26 26 Simply reducing the amount of energy required, as optical transport enables, reduces the overall size, HVAC and environmental costs. As the value of optical methods to reduce these soft costs becomes better known, optical methods will be more widely implemented. Size and Weight Reduction Optical fiber is smaller in cross section, often by 75%, lighter in weight and will usually bend in a tighter radius than the copper cables it replaces. In today s large installations, this size reduction is an important advantage. Greater Reach (Transmission distance) Optical methods have greater reach for the high data rates demanded. That relaxes the computation center layouts requirements as well as provides data transfer at lower power levels. Reduced Latency Optical methods sometimes reduce latency. That is particularly true when the electrical methods require coding to provide low BERs in low signal-to-noise electrical environments but also when signal pre and post transmission conditioning to characterize or compensate for copper distortions, crosstalk, reflections and interference is required. Finally, in a few cases, the velocity of transmission through the media (fiber vs cables) favors optical methods but that is not generally true. Converting electrical signals to optical and back is an inherent disadvantage of optical methods. Fortunately, this conversion takes very little time; on the order of 2 ns. An offsetting factor is that optical signals generally have a higher signal to noise ratio so the latency associated with coding and decoding used in low S/N environments is avoided. Another factor is the velocity of propagation through the media. The index of refraction of most fiber is ~ 1.4 implying 35 a velocity of ~70% of c, the velocity of light in a vacuum. The velocity of electrical signals varies greatly because the dielectric constant surrounding the copper conductor typically used ranges from 4 to 1.2 implying 36 velocities of propagation of 50% to 90% of c. Whether copper or optical transmission methods provide the lowest latency is a strong function of the application so a definitive statement cannot be made. 35 Thevelocityoflightthroughatransparentsolidisinverselyproportionaltotheindexofrefraction. 36 Velocityofanelectricalsignalisproportionalto1dividedbythesquarerootofthedielectricconstant. WhitePaper#4, ScalingCopperinterconnects

27 27 Major Applications Where Copper Is Displaced by Optical Data Transmission A Figure of Merit for Optical Data Transmission Products The table below shows the three major applications where optical technology is currently replacing, or competing with, copper for data communication. One useful parameter for comparing optical technology products is a figure of merit. The table below shows the estimated value of such a FOM for 3 current applications. The figure of merit is a simple equation: The FOM is: where FOM = Figure of Merit R = range in meters G = data rate through the link in Gb/s A = the maximum area of the interface per link in mm 2 $ = the cost in dollars per link J = the energy required in Joules The FOM for 4 actual or proposed commercial optical data transmission products for 4 major applications is estimated in the table below. Appendix F provides the details. These FOMs are only estimates as the exact values of some of the parameters, especially cost but area on the PCB too, are estimated. WhitePaper#4, ScalingCopperinterconnects

28 28 Product FOM for Major Applications of Optical Data Transmission Application Major Optical Benefits Current Status of Optical Technology Product for which FOM is estimated. Estimated FOM High Performance Computing Ability to transmit 1Tb/s between processors and memory Major application MicroPod. 100 meter reach. 14,249 Data Centers Data capacity, power and size reduction Major application Typical Active Optical Cable (AOC) 100 meter reach. 1,231 Data Centers Data capacity, power and size reduction Commercially available Fully integrated SM AOC such as that from Luxtera.100 meter reach. 5,663 23,302 at 4000 meter reach. Consumer Applications Enabling new applications, smaller size. Applications in a few years. Light Peak. 100 meter reach 5,106 High Performance Computing and Data Centers The high data rates, lower energy consumption, reduced heat dissipation, smaller size, tighter bend radius, reduced EMI and longer reach are the important attractions of optical methods. The cost and complexity of implementing optical data transmission are the major impediments. Active Optical Cables (AOC) While data centers were the initial users of AOCs, these cables are finding additional application. Replacing a copper cable with an AOC is a low risk change because the AOC can replaced with the copper cable if it does not perform. WhitePaper#4, ScalingCopperinterconnects

29 29 AOCs offer these advantages; The negatives are, WhitePaper#4, ScalingCopperinterconnects o typically 75% lower power consumption o 75% smaller cross section o no EMI o longer reach a., some increased initial cost that is partially offset by the lifetime power savings b., added latency in some cases. The AOC concept can be extended and applied to many situations where data is sent over copper wires between points. USB cables, HDMI cables, etc., are all candidates for conversion from copper to optical methods using the AOC concept. The transition depends on cost, the data rates, the distances and the willingness of the end user to change from the traditional copper solution to the somewhat unproven and unknown optical technology. On-card and off-of card While the Avago MicroPod developed for IBM by a group of companies is the most recent example of this technology, several other vendors offer similar solutions. The MicroPod utilizes complementary Tx and Rx modules, both of which are ~7.8 mm x 8.2 mm. The modules are mounted on cards near the chips that generate or receive the data. Transmission from the Tx to the Rx is through a 12 fiber ribbon cable at data rates of 10Gb/s in each of the 12 fibers. The result is unusually high off-of card and on-to card data transmission density between multi-core processor chips and memory chips at a power level of 20 mw/gbs. The high density data transfer at low power that optical technology attains is not viable utilizing electrical (copper) data transmission. The MicroPod may be the first of the on-card and off-of card applications of optical data transmission. Transportation Optical data transmission is replacing copper in some transportation applications, especially automotive, but also in both commercial and military aircraft. The attraction of optical technology is the lower weight of the plastic fiber that is often used vs copper. In some cases a more important benefit is the elimination of actual or potential EMI that optical methods offer. Europeans are the leaders in replacing copper with optical fiber in automobiles. Plastic optical fiber (POF) configured to the MOST standard is used. MOST standard supports a data rate of

30 30 100Mb/s and very low cost terminations that can be made by cutting the POF and inserting the cut end into a connector. Other Applications Audio Systems - Many audio systems offer optical ports. While the use has not been extensive to date, these ports will continue to be available. HDMI - An AOC like solution utilizing 4 links+ clock at 2.97 Gb/s/pair is viable and offers smaller size and longer reach in optical cables than in copper. The major impediment is the cost of the optical solution vs copper. Security Applications- Tapping into an optical signal in a fiber, especially a single mode fiber, is quite difficult and almost impossible to do without the owner of the fiber knowing the fiber is being tapped. That is not true with copper, of course, where tapping of phone lines is widely practiced. Thus, for secure communications, optical data transmission is replacing electrical methods. Conclusion Electrical data transmission over copper will continue to be used in many applications in the foreseeable future. Additionally, the ability to perform more complex processes to extract data from distorted and low level electrical signals enabled by the continuing improvement in highspeed silicon technology provides a path to extend copper life through the use of more advanced modulation formats, equalization and coding. For very high capacity density applications and for distance-bandwidth products >100 Gb/s x meter, however, optical methods offer important advantages. The primary advantages are lower power, smaller size, longer reach and lower cost at high (>10 Gb/s) data rates. In addition, copper is being displaced in some specific applications due to advantages unique to the application; lower weight and reduced EMI in transportation equipment; smaller size and greater fidelity for consumer video and other electronics; and greater security for sensitive communications. WhitePaper#4, ScalingCopperinterconnects

31 31 Appendix A This Appendix will be an Executive Summary and may contain the following simplified table. Electrical (copper) vs Photonic Data Transmission Electrical (copper) Photonic Pros Cons Pros Cons Low cost Much energy loss due to electrical resistance, skin effect and loss tangent, especially as data rates increase. Very low energy loss once the optical signal is launched. <10 pj/bit Some power and more components are required to convert from electrical to optical and back. Well established & understood. Low risk. Limited bandwidth vs photonic. 10Gbs at 100 meters per Ethernet standards. Able to transmit 100+Gbs over distances as great as 100 Kilometers. Generally more expensive if copper will work Widely available. Higher power/bit if transmission distance is > 3 cm. Extremely high bandwidth (10 s of Terahertz) and data rates (100Terabits/second) Reliability of optical devices, especially VCSELs, is unproven. Data density of 10Gbs through 1/16 of a mm 2 Generally larger and heavier than the equivalent photonic replacement. Data density of 1 Terabit/s through 1/16 of a mm 2 Generally not as well understood or accepted More energy efficient over distances < 3 cm. Requires 0.1pJ/bit over 0.1 mm. Often more expensive per bit over time due to energy cost. Generally smaller in cross section, bends with a shorter radius and weighs less. Requires more skill to terminate and install No EMI or radiation Less available WhitePaper#4, ScalingCopperinterconnects

32 32 Appendix B Limits of a Data Transmission Channel Transmitting information through any communications channel, either copper or optical, is limited by a fundamental parameter called the channel capacity. The channel capacity results from the bandwidth and signal-to-noise ratio (SNR) of the channel. Considering 37 all possible multi-level and multi-phase encoding techniques, the Shannon Hartley theorem states the channel capacity C, meaning the theoretical tightest upper bound on the information rate (excluding error correcting codes) of clean (or arbitrarily low bit error rate) data that can be sent with a given average signal power S through an analog communication channel subject to additive white Gaussian noise of power N, is: where C is the channel capacity in bits per second; B is the bandwidth of the channel in hertz (passband bandwidth in case of a modulated signal); S is the total received signal power over the bandwidth (in case of a modulated signal, often denoted C, i.e. modulated carrier), measured in watt or volt 2 ; N is the total noise or interference power over the bandwidth, measured in watt or volt 2 ; and S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the Gaussian noise interference expressed as a linear power ratio (not as logarithmic decibels). Thus, the channel capacity is proportional to the bandwidth of the channel and to the logarithm of SNR. This means channel capacity can be increased two ways; by increasing the bandwidth of the channel with the same SNR OR, with a fixed bandwidth, by utilizing complex, higher order modulation methods that require high SNR. With the higher order modulation rate, the channel capacity and the spectral efficiency (bits/per cycle of bandwidth) improve but at the cost of an exponentially higher SNR. For example, 16QAM modulation, (see: Quadrature amplitude modulation) transmits 4 bits per symbol whereas 64QAM transmits 6 bits. This 50% 37 ThisdiscussionistakenfromWikipediawithsomemodificationinstructurebutnotbasiccontent. WhitePaper#4, ScalingCopperinterconnects

33 33 improvement in bits/symbol (or cycle of bandwidth) requires a 6db (4X) increase in SNR. 4 times the energy for a 50% data rate increase is not always a good tradeoff. The Shannon limit, C, discussed above applies to data transmission channels using any transmission method including copper and photonic methods. The theory makes clear that the Signal to Noise power ratio is important and that as the signal power decreases compared to noise, the amount of data, C, that can be transmitted decreases. So, to understand the Scalability of copper vs photonic methods, the combination of bandwidth and signal to noise power must be considered. Comparing the signal to noise power loss and bandwidth of copper vs photonics will provide insight at a fundamental level to the capability of each. WhitePaper#4, ScalingCopperinterconnects

34 34 Appendix C Data Transmission with Copper Energy Loss Phenomena Transmitting a data signal requires receiving transmitted energy. The sources and rate of loss of energy with distance determine how much data and how far data can be transmitted through a link. Copper conductors lose energy due to a variety of physical phenomena including: Bulk electrical resistance the skin effect the loss tangent of nearby dielectrics scattering of electronics in small conductors radiation a few other phenomena For data transmission purposes, the major losses are the first 3; bulk resistance, the skin effect and the loss tangent associated with dielectrics. The loss through radiation is typically not high, but the effect on other parts of a related or nearby system manifest themselves as electromagnetic interference (EMI), and that effect can be important to avoid. The table below summarizes these three main mechanisms and quantifies them. Sources of Energy Loss Using Copper for Data Transmission Energy Loss Phenomena Loss dependence factors Value in Copper Electrical resistance Skin effect Tan delta dielectric losses Bulk resistance of the conductor at DC Square root of conductivity divided by permeability X frequency Loss proportional to the frequency X the tan delta of Rho, bulk resistivity Loss = f x tan delta WhitePaper#4, ScalingCopperinterconnects

35 35 the dielectric Energy Loss in Copper The total power loss in a copper conductor is the sum of the loss from the skin effect and dielectric tan delta. Mathematically, the loss in proportional to the sum of the square root of the frequency times a constant related to the geometry and conductor conductivity and permeability plus the frequency times another constant related to the dielectric loss tangent. At low frequencies in copper, the first term dominates; at higher frequencies the tan delta losses dominate. The total energy loss is the sum of the losses from the skin effect and tan delta. Skin Effect Loss 38 The skin depth is defined as the depth below the surface of the conductor at which the current density decays to 1/e (about 0.37) of J S. It can be calculated as follows: where ρ = resistivity of conductor ω = angular frequency of current = 2π frequency µ = absolute magnetic permeability of conductor, where µ 0 is the permeability of free space (4π 10 7 N A -2 ) and µ r is the relative permeability of the conductor. A tabulation of the skin depth vs frequency in copper is shown below. Skin depth vs Frequency in Copper Signal frequency Skin depth in microns 60 Hz 8, KHz KHz MHz Mhz FromWikipediawithsomemodificationofthetextbutnotthebasiccontent. WhitePaper#4, ScalingCopperinterconnects

36 36 100MHz GHz GHz GHz 0.21 The Tan delta Loss (This paragraph needs some work. Maybe a simple equation with a better explanation of the terms. Also filling the table of dissipation factors for various materials.) The tan delta loss is:. Where: sigma is the bulk electrical conductivity of the dielectric epsilon prime is the real part of the dissipation factor of the dielectric omega is the frequency in radians or frequency x 2 pi. Loss tangent of Typical Dielectric Materials Material Tan delta FR-4 ~0.012 at 10GHz 39 Teflon dielectric Al 2 O at 100MHz 41 Rogers 4003C at 10GHz TheFR 4tandeltawasestimatedfromtheRogerssitechartcomparingFR 4andRogers4003Clossesat10GHz. 40 TheTeflontandeltaisfromwww.matweb.com.Afrequencyisnotspecified. 41 TheAl 2 O 3 tandeltaisfromwww.matweb.com. 42 TheRogers4003Closstangentisfromthewww.rogers.com. WhitePaper#4, ScalingCopperinterconnects

37 37 Appendix D The chart on page 16 repeated below is based on the data that follows. WhitePaper#4, ScalingCopperinterconnects

38 38 WhitePaper#4, ScalingCopperinterconnects

39 39 Appendix E The table below shows the physical implementation options established by IEEE 802.3ba. FromElectronicDesign,LouisE.Frenzel,April22,2010,12:00AM. WhitePaper#4, ScalingCopperinterconnects